**Meet the editor**

Dr. Mark Zimering is the Chief of Endocrinology at the Department of Veterans Affairs in East Orange, New Jersey and Associate Professor of Medicine Co-Terminous at UMDNJ/Robert Wood Johnson Medical School. Dr. Zimering received his undergraduate training at Harvard College, MD and PhD degrees from the Albert Einstein College of Medicine, and completed an endocri-

nology fellowship at the NIH. His research has focused on roles for basic fibroblast growth factor (or autoantibodies which mimic or inhibit its effects) in diabetic vascular complications. He reported markedly increased plasma basic fibroblast growth in a subset of obese adult participants from the Veterans Affairs Diabetes Trial having increased coronary heart disease occurrence. His group reported low levels of plasma basic fibroblast growth factor in adult diabetes having a cluster of microvascular complications (macular edema, albuminuria, painful neuropathy) in association with endothelial cell inhibitory autoantibodies which activated the RhoA/ Rho kinase signaling pathway in endothelial cells or caused global increases in intracellular calcium in endothelial cells, neurons or cardiomyocytes.

Contents

**Preface IX**

Chapter 1 **Burden of Diabetes Type 2**

**Part 2 Novel Treatments 75**

**Part 1 Economic Burden & Relation to Alzheimer's Disease 1**

**Different Pathologies and Same Features 29**  Marta Di Carlo, Pasquale Picone, Rita Carrotta, Daniela Giacomazza and P.L. San Biagio

Sung Min Son, Hong Joon Shin and Inhee Mook-Jung

**Agonists (GLP-1R) or So-Called Incretin Mimetics 77**

**Compounds in Established and Investigational Therapies of Type 2 Diabetes Mellitus 103**  László Somsák, Éva Bokor, Katalin Czifrák,

**on Insulin Sensitivity and Adipocyte Growth in Otsuka Long-Evans Tokushima-Fatty Rats 127**

Tatsuo Ishizuka, Kazuo Kajita, Kei Fujioka, Takayuki Hanamoto, Takahide Ikeda, Ichiro Mori, Masahiro Yamauchi, Hideyuki Okada, Taro Usui,

Noriko Takahashi, Hiroyuki Morita, Yoshihiro Uno and Atsushi Miura

**Through Modelling and Simulation 3**  Maja Atanasijević-Kunc and Jože Drinovec

Chapter 2 **Alzheimer's Disease and Type 2 Diabetes:**

Chapter 3 **Insulin Resistance and Alzheimer's Disease 53**

Chapter 4 **Incretin-Based Treatment Strategy - GLP-1 Receptor**

Jindra Perusicova and Klara Owen

Chapter 5 **Carbohydrate Derivatives and Glycomimetic**

László Juhász and Marietta Tóth

Chapter 6 **Effect of Dehydroepiandrosterone**

### Contents

#### **Preface XIII**

#### **Part 2 Novel Treatments 75**

	- **Part 3 Prevention 161**
	- **Part 4 Complications 191**

### Preface

Type 2 diabetes is estimated to affect 120 million people worldwide- and according to projections from the World Health Organization this number is expected to double over the next two decades. Novel, cost-effective strategies are needed to reverse the global epidemic of obesity which is driving the increased occurrence of type 2 diabetes and to less the burden of diabetic vascular complications. In the current volume, *Topics in the Prevention, Treatment and Complications of Type 2 Diabetes* experts in biology and medicine from four different continents contribute important information and cutting-edge scientific knowledge on a variety of topics relevant to the management and prevention of diabetes and related illnesses.

In the opening section, *Economic burden and Relation to Alzheimer's Disease,* Atanasijevic-Kunc & Drinovec use mathematical modeling and simulation to forecast the economic burden from type 2 diabetes in the coming decades. Alzheimer's disease has been referred to as 'type 3 diabetes' because of its increased prevalence in populations having obesity, insulin resistance and dyslipidemia. In two excellent chapters-DiCarlo et al present evidence suggesting that type 2 diabetes has manifestations of a protein misfolding disease akin to several well-known neurodegenerative diseases and then Sung Min Son and colleagues argue in favor of mechanistic links underlying an association between insulin resistance and Alzheimer's disease.

The section on *Treatment* starts with a concise review of GLP-1 receptor analogues by Perusicova & Owen. Next, Somsak and colleagues summarize experimental and clinical data supporting the efficacy of new glycomimetic compounds for the treatment of type 2 diabetes in animal models. Ishizuka et al review data showing that the adrenal androgen DHEA can improve glucose sensitivity and protect against the development of diabetes in obese rats. Finally, Cheow Peng Ooi et al summarize the results of clinical trials using various botanical compounds for the treatment of type 2 diabetes.

In a brief section *Prevention*, McLellan et al present the results of their study of lifestyle interventions in preventing type 2 diabetes. Maki and Rains review existing data on how the consumption of dietary fiber can lower the risk for development of type 2 diabetes.

#### XII Preface

Finally, the closing section on *Complications* offers an in-depth, expert treatment on such diverse topics as vitamin B12 deficiency, the microcirculation, hypertriglyceridemic-waist as a predictor of cardiovascular disease, and psychological aspects of type 2 diabetes, all by notable contributors in each field.

#### **Mark B. Zimering, MD, PhD**

Chief, Endocrinology Veterans Affairs New Jersey Healthcare System East Orange, New Jersey, USA Associate Professor of Medicine University of Medicine and Dentistry of New Jersey, Robert Wood Johnson Medical School, New Brunswick, New Jersey, USA

X Preface

Finally, the closing section on *Complications* offers an in-depth, expert treatment on such diverse topics as vitamin B12 deficiency, the microcirculation, hypertriglyceridemic-waist as a predictor of cardiovascular disease, and psychological

**Mark B. Zimering, MD, PhD**

Associate Professor of Medicine

Veterans Affairs New Jersey Healthcare System

University of Medicine and Dentistry of New Jersey,

Robert Wood Johnson Medical School, New Brunswick, New Jersey,

Chief, Endocrinology

USA

USA

East Orange, New Jersey,

aspects of type 2 diabetes, all by notable contributors in each field.

**Part 1**

**Economic Burden & Relation**

**to Alzheimer's Disease**

## **Part 1**

**Economic Burden & Relation to Alzheimer's Disease**

**1**

*Slovenia*

**Burden of Diabetes Type 2 Through**

Modelling and simulation represent well established approaches when analyzing systems' properties, their behaviour, predicting possible scenarios, or estimating potential results or responses when influencing the observed system (Cellier, 1991; Cassandras & Lafortune, 1999; Cellier & Kofman, 2006; D'Inverno & Luck, 2010). Such **knowledge organization about a given problem** can help in its presentation, understanding, explanation and it is

Modelling and model usage can be classified and/or chosen as methodology regarding different criteria which can in addition be interdependent due to important activities needed in such situations. Criteria can represent the way of data collecting, their form and degree of confidence, model structure and possibilities of model experimentations, the level of problem abstraction and its aggregation, the selection of time granulation, etc. One of the most important aspect (in spite of the fact that it is often not mentioned) which has to be taken into account, is also *the goal of modelling* which should lead the designer through the whole procedure of model development, its interpretation and experimentation. The last two facts are very important also for the user of developed model. This is perhaps also one of important reasons why very different mathematical approaches and descriptions are used, where the disciplines like medicine, pharmacy and the life sciences are no exception (Hoppensteadt & Peskin, 2002; Atanasijević-Kunc et al., 2008a; Stahl, 2008; Belič, 2009; Arnold 2010). This is true even in the cases where the same problem, like certain disease

also frequently used through system design (Matko et al., 1992).

development (diabetes for example) is observed.

Here the following questions can arise:

important or relevant one?

similar results?

problem?

**1. Introduction**

**Modelling and Simulation**

*2University of Maribor, Faculty for Medicine*

Maja Atanasijević-Kunc1 and Jože Drinovec2 *1University of Ljubljana, Faculty of Electrical Engineering*

## **Burden of Diabetes Type 2 Through Modelling and Simulation**

Maja Atanasijević-Kunc1 and Jože Drinovec2 *1University of Ljubljana, Faculty of Electrical Engineering 2University of Maribor, Faculty for Medicine Slovenia*

#### **1. Introduction**

Modelling and simulation represent well established approaches when analyzing systems' properties, their behaviour, predicting possible scenarios, or estimating potential results or responses when influencing the observed system (Cellier, 1991; Cassandras & Lafortune, 1999; Cellier & Kofman, 2006; D'Inverno & Luck, 2010). Such **knowledge organization about a given problem** can help in its presentation, understanding, explanation and it is also frequently used through system design (Matko et al., 1992).

Modelling and model usage can be classified and/or chosen as methodology regarding different criteria which can in addition be interdependent due to important activities needed in such situations. Criteria can represent the way of data collecting, their form and degree of confidence, model structure and possibilities of model experimentations, the level of problem abstraction and its aggregation, the selection of time granulation, etc. One of the most important aspect (in spite of the fact that it is often not mentioned) which has to be taken into account, is also *the goal of modelling* which should lead the designer through the whole procedure of model development, its interpretation and experimentation. The last two facts are very important also for the user of developed model. This is perhaps also one of important reasons why very different mathematical approaches and descriptions are used, where the disciplines like medicine, pharmacy and the life sciences are no exception (Hoppensteadt & Peskin, 2002; Atanasijević-Kunc et al., 2008a; Stahl, 2008; Belič, 2009; Arnold 2010). This is true even in the cases where the same problem, like certain disease development (diabetes for example) is observed.

Here the following questions can arise:

Burden of Diabetes Type 2 Through Modelling and Simulation 5

also the treatment efficacy can be taken into account which can compare different treatment strategies and/or their influence to further complications development. In addition, of course, also the reasons which influence D2 development can be taken into account, as usually the prevention offers the most effective positive influence to economical and social

This chapter is organized in the following manner. In the next session some modelling structures are indicated which have been used for modelling purposes of D2 presentation. Special attention is devoted to the possibilities of coexistence of different modelling descriptions. Simulation results are illustrated in session 3, where also some of expenses, related to observed patients are estimated. The work ends with conclusion remarks and some ideas for future investigations. It is also important to mention that all presented results

One of the simplest presentation which is describing the D2 population, two – compartment linear model, is illustrated in Fig. 1 (Boutayeb et al., 2004). Input signal *u(t)* represents the incidence of D2, while *C(t)* and *D(t)* are the numbers of D2 patients with and without complications, respectively. It is expected that patients with D2 are developing complications with *k1D(t)* rate, in the compartment *C(t)* they can recover and therefore return to *D(t)* compartment (with *k2C(t)* rate), they can die due to natural causes (with *c1C(t)* rate) or due to severe complications (with *c2C(t)* rate), and they can also become seriously disabled (with *c3C(t)* rate). The authors have suggested stability analysis with respect to model parameters and numerical problem solving. In this simple description the population in each compartment is observed as a homogeneous set of patients and it is expected that parameters are time – independent. Important aspects as for example patients' age, life style, body mass, simultaneous joint diseases and similar are not presented explicitly, they can only influence (through the identification process) the values of model parameters. Further extension to nonlinear description was proposed in (Boutayeb et al., 2006), but basic

Far more complex dynamical nonlinear model, as schematically presented in Fig. 2, was originally developed and tuned for the USA (Homer et al., 2004) and later on also adapted with some improvements to the population of Austria (Kristöfel et al., 2007). In comparison to the structure in Fig. 1 this one recognises also the patients with pre-diabetes, not only those where D2 is completely developed, while both groups can be diagnosed or not. So additional four compartments are needed, while special attention was devoted also to the transition flows, which are dependent on a great number of important factors and ratios, like population age, obesity, activity and similar. One difference in comparison to model in Fig. 1 is also the interpretation regarding patients with complications, as they can't reach the

It is important to mention that authors have in this last case devoted detailed attention to the validation and verification of proposed models using extensive data, which are in general not available for all countries. Due to model complexity sensitivity and stability analysis demanded the introduction of expected range of variables' changes and simulation testing. When economical burden of disease treatment and/or treatment efficacy is of interest in many cases the so called decision modelling techniques are used (Arnold, 2010). Decision trees have been for more than forty years the most common and simplest formalism,

were realized using Matlab (Matlab, 2005) with Simulink (Simulink, 2005).

situation.

**2. Modelling structures**

viewpoint remains unchanged.

state without complications anymore.

The answers to the first questions are not surprising. Process descriptions should be suitably chosen regarding modelling goal(s), modelling phase and other important design factors. As indicated in (Stahl, 2008) the investigators should choose the modelling methods that fit the defined problem. It means that different descriptions can predict similar or complementary results using, for example, *different complexity* (nonlinear or linear descriptions, high or low order descriptions) or *different granularity* (observation of the whole population, observation of an individual patient, observation of dynamical processes on molecular level), *different aggregation* (development of one or several diseases) or perhaps only *different model presentations* are suitable when performing different analysis functions (state space or transfer function description, continuous or discrete time description, time or frequency domain description, ...). Whenever a new point of view of certain problem is under investigation, whenever some new facts or perhaps only different assumptions are taken into account, when modelling results are meant to be used by different groups of people also a new or improved description can be important. All mentioned facts can be verified also when observing different aspects of diabetes mellitus. But, in spite of great diversity of results' description regarding this dangerous chronic disease practically nowhere attention is devoted to the idea of their complementary usage. This viewpoint can become especially interesting when several factors influencing the problem are taken into account.

