**1. Introduction**

The manufacturing sector has one of the largest impacts on worldwide energy use and natural resource consumption. Traditionally, research on manufacturing processes was mainly conducted to improve efficiency and accuracy and to lower costs [1]. One of the modern challenges in the field of designing manufacturing systems is to determine the optimal level of their flexibility from the point of view of the production tasks being performed. Whether or not a production process to be executed is capable of achieving the assumed performance parameters depends, among others, on the reliability of the machines and technological devices that make up the system under design [2]. As commonly known, the oldest manufacturing techniques used by humans are the grinding, chopper, and milling processes. Research on grinding tries to enhance economic and ecological properties and performance to extend grinding applications in the overall process chain—on the one hand, in the direction of increased material removal rates, avoiding turning and milling, and on the other hand, in the direction of fine finishing, thus making further abrasive finishing processes, such as lapping and polishing, obsolete [3].

Many factors influence the sustainability of a manufacturing process, and a combination of qualitative and quantitative methods are needed to discover them [4]. To resolve these issues, namely, the identification of the type of underlying impact factors, the uncertainty of the influencing factors, and the incompleteness of the evaluation information, the researchers used the evaluation method with analytical hierarchy process [5,6] and simulations [2,7–9] in the manufacturing sector. Sustainability encompasses the three pillars of economic, environmental, and social sustainability [10–12]. In the investigation of Ahmad [10], generally, there were approximately 44% (25/57) of highly applicable indicators. Among them, there were 28% (7/25) environmental, 28% (7/25) economic, and 44% (11/25) social indicators [10]. We can, therefore, see that economic and environmental factors are treated on an equal level. Social indicators in sustainable development are highly rated. Nevertheless, in the case of the two previous ones, they are more adequate for production processes, which have a more indirect nature on social impact. Beekaroo et al. [13] revealed an index with nine environmental, four economic, and two social indicators which were pertinent in sustainability measurement.

One of the most commonly used methods focusing on environmental sustainability is the product life cycle assessment (LCA). This method is used in many sectors of the economy [14–16] such as energy sector [17–19], transport sector [18,19], and food and agricultural industry [20,21]. The limitation of using this method is the need for specific and very detailed databases covering a lot of quantitative data.

Another method uses sustainability indicators (SI). In this method, the indicator can be defined "as a measure or aggregation of measures from which one can infer about the phenomenon of interest" [11]. This method can capture all three dimensions of sustainable development and help with the evaluation on many levels (e.g., enterprises, objects, processes, and products). In particular, for perpetrators with limited means and resources, SI provide a good method of analyzing sustainable development. Enterprises can assess their real situation using indicators, raise awareness, and set targets. The results of a literature review show that energy costs and GHG (Greenhouse Gas) indicators [10,11,13,19,22–25] are becoming the most commonly used indicators in sustainable planning. On this basis [11,26], four main directions of future research on sustainability indicators can also be mentioned: implementation of new optimization methods; adding further sustainable development indicators; extension of the model on a larger scale of the production system; and loosening certain assumptions. Finding optimal indicators in production processes is not an easy task; generally, we focus on minimizing energy consumption, waste production, improving the efficiency of machinery and equipment, as well as production and logistic processes in a given company. Sustainability indicators are based on measured and/or estimated data that have to be normalized, scaled, and aggregated consistently [27].

The evolution of design criteria for grinding and chopper machines is driven by functional requirements, general trends in machine tools, and cost [28]. The primary functional requirements, as named by Möhring et al. [29], are similar for all machine tools: high static and dynamic stiffness, fatigue strength, damping, thermal and long-term stability, and low weight of moving parts. The grinding and chopper process is carried out in many areas of food manufacturing [30–32] and agriculture [33–35], as well as in the industrial sector [36–38]. The mixing process is highly complicated, with a number of affecting parameters, such as the particle properties, the structure and performance of the mixer, the mixing process parameters, and the particle feeding order [38]. The crushing method and the machinery used for this purpose should be adapted to the type of material being ground and, in particular, to its mechanical properties [33,39].

