Computational and Mathematical Methods in Medicine

Volume 2019, Article ID 7525834, 8 pages

https://doi.org/10.1155/2019/7525834

## Modeling the Effect of High Calorie Diet on the Interplay between Adipose Tissue, Inflammation, and Diabetes

^{1}Institute for Applied Computing (IAC) “M. Picone”, National Research Council of Italy (CNR), Via dei Taurini, 19-00185 Rome, Italy^{2}Institute for Advanced Study (IAS), University of Amsterdam (UvA), Oude Turfmarkt, 147-1012 GC Amsterdam, Netherlands

Correspondence should be addressed to F. Castiglione; ti.rnc.cai@enoilgitsac.f

Received 11 August 2018; Accepted 6 January 2019; Published 3 February 2019

Academic Editor: Zoran Bursac

Copyright © 2019 V. Prana et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

*Background*. Type 2 diabetes (T2D) is a chronic metabolic disease potentially leading to serious widespread tissue damage. Human organism develops T2D when the glucose-insulin control is broken for reasons that are not fully understood but have been demonstrated to be linked to the emergence of a chronic inflammation. Indeed such low-level chronic inflammation affects the pancreatic production of insulin and triggers the development of insulin resistance, eventually leading to an impaired control of the blood glucose concentration. On the contrary, it is well-known that obesity and inflammation are strongly correlated. *Aim*. In this study, we investigate *in silico* the effect of overfeeding on the adipose tissue and the consequent set up of an inflammatory state. We model the emergence of the inflammation as the result of adipose mass increase which, in turn, is a direct consequence of a prolonged excess of high calorie intake. *Results*. The model reproduces the fat accumulation due to excessive caloric intake observed in two clinical studies. Moreover, while showing consistent weight gains over long periods of time, it reveals a drift of the macrophage population toward the proinflammatory phenotype, thus confirming its association with fatness.

#### 1. Introduction

Diabetes is a chronic disease characterized by a decreased production of insulin and by a reduced efficacy of the insulin produced. This impaired condition is differently caused by both type 1 and type 2 diabetes. In type 1 diabetes, insulin-producing cells in the pancreas (*i.e.*, the beta cells) have been damaged by the immune system in a *de facto* autoimmune response. In type 2 diabetes, the origin of beta cell malfunctioning is diverse and mainly attributed to a systemic low-grade inflammation which also impairs the various organs ability to make use of insulin and remove glucose from the blood.

If untreated, both forms of diabetes result over time in a persistent high concentration of glucose in blood which leads to serious tissue damage, especially to the nervous and circulatory system with potentially fatal consequences. In 2015, diabetes caused five million deaths worldwide. The number of diabetic individuals has risen over the years from 285 million in 2010 to 387 million in 2014 and 415 in 2015, while projections estimate 642 million in 2040 [1].

There is no doubt that this kind of “pandemic” requires maximum attention and that besides clinical and biological research, mathematics could contribute to shed light on this complex pathology. In our study, we employed computational modeling and simulation to describe the effects of high calorie diets on the pathology of type 2 diabetes limiting our observation to the process of weight gain ultimately leading to the onset of an inflammation state.

##### 1.1. About Type 2 Diabetes

Symptoms of type 2 diabetes (T2D) are not very pronounced, and as a result, the disease is usually diagnosed several years after its onset, once complications have already become established. The International Diabetes Federation estimated that 193 million people with diabetes are undiagnosed and are therefore at risk of developing complications. Since T2D comprises 90% of diabetes cases worldwide, by 2040, more than 570 million people will likely be living with diabetes, the majority of them being unaware of it [2]. Another cause of concern is the fact that while T2D was previously prognosticated only in adults, it is now also found in children [3]. It is also worth to be mentioned that T2D is becoming worrying in developing countries which have recently taken up higher calorie diets. For all these reasons, there is an urgent need to understand the complex mechanisms underpinning the onset of T2D and to identify early diagnostic parameters and related inflammatory indicators, possibly using a personalized medicine approach.

A number of conceivable stress mechanisms (herein indicated as “stressors”) leading to and participating in insulin resistance and beta-cell dysfunction have been hypothesized to explain the complex landscape of T2D onset, such as oxidative stress, endoplasmic reticulum stress, amyloid (*i.e.*, insoluble fibrous proteins) deposition in the pancreas, and ectopic lipid deposition in the muscle, liver, and pancreas [4]. All of these stressors are potentially linked to overnutrition although it has been difficult, so far, to identify the precise mechanisms determining the decreased rate of glucose uptake by the different tissues in individuals proceeding to T2D. However, it is noteworthy that each of these cellular stressors is thought to also either induce an inflammatory response by itself or to be exacerbated by or associated with inflammation [5]. Inflammation is a complex, systemic, multiscale physiological process necessary to cope with damaging agents, involving a variety of cells, organs, and organ systems. The complexity of the inflammatory process escapes reductionist approaches, since it is characterized, among other things, by nonlinear kinetics as well as numerous and nested feedback loops.

The ultimate conceptualization identifies the hallmark of T2D in a chronic inflammatory state initiated by an excess of nutrients and referred to as metabolic inflammation or *metaflammation*. Indeed, proof-of-concept clinical studies demonstrated the potential of using an anti-inflammatory molecule in T2D therapy, thus strongly linking inflammation with the pathogenesis of T2D [4].