The literature dealing with different aspects of diabetes has become enormous and very heterogeneous even in the case when searching is limited to mathematical modelling and simulation processes of this disease. Some of them are describing **glucose-insulin dynamics** (Boutayeb & Chetouani 2006; Makroglou et al., 2006; Shianga & Kandeelc 2010), some represent **epidemiological descriptions** of this non communicable disease (Boutayeb et al., 2004; Boutayeb et al., 2006; Atanasijević-Kunc et al., 2008b), while others describe **disease development** (Eddy & Schlessinger, 2003a; 2003b; Kristöfel, et al., 2007) or the **relations to risk factors** which are in correlation with diabetes development (Brock et al., 2009; MMWR 2004; Atanasijević-Kunc et al., 2008c). Diabetes can represent by itself or even more intense in combination with other possible chronic diseases (dislipidemia, hypertension) or life style (smoking, alcohol consumption, inactivity) the risk for developing different cardiovascular diseases (Levenson et al., 2002; Atanasijević-Kunc et al., 2008c; 2011). Additional aspect, important for modelling structure, can represent **social and economical burden** of the discussed disease and/or **treatment efficacy**, which is often interpreted through different **pharmacoeconomical studies** (Boutayeb et al., 2004; Tarride et al., 2010; Arnold, 2010; Atanasijević-Kunc et al., 2011), where cost-effectiveness analysis and cost – utility analysis provide a basic comparison of different treatment policies or drug efficacy. All mentioned situations can be interpreted as **open** or **closed – loop problems (**Atanasijević-Kunc et al., 2008c; 2011; Bellazzi, 2001; Lam, 2002; Makroglou, 2006), where especially in the second case the analysis should take into account stability and sensitivity of system behaviour.

The modelling and simulation approach aims to indicate, use and/or develop mathematical problem presentations which can be used for the evaluation of the burden of diabetes type 2 (D2) mellitus and correlated processes which can contribute to disease development or can represent the source of expenses (direct and/or indirect). This burden is not important only from the economical but also from the social point of view due to the possible severe health complications which usually essentially influence the quality of life.

For the evaluation of mentioned disease burdens regarding certain population it is of most importance first to estimate the number of patients and the treatment expenses. In addition also the treatment efficacy can be taken into account which can compare different treatment strategies and/or their influence to further complications development. In addition, of course, also the reasons which influence D2 development can be taken into account, as usually the prevention offers the most effective positive influence to economical and social situation.

This chapter is organized in the following manner. In the next session some modelling structures are indicated which have been used for modelling purposes of D2 presentation. Special attention is devoted to the possibilities of coexistence of different modelling descriptions. Simulation results are illustrated in session 3, where also some of expenses, related to observed patients are estimated. The work ends with conclusion remarks and some ideas for future investigations. It is also important to mention that all presented results were realized using Matlab (Matlab, 2005) with Simulink (Simulink, 2005).

#### **2. Modelling structures**

4 Topics in the Prevention, Treatment and Complications of Type 2 Diabetes

The answers to the first questions are not surprising. Process descriptions should be suitably chosen regarding modelling goal(s), modelling phase and other important design factors. As indicated in (Stahl, 2008) the investigators should choose the modelling methods that fit the defined problem. It means that different descriptions can predict similar or complementary results using, for example, *different complexity* (nonlinear or linear descriptions, high or low order descriptions) or *different granularity* (observation of the whole population, observation of an individual patient, observation of dynamical processes on molecular level), *different aggregation* (development of one or several diseases) or perhaps only *different model presentations* are suitable when performing different analysis functions (state space or transfer function description, continuous or discrete time description, time or frequency domain description, ...). Whenever a new point of view of certain problem is under investigation, whenever some new facts or perhaps only different assumptions are taken into account, when modelling results are meant to be used by different groups of people also a new or improved description can be important. All mentioned facts can be verified also when observing different aspects of diabetes mellitus. But, in spite of great diversity of results' description regarding this dangerous chronic disease practically nowhere attention is devoted to the idea of their complementary usage. This viewpoint can become especially

interesting when several factors influencing the problem are taken into account.

the analysis should take into account stability and sensitivity of system behaviour.

complications which usually essentially influence the quality of life.

The modelling and simulation approach aims to indicate, use and/or develop mathematical problem presentations which can be used for the evaluation of the burden of diabetes type 2 (D2) mellitus and correlated processes which can contribute to disease development or can represent the source of expenses (direct and/or indirect). This burden is not important only from the economical but also from the social point of view due to the possible severe health

For the evaluation of mentioned disease burdens regarding certain population it is of most importance first to estimate the number of patients and the treatment expenses. In addition

The literature dealing with different aspects of diabetes has become enormous and very heterogeneous even in the case when searching is limited to mathematical modelling and simulation processes of this disease. Some of them are describing **glucose-insulin dynamics** (Boutayeb & Chetouani 2006; Makroglou et al., 2006; Shianga & Kandeelc 2010), some represent **epidemiological descriptions** of this non communicable disease (Boutayeb et al., 2004; Boutayeb et al., 2006; Atanasijević-Kunc et al., 2008b), while others describe **disease development** (Eddy & Schlessinger, 2003a; 2003b; Kristöfel, et al., 2007) or the **relations to risk factors** which are in correlation with diabetes development (Brock et al., 2009; MMWR 2004; Atanasijević-Kunc et al., 2008c). Diabetes can represent by itself or even more intense in combination with other possible chronic diseases (dislipidemia, hypertension) or life style (smoking, alcohol consumption, inactivity) the risk for developing different cardiovascular diseases (Levenson et al., 2002; Atanasijević-Kunc et al., 2008c; 2011). Additional aspect, important for modelling structure, can represent **social and economical burden** of the discussed disease and/or **treatment efficacy**, which is often interpreted through different **pharmacoeconomical studies** (Boutayeb et al., 2004; Tarride et al., 2010; Arnold, 2010; Atanasijević-Kunc et al., 2011), where cost-effectiveness analysis and cost – utility analysis provide a basic comparison of different treatment policies or drug efficacy. All mentioned situations can be interpreted as **open** or **closed – loop problems (**Atanasijević-Kunc et al., 2008c; 2011; Bellazzi, 2001; Lam, 2002; Makroglou, 2006), where especially in the second case One of the simplest presentation which is describing the D2 population, two – compartment linear model, is illustrated in Fig. 1 (Boutayeb et al., 2004). Input signal *u(t)* represents the incidence of D2, while *C(t)* and *D(t)* are the numbers of D2 patients with and without complications, respectively. It is expected that patients with D2 are developing complications with *k1D(t)* rate, in the compartment *C(t)* they can recover and therefore return to *D(t)* compartment (with *k2C(t)* rate), they can die due to natural causes (with *c1C(t)* rate) or due to severe complications (with *c2C(t)* rate), and they can also become seriously disabled (with *c3C(t)* rate). The authors have suggested stability analysis with respect to model parameters and numerical problem solving. In this simple description the population in each compartment is observed as a homogeneous set of patients and it is expected that parameters are time – independent. Important aspects as for example patients' age, life style, body mass, simultaneous joint diseases and similar are not presented explicitly, they can only influence (through the identification process) the values of model parameters. Further extension to nonlinear description was proposed in (Boutayeb et al., 2006), but basic viewpoint remains unchanged.

Far more complex dynamical nonlinear model, as schematically presented in Fig. 2, was originally developed and tuned for the USA (Homer et al., 2004) and later on also adapted with some improvements to the population of Austria (Kristöfel et al., 2007). In comparison to the structure in Fig. 1 this one recognises also the patients with pre-diabetes, not only those where D2 is completely developed, while both groups can be diagnosed or not. So additional four compartments are needed, while special attention was devoted also to the transition flows, which are dependent on a great number of important factors and ratios, like population age, obesity, activity and similar. One difference in comparison to model in Fig. 1 is also the interpretation regarding patients with complications, as they can't reach the state without complications anymore.

It is important to mention that authors have in this last case devoted detailed attention to the validation and verification of proposed models using extensive data, which are in general not available for all countries. Due to model complexity sensitivity and stability analysis demanded the introduction of expected range of variables' changes and simulation testing.

When economical burden of disease treatment and/or treatment efficacy is of interest in many cases the so called decision modelling techniques are used (Arnold, 2010). Decision trees have been for more than forty years the most common and simplest formalism,

Burden of Diabetes Type 2 Through Modelling and Simulation 7

Such problem presentations are static and they don't enable the observation of patients' history, as in the previously mentioned cases. In problems that lead to long – term differences in outcome such presentation can be insufficient. One way to avoid (at least partly) this drawback is to use the description in the form of the so called Markov process (Stahl, 2008; Shih, 2007) or to extend the decision tree to include also Markov processes, for example at the outcome node as illustrated in Fig. 4 (Arnold, 2010). The advantages of such presentations are that they are relatively simple, frequently used and therefore also well accepted as abstract problem presentation. But there are also two main limitations (Stahl, 2008; Arnold, 2010). State transitions can only occur at the end of a cycle, which can create some biases, and Markov cycle time may force the analyst to make simplifying assumptions

Economical burden regarding the situation inside the observed population was investigated also by (Briggs & Sculpher, 1998; Atanasijević-Kunc et al., 2008b; 2008c; 2011). When summarizing the mentioned results the modelling structure can be presented as illustrated in Fig. 5. The problem presentation and design is separated into three main phases. Through the first phase risk factors and chronic diseases are described in the form of prevalence distribution regarding patients' age, in the second design phase also the prevalence of different complications are added, where among the patients with more problems indicated in the first phase or in the case where chronic diseases were not correspondingly treated, also the development of complications was more frequent. Input signal to the first phase is

Fig. 3. Decision tree modelling structure

regarding transition probabilities.

comprising choices, chances, and outcomes. For the similar situation as in previous two presentations the idea is indicated in Fig. 3.

Fig. 1. Two - compartment modelling structure

Fig. 2. System dynamics model for the diabetes prevalence

comprising choices, chances, and outcomes. For the similar situation as in previous two

presentations the idea is indicated in Fig. 3.

Fig. 1. Two - compartment modelling structure

Fig. 2. System dynamics model for the diabetes prevalence

Fig. 3. Decision tree modelling structure

Such problem presentations are static and they don't enable the observation of patients' history, as in the previously mentioned cases. In problems that lead to long – term differences in outcome such presentation can be insufficient. One way to avoid (at least partly) this drawback is to use the description in the form of the so called Markov process (Stahl, 2008; Shih, 2007) or to extend the decision tree to include also Markov processes, for example at the outcome node as illustrated in Fig. 4 (Arnold, 2010). The advantages of such presentations are that they are relatively simple, frequently used and therefore also well accepted as abstract problem presentation. But there are also two main limitations (Stahl, 2008; Arnold, 2010). State transitions can only occur at the end of a cycle, which can create some biases, and Markov cycle time may force the analyst to make simplifying assumptions regarding transition probabilities.

Economical burden regarding the situation inside the observed population was investigated also by (Briggs & Sculpher, 1998; Atanasijević-Kunc et al., 2008b; 2008c; 2011). When summarizing the mentioned results the modelling structure can be presented as illustrated in Fig. 5. The problem presentation and design is separated into three main phases. Through the first phase risk factors and chronic diseases are described in the form of prevalence distribution regarding patients' age, in the second design phase also the prevalence of different complications are added, where among the patients with more problems indicated in the first phase or in the case where chronic diseases were not correspondingly treated, also the development of complications was more frequent. Input signal to the first phase is

Burden of Diabetes Type 2 Through Modelling and Simulation 9

Fig. 5. Diseases prevalence, number of patients and expenses presentation

et al., 2001; DPPRSG, 2002; Kriska et al., 2003; Mokdad et al., 2003; ADA, 2007;).

interventions in prevention or delayed D2 development.

reformulated to indicate the results of economical and financial flows.

system's states at the first level.

Here D2 is a disease of the third level due to the fact that on one side risky and/or unhealthy life style (population status observed in the second level of the structure) can influence the development of this chronic disease, but D2, as already mentioned, can also contribute to development of different health complications (presented at the fourth level of the proposed structure). At the second level two important problems, namely activity or inactivity and obesity are taken into account, which are two most important problems leading to D2 (Defay

D2 is usually preceded by a pre-diabetes ("a metabolic condition characterised by insulin resistance and primary or secondary beta cell dysfunction which increases the risk of developing type 2 diabetes and cardiovascular disease" (Tuomilehto et al., 2001; Valensi et al., 2005). It is extremely common, especially in elder population (40+). Efficient pharmacological therapies are known, which can be very efficient together with lifestyle

As mentioned processes are observed regarding certain population, an important influence to overall situation can contribute also demographic changes which are influencing the

Expenses are here presented as a static property, but can be in the future extensions

unity step indicating the start of problem observation, namely at the birth. The results from the first and the second phase are entering the third phase together with input signals *u2(t)* and *u3(t)*. Input signal *u2(t)* provides the information regarding the number of people in the observed population with respect to their age, while with *u3(t)* also the prices for needed treatment are defined. Combining the signal *u2(t)* with calculated prevalence distribution enables the definition of patients' number in the observed population, and using the prices from *u3(t)* also the economical burden can be calculated.

Fig. 4. Usage of Markov processes in decision tree structure

Presented structure gives very good insight how patients are distributed regarding their age and also how this influences the economical burden of observed population. In the case of similar disease distribution only demographic data can be changed and perhaps (if essentially different also) prices and model gives the estimation of patients' number or treatment economical burden for another country or group of people. This approach is therefore especially interesting for the countries or areas for which national diseases registers are not available. But, the drawback of this mathematical presentation is, that it is very difficult to identify the influence on population, which is the result of some actions realized on only one part of the population where also the transient response due to dynamical system properties should be taken into account. To indicate how to overcome this problem let's present only one part of the situation from Fig. 5 and from a slightly different view point. The idea is illustrated in Fig. 6 taking into account also the possibility of coexistence of different dynamical processes descriptions.

unity step indicating the start of problem observation, namely at the birth. The results from the first and the second phase are entering the third phase together with input signals *u2(t)* and *u3(t)*. Input signal *u2(t)* provides the information regarding the number of people in the observed population with respect to their age, while with *u3(t)* also the prices for needed treatment are defined. Combining the signal *u2(t)* with calculated prevalence distribution enables the definition of patients' number in the observed population, and using the prices

from *u3(t)* also the economical burden can be calculated.