Laboratories and modern industry require fast and effective grinding in small volumes [40]. In the field of agricultural mechanization, centrifugal chopper machines with a horizontal rotor have recently attracted increasing interest. Their principle of action lies in the acceleration of grains due to centrifugal inertia forces with their subsequent grinding (fragmentation) by impact or cutting [41,42]. This is due to the lower energy consumption for the grinding process in comparison with other choppers (crushers), which, in addition to the direct costs of grain destruction, have the energy costs for drifting whole and crushed grain using air. In centrifugal rotary chopper machines, the material can be supplied to crusher/shredder hammers or to a cutting pair by centrifugal inertia forces created by a horizontally rotating rotor with working elements. In this, one of the key roles of a centrifugal rotary material grinding machine is the distribution bowl or accelerator, which functions to provide a uniform and stable supply of material to the chopper bodies and impart to the material (particles) located on its surface the necessary linear velocity and trajectory of motion. Despite the rotary blenders relying upon the action of gravity to cause the powder to cascade and mix within a rotating vessel, the convective blenders employ a paddle, impeller, blade, or screw which stirs the powder inside a static vessel [43].

Most of the centrifugal rotary grinding machines in their design have a central feed of the material into the accelerator made in the form of a flat disc. However, with this material feed, the acceleration of a particle that is closest to the axis of rotation will be difficult because of the lack of initial velocity and centrifugal forces to overcome the friction forces, which provokes the appearance of a stagnant zone and an increase in the cost of overcoming them. To solve this problem, two approaches can be used: feeding the material with an offset from the axis of rotation, leading to design complexity, or using the reflective surface of the splitter, which is a straight conical surface located coaxially with the axis of rotation, ensuring the separation of the particles to be ground from the axis of rotation and giving them the initial velocity. In centrifugal impact grinders using the "stone-crushing-stone" principle with self-lining, the trajectory of the particles to be ground (milled) is equally important.

Figure 1 shows the rotary chopper machine analyzed in this study.

**Figure 1.** Tornado chopper machine: 1—feed-in tube; 2—case cover; 3—accelerator; 4—accelerating blade; 5—shredding element; 6—electric motor; 7—V-belt drive.

Figure 2 shows a scheme of self-lining formation in the accelerator.

**Figure 2.** Scheme of self-lining formation in the accelerator: 1—a splitter; 2—wear plate; 3—self-lining pocket; 4—carbide blade; 5—descent of the material from the accelerator; 6—accelerator case.

The main contribution of this study is the modeling (simulating) of the particle motion on an axisymmetric rotating curved surface with a vertical axis of rotation, whose calculation can be used for the study and design of machines, for example, centrifugal rotary chopper machines. A mathematical model of motion was developed on the basis of step-by-step numerical integration of the obtained closed system of differential equations with an equation of constraint describing the surface of revolution. An application based on the algorithm in C# under MS Visual Studio (Microsoft, Redmond, Washington, USA) was developed that enables graphical and numerical control of the calculation results. Moreover, the results of the calculations of the particle motion trajectory and kinematic indicators are presented. The conducted simulation tests show possibilities of improving the process efficiency and shortening the operation times, which results in economic benefits during sustainable manufacturing.

#### **2. Materials and Methods**

Hypothesis. One of the methods to achieve this goal takes into account the form of the accelerator, allowing us to set the initial kinematic parameters and particle trajectory, which in turn will affect the geometric dimensions, metal consumption, and technological modes of operation of a centrifugal rotary chopper or its nodes, for example, rotor (crusher) speed and material feed rate, which would then reduce the specific energy consumption per unit of output.

Methods. To solve this problem, we modeled the motion of a particle of the material on a rotating curved surface. To do this, we used the basic law of particle dynamics (dynamics of a material point) and considered the motion of a particle on the surface of an axisymmetric spinning bowl. We used step-by-step numerical integration, which allowed us to obtain data for analyzing the particle.

#### **3. Results and Discussion**

#### *3.1. Modeling Results*

The curved surface rotates around the vertical axis *z* (Figure 3). The equation of the surface is described in cylindrical coordinates by the equation

$$
\eta(\rho, \,\varphi, z) = 0 \tag{1}
$$

where ρ is the cylindrical radius, ϕ is the polar (vectorial) angle, and *z* is the application (*z*-axis).