This clear evidence is at the core of the present computer simulation study as it constitutes the primary working hypothesis of a mathematical model developed and used to assess the risk of developing an inflammatory state thus leading to T2D.

#### 2. Computational Modeling

We used an agent-based model (ABM) of the immune system to study *in silico* the emergence of a low-level chronic inflammation in the adipose tissue, as the main place of accrual of inflammatory evidences due to prolonged excessive calorie intake.

The model is a derivation of a well-established general-purpose immune system simulator [6], a modeling framework that has been used over the past two decades to study different human pathologies [7–9], specific aspects of the immune response [10, 11], and also nonhuman immunity [12].

It is a multiscale discrete-event model, generic enough to account for the major hallmarks of the immune response. This computational model has been conceived to allow the dynamic representation of hypotheses and their preliminary testing [13]. The model represents several primary and secondary immune compartments playing a critical role in the immune response: generic tissue (e.g., epithelial and adipose tissue), lymphoid tissue, thymus gland, and bone marrow. These components are bundled together in a complex yet parsimonious model of immunity focused at the mesoscopic (i.e., cellular) level.

Agent-based modeling is based on a general paradigm for complex systems inspired by von Neumann’s “cellular automata” [14]. It consists of discrete dimensional entities (three-dimensional space and time in discrete steps), where the agents are the relevant entities (cells or molecules) equipped with virtual receptors and capabilities, which reflect biological observations.

In the used modeling framework, key immune cells such as monocytes-derived macrophages, dendritic cells, and B and T lymphocytes are represented by agents and follow a set of rules describing the different phases of the recognition and response of the immune system against a pathogen. In particular, the model incorporates key immune processes such as phagocytosis, antigen presentation, cytokine release, cell activation from inactive or anergic states, development of the immune memory, cytotoxicity, and antibody secretion [6]. Additionally, this model reproduces the gene-regulation mechanisms leading to macrophage differentiation during the different stages of inflammation [11].

The model represents a small volume of the body populated by a fraction of immune cells which is calculated according to generic leukocyte formulas. The discrete time step is equivalent to eight hours of real life.

For the work here presented, the above described model has been enriched for the ongoing purpose of studying the effects of excessive caloric intake by including specific mechanisms pertaining the (i) accumulation of fat in the adipose tissue, (ii) consequential growth of the adipose tissue, (iii) the generation of proinflammatory cytokines, and (iv) the endmost polarization of key innate immune mediators such as the macrophages into the proinflammatory phenotype establishing *de facto* a low-grade inflammatory state. This implementation is described in the following section.

##### 2.1. Modeling the Effect of Excess Calories on Adipocytes

Among the main risk factors of T2D is an excess in body weight which is often the result of fat accumulation over an extended period of time. This process is the result of an excess of caloric intake which is not balanced by a comparable caloric consumption due, for instance, to physical activity.

In the literature, there are very few attempts to quantify and model the link between the effects of high caloric intake [15–18] and the emergence of the inflammation state. In the present study, therefore, we present a model on the effects of food intake linked to a model of weight gain eventually driving a systemic low-grade inflammation. Our model represents besides key immune cells responsible for the inflammation process, a population of adipocytes as the sum of individual cells acting as reservoirs for fat and originators of inflammatory signals. Model’s anthropometric inputs include the subject initial body weight (BW) in kilograms, height (H) in meters, age (A) in years, and gender (G) male or female. Starting from these parameters, the relationship between adipocyte diameter and body mass index (BMI) is determined as in equation (1) to set the initial distribution of the volume of adipocytes. This relationship has been estimated in [19] from data on 54 men and 207 women and links the diameter of an adipocyte of the *omental* adipose tissue (*ϕ*) with the BMI:where, respectively, for female and male, and , and 74.905 *μ*m, and and 0.049 /kg [19]. These values for the parameter for male and female are in accordance with another experimental finding [18], which shows a maximal cell diameter value ranging from 120 to 130 *μ*m. Omental fat constitutes the larger part of visceral adipose tissue (VAT, i.e., the main spot of the inflammation), and hence, we surmise that relation in equation (1) is valid for all adipocytes in VAT. Moreover, since the body mass index is calculated as , the relationship in equation (1) links the average diameter of a visceral adipocyte *ϕ* to BW and therefore it allows the estimation of the distribution of the initial diameter of the adipocytes making up the fraction of the adipose tissue given the BMI of the subject at the beginning of the simulated period.

Another value of use to set the initial condition of the model is the initial value of the fat mass FM. To this purpose, the following compartmental relation between fat and body weight [20] allows to compute FM as a function of the body weight and the free fat mass (FFM):

According to Westerterp’s regression equations in [21], different values of FFM for men and women can be estimated on the basis of the age *A*, body weight BW, and height *H* as follows:where the parameters depend on the gender and are, respectively, kg, kg/years, kg/m, and for female and kg, kg/years, kg/m, and for male.

During periods of excessive calorie intake, adipocytes grow in order to stock the energy surplus (*swelling*). The growth continues until a *critical* size for the diameter of a visceral adipocyte () is reached (equation (1)). Beyond this value, the adipocyte stimulates the generation (*adipogenesis*) of new adipocytes from precursor cells [15–17].

To model the enlargement of the adipocyte due to a (daily) surplus of calorie intake indicated by *E*, we assume a spherical shape and define the critical value for the volume for the cells where, as already mentioned above, is set to 123 *μ*m for females and 120 *μ*m for males [18, 19] (Figure 1).