Fig. 4. Usage of Markov processes in decision tree structure

of coexistence of different dynamical processes descriptions.

Presented structure gives very good insight how patients are distributed regarding their age and also how this influences the economical burden of observed population. In the case of similar disease distribution only demographic data can be changed and perhaps (if essentially different also) prices and model gives the estimation of patients' number or treatment economical burden for another country or group of people. This approach is therefore especially interesting for the countries or areas for which national diseases registers are not available. But, the drawback of this mathematical presentation is, that it is very difficult to identify the influence on population, which is the result of some actions realized on only one part of the population where also the transient response due to dynamical system properties should be taken into account. To indicate how to overcome this problem let's present only one part of the situation from Fig. 5 and from a slightly different view point. The idea is illustrated in Fig. 6 taking into account also the possibility

Fig. 5. Diseases prevalence, number of patients and expenses presentation

Here D2 is a disease of the third level due to the fact that on one side risky and/or unhealthy life style (population status observed in the second level of the structure) can influence the development of this chronic disease, but D2, as already mentioned, can also contribute to development of different health complications (presented at the fourth level of the proposed structure). At the second level two important problems, namely activity or inactivity and obesity are taken into account, which are two most important problems leading to D2 (Defay et al., 2001; DPPRSG, 2002; Kriska et al., 2003; Mokdad et al., 2003; ADA, 2007;).

D2 is usually preceded by a pre-diabetes ("a metabolic condition characterised by insulin resistance and primary or secondary beta cell dysfunction which increases the risk of developing type 2 diabetes and cardiovascular disease" (Tuomilehto et al., 2001; Valensi et al., 2005). It is extremely common, especially in elder population (40+). Efficient pharmacological therapies are known, which can be very efficient together with lifestyle interventions in prevention or delayed D2 development.

As mentioned processes are observed regarding certain population, an important influence to overall situation can contribute also demographic changes which are influencing the system's states at the first level.

Expenses are here presented as a static property, but can be in the future extensions reformulated to indicate the results of economical and financial flows.

Burden of Diabetes Type 2 Through Modelling and Simulation 11

divided by the square of the height in meters (kg/m2). BMI is used because, for most people, it correlates with their amount of body fat. However, it should be considered as a rough guide because it may not correspond to the same degree of fatness in different individuals. WHO defines "overweight" as a BMI equal to or more than 25, and "obesity" as a BMI equal to or more than 30 (WHO, 2011b). WHO's latest projections indicate that globally in 2005 approximately 1.6 billion adults (age 15+) were overweight and at least 400 million adults were obese. Children were defined as overweight or obese using the 85th and 95th percentiles of the reference curves. At least 20 million children under the age of 5 years were overweight globally in 2005. Once considered a problem only in high-income countries, overweight and obesity are now dramatically rising in low- and middle-income countries, particularly in urban settings. The prevalence of obesity differs from country to country and is also different regarding men and women. An average situation, which can be taken into account for most European countries, is presented in Table 2 (British Heart Foundation

From data given in Tables 1 and 2 it is clear that activity or inactivity, as well as overweight and obesity can, regarding the whole observed population, be interpreted as dynamical

In Fig. 7 the model response is illustrated which shows that activity is decreasing through the whole life time and is becoming especially intensive after the age of 40. When activity is defined also the prevalence of inactive are known, as is indicated in Fig. 8. The dynamical structure which gives the responses presented in Figs. 7 and 8 was identified so that good matching was achieved with data in Table 1 (dynamical nonlinear model of 11th order).

[years] 0 1 2 3 4 5 6 7

[%] 70 69 68.5 69 70 62 62.5 69

[years] 8 9 10 11 12 13 14 15

[years] 16-24 25-34 35-44 45-54 55-64 65-74 75+

[%] 43 44 40.5 36 31 18.5 6.5

age [years] 2-15 16-34 35-54 55-74 75+

25=<BMI<30 [%] 13.5 27 39 41.5 37.5

BMI=>30 [%] 16 19 33.5 31.5 22.5

BMI=>25 [%] 29.5 46 72.5 73 60

Table 2. Prevalence of overweight (25=<BMI<30) and obese population (BMI=>30)

[%] 68.5 64.5 64.5 64 64.5 64.5 58.5 56.5

processes where age of people is represented as independent variable.

Statistics Website, 2010).

age

average

age

average

age

average

average prevalence:

average prevalence:

average prevalence:

Table 1. Prevalence of high active population

Fig. 6. Limited sub-problem with dynamic processes at different levels

#### **3. Simulation results**

Modelling procedure of the structure indicated in Fig. 6 has started by observing the available information regarding the prevalence of population activity/inactivity and obesity as they are closely related to the probability of developing D2. It is important to mention that statistical data differ slightly for different world areas (Berghöfer et al., 2008; WHO, 2011a), but data for larger countries seem to be reliable also for the countries with comparable demographic, economic and social situation.

As very well known, activity has a significant direct influence to body weight and especially to adequate body mass maintainance, but is important also by itself as a prevention regarding the development of D2 (Defay, 2001; Brock, 2009). In adult population to the group of high active are classified those, who are active 30 minutes or more on at least five days a week, medium active are those, who are active 30 minutes or more 1 to 4 days a week, other are low active. In children the following division was adopted: high (recommended): 60 minutes or more on all 7 days per week; medium: 30–59 minutes on all 7 days per week; low: lower level of activity. Usually activity in men and women slightly differ (men and boys are slightly more active), but average data, which were used for modelling purposes, are summarized in Table 1 (British Heart Foundation Statistics Website, 2008).

Overweight and obesity are defined as abnormal or excessive fat accumulation that may impair health. The number of these people is constantly increasing and consequently the World Health Organization (WHO, 2000) has recognized obesity being a disease too and as such it deserves far more attention. It is mainly a consequence of unbalance between energy intake and energy expenditure in each individual.

For adults, overweight and obesity ranges are determined by using weight and height to calculate a number called "body mass index" (BMI). It is defined as the weight in kilograms

Fig. 6. Limited sub-problem with dynamic processes at different levels

comparable demographic, economic and social situation.

intake and energy expenditure in each individual.

Modelling procedure of the structure indicated in Fig. 6 has started by observing the available information regarding the prevalence of population activity/inactivity and obesity as they are closely related to the probability of developing D2. It is important to mention that statistical data differ slightly for different world areas (Berghöfer et al., 2008; WHO, 2011a), but data for larger countries seem to be reliable also for the countries with

As very well known, activity has a significant direct influence to body weight and especially to adequate body mass maintainance, but is important also by itself as a prevention regarding the development of D2 (Defay, 2001; Brock, 2009). In adult population to the group of high active are classified those, who are active 30 minutes or more on at least five days a week, medium active are those, who are active 30 minutes or more 1 to 4 days a week, other are low active. In children the following division was adopted: high (recommended): 60 minutes or more on all 7 days per week; medium: 30–59 minutes on all 7 days per week; low: lower level of activity. Usually activity in men and women slightly differ (men and boys are slightly more active), but average data, which were used for modelling purposes, are summarized in Table 1 (British Heart Foundation Statistics

Overweight and obesity are defined as abnormal or excessive fat accumulation that may impair health. The number of these people is constantly increasing and consequently the World Health Organization (WHO, 2000) has recognized obesity being a disease too and as such it deserves far more attention. It is mainly a consequence of unbalance between energy

For adults, overweight and obesity ranges are determined by using weight and height to calculate a number called "body mass index" (BMI). It is defined as the weight in kilograms

**3. Simulation results**

Website, 2008).

divided by the square of the height in meters (kg/m2). BMI is used because, for most people, it correlates with their amount of body fat. However, it should be considered as a rough guide because it may not correspond to the same degree of fatness in different individuals.

WHO defines "overweight" as a BMI equal to or more than 25, and "obesity" as a BMI equal to or more than 30 (WHO, 2011b). WHO's latest projections indicate that globally in 2005 approximately 1.6 billion adults (age 15+) were overweight and at least 400 million adults were obese. Children were defined as overweight or obese using the 85th and 95th percentiles of the reference curves. At least 20 million children under the age of 5 years were overweight globally in 2005. Once considered a problem only in high-income countries, overweight and obesity are now dramatically rising in low- and middle-income countries, particularly in urban settings. The prevalence of obesity differs from country to country and is also different regarding men and women. An average situation, which can be taken into account for most European countries, is presented in Table 2 (British Heart Foundation Statistics Website, 2010).

From data given in Tables 1 and 2 it is clear that activity or inactivity, as well as overweight and obesity can, regarding the whole observed population, be interpreted as dynamical processes where age of people is represented as independent variable.

In Fig. 7 the model response is illustrated which shows that activity is decreasing through the whole life time and is becoming especially intensive after the age of 40. When activity is defined also the prevalence of inactive are known, as is indicated in Fig. 8. The dynamical structure which gives the responses presented in Figs. 7 and 8 was identified so that good matching was achieved with data in Table 1 (dynamical nonlinear model of 11th order).

Table 2. Prevalence of overweight (25=<BMI<30) and obese population (BMI=>30)

Burden of Diabetes Type 2 Through Modelling and Simulation 13

Fig. 8. Prevalence of activity and inactivity in observed population illustrated through

0 10 20 30 40 50 60 70 80 90 100 0

age [years]

decision tree

0.5

Fig. 9. Number of people in Slovenia

1

1.5

number

2

2.5

3

3.5 x 104

It is important to note that such representation enables the extension of decision tree formalism to comprise also a time component, namely the age of observed people (and/or patients). This time component is of crucial importance also regarding the prevalence of great number of chronic diseases and corresponding consequences. Another advantage is that when certain population is observed these responses can be combined with demographic data to evaluate the number of observed people.

In Fig. 9 the result of the last count of the population in Slovenia in 2003 is illustrated. When combined with the prevalence of activity in Fig. 7 it becomes clear that in Slovenia around 780 000 people or 39% are active, while other 61% do not match this criteria. Distribution of the number of active people regarding their age is presented in Fig. 10.

Fig. 7. Prevalence of activity

Two output signals from the block "activity" (see Fig. 6) are entering the block "obesity". For modelling purposes the information from Table 2 was used. It is clear that the ratio between overweight and obese population is slightly changing through the life time, but as these changes are not very distinctive the assumption that it is equal to 1.33 (average value from Table 2) is taken into account.

It is also very well known that active life style has very good influence also to body mass and in contrary people who are obese are inclined to inactivity, but there is practically no quantitative data available regarding the statistical correlation on the population level among these two variables. The interesting exception represents the paper of Brock (Brock et al, 2009), where the association between insufficiently physically active and the prevalence of obesity is described for the USA in the form of linear regression model. Testing this description in comparison to information from Table 2 and presented activity response showed that it is expected the prevalence of obesity to be slightly lower in EU countries. Further nonlinearity can be presumed which can mainly be the reason of the fact that activity is essentially decreasing especially after the age of 45 (see Fig. 7).

It is important to note that such representation enables the extension of decision tree formalism to comprise also a time component, namely the age of observed people (and/or patients). This time component is of crucial importance also regarding the prevalence of great number of chronic diseases and corresponding consequences. Another advantage is that when certain population is observed these responses can be combined with

In Fig. 9 the result of the last count of the population in Slovenia in 2003 is illustrated. When combined with the prevalence of activity in Fig. 7 it becomes clear that in Slovenia around 780 000 people or 39% are active, while other 61% do not match this criteria. Distribution of

0 10 20 30 40 50 60 70 80 90 100 0

age [years]

Two output signals from the block "activity" (see Fig. 6) are entering the block "obesity". For modelling purposes the information from Table 2 was used. It is clear that the ratio between overweight and obese population is slightly changing through the life time, but as these changes are not very distinctive the assumption that it is equal to 1.33 (average value

It is also very well known that active life style has very good influence also to body mass and in contrary people who are obese are inclined to inactivity, but there is practically no quantitative data available regarding the statistical correlation on the population level among these two variables. The interesting exception represents the paper of Brock (Brock et al, 2009), where the association between insufficiently physically active and the prevalence of obesity is described for the USA in the form of linear regression model. Testing this description in comparison to information from Table 2 and presented activity response showed that it is expected the prevalence of obesity to be slightly lower in EU countries. Further nonlinearity can be presumed which can mainly be the reason of the fact that

activity is essentially decreasing especially after the age of 45 (see Fig. 7).

demographic data to evaluate the number of observed people.

10

Fig. 7. Prevalence of activity

from Table 2) is taken into account.

20

30

40

prevalence [%]

50

60

70

80

the number of active people regarding their age is presented in Fig. 10.

Fig. 8. Prevalence of activity and inactivity in observed population illustrated through decision tree

Fig. 9. Number of people in Slovenia

Burden of Diabetes Type 2 Through Modelling and Simulation 15

Both, inactivity and obesity are very important regarding the development of D2 (Valensi et al., 2005). It was discovered that most adults (85.4 - 86% in average) with diagnosed diabetes were overweight or obese (MMWR, 2004), 52% were obese, and 8.1% had morbid obesity (Daousi, 2006). Before this chronic disease is fully developed patients have a pre-diabetes which in general significantly differ from D2 regarding the fact that when strict life change is adopted taking into account corresponding diet and activity, sometimes complemented by drug treatment, patients can return to normal state. Sometimes this transition is (for example due to long lasting pre-diabetes) not possible, but in such situations D2 development is in most cases significantly postponed. Pre-diabetes is not a true disease but can be interpreted as a serious risk factor for developing D2 and cardiovascular diseases. Over 30% of people with pre-diabetes develop D2 within 5 years (Valensi, 2005). The average conversion rate was estimated at 5.8% per year with wide variations which depend on differences in age, BMI, ethnicity, etc.. It is very important to accent that several welldesigned randomized controlled trials (Valensi, 2005) have been reported that categorically confirm the benefits of interventions in pre-diabetes. Standardized diet with reduced food intake, increased physical activity and sometimes also additional drug treatment can reduce the incidence of D2 for almost 60% (in mentioned studies from 25% to 58%). But, it is important to point out that intensive lifestyle modification was nearly twice as effective in preventing D2. It is therefore evident that active management of pre-diabetes can be very

For modelling purposes the information given in Tables 3 (Narayanappa et al., 2011; Li, et al., 2009; NDS, 2011; Valensi et al., 2005) and 4 (Behl et al., 2004) was taken into account.