The radius vector of a material point moving on a curved surface in the coordinate axes, rotating with it, is a function of these three coordinates, which can transform over time without breaking Equation (1):

$$
\overrightarrow{r} = \overrightarrow{r}(\rho, \varphi, z). \tag{2}
$$

The differential equation of the relative motion of a point on a rotating surface is written in vector form [40]

$$m\frac{d^2\overrightarrow{r}}{dt^2} = m\overrightarrow{\mathcal{g}} + \overrightarrow{N} + F\_{TR} + \overrightarrow{\Phi\_c} + \overrightarrow{\Phi\_c} \tag{3}$$

where *m* is the mass of a particle, *d*2→ *r dt*2 is its acceleration, *m*→ *g* is the gravity force, → *N* is the normal reaction of a bowl surface, → *FTR* is the friction force from the surface directed opposite to the relative velocity of a particle, → Φ*e* is the centrifugal inertial force, and → Φ*c* is the Coriolis inertial force.

Forces and accelerations on the direction of the cylindrical axes of coordinates are projected. The gravity force is opposite to the *z* axis,

$$m\overrightarrow{\mathcal{g}} = m\overrightarrow{\mathcal{g}}(0, \ 0, \ -mg), \tag{4}$$

where → *g* is free-fall acceleration. The normal reaction of a rotating curved surface is

$$
\overrightarrow{N} = \lambda \cdot \text{grad}(\,\,\eta),
\tag{5}
$$

where λ = λ(*t*) is Lagrange's indeterminate multiplier [44], *grad*(η) is the vector gradient to the equation of surface (1), which has projections on the axial cylindrical coordinate system with the ϕ axis directed perpendicular to the ρ, *z*, axes and passing through the moving point, so that the axes ρ*,* ϕ*, z* form the right-hand system of vectors:

$$\begin{cases} \left( \operatorname{grad}(\eta) \right)\_{\rho} = \frac{\partial \eta}{\partial \rho} \\ \left( \operatorname{grad}(\eta) \right)\_{\rho} = \frac{\partial \eta}{\partial \psi} \cdot \frac{1}{\rho} . \end{cases} \tag{6}$$

$$\begin{cases} \left( \operatorname{grad}(\eta) \right)\_{z} = \frac{\partial \eta}{\partial z} \end{cases} \tag{6}$$

**Figure 3.** Design diagram of the motion of a particle on a rotating curved surface.

The projections of the normal reaction → *N* are:

$$\begin{cases} N\_{\rho} = \lambda \frac{\partial \eta}{\partial \rho} \\ N\_{\phi} = \lambda \frac{\partial \eta}{\partial \phi} \cdot \frac{1}{\rho} . \\ N\_{z} = \lambda \frac{\partial \eta}{\partial z} \end{cases} \tag{7}$$

The modulus of the normal reaction is found by

$$N = \left| \vec{\mathbf{N}} \right| = |\lambda| \sqrt{\left(\frac{\partial \eta}{\partial \rho}\right)^2 + \left(\frac{\partial \eta}{\partial \rho} \frac{1}{\rho}\right)^2 + \left(\frac{\partial \eta}{\partial z}\right)^2}. \tag{8}$$

At a constant angular velocity of rotation (spin rate) of the curved surface → ω, the centrifugal inertial force → Φ*e* is directed along the radius ρ in accordance with the result of vector products in its definition →

$$
\overrightarrow{\Phi\_{\varepsilon}} = -m\overrightarrow{\omega} \times \left(\overrightarrow{\omega} \times \overrightarrow{r}\right),
\tag{9}
$$

where → *r* is determined by Equation (2), then

$$\begin{cases} \Phi\_{\epsilon\wp} = m\nu^2 \rho \\ \quad \Phi\_{\epsilon\wp} = 0 \\ \quad \Phi\_{\epsilon z} = 0 \end{cases} . \tag{10}$$

Coriolis inertial force → Φ*c* is by definition equal to

$$
\overrightarrow{\Phi\_c} = -2m\overrightarrow{\omega} \times \overrightarrow{\upsilon}\_{\prime} \tag{11}
$$

where → *v* is the relative velocity of a material point in the moving axes of coordinates, and the modulus of relative velocity is associated with the cylindrical coordinates by

$$v = \sqrt{\dot{\rho}^2 + \left(\rho \dot{\phi}\right)^2 + \dot{z}^2}.\tag{12}$$

Then, the projections of the Coriolis force equal

$$\begin{cases} \Phi\_{c\rho} = 2ma\dot{\varphi}\rho\\ \Phi\_{c\rho} = -2m\dot{\rho}a \end{cases} \tag{13}$$