BMI=>25

0 10 20 30 40 50 60 70 80 90 100 0

inactive

age[yeas]

effective in preventing the progression of diabetes.

0.5

1

1.5

number of people

2

2.5 x 104

Again the average data between men and women are presented.

active

Fig. 12. Number of people in Slovenia with BMI=>25 (active and inactive)

Fig. 10. Number of active people in Slovenia

Taking into account all mentioned data the mathematical model (11th order with time delays) of overweight and obese population was identified and responses are presented in Fig. 11. It is also possible to differ among overweight and obese taking into account mentioned ratio.

When prevalence functions are defined also the number of these people can be calculated (Fig. 12). Regarding the presented model in Slovenia live over 1 million people who have BMI equal to or greater than 25 or with other words almost 55% of population have higher body mass as recommended. Among these people around 300 000 are active while others are not.

Fig. 11. Prevalence of population with BMI=>25

0 10 20 30 40 50 60 70 80 90 100 0

age [years]

Taking into account all mentioned data the mathematical model (11th order with time delays) of overweight and obese population was identified and responses are presented in Fig. 11. It is also possible to differ among overweight and obese taking into account

When prevalence functions are defined also the number of these people can be calculated (Fig. 12). Regarding the presented model in Slovenia live over 1 million people who have BMI equal to or greater than 25 or with other words almost 55% of population have higher body mass as

BMI=>25

0 20 40 60 80 100 0

inactive

active

age [years]

recommended. Among these people around 300 000 are active while others are not.

2000

mentioned ratio.

10

Fig. 11. Prevalence of population with BMI=>25

20

30

40

prevalence [%]

50

60

70

80

Fig. 10. Number of active people in Slovenia

4000

6000

8000

number

10000

12000

14000

Both, inactivity and obesity are very important regarding the development of D2 (Valensi et al., 2005). It was discovered that most adults (85.4 - 86% in average) with diagnosed diabetes were overweight or obese (MMWR, 2004), 52% were obese, and 8.1% had morbid obesity (Daousi, 2006). Before this chronic disease is fully developed patients have a pre-diabetes which in general significantly differ from D2 regarding the fact that when strict life change is adopted taking into account corresponding diet and activity, sometimes complemented by drug treatment, patients can return to normal state. Sometimes this transition is (for example due to long lasting pre-diabetes) not possible, but in such situations D2 development is in most cases significantly postponed. Pre-diabetes is not a true disease but can be interpreted as a serious risk factor for developing D2 and cardiovascular diseases. Over 30% of people with pre-diabetes develop D2 within 5 years (Valensi, 2005). The average conversion rate was estimated at 5.8% per year with wide variations which depend on differences in age, BMI, ethnicity, etc.. It is very important to accent that several welldesigned randomized controlled trials (Valensi, 2005) have been reported that categorically confirm the benefits of interventions in pre-diabetes. Standardized diet with reduced food intake, increased physical activity and sometimes also additional drug treatment can reduce the incidence of D2 for almost 60% (in mentioned studies from 25% to 58%). But, it is important to point out that intensive lifestyle modification was nearly twice as effective in preventing D2. It is therefore evident that active management of pre-diabetes can be very effective in preventing the progression of diabetes.

For modelling purposes the information given in Tables 3 (Narayanappa et al., 2011; Li, et al., 2009; NDS, 2011; Valensi et al., 2005) and 4 (Behl et al., 2004) was taken into account. Again the average data between men and women are presented.

Fig. 12. Number of people in Slovenia with BMI=>25 (active and inactive)

Burden of Diabetes Type 2 Through Modelling and Simulation 17

0 10 20 30 40 50 60 70 80 90 100 0

D2

Fig. 14. Number of patients with pre-diabetes and D2 in Slovenia

from the group of obese or overweight persons.

decades this burden can become even more serious.

age [years]

In this design phase also some of expenses needed for observed patients can be indicated. For the population with higher mass it is possible to find out that a great majority of these people would like to loose their overweight. Some of them are experimenting with different diets, around 20% of adult population (from 18 to 60) also use drugs, and around 5% from the age window of 40 to 60 use the help of medical experts. In some special cases also surgical help is needed. In Slovenia in average around 100 such surgical operations per year can be expected. More and more frequent are also cosmetic surgical operations, but were not taken into account here as they are mainly performed in private institutions and data are not

It was estimated, that for one overweight or obese patient the year price for drugs is €447.96, what represents an economic burden of €66.88 million per year (for 20% of adult population between 18 to 60). As year treatment by medical expert represents economical burden of around €3000 for this group additional €63.4 million is used (for 5% from the age window of 40 to 60). Prices for surgical operations differ drastically. In Slovenia for such intervention €7200 is needed for one patient or €720 000 per year for the whole country. All together this represents €131 million per year of direct costs or in average around €130 each year for each

An average year treatment price for one D2 patient was estimated to be €355 (Atanasijević-Kunc et al., 2008c) (general practitioner: 4 times / year, laboratory: 2 times / year, drugs), representing economical burden of over €51 million per year. It is important to observe that the maximum number of these patients can be expected inside the age window of 55 to 75. As population in Slovenia, similar to other EU countries, is getting older, in the future

To estimate such population changes mathematical model was developed taking into account average statistical parameters using data (fertility, mortality and migrations) from 2004 to 2007 as presented by Statistical Office of the Republic of Slovenia (SORS, 2011). Fertility was calculated regarding the number of people in the age window from 18 to 45. It

2000

4000

6000

8000

number

available.

10000

12000

pre-D2

14000

Table 3. Prevalence of pre-diabetes

Table 4. Prevalence of diabetes type 2

In Fig. 13 model responses are given regarding pre-diabetes (16th order model with time delays) and D2 (5th order with time delays), what further enable the calculation of observed patients with respect to their age, what shows Fig. 14. It can be concluded that in Slovenia live around 611 000 patients with pre-diabetes, or with other words, approximately 30% of the population is in such state. In addition almost 144 000 are D2-patients, or over 7% have developed this serious chronic disease. Among this group of patients 85.7% are overweight or even obese.

Fig. 13. Prevalence of pre-diabetes and D2

[years] 5-11 12-19 20+ 40-75 65+

[years] 25-34 35-44 45-54 55-64 65+

In Fig. 13 model responses are given regarding pre-diabetes (16th order model with time delays) and D2 (5th order with time delays), what further enable the calculation of observed patients with respect to their age, what shows Fig. 14. It can be concluded that in Slovenia live around 611 000 patients with pre-diabetes, or with other words, approximately 30% of the population is in such state. In addition almost 144 000 are D2-patients, or over 7% have developed this serious chronic disease. Among this group of patients 85.7% are overweight

pre-D2

0 10 20 30 40 50 60 70 80 90 100 0

D2

age [years]

3.7 16.1 35 40 50

3.5 4.2 8.9 15.5 19

age

average prevalence [%]

age

average prevalence [%]

or even obese.

10

Fig. 13. Prevalence of pre-diabetes and D2

20

30

40

prevalence [%]

50

60

70

Table 3. Prevalence of pre-diabetes

Table 4. Prevalence of diabetes type 2

Fig. 14. Number of patients with pre-diabetes and D2 in Slovenia

In this design phase also some of expenses needed for observed patients can be indicated. For the population with higher mass it is possible to find out that a great majority of these people would like to loose their overweight. Some of them are experimenting with different diets, around 20% of adult population (from 18 to 60) also use drugs, and around 5% from the age window of 40 to 60 use the help of medical experts. In some special cases also surgical help is needed. In Slovenia in average around 100 such surgical operations per year can be expected. More and more frequent are also cosmetic surgical operations, but were not taken into account here as they are mainly performed in private institutions and data are not available.

It was estimated, that for one overweight or obese patient the year price for drugs is €447.96, what represents an economic burden of €66.88 million per year (for 20% of adult population between 18 to 60). As year treatment by medical expert represents economical burden of around €3000 for this group additional €63.4 million is used (for 5% from the age window of 40 to 60). Prices for surgical operations differ drastically. In Slovenia for such intervention €7200 is needed for one patient or €720 000 per year for the whole country. All together this represents €131 million per year of direct costs or in average around €130 each year for each from the group of obese or overweight persons.

An average year treatment price for one D2 patient was estimated to be €355 (Atanasijević-Kunc et al., 2008c) (general practitioner: 4 times / year, laboratory: 2 times / year, drugs), representing economical burden of over €51 million per year. It is important to observe that the maximum number of these patients can be expected inside the age window of 55 to 75. As population in Slovenia, similar to other EU countries, is getting older, in the future decades this burden can become even more serious.

To estimate such population changes mathematical model was developed taking into account average statistical parameters using data (fertility, mortality and migrations) from 2004 to 2007 as presented by Statistical Office of the Republic of Slovenia (SORS, 2011). Fertility was calculated regarding the number of people in the age window from 18 to 45. It

Burden of Diabetes Type 2 Through Modelling and Simulation 19

The number of D2 patients in younger population is expected to decrease as the number of younger population is also decreasing, but after the age of 60 the number of D2 patients is essentially higher. The ratio between the number of D2 patients and the number of active people (people between 20 and 60) in 2003 equals 0.1208, while in 2052 it is expected to rise to 0.2036. This means that for active population only regarding D2 patients the economic burden is expected to increase for 68.5% if the prevalence of this disease remains

Therefore it would be of great importance to indicate and evaluate some solutions which

The increase of activity is, regarding medical recommendation, the first step which can represent an improvement in desired direction, and the second is of course body mass reduction. To estimate the interdependence of mentioned variables in a quantitative manner two-compartment mathematical model was used (Chow & Hall, 2008), enabling to differ among fat-free body mass (*ffm*) and fat mass (*fm*). Equation for daily energy balance is:

where *ei(t)* represents daily energy intake and *ee(t)* daily energy expenditure in *kcal*. Energy

*ci(t)* indicating carbohydrate intake, *fi(t)* fat intake and *pi(t)* protein intake while constants *ki* are: *k1=4kcal/gram, k2=9kcal/gram, k3=4 kcal/gram*. It is recommended that protein intake represents 20-30%, fat intake 15-20% and carbohydrate intake 55-60% of daily food intake.

where *tef(t)* is thermic effect of feeding which usually ranges from 7 to 15% of the total energy intake (11% in our case), *pa(t)* represents energy spent on physical activity and *rmr(t)* is the so called resting metabolic rate. It refers to the energy needed to maintain basic physiological processes. It represents a substantial percentage (45-70%) of energy expenditure for the typical individual (HER, 2001). It mainly depends on *ffm(t)* and was

The daily energy balance *eb(t)* is partitioned into one of two compartments for fat mass and

1

*dfm t r t eb t dt ρ*

*fm*

*eb t ei t ee t* (1)

*ei t k ci t k* 123 *fit k pi t* (2)

*ee t te f t pa t rmr t* (3)

*rmr t* 500 22 *ffm t* (4)

(5)

diagnosed D2 are 2.3 times higher than that for the people without D2.

among older population (Atanasijević-Kunc et al., 2008a, 2008b, 2008c).

Here it is important to point out also the following additional facts:

would decrease this enormous social and economical burden.

intake depends on food and its caloric value:

Daily energy expenditure is calculated as follows:

approximated with:

for fat-free mass:

unchanged.

was estimated that each year 2.2715% newborns are expected regarding the mentioned group of people. The realized prediction starts in 2003 and illustrates the expectations till the year 2052. The situation is illustrated in Fig. 15. An important observation from this figure is that the number of people after the age of 60 is expected to increase while the younger population, including also the majority of working people, is diminished. Combination of modelling results from Fig. 15 and the prevalence of D2 model is shown in Fig. 16.

Fig. 15. Number of people in Slovenia from 2003 to 2052

Fig. 16. Number of D2 patients from 2003 to 2052

was estimated that each year 2.2715% newborns are expected regarding the mentioned group of people. The realized prediction starts in 2003 and illustrates the expectations till the year 2052. The situation is illustrated in Fig. 15. An important observation from this figure is that the number of people after the age of 60 is expected to increase while the younger population, including also the majority of working people, is diminished. Combination of

0 10 20 30 40 50 60 70 80 90 100 0

age [years]

2052

0 10 20 30 40 50 60 70 80 90 100 0

age [yeas]

0.5

1000

2000

3000

number

4000

5000

6000

1

1.5

number of people from 2003 to 2052

2

2.5

3

3.5 x 104

2003

modelling results from Fig. 15 and the prevalence of D2 model is shown in Fig. 16.

2052

2003

Fig. 15. Number of people in Slovenia from 2003 to 2052

Fig. 16. Number of D2 patients from 2003 to 2052

The number of D2 patients in younger population is expected to decrease as the number of younger population is also decreasing, but after the age of 60 the number of D2 patients is essentially higher. The ratio between the number of D2 patients and the number of active people (people between 20 and 60) in 2003 equals 0.1208, while in 2052 it is expected to rise to 0.2036. This means that for active population only regarding D2 patients the economic burden is expected to increase for 68.5% if the prevalence of this disease remains unchanged.

Here it is important to point out also the following additional facts:

Therefore it would be of great importance to indicate and evaluate some solutions which would decrease this enormous social and economical burden.

The increase of activity is, regarding medical recommendation, the first step which can represent an improvement in desired direction, and the second is of course body mass reduction. To estimate the interdependence of mentioned variables in a quantitative manner two-compartment mathematical model was used (Chow & Hall, 2008), enabling to differ among fat-free body mass (*ffm*) and fat mass (*fm*). Equation for daily energy balance is:

$$
\epsilon eb(t) = ei(t) - ee(t) \tag{1}
$$

where *ei(t)* represents daily energy intake and *ee(t)* daily energy expenditure in *kcal*. Energy intake depends on food and its caloric value:

$$
\dot{e}i(t) = k\_1 c i(t) + k\_2 f(t) + k\_3 p i(t) \tag{2}
$$

*ci(t)* indicating carbohydrate intake, *fi(t)* fat intake and *pi(t)* protein intake while constants *ki* are: *k1=4kcal/gram, k2=9kcal/gram, k3=4 kcal/gram*. It is recommended that protein intake represents 20-30%, fat intake 15-20% and carbohydrate intake 55-60% of daily food intake. Daily energy expenditure is calculated as follows:

$$
\det(t) = \text{tf}\left(t\right) + pa(t) + rmr\left(t\right)\tag{3}
$$

where *tef(t)* is thermic effect of feeding which usually ranges from 7 to 15% of the total energy intake (11% in our case), *pa(t)* represents energy spent on physical activity and *rmr(t)* is the so called resting metabolic rate. It refers to the energy needed to maintain basic physiological processes. It represents a substantial percentage (45-70%) of energy expenditure for the typical individual (HER, 2001). It mainly depends on *ffm(t)* and was approximated with:

$$rmr(t) = 500 + 22\, ft \text{m(t)}\tag{4}$$

The daily energy balance *eb(t)* is partitioned into one of two compartments for fat mass and for fat-free mass:

$$\frac{dfm(t)}{dt} = \frac{(1 - r(t))eb(t)}{\rho\_{fm}}\tag{5}$$

$$\frac{d\mathcal{f}m(t)}{dt} = \frac{r(t)eb(t)}{\rho\_{\mathcal{f}^{\text{fin}}}} \tag{6}$$

Burden of Diabetes Type 2 Through Modelling and Simulation 21

0 500 1000 1500 2000 2500 3000 3500 4000 0

time [days]

0 10 20 30 40 50 60 70 80 90 100 0

age [years]

5

0.5

Fig. 18. Activity is increasing

1

1.5

number

2

2.5

3x 104

Fig. 17. BMI changing in an average person

10

15

20

BMI

25

30

35

40

where *r(t)* ratio is the parameter that assigns a percentage of the imbalance denoted by *eb(t)* to the compartments fat mass and fat-free mass, respectively (Dugdale & Payne, 1977):

$$r\left(t\right) = \frac{K}{K + fm\left(t\right)}; \quad K = 10.4 \frac{\rho\_{f\text{fm}}}{\rho\_{fm}}\tag{7}$$

$$\rho\_{f\text{fm}} = 1800 \text{ kcal/kg}$$

$$\rho\_{f^{\rm fm}} = 9400 \text{ kcal/kg}$$

It is important to mention that also more precise (and complex) mathematical models describing the influence of eating and physical activity to body mass exist. But in our case the goal was mainly to present the interdependence of different models and information which can be shared to obtain better insight into population behaviour what is also the reason why in this modelling step only an average person (between men and women) was taken into account. From the average height (1.72m regarding 11 European countries) and average BMI=32 also the average mass of this person is estimated to be 94.7kg. Regarding medical recommendations such person should loose around 30kg to satisfy BMI=22 in the middle of desired BMI interval. The initial fat mass was estimated from the regression equations (Jackson et al., 2002): *fm(0)=34.7 kg*.

Model response is given in Fig. 17 for observation time of 10 years. During the first year (365 days) energy intake is equal to energy expenditure (2460kcal) (for control purposes) and therefore the body mass remains unchanged. After the first year physical activity is increased from 370kcal per day (representing minimal physical activity) for 210 kcal per day. This energy expenditure can be realized by a half an hour walk, but without the increase of energy intake. Such minimal increase of activity, which is in general suitable also for obese persons, would change in three years BMI to 25.

In our case however, at the beginning of the third year of observation also the energy intake is decreased for 300 kcal per day, but only for one year. In this way desired range of BMI is reached during the second year as presented in Fig. 17. If the person remains active for half an hour per day he-she is reaching desired mass at the end of the third year.

What direct changes could such a regime of activity and diet represent for observed population and why the problems are expected in practice?

Let's take into account the following assumptions. 80% of obese and inactive people between the age of 20 to 50 are motivated to undertake the presented regime of increased activity and diet. With this they are immediately transferred into the group of active population, where they remain. After two years of activity they are also transferred out from obese population and they remain in the group of people with healthy body mass. Each year also 80% of 20 years old obese and inactive are motivated to join the motivated group.

The consequences of life – lasting increased activity together with corresponding diet are shown in Figs. 18 to 20. The increased number of active population (Fig. 18) would together with proposed diet slowly changing the number of overweight and obese people (Fig. 19).

*dffm t r t eb t*

where *r(t)* ratio is the parameter that assigns a percentage of the imbalance denoted by *eb(t)* to the compartments fat mass and fat-free mass, respectively (Dugdale & Payne, 1977):

; 10.4 *ffm*

1800 / 9400 /

*ρ kcal kg ρ kcal kg*

It is important to mention that also more precise (and complex) mathematical models describing the influence of eating and physical activity to body mass exist. But in our case the goal was mainly to present the interdependence of different models and information which can be shared to obtain better insight into population behaviour what is also the reason why in this modelling step only an average person (between men and women) was taken into account. From the average height (1.72m regarding 11 European countries) and average BMI=32 also the average mass of this person is estimated to be 94.7kg. Regarding medical recommendations such person should loose around 30kg to satisfy BMI=22 in the middle of desired BMI interval. The initial fat mass was estimated from the regression

Model response is given in Fig. 17 for observation time of 10 years. During the first year (365 days) energy intake is equal to energy expenditure (2460kcal) (for control purposes) and therefore the body mass remains unchanged. After the first year physical activity is increased from 370kcal per day (representing minimal physical activity) for 210 kcal per day. This energy expenditure can be realized by a half an hour walk, but without the increase of energy intake. Such minimal increase of activity, which is in general suitable also

In our case however, at the beginning of the third year of observation also the energy intake is decreased for 300 kcal per day, but only for one year. In this way desired range of BMI is reached during the second year as presented in Fig. 17. If the person remains active for half an hour per day he-she is reaching desired mass at the end of the third

What direct changes could such a regime of activity and diet represent for observed

Let's take into account the following assumptions. 80% of obese and inactive people between the age of 20 to 50 are motivated to undertake the presented regime of increased activity and diet. With this they are immediately transferred into the group of active population, where they remain. After two years of activity they are also transferred out from obese population and they remain in the group of people with healthy body mass. Each year also 80% of 20 years old obese and inactive are motivated to join the motivated

The consequences of life – lasting increased activity together with corresponding diet are shown in Figs. 18 to 20. The increased number of active population (Fig. 18) would together with proposed diet slowly changing the number of overweight and obese people (Fig. 19).

*K ρ r t K K fm t ρ*

> *ffm fm*

equations (Jackson et al., 2002): *fm(0)=34.7 kg*.

year.

group.

for obese persons, would change in three years BMI to 25.

population and why the problems are expected in practice?

*ffm*

*dt ρ* (6)

(7)

*fm*

Fig. 17. BMI changing in an average person

Fig. 18. Activity is increasing

Burden of Diabetes Type 2 Through Modelling and Simulation 23

The consequence would be that among this group of patients from pre-diabetes only 50% would develop D2, while other would return to the population with healthy body mass and

In this way the number of obese and overweight people would be decreased for over 53% and the number of D2 patients for 35%. In the same proportion also the corresponding

The proposed strategy has one important deficiency, namely the lack of patients' motivation and discipline as the success is completely dependent on these two important factors. Therefore our further goal is to extend the presented model with motivation aspects and

Four-level mathematical description structure is proposed which can be efficiently used for the estimation of the number of observed patients, the distribution regarding their age and for the estimation of their economical burden. It can comprise different mathematical descriptions important for observed processes. In our case it consists of dynamical decision tree describing the prevalence of population activity and inacivity, overweight and obesity, pre-diabetes and diabetes type 2. In combination with dynamical population model predicting the number of people, two-compartment dynamical model for estimation of body mass changes and evaluated treatment expenses also the number of observed patients and treatment burden were calculated for Slovenia. As similar results can be expected in the countries with comparable social and economical situation (the great majoity of EU countries), the following can be concluded for the population of one

overweight and obese patients spend around €65.5 million per year for body mass

in this way the number of obese and overweight people could be decreased for over

It is obvious that motivation is the most important obstacle in achieving the efficient improvement in reduction of D2 patients and corresponding economical burden. Therefore our future interest will be directed in developing corresponding mathematical model to complement the presented structure and to indicate the potentially important further

The authors sincerely thank prof. dr. Rihard Karba, University of Ljubljana, Faculty of Electrical Engineering, for the fruitful discussions and his suggestions which have

without D2 (Fig 20).

**4. Conclusion**

million people:

reduction,

activities.

**5. Acknowledgment**

significantly influenced the work.

over 60% are inacive,

only 45% have body mass in normal range,

over 7% have developed diabetes type 2,

 direct tratment expenses for D2 patients are around €25.5 million, essential savings could be expected with minimal life-style changes,

53% and the number of D2 patients for over 35%.

30% of people has pre-diabetes,

expenses would be reduced.

expenses needed for its stimulation.

Fig. 19. Number of overweight and obese patients is decreasing

Fig. 20. Number of D2 patients is decreasing

The consequence would be that among this group of patients from pre-diabetes only 50% would develop D2, while other would return to the population with healthy body mass and without D2 (Fig 20).

In this way the number of obese and overweight people would be decreased for over 53% and the number of D2 patients for 35%. In the same proportion also the corresponding expenses would be reduced.

The proposed strategy has one important deficiency, namely the lack of patients' motivation and discipline as the success is completely dependent on these two important factors. Therefore our further goal is to extend the presented model with motivation aspects and expenses needed for its stimulation.

### **4. Conclusion**

22 Topics in the Prevention, Treatment and Complications of Type 2 Diabetes

0 10 20 30 40 50 60 70 80 90 100 0

age [years]

0 10 20 30 40 50 60 70 80 90 100 0

age [years]

Fig. 19. Number of overweight and obese patients is decreasing

0.5

500

Fig. 20. Number of D2 patients is decreasing

1000

1500

2000

number

2500

3000

3500

4000

1

1.5

number

2

2.5 x 104

Four-level mathematical description structure is proposed which can be efficiently used for the estimation of the number of observed patients, the distribution regarding their age and for the estimation of their economical burden. It can comprise different mathematical descriptions important for observed processes. In our case it consists of dynamical decision tree describing the prevalence of population activity and inacivity, overweight and obesity, pre-diabetes and diabetes type 2. In combination with dynamical population model predicting the number of people, two-compartment dynamical model for estimation of body mass changes and evaluated treatment expenses also the number of observed patients and treatment burden were calculated for Slovenia. As similar results can be expected in the countries with comparable social and economical situation (the great majoity of EU countries), the following can be concluded for the population of one million people:

It is obvious that motivation is the most important obstacle in achieving the efficient improvement in reduction of D2 patients and corresponding economical burden. Therefore our future interest will be directed in developing corresponding mathematical model to complement the presented structure and to indicate the potentially important further activities.

#### **5. Acknowledgment**

The authors sincerely thank prof. dr. Rihard Karba, University of Ljubljana, Faculty of Electrical Engineering, for the fruitful discussions and his suggestions which have significantly influenced the work.

Burden of Diabetes Type 2 Through Modelling and Simulation 25

Boutayeb, A. & Chetouani, A. (2006). A critical review of mathematical models and data

Boutayeb, A., Chetouani, A., Achouyab, K. & Twizell, E. H. (2006). A non-linear population

British Heart Foundation Statistics Website (2008). Age differences and physical activity,

British Heart Foundation Statistics Website (2010). Trends in the prevalence of overweight

Briggs, A. & Sculpher, M. (1998). An Introduction to Markov Modeling for Economic Evaluation. *PharmacoEconomics*, 13(4), 1998 , pp. 397-409, ISSN 1170-7690. Brock, D. W., Thomas, O., Cowan, C. D., Allison, D. B., Gaesser, G. A. & Hunter, G. R.

Cassandras, C.G., Lafortune S. (1999). *Introduction to Discrete Evant Systems*. Kluwer

Cellier, F. E.(1991). *Continuous System Modeling*. Springer-Verlag, New York, ISBN 0-387-

Cellier, F. E. & Kofman, E. (2006). *Continuous System Simulation*, Springer Science + Business

Chow, C. C. & Hall, K. D. (2008). The dynamics of human body weight change, *PLoS*

Daousi, C., Casson, I. F., Gill, G. V., MacFarlane, I. A., Wilding, J. P. H.& Pinkney, J. H.