The friction force of a particle on the bowl surface → *FTR* is determined by Coulomb's law through a normal reaction and it is opposite in direction to the relative velocity:

$$
\overrightarrow{F\_{TR}} = -\left|\overrightarrow{\mathbf{N}}\right| f \frac{\overrightarrow{\boldsymbol{\upsilon}}}{\boldsymbol{\upsilon}} \tag{14}
$$

$$\begin{cases} \begin{aligned} F\_{TR\rho} &= -\overrightarrow{\text{N}} \Big| f \frac{\dot{\rho}}{v} \\ F\_{TR\rho} &= -\overrightarrow{\text{N}} f \frac{\dot{\varphi}\rho}{v} \\ F\_{TRz} &= -\overrightarrow{\text{N}} \Big| f \frac{\dot{z}}{v} \end{aligned} \end{cases} \tag{15}$$

Let us project Equation (3) on the axis of the moving system of cylindrical coordinates rotating together with the curved surface by using the found projections of all forces:

$$\begin{cases} m\left(\ddot{\rho} - \rho \dot{\varphi}^2\right) = \lambda \frac{\partial \eta}{\partial \rho} - Nf \frac{\dot{\rho}}{v} + m\omega^2 \rho + 2m\omega \dot{\varphi}\rho \\\ m \frac{1}{\rho} \frac{d}{dt} \{\rho^2 \dot{\varphi}\} = -Nf \frac{\dot{\varphi}\rho}{v} - 2m\dot{\rho}\omega \\\ m\ddot{z} = -mg + \lambda \frac{\partial \eta}{\partial z} - Nf \frac{\dot{z}}{v} \end{cases} \tag{16}$$

Let us transform the second equation of the system, taking into account the projection of acceleration on the ϕ axis:

$$\frac{1}{\rho} \frac{d}{dt} (\rho^2 \dot{\phi}) = 2\dot{\rho}\dot{\phi} + \rho \ddot{\phi}.\tag{17}$$

By bringing all forces to a unit mass of a particle *m* = 1, we obtain

$$\begin{cases} \ddot{\rho} = \rho \dot{\rho}^2 + \lambda \frac{\partial \eta}{\partial \rho} - Nf \frac{\dot{\rho}}{\overline{v}} + \omega^2 \rho + 2a \dot{\rho} \rho \\\ \ddot{\rho} = \frac{1}{\rho} (-2\dot{\rho}\dot{\rho} - Nf \frac{\dot{\rho}\rho}{\overline{v}} - 2\dot{\rho}\omega) \\\ \ddot{z} = -g + \lambda \frac{\partial \eta}{\partial \overline{z}} - Nf \frac{\dot{z}}{\overline{v}} \end{cases} \tag{18}$$

To obtain a closed system of equations, we supplement the system (18) with a coupling equation (of constraints) (1) (see Supplementary Material). Then, four unknown functions ρ(*t*), ϕ(*t*), *z*(*t*), λ(*t*) can be found by solving a system of three differential (18) and one algebraic (1) equations.

In the equation, various forms of execution of the surface of revolution are possible (1). Let us define the coupling equation in the form of an axisymmetric surface described by a power function passing through the given starting and final points of motion, written as

$$\frac{z}{z\_K} = a\_0 + \left(\frac{\rho}{\rho\_K}\right)^n,\tag{19}$$

where *a*0 is a summand determined from the condition of belonging to a given surface of revolution of the initial point of the trajectory with the coordinates

$$
\rho(0) = \rho\_0, \ q(0) = 0, \ z(0) = 0 \tag{20}
$$

ρ*K*, *zK* are coordinates of the final point of the trajectory, where the surface described by Equation (19) ends for all values of the polar (vectorial) angle ϕ; *n* is an exponent in the equation of surface, which changes the degree of the bowl concavity and which can be varied to achieve the required parameters of the particle motion.

Thus, the origin of coordinates of the moving frame of reference, in which the particle motion is described, always corresponds along the *z* axis to the starting point of the motion trajectory, and the parabola vertex in the axial section of the surface of revolution lies on this axis below zero by the value *a*0:

$$a\_0 = -\left(\frac{\rho\_0}{\rho\_K}\right)^n. \tag{21}$$

Let us reduce Equation (19) to the form (1)

$$\eta(\rho,\rho,z) = \frac{z}{z\_{\mathbb{K}}} - a\_0 - \left(\frac{\rho}{\rho \mathbb{K}}\right)^n = 0,\tag{22}$$

and calculate the partial derivatives in the gradient expression to the constraint surface

$$\begin{cases} \frac{\partial \eta}{\partial \rho} = -n \left(\frac{\rho}{\rho \chi}\right)^{n-1} \frac{1}{\rho \chi} \\ \qquad \frac{\partial \eta}{\partial \varphi} = 0 \\ \qquad \frac{\partial \eta}{\partial z} = \frac{1}{z\_K} \end{cases} \tag{23}$$

These expressions in Equation (23) should be substituted in the projection of force → *N* , a normal reaction to the constraint surface in Equation (18).