Defay, R., Delcourt, C., Ranvier, M., Lacroux, A. & Papoz, L. (2001). Relationships between

DPPRG - Diabetes Prevention Program Research Group, (2002). Reduction in the Incidence

Dugdale, A. & Payne, P. (1977). Pattern of lean and fat deposition in adults, *Nature*, Vol. 266,

Eddy, D. M. & Schlessinger, L. (2003a). Archimedes, A trial-validated model of diabetes. *Diabetes Care*, Vol. 26, No. 11, (2003), pp. 3093–3101, Online ISSN 1935-5548 Eddy, D. M. & Schlessinger, L. (2003b). Validation of the Archimedes Diabetes Model. *Diabetes Care*, Vol. 26, No. 11, (2003), pp. 3102–3110, Online ISSN 1935-5548. HER (2001). Human energy requirements, Report of a Joint FAO/WHO/UNU Expert

(2006). Prevalence of obesity in type 2 diabetes in secondary care: association with cardiovascular risk factors, *Postgraduate Medical Journal*, 2006; Vol. 82, pp. 280-284

physical activity, obesity and diabetes mellitus in a French elderly population: the POLA study, *International Journal of Obesity*, 2001, Vol. 25, No. 4, pp. 512-518, ISSN

of Type 2 Diabetes with Lifestyle Intervention or Metformin, *The New England*

Consultation, Rome, 17-24 October 2001, ISBN 92-5-105212-3, ISSN 1813-3932,

*Computational Biology*, Vol. 4, No. 3, pp. 1–13, ISSN 1553-734X.

*Journal of Medicine*, 2002, Vol. 346, pp. 393-403, ISSN 1533-4406.

<http://www.fao.org/docrep/007/y5686e/y5686e00.htm>.

and obesity, <http://www.heartstats.org/datapage.asp?id=1011>.

1475-925X, doi:10.1186/1475-925X-5-43.

<http://www.heartstats.org/atozpage.asp?id=4955>.

Academic Publishers, Boston, ISBN 0-7923-8609-4.

21, pp. 127-139, ISSN 15985865.

6, No. 1, pp.1–5, ISSN 1543-3080.

Media, New York, ISBN 0-387-26102-8.

doi:10.1136/pmj.2005.039032, ISSN 00325473.

97502-0.

0307-0565.

pp. 349–351, ISSN 0028-0836.

used in diabetology, *BioMedical Engineering OnLine*, Vol. 5, No. 43, (2006), ISSN:

model of diabetes mellitus. Journal of Applied Mathematics and computing, Vol.

(2009). Association Between Insufficiently Physically Active and the Prevalence of Obesity in the United States, *Journal of physical activity & health*, 2009, January, Vol.

#### **6. References**

<http://dx.doi.org/10.1080/13873950903375304>, doi:10.1080/13873950903375304.

ADA - American Diabetes Association (2007). Standards of medical care in diabetes—2007,

Arnold, R. J. G. (Editor) (2010). *Pharmacoeconomics, From Theory to Practice*, CRC Press,

Atanasijević-Kunc, M.; Drinovec, J. & Mrhar, A. (2008a). Usage of Modelling and Simulation

Atanasijević-Kunc, M.; Drinovec, J.; Ručigaj, S. & Mrhar, A. (2008b). Modelling of the risk

Atanasijević-Kunc, M.; Drinovec, J.; Ručigaj, S. & Mrhar, A. (2008c). Modeling the

Atanasijević-Kunc, M.; Drinovec, J.; Ručigaj, S. & Mrhar, A. (2011). Simulation analysis of

Behl, G. F. E., Copeland, J. A., Wiggins, J. (2004). *The District of Columbia Diabetes Surveillance*

final data\_and\_stat\_diabetes.pdf. #search=%22columbia%20diabetes%20

Bellazzi R., Nucci G. & Cobelli C. (2001). The Subcutaneous Route to Insulin Dependent

Medicine and Biology Magazine, 2001, 20(1), pp.54-64, ISSN: 0739-5175. Belič, A. (2009). Modelling in systems biology, neurology and pharmacy. *Mathematical and*

Berghöfer, A., Pischon, T., Reinhold, T., Apovian, C. M., Sharma, A. M. & Willich, S.

Boutayeb, A.; Twizell, E. H.; Achouayb, K. & Chetouani, A. (2004). A mathematical model

Vol. 3, No. 20, (2004), doi:10.1186/1475-925X-3-20.

4754,<http://dx.doi.org/10.1016/j.matcom.2010.10.024>,

doi: 10.1016/j.matcom.2010.10.024.

Taylor & Francis Group, Drug Discovery Series/13, ISBN 978-1-4200-8422, Boca

in Medicine and Pharmacy. *Journal of Slovene Medical Society*, Vol. 77, No. 1, (2008),

factors and chronic diseases that influence the development of serious health complications. *Journal of Slovene Medical Society*, Vol. 77, No. 8, (2008), pp. 487-498,

influence of risk factors and chronic diseases on the development of strokes and peripheral arterial-vascular disease. *Simulation modelling practice and theory*, Vol. 16, No. 8, (2008), pp. 998 -1013, ISSN 1569-190X, doi: DOI:10.1016/j.simpat.

coronary heart disease, congestive heart failure and end-stage renal disease economic burden. *Mathematics and Computers in simuation*, pp. 1-14, ISSN 0378 -

*Report*, DC Department of Health, Washington, DC, September 2004, <http://dchealth.dc.gov/doh/lib/doh/services/special\_programs/diabetes/pdf/

Diabetes Therapy: Closed-Loop and Partially Closed-Loop Control Strategies for insulin Delivery and Measuring Glucose Concentration. IEEE Engineering in

*Computer Modelling of Dynamical Systems*, Vol. 15, No. 6, (2009), pp. 479 – 491, ISSN

<http://dx.doi.org/10.1080/13873950903375304>, doi:10.1080/13873950903375304.

N. (2008). Obesity prevalence from a European perspective: a systematic review, *BMC Public Health*, 2008, 8:200, doi:10.1186/1471-2458-8-200, ISSN 1471-

for the burden of diabetes and its complications. *BioMedical Engineering OnLine*,

*Diabetes Care*, 2007, Jan;30, Suppl 1:S4-S41, ISSN 0149-5992.

**6. References**

Raton.

pp. 57-71, ISSN 1318-0347.

ISSN 1318-0347.

2008.03.008.

prevalence%22>.

1387-3954,

2458.

Burden of Diabetes Type 2 Through Modelling and Simulation 27

Mokdad, A. H., Ford, E. S., Bowman, B. A., Dietz, W. H., Vinicor, F., Bales, V. S. & Marks, J.

Narayanappa, D., Rajani, H. S., Mahendrappa, K. B. & Prabhakar, A. K. (2011). Prevalence of

NDS (2011). National Diabetes Statistics, 2011, U.S. Department of Health and Human

 <http://diabetes.niddk.nih.gov/DM/PUBS/statistics/DM\_Statistics.pdf>. Shianga, K.D. & Kandeelc, F. (2010). A computational model of the human glucose-insulin

Shih, H.C., Chou, P., Liu, C. M. & Tung, T. H. (2007). Estimation of progression of multi-

Stahl, J. E. (2008). Modelling Methods for Pharmacoeconomics and Health Technology

Tarride, J. E., Hopkins, R., Blackhouse, G., Bowen, J. M., Bischof, M., Von Keyserlingk, C.,

Tuomilehto, J., Lindström, J. E. J. G., Valle, T. T., Hämäläinen, H., Ilanne-Parikka, P.,

Valensi, P., Schwarz, P., Hall, M., Felton, A. M., Maldonato, A. & Mathieu, C. (2005). Pre-

WHO - World Health Organization (2000), Technical report series 894: Obesity:

<http://www.who.int/diabetes/facts/world\_figures/en/index.html>.

*Medicine*, 2001, Vol. 344, No. 18, pp. 1343-1350, ISSN 1533-4406.

<http://whqlibdoc.who.int/trs/WHO\_TRS\_894\_(part1).pdf>.

WHO - World health organization (2011a). Diabetes Programme, Prevalence data,

76-79, doi: 10.1001/jama.289.1.76, ISSN 00987484.

ISSN 0019-6061.

364, ISSN 1552-4965.

ISSN 1472-6947.

200516342.

Simulink (2005). *User's Guide*, The MathWorks Inc. SORS (2011). Statistical Office of the Republic of Slovenia,

Vol. 28, No. 4, pp. 255-277, ISSN 1170-7690.

Organization. ISBN 92-4-120894-5,

<http://www.stat.si/eng/index.asp>.

131-148, ISSN 1170-7690.

2011,

S. (2003). Prevalence of Obesity, Diabetes, and Obesity-Related Health Risk Factors, 2001, *JAMA, The Journal of the American Medical Association*, 2003; Vol. 289, No. 1, pp.

Prediabetes in School-Going Children, Indian Pediatrics, Vol. 48, 2011, pp. 295-299,

Services, National Institutes of Health, NIH Publication No. 11–3892, February

regulatory system. Journal of Biomedical Research, Vol. 24, Iss. 5, (2010), pp. 347-

state chronic disease using the Markov model and prevalence pool concept. BMC Medical Informatics and Decision Making, 2007, 7:34, doi:10.1186/1472-6947-7-34,

Assessment, An Overview and Guide, *Pharmacoeconomics*, 2008, Vol. 26, No. 2, pp.

O'Reilly, D., Xie, F. & Goeree, R. (2010). A Review of Methods Used in Long-Term Cost-Effectiveness Models of Diabetes Mellitus Treatment, *Pharmacoeconomics*, 2010,

Keinänen-Kiukaanniemi, S., Laakso, M., Louheranta, A., Rastas, M., Salminen, V., Uusitupa, M. (2001). Prevention of type 2 diabetes mellitus by changes in lifestyle among subjects with impaired glucose tolerance, *The New England Journal of*

diabetes essential action: a European perspective, *Diabetes & Metabolism*, Vol 31, No. 6, 2005, pp. 606-620, ISSN 1262-3636, doi : DM-12-2005-31-6-1262-3636-101019-

Preventing and managing the global epidemic. Geneva: World Health

Homer, J., Jones, A., Seville, D., Essien, J., Milstein, B. & Murphy, D. (2004). The CDC's Diabetes Systems Modeling Project: Developing a New Tool for Chronic Disease Prevention and Control. 22nd International Conference of the System Dynamics Society, July 25-29, 2004 (Oxford, England),

<http://www.sustainabilityinstitute.org/pubs/Diabetes\_System(ISDC04).pdf>.

<http://www.cdc.gov/mmwr/preview/mmwrhtml/mm5345a2.htm>.

Homer, J., Jones, A., Seville, D., Essien, J., Milstein, B. & Murphy, D. (2004). The CDC's

 <http://www.sustainabilityinstitute.org/pubs/Diabetes\_System(ISDC04).pdf>. Hoppensteadt, F. C. & Peskin, C. S. (2002). *Modeling and Simulation in Medicine and the Life*

D'Inverno, M. & Luck, M. (2010). *Understanding Agent Systems*. Springer-Verlag, Berlin, ISBN

Jackson, A. S., Stanforth, P. R., Gagnon, J., Rankinen, T., Leon, A. S., Rao, D. C., Skinner, J.

Kriska, A. M., Saremi, A., Hanson, R. L., Bennett, P. H., Kobes, S., Williams, D. E. &

Kristöfel, P., Breitenecker, F., Gyimesi, M. & Popper, N. (2007). A System Dynamics Model

Lam, Z. H., Hwang, K.S., Lee, J. Y., Chase, J. G. & Walker, G. C. (2002). Active insulin

Levenson, J. W., Skerrett, P. J., Gaziano, J. M. (2002). Reducing the Global Burden of

Li C., Ford, E. S., Zhao, G. & Mokdad, A. H. (2009). Prevalence of Pre-Diabetes and Its

Makroglou, A.; Li, J. & Kuang, Y. (2006). Mathematical models and software tools for the

Matko, D.; Karba, R. & Zupančič, B. (1992). Simulation and Modelling of Continuous Systems, A Case Study Approach, Prentice Hall, New York, ISBN 0-13-808064-X

MMWR (2004). Prevalence of Overweight and Obesity Among Adults with Diagnosed

<http://www.cdc.gov/mmwr/preview/mmwrhtml/mm5345a2.htm>.

S., Bouchard, C. & Wilmore, J. H. (2002). The effect of sex, age and race on estimating percentage body fat from body mass index: The heritage family study, *International Journal of Obesity*, Vol. 26, pp. 789–796, doi:10.1038/sj.ijo.0802006,

Knowler, W. C. (2003). Physical Activity, Obesity, and the Incidence of Type 2 Diabetes in a High-Risk Population, *American Journal of Epidemiology*, 2003, Vol. 158,

for the Diabetes Prevalence in Austria, Proc. EUROSIM 2007, 9-13 Sept. 2007,

infusion using optimal and derivative weighted control. *Medical engineering physics*,

Cardiovascular Disease: The Role of Risk Factors. *Preventive Cardiology*, Fall 2002,

Association With Clustering of Cardiometabolic Risk Factors and Hyperinsulinemia Among U.S. Adolescents, Diabetes Care, Vol. 32, No. 2, 2009, pp.

glucose-insulin regulatory system and diabetes: an overview. *Applied Numerical Mathematics*, Vol. 56, Iss. 3-4, (2006), pp. 559-573, Selected Papers, The Third International Conference on the Numerical Solutions of Volterra and Delay

Diabetes - United States, 1988--1994 and 1999—2002, (2004). *Morbidity and Mortality Weekly Report (MMWR)*, 53(45); pp. 1066-1068, 2004, Centers for Disease Control

*Sciences*, Springer-Verlag, New York, ISBN 0-387-95072-9.

No. 7, DOI: 10.1093/aje/kwg191, ISSN 0002-9262.

Ljubljana, Slovenia, ISBN 978-3-901608-32-2.

2002, Vol. 24, pp. 663-672, ISSN 1350-4533.

Vol. 5, pp. 188-199, ISSN 1520-037X.

342-347, ISSN: 1935-5548.

Equations, ISSN 0168-9274.