From the last equation of the system (18) we find the Lagrange multiplier

$$
\lambda = \frac{1}{\left(\frac{\partial \eta}{\partial z}\right)} \left(\ddot{z} + g + Nf \frac{\dot{z}}{v}\right). \tag{24}
$$

Since, when moving along the surface, only two cylindrical coordinates are independent, then for step-by-step numerical integration, we take the first two differential Equations (18) as the basis and calculate the coordinate *z* and its time derivatives through coupling Equation (22):

$$z = z\_K a\_0 + z\_\mathcal{K} \left(\frac{\rho}{\rho\_\mathcal{K}}\right)^n \tag{25}$$

$$\dot{z} = nz\kappa \frac{1}{\rho\_{\mathbb{K}}} \left(\frac{\rho}{\rho\_{\mathbb{K}}}\right)^{n-1} \dot{\rho} \tag{26}$$

$$\bar{z} = nz\_{\bar{K}} \frac{1}{\rho\_{\bar{K}}} (n-1) \left(\frac{\rho}{\rho\_{\bar{K}}}\right)^{n-2} \frac{\bar{\rho}^2}{\rho\_{\bar{K}}} + nz\_{\bar{K}} \frac{1}{\rho\_{\bar{K}}} \left(\frac{\rho}{\rho\_{\bar{K}}}\right)^{n-1} \bar{\rho}. \tag{27}$$

In Equations (24)–(27), the coordinate values ρ and ϕ, as well as their time derivatives . ρ, . ϕ at the next integration step, are assumed to be equal to their value at the end of the previous integration step. The procedure of numerical integration of the system of Equation (18) was carried out by the method of averaged acceleration [45], using the original algorithmic program for "Windows" coded in C# under MS Visual Studio.

#### *3.2. Results and Discussion*

The results of the analysis of the kinematic parameters of the motion and trajectory of the particle, which initiate motion, with no initial linear velocity *v*0 and with an angular velocity ω0 equal in magnitude to the angular velocity of rotation ω*e*, for different curvilinear surfaces (Figure 4) of the accelerator, are presented in Figure 5. It shows that the use of a concave curvilinear surface (*na* = 2) allowed to double the value of the acquired velocity *vabs* in comparison with the flat surface (*na* = 0) and to increase it 1.7 times compared to a conical surface (*na* = −0.1) at a descent from a rotating surface, which is a consequence of the time spent by the particle on the surface, for example, when *na* = 2, the time was *t* = 2.05 s, when *na* = 0, the time was *t* = 0.84 s, and when *na* = −0.1, the time was *t* = 0.38 s. When the shape of the rotating surface changed from concave *na* = 2 to convex *na* = −0.1, the total length of the path traveled by the particle—that is, its trajectory—decreased.

**Figure 4.** Variants of generates of the studied curvilinear surfaces of the accelerator.

**Figure 5.** *Cont.*

**Figure 5.** Data for analyzing the velocity and trajectory of the particle motion, which is introduced with no initial linear velocity and with angular velocity equal in magnitude to the angular velocity of rotation for different curvilinear surfaces of the accelerator: (**a**) *na* = 2 (concave); (**b**) *na* = 0 (straight line); (**c**) *na* = −0.1 (conical curvilinear).

The calculations were carried out for different variable characteristics of the surface, initial indicators of kinematic parameters, and friction coefficient. Figure 6a presents an example of tabular data with the results of calculations and diagrams of changes in the motion trajectory, velocity, and acceleration of a particle along the cylindrical axes ρ and *z*.

Analysis of the diagrams presented in Figure 6b, c made it possible to note that the particle reached its maximum velocity in 0.313 s, being at a distance of ρ = 0.0092 m from the axis of rotation. At the same time, the subsequent changes in velocity, down to its descent from the concave surface, had a damped harmonic nature.

Thus, curvilinear surfaces of concave nature combining conical and concave surfaces are of great interest for further research. The trajectories of the particles and their kinematic indicators can be used to determine the relationship between the design factors and the process parameters of centrifugal choppers, such as the time when the particle is on a dispensing bowl, the descent velocity of the particle from the bowl, and the shape of accelerating blades.