Matlab, (2005). *Reference Guide*, The MathWorks Inc.

and Prevention (CDC), ISSN 0149-2195,

Society, July 25-29, 2004 (Oxford, England),

978-3-642-07382-3.

ISSN 0307-0565.

Diabetes Systems Modeling Project: Developing a New Tool for Chronic Disease Prevention and Control. 22nd International Conference of the System Dynamics

<http://diabetes.niddk.nih.gov/DM/PUBS/statistics/DM\_Statistics.pdf>.

<http://whqlibdoc.who.int/trs/WHO\_TRS\_894\_(part1).pdf>.

WHO - World health organization (2011a). Diabetes Programme, Prevalence data, <http://www.who.int/diabetes/facts/world\_figures/en/index.html>.

**2**

*Italy*

**Alzheimer's Disease and Type 2 Diabetes:**

**Different Pathologies and Same Features**

Protein aggregation is a very fascinating matter due to its implication in many human neurodegenerative diseases and its relevance in food and pharmaceutical industries. In some cases, the aggregation of protein is a natural phenomenon occurring in living organisms. For example, in the reaction leading from the globular (G) monomeric actin to its

n (G-Actin) (F-Actin)n or the case of polymerization of tropocollagen to obtain collagen fibrils, a process leading, in the case of type I Collagen, to the formation of long fibrils having a wave pattern (Yadavalli

In general, a non-physiological aggregation, that is an aggregation process not naturally occurring, starts from "activated" molecules having secondary and/or tertiary structures different from those corresponding to the "native state" (Manno et al., 2006, 2010; Morris et al., 2009). Increasing evidence suggests that the non-physiological aggregation of proteins such beta-amyloid, alpha-synuclein, huntingtin and ataxin, superoxide-dismutase 1 (SOD1), Tau and Amylin, is responsible for the onset of many neurodegenerative pathologies such as Alzheimer's, Parkinson's and Huntington's diseases, Amyotrophic Lateral Sclerosis, Frontotemporal Lobar Degeneration (Figure 1) and Type 2 Diabetes (or diabetes mellitus),

The question of what triggers the transformation of a biologically active protein into a "pathogenic agent" with high self-assembly propensity is still unanswered. Some of the

i. the propensity of some proteins to assume a pathological conformation which increases

ii. the persistently high cellular or plasma concentrations (Singleton et al., 2003; Farrer et

iii. an amino acid mutation or a genetic expansion of DNA sequences encoding proteins, as

iv. an abnormal post-traslational modification of the protein responsible for the disease

in the case of Huntington disease (Cummings & Zoghbi, 2000);

**1. Introduction**

et al., 2010).

polymeric fibrillar (F) structure (Morris et al., 2009):

respectively (Chiti & Dobson, 2006).

with aging (Uversky, 2007; Saraiva, 2001);

proposed explainations include:

(Goedert et al., 1993);

al., 2004);

Marta Di Carlo1, Pasquale Picone1, Rita Carrotta2,

*1Istituto di Biomedicina e Immunologia Molecolare (IBIM) – CNR*

Daniela Giacomazza2 and P.L. San Biagio2

*2Istituto di Biofisica (Palermo unit) – CNR*

WHO - World health organization (2011b), Obesity and overweight, Fact sheet N°311, March 2011,

<http://www.who.int/mediacentre/factsheets/fs311/en/>.

### **Alzheimer's Disease and Type 2 Diabetes: Different Pathologies and Same Features**

Marta Di Carlo1, Pasquale Picone1, Rita Carrotta2, Daniela Giacomazza2 and P.L. San Biagio2 *1Istituto di Biomedicina e Immunologia Molecolare (IBIM) – CNR 2Istituto di Biofisica (Palermo unit) – CNR Italy*

#### **1. Introduction**

28 Topics in the Prevention, Treatment and Complications of Type 2 Diabetes

WHO - World health organization (2011b), Obesity and overweight, Fact sheet N°311,

<http://www.who.int/mediacentre/factsheets/fs311/en/>.

March 2011,

Protein aggregation is a very fascinating matter due to its implication in many human neurodegenerative diseases and its relevance in food and pharmaceutical industries. In some cases, the aggregation of protein is a natural phenomenon occurring in living organisms. For example, in the reaction leading from the globular (G) monomeric actin to its polymeric fibrillar (F) structure (Morris et al., 2009):

#### n (G-Actin) (F-Actin)n

or the case of polymerization of tropocollagen to obtain collagen fibrils, a process leading, in the case of type I Collagen, to the formation of long fibrils having a wave pattern (Yadavalli et al., 2010).

In general, a non-physiological aggregation, that is an aggregation process not naturally occurring, starts from "activated" molecules having secondary and/or tertiary structures different from those corresponding to the "native state" (Manno et al., 2006, 2010; Morris et al., 2009). Increasing evidence suggests that the non-physiological aggregation of proteins such beta-amyloid, alpha-synuclein, huntingtin and ataxin, superoxide-dismutase 1 (SOD1), Tau and Amylin, is responsible for the onset of many neurodegenerative pathologies such as Alzheimer's, Parkinson's and Huntington's diseases, Amyotrophic Lateral Sclerosis, Frontotemporal Lobar Degeneration (Figure 1) and Type 2 Diabetes (or diabetes mellitus), respectively (Chiti & Dobson, 2006).

The question of what triggers the transformation of a biologically active protein into a "pathogenic agent" with high self-assembly propensity is still unanswered. Some of the proposed explainations include:

Alzheimer's Disease and Type 2 Diabetes: Different Pathologies and Same Features 31

insulin deficiency. The third type, gestational diabetes, is when pregnant women, who have never had diabetes before, have a high blood glucose level during pregnancy and it may precede development of T2D. Ninety percent of diabetes patients have T2D, which usually has its onset in adulthood. Diabetes is increasing and the World Health Organization estimates that there will be a doubling of cases by 2025, largely as a result of lack of physical activity and poor dietary habits, both of which are risk factors for the disease. Obesity, hypertension, hyper-cholesterolemia and hyperlipidemia are all associated with T2D

 Alzheimer's disease (AD) is the most common form of dementia in the elderly. It is characterized by neuronal cell loss and increasing accumulation of neurofibrillary tangles (NTF) in neurons and amyloid fibers in neuritic plaques and in the walls of blood vessels (Wisniewski et al., 1997). Amyloid beta-peptides of varying length (39–43 residues) are produced by cleavage of a transmembrane protein, the amyloid beta-protein precursor (APP) (Wilquet & De Strooper, 2004). The 42 residue beta-peptide (Abeta-42) is the predominant form found in plaques and under physiological condition the ratio between Abeta42 and Abeta40 is about 1:10 (Iwatsubo et al., 1994). Abeta42 has a much greater neurotoxity than Abeta40 and its aggregation kinetics is faster than other beta-petides (Davis & Van Nostrand, 1996). The proteinaceous material is organized in structured linear aggregates (amyloid fibrils). A recent and now convincing belief is that small diffusible oligomers of Abeta-42, called ADDLs, are the determining pathogenic species causing synaptic dysfunction and eventually neuronal degeneration (Lambert et al., 1998; Picone et

AD accounts for 50–70% of all dementia cases and is characterized by cognitive deficits. This incurable, degenerative, and terminal disease was first described by the German psychiatrist and neuropathologist Alois Alzheimer in 1906. Several factors have been considered relevant for the AD pathogenesis and among these the most important is age. During life small variations occurring in cellular metabolism and structure can modify the functional state of susceptible neurons, leading to dramatic or even lethal changes. Thus, while the the monomeric Abeta is not neurotoxic, for not yet known reasons it starts to form

Familial AD is a rare form of dementia and is caused by autosomal dominant mutations in one or more of the genes encoding the amyloid precursor protein (APP), presenilin 1 or presenilin 2 (the latter two proteins form the catalytic core of *γ*-secretase) (Gotz et al., 2004). By contrast, late-onset AD might be caused by environmental and/or life style factors (Rocchi et al., 2003). Interestingly, late-onset AD is characterized not only by the neuropathological markers mentioned above, but also by vascular lesions, and hyperglycemia, hyperinsulinemia, insulin resistance, glucose intolerance, adiposity,

Diabetes and AD are considered age-related diseases and are both increasing. In the USA, diabetes and AD affect ≈ 23.6 and ≈ 5.3 million people, respectively, and these numbers are projected to rise considerably. The Centers for Disease Control and Prevention predict that more than 29 million people in the US will be affected by diabetes by 2050, while the Alzheimer's association forecasts that by this date, 11–16 million Americans will have AD (Han & Li, 2010). Numerous studies report that patients with diabetes have an increased risk of developing AD compared with healthy individuals (Arvanitakis et al., 2004; Neumann et al., 2008; Roriz-Filho et al. 2009). In fact, some studies revealed that 80% of

supramolecular aggregates accumulating in the AD brain.

atherosclerosis and hypertension (Haan, 2006).

(MedScape).

al., 2009)

v. the proteolitic cleavage of the precursor protein, as in the case of Abeta-peptide;

vi. the influence of environmental factors.

Fig. 1. *Protein misfolding and aggregation as the common molecular pathogenesis of neurodegenerative diseases*. Some genetic mutations responsible of neurodegenerative diseases render the causative proteins prone to misfold and to form beta-sheet-rich oligomers and amyloid fibrillar aggregates, resulting in their accumulation in the affected neurons and eventually leading to degeneration in the brain. This mechanism is retained common to a broad variety of neurodegenerative diseases, such as Alzheimer's, Parkinson's and Huntington disease, Amyothophic Lateral Sclerosis and Frontotemporal Lobar degeneration.

Type 2 diabetes (T2D) is classified as a metabolism disorder and it is often associated with microvascular and macrovascular complications, including retinopathy, nephropathy, neuropathy and cardiovascular disease. A diabetes affected person has an elevated quantity of glucose in the blood (hyperglycemia) that is caused by the inability of the body either to produce any insulin or enough insulin, or by the inability of the cells to respond properly to the insulin producted in the pancreas. This excess blood glucose eventually passes out of the body in the urine. So, even though the blood has plenty of glucose, the cells are incapable of getting it for their essential energy and growth requirements. There are three main types of diabetes: Type 1 diabetes (T1D) (referred to as *insulin-dependent* diabetes and *juvenile* diabetes), results from the body's failure to produce insulin, and presently requires the person to inject insulin. Type 2 diabetes (referred to as *non-insulin-dependent* diabetes mellitus, and *adult-onset* diabetes.) is associated with a reduced ability of insulin to stimulate glucose utilization (insulin resistance) and sometimes it is combined with an absolute

v. the proteolitic cleavage of the precursor protein, as in the case of Abeta-peptide;

Fig. 1. *Protein misfolding and aggregation as the common molecular pathogenesis of*

*neurodegenerative diseases*. Some genetic mutations responsible of neurodegenerative diseases render the causative proteins prone to misfold and to form beta-sheet-rich oligomers and amyloid fibrillar aggregates, resulting in their accumulation in the affected neurons and eventually leading to degeneration in the brain. This mechanism is retained common to a broad variety of neurodegenerative diseases, such as Alzheimer's, Parkinson's and Huntington disease, Amyothophic Lateral Sclerosis and Frontotemporal Lobar

Type 2 diabetes (T2D) is classified as a metabolism disorder and it is often associated with microvascular and macrovascular complications, including retinopathy, nephropathy, neuropathy and cardiovascular disease. A diabetes affected person has an elevated quantity of glucose in the blood (hyperglycemia) that is caused by the inability of the body either to produce any insulin or enough insulin, or by the inability of the cells to respond properly to the insulin producted in the pancreas. This excess blood glucose eventually passes out of the body in the urine. So, even though the blood has plenty of glucose, the cells are incapable of getting it for their essential energy and growth requirements. There are three main types of diabetes: Type 1 diabetes (T1D) (referred to as *insulin-dependent* diabetes and *juvenile* diabetes), results from the body's failure to produce insulin, and presently requires the person to inject insulin. Type 2 diabetes (referred to as *non-insulin-dependent* diabetes mellitus, and *adult-onset* diabetes.) is associated with a reduced ability of insulin to stimulate glucose utilization (insulin resistance) and sometimes it is combined with an absolute

vi. the influence of environmental factors.

degeneration.

insulin deficiency. The third type, gestational diabetes, is when pregnant women, who have never had diabetes before, have a high blood glucose level during pregnancy and it may precede development of T2D. Ninety percent of diabetes patients have T2D, which usually has its onset in adulthood. Diabetes is increasing and the World Health Organization estimates that there will be a doubling of cases by 2025, largely as a result of lack of physical activity and poor dietary habits, both of which are risk factors for the disease. Obesity, hypertension, hyper-cholesterolemia and hyperlipidemia are all associated with T2D (MedScape).

 Alzheimer's disease (AD) is the most common form of dementia in the elderly. It is characterized by neuronal cell loss and increasing accumulation of neurofibrillary tangles (NTF) in neurons and amyloid fibers in neuritic plaques and in the walls of blood vessels (Wisniewski et al., 1997). Amyloid beta-peptides of varying length (39–43 residues) are produced by cleavage of a transmembrane protein, the amyloid beta-protein precursor (APP) (Wilquet & De Strooper, 2004). The 42 residue beta-peptide (Abeta-42) is the predominant form found in plaques and under physiological condition the ratio between Abeta42 and Abeta40 is about 1:10 (Iwatsubo et al., 1994). Abeta42 has a much greater neurotoxity than Abeta40 and its aggregation kinetics is faster than other beta-petides (Davis & Van Nostrand, 1996). The proteinaceous material is organized in structured linear aggregates (amyloid fibrils). A recent and now convincing belief is that small diffusible oligomers of Abeta-42, called ADDLs, are the determining pathogenic species causing synaptic dysfunction and eventually neuronal degeneration (Lambert et al., 1998; Picone et al., 2009)

AD accounts for 50–70% of all dementia cases and is characterized by cognitive deficits. This incurable, degenerative, and terminal disease was first described by the German psychiatrist and neuropathologist Alois Alzheimer in 1906. Several factors have been considered relevant for the AD pathogenesis and among these the most important is age. During life small variations occurring in cellular metabolism and structure can modify the functional state of susceptible neurons, leading to dramatic or even lethal changes. Thus, while the the monomeric Abeta is not neurotoxic, for not yet known reasons it starts to form supramolecular aggregates accumulating in the AD brain.

Familial AD is a rare form of dementia and is caused by autosomal dominant mutations in one or more of the genes encoding the amyloid precursor protein (APP), presenilin 1 or presenilin 2 (the latter two proteins form the catalytic core of *γ*-secretase) (Gotz et al., 2004). By contrast, late-onset AD might be caused by environmental and/or life style factors (Rocchi et al., 2003). Interestingly, late-onset AD is characterized not only by the neuropathological markers mentioned above, but also by vascular lesions, and hyperglycemia, hyperinsulinemia, insulin resistance, glucose intolerance, adiposity, atherosclerosis and hypertension (Haan, 2006).

Diabetes and AD are considered age-related diseases and are both increasing. In the USA, diabetes and AD affect ≈ 23.6 and ≈ 5.3 million people, respectively, and these numbers are projected to rise considerably. The Centers for Disease Control and Prevention predict that more than 29 million people in the US will be affected by diabetes by 2050, while the Alzheimer's association forecasts that by this date, 11–16 million Americans will have AD (Han & Li, 2010). Numerous studies report that patients with diabetes have an increased risk of developing AD compared with healthy individuals (Arvanitakis et al., 2004; Neumann et al., 2008; Roriz-Filho et al. 2009). In fact, some studies revealed that 80% of

Alzheimer's Disease and Type 2 Diabetes: Different Pathologies and Same Features 33

The islet amyloid polypetide (IAPP), identified for the first time in 1987 (Westermark et al.) and also known as amylin, is secreted by the beta cells of the pancreatic islets of Langerhans, which also secrete the insulin. The occurrence of IAPP in the membranes of beta-cells and the presence of alterations in the membranes of the same cells (Lorenzo et al., 1994; Janson et al., 1999) suggest that this interaction is responsible for the cytotoxic effect of these formations. The primary sequence of the peptide is well conserved in organisms and, in particular human and mouse IAPPs differ by only six amino acids but the latter does not form fibrils neither in vitro nor in vivo. The development of IAPP deposits is deeply associated with T2D because more than 90% of T2D patients presents this type of amyloid formations as evidenced by autopsy and, further, the amount of aggregates appears to be

Human IAPP (hIAPP) consists of 37 amino acids with a S-S bridge between the Cys 2 and Cys 7. As in Abeta, IAPP is non-toxic in its monomeric form but it exhibits high toxicity levels when it aggregates into beta-rich amyloid structures. As in other amyloid peptides, the mechanism of fibrillation occurs through the formation of nuclei with a lag phase whose duration is concentration-dependent and proceeds by addition of monomers or oligomers to both fibril terminals. The secondary structure of hIAPP mainly consists of unstructured regions, with small alpha-helical and beta-sheet components (Goldsbury et al., 2000). Recently has been suggested that hIAPP oligomers in presence of membranes could exhibit

The three dimensional structure of hIAPP has been extensively studied with different techniques and the results show that, similarly to other amyloid proteins, the amylin mature amyloid fibrils show a relevant amount of beta-structure (McLean, 1992; Goldsbury, 2000). Studies on the mechanism of hIAPP fibrillation indicate that during the process, hIAPP undergoes a conformational change from an unstructured peptide to beta-sheets and alpha-

The IAPP decapeptide sequence between residues 20-29 seems to play an important role in the fibrillization process (Westermark et al., 1990) even if it does not appear to be the only region involved in fibril formation. In fact, recent studies have evidenced the importance of the residues in position 13-18 in the interaction leading to the formation of fibrils (Gilead & Gazit, 2008). Also the aromatic-aromatic interactions between residues 15, 23 and 37 seem to be important in amyloid formation althought not essential for fiber formation as evidenced

The brain has a high energy demand and, although it represents only 2% of body weight, it accounts for 20% of total body oxygen consumption. This energy requirement is largely driven by neuronal request of energy to maintain the ion gradients across the plasma membrane, which are critical for the generation of action potentials. This intense energy requirement is continuous; even brief periods of oxygen or glucose deprivation result in neuronal death. Diabetes mellitus leads to functional and structural changes in the brain, which appear to be most pronounced in the elderly. Furthermore, increased age is associated with insulin resistance. Increasing data support the idea that mitochondrial

Normal glucose metabolism is required for the performance of cognitive functions, and impairments in glucose metabolism might contribute to cognitive dysfunction. Imaging

function declines with aging and in age-related diseases such as diabetes and AD.

correlated with the pathology seriousness.

an alpha-helical structure (Knight et al., 2006).

using IAPP with a triple mutation (Marek et al., 2007).

helical structures (Goldsbury, 2000).

**3. The effect of oxidative stress**

patients with AD exhibited either impairments in glucose tolerance or frank diabetes (Schrijvers et al., 2010). In particular, similarities between T2D and AD include: agingrelated processes, degeneration, high cholesterol levels, peripheral and CNS insulin resistance, dysfunctional IR and IR-mediated signaling pathways, decreased glucose transport and metabolism, despite the higher non-metabolized glucose levels in cerebral blood (Hoyer, 1998; Salkovic-Petrisic & Hoyer, 2007; Schulingkamp et al., 2000). The inbalance between low and high glucose levels in T2D patients may be responsible for brain vascular damage and neurodegeneration thus facilitating the AD onset.

#### **2. Alzheimer's disease and type 2 diabetes: Two amyloidogenic pathologies**

AD and T2D are two pathologies characterized by the presence of large insoluble aggregates having an amyloidogenic fibrillar conformation, amylin in T2D pancreatic islets and Abeta and the microtubule protein Tau in the brain of AD patients. In particular, amylin aggregation is associated with pancreatic b-cell loss, whereas Abeta and Tau aggregation is associated with neuronal cell loss and synaptic dysfunction (Lupi & Del Prato, 2008; Schroeder & Koo, 2005; Resende et al., 2008a). The formation of amyloid aggregate occurs both in the intra- and extra-cellular environments; further the proteinaceous aggregates are strictly bound with membranes and calcified. Despite their common secondary structure conformation, it is well accepted that a correlation does not exit between amino acid sequence and tendency to amyloid structure formation; thus it is assumed that amyloid formation is a generic properties of all polypeptides (Chiti & Dobson, 2006). In particular, amyloid fibers share the following features (Xu, 2007):

 On a molecular lengthscale, Abeta can form aggregates of different shape originated in vitro under different conditions.

X-ray fiber diffraction showed that amyloid fibrils contain beta-sheet structure lying orthogonally to the major fibril axis (Serpell, 2000). In the early 2000s, Tycko's group (Antzutkin et al., 2000; Balbach et al., 2002) obtained, for the first time, evidence of an extended parallel beta-sheet organization for the Abeta40 fibrils using solid-state NMR. They showed that the methyl carbons of Ala-21 and Ala-30 must be placed in groups of at least four with internuclear distances of less than 5.5 Å. Although beta-sheets are the main constituent of the amyloid fibrils they are not the only structure present in the fibrils. Liquid state NMR, FTIR and CD measurements in Abeta40 have demonstrated the existence of a turn formed by the amino acids at position 26-29. Little information is known about the Abeta42 fibril structure and many mutant peptides have been synthetized to obtain an explanation about its secondary structure. The results have showed that the residues at positions 15–21 and 24–32 are involved in the beta-sheet formation and that the turn at positions 22 and 23 plays a crucial role in the aggregation of Abeta42.

patients with AD exhibited either impairments in glucose tolerance or frank diabetes (Schrijvers et al., 2010). In particular, similarities between T2D and AD include: agingrelated processes, degeneration, high cholesterol levels, peripheral and CNS insulin resistance, dysfunctional IR and IR-mediated signaling pathways, decreased glucose transport and metabolism, despite the higher non-metabolized glucose levels in cerebral blood (Hoyer, 1998; Salkovic-Petrisic & Hoyer, 2007; Schulingkamp et al., 2000). The inbalance between low and high glucose levels in T2D patients may be responsible for brain

**2. Alzheimer's disease and type 2 diabetes: Two amyloidogenic pathologies**  AD and T2D are two pathologies characterized by the presence of large insoluble aggregates having an amyloidogenic fibrillar conformation, amylin in T2D pancreatic islets and Abeta and the microtubule protein Tau in the brain of AD patients. In particular, amylin aggregation is associated with pancreatic b-cell loss, whereas Abeta and Tau aggregation is associated with neuronal cell loss and synaptic dysfunction (Lupi & Del Prato, 2008; Schroeder & Koo, 2005; Resende et al., 2008a). The formation of amyloid aggregate occurs both in the intra- and extra-cellular environments; further the proteinaceous aggregates are strictly bound with membranes and calcified. Despite their common secondary structure conformation, it is well accepted that a correlation does not exit between amino acid sequence and tendency to amyloid structure formation; thus it is assumed that amyloid

vascular damage and neurodegeneration thus facilitating the AD onset.

formation is a generic properties of all polypeptides (Chiti & Dobson, 2006).

 their formation can be enhanced either by the stirring or the presence of seeds; all aggregate starts from spherical oligomers that in turn self-assemble linearly; all can incorporate a special kind of dye molecules such as Congo Red or Thioflavin T. On a molecular lengthscale, Abeta can form aggregates of different shape originated in vitro under different conditions. These structures include amyloid fibrils (Ban et al., 2004), small oligomers (Walsh et al., 1999), spherical amyloid oligomers (Westlind-Danielsson & Arnerup, 2001) and annular pore-forming structures (Lashuel et al., 2002), amyloid protofibrils (Harper et al., 1997), beaded chain protofibrils (Huang et al., 2000) and

X-ray fiber diffraction showed that amyloid fibrils contain beta-sheet structure lying orthogonally to the major fibril axis (Serpell, 2000). In the early 2000s, Tycko's group (Antzutkin et al., 2000; Balbach et al., 2002) obtained, for the first time, evidence of an extended parallel beta-sheet organization for the Abeta40 fibrils using solid-state NMR. They showed that the methyl carbons of Ala-21 and Ala-30 must be placed in groups of at least four with internuclear distances of less than 5.5 Å. Although beta-sheets are the main constituent of the amyloid fibrils they are not the only structure present in the fibrils. Liquid state NMR, FTIR and CD measurements in Abeta40 have demonstrated the existence of a turn formed by the amino acids at position 26-29. Little information is known about the Abeta42 fibril structure and many mutant peptides have been synthetized to obtain an explanation about its secondary structure. The results have showed that the residues at positions 15–21 and 24–32 are involved in the beta-sheet formation and that the turn at

In particular, amyloid fibers share the following features (Xu, 2007):

spherocylindrical micelles (Lomakin et al., 1996; Yong et al., 2002).

positions 22 and 23 plays a crucial role in the aggregation of Abeta42.

all have a rope-like appearance;

all show a dominant beta-sheet structure;

The islet amyloid polypetide (IAPP), identified for the first time in 1987 (Westermark et al.) and also known as amylin, is secreted by the beta cells of the pancreatic islets of Langerhans, which also secrete the insulin. The occurrence of IAPP in the membranes of beta-cells and the presence of alterations in the membranes of the same cells (Lorenzo et al., 1994; Janson et al., 1999) suggest that this interaction is responsible for the cytotoxic effect of these formations. The primary sequence of the peptide is well conserved in organisms and, in particular human and mouse IAPPs differ by only six amino acids but the latter does not form fibrils neither in vitro nor in vivo. The development of IAPP deposits is deeply associated with T2D because more than 90% of T2D patients presents this type of amyloid formations as evidenced by autopsy and, further, the amount of aggregates appears to be correlated with the pathology seriousness.

Human IAPP (hIAPP) consists of 37 amino acids with a S-S bridge between the Cys 2 and Cys 7. As in Abeta, IAPP is non-toxic in its monomeric form but it exhibits high toxicity levels when it aggregates into beta-rich amyloid structures. As in other amyloid peptides, the mechanism of fibrillation occurs through the formation of nuclei with a lag phase whose duration is concentration-dependent and proceeds by addition of monomers or oligomers to both fibril terminals. The secondary structure of hIAPP mainly consists of unstructured regions, with small alpha-helical and beta-sheet components (Goldsbury et al., 2000). Recently has been suggested that hIAPP oligomers in presence of membranes could exhibit an alpha-helical structure (Knight et al., 2006).

The three dimensional structure of hIAPP has been extensively studied with different techniques and the results show that, similarly to other amyloid proteins, the amylin mature amyloid fibrils show a relevant amount of beta-structure (McLean, 1992; Goldsbury, 2000). Studies on the mechanism of hIAPP fibrillation indicate that during the process, hIAPP undergoes a conformational change from an unstructured peptide to beta-sheets and alphahelical structures (Goldsbury, 2000).

The IAPP decapeptide sequence between residues 20-29 seems to play an important role in the fibrillization process (Westermark et al., 1990) even if it does not appear to be the only region involved in fibril formation. In fact, recent studies have evidenced the importance of the residues in position 13-18 in the interaction leading to the formation of fibrils (Gilead & Gazit, 2008). Also the aromatic-aromatic interactions between residues 15, 23 and 37 seem to be important in amyloid formation althought not essential for fiber formation as evidenced using IAPP with a triple mutation (Marek et al., 2007).

#### **3. The effect of oxidative stress**