**Figure 6.** *Cont.*

**Figure 6.** Example of the results of calculations of the particle motion trajectory and kinematic indicators for *na* = 2; (**a**) tabular data; (**b**) diagrams of particle displacement, velocity, and acceleration along the axis ρ; (**c**) diagrams of particle displacement, velocity, and acceleration along the axis *z*.

The ability to achieve the assumed performance parameters of the production process planned for implementation depends on the degree of reliability of the machines and technological devices included in the designed system [2]. Based on previous research [34], it can be confirmed that with the optimal values of the technological process (efficiency, time of a given operation—mixing or mining, coefficient of friction, and particle movement), it is possible to reduce energy consumption. Data on the possibility of improving the operation of production processes of various enterprises in Germany are presented by Steinhofel and others [46]. As we know, many factors influence the production process, for example, technical, economic, and social factors. Due to the above reasons, obtaining such large benefits in the whole production process, where various technological machines operate (technological operations), is difficult; nevertheless, it enables the introduction of sustainable production processes. The conducted simulation tests show possibilities of improving process efficiency and shortening the operation times, which results in economic benefits. The lower energy consumption and the increase in the efficiency of technological processes will also lead to the generation of less post-production waste (ecological benefits), which is in line with the principles of sustainable development.

#### **4. Conclusions**

In this study, a closed system of equations was obtained with a coupling equation (of constraints) that allows modeling a particle motion on a rotating surface; when numerically integrating them, it is possible to evaluate the use of a particular accelerator surface of a centrifugal rotary chopper machine to achieve the desired results in terms of downsizing, increasing productivity, or improving the quality of shredding. The use of numerical integration methods allows to consider the influence of physical and geometrical processes and kinematic parameters on the output result, for example, traveling time and velocity in cylindrical coordinates. Thus, the simulation of the particle motion

along an accelerator allows choosing rational geometrical dimensions of the chopper machine and its optimal operating practice.

**Supplementary Materials:** The Supplementary Materials are available online at http://www.mdpi.com/2071-1050/ 11/18/4873/s1.

**Author Contributions:** Conceptualization, J.C., P.A.S. and I.I.I.; Data curation, A.V.A.; Formal analysis, A.M., A.V.A., A.Y.I. and I.I.I.; Methodology, A.V.A., P.A.S. and A.Y.I.; Resources, J.C.; Software, P.A.S.; Writing—original draft, J.C., P.A.S. and A.Y.I.; Writing—review & editing, J.C. and I.I.I.

**Funding:** This research received no external funding.

**Acknowledgments:** We are thankful to the Editor and the reviewers for their valuable comments and detailed suggestions to improve the paper.

**Conflicts of Interest:** The authors declare no conflict of interest.


**5. Importance of genetics for the clinician**

In the last 15 to 20 years, clinicians have been concerned with grasping the increasing complexity of this disease, with a gradual worldwide increase of its prevalence that has turned it into a pandemic disease. The latest evidence shows that, despite correcting their lifestyle, we cannot always achieve good metabolic control in patients in complex clinical situations.

There is a population, which is probably formed by most of our patients, with clinical features where their phenotype is a good reflection of their genotype; but we are finding with increasingly frequency clinical cases that are difficulty to classify with the current criteria.

In these cases, a high percentage of patients had severe difficulties with their metabolic control. It is precisely here where we need to carry out a proper genetic diagnosis, and eventually an immunologic one, to allow us a broader view of their pathology. Several clinical observations and systematic studies have shown that classical type 1 diabetes, whether in children, late onset in adults, or individuals over 65, can coexist in the same individual with "classic" type 2 diabetes where insulin secretion deficiency and insulin resistance are detected simultaneously (Serrano Rios, 2009). This group of patients is usually referred to a diabetes specialist because the primary care physician cannot decide about or control them. Once reached this stage and after correcting the variables that affect proper metabolic control, such as nutritional plan and regular physical activity, we can see that many of these patients keep having a poor metabolic control. These patients are usually overweight and / or obese with a very erratic response to anti-diabetic drugs alone or in combination, both between them and with insulin.

Complying with the algorithms, we almost always end up giving insulin to our patients, but in many cases this is probably done too late. This was analyzed by many authors that described as final: "therapeutic inertia". They are usually described as patients with a poor adherence to the treatment plan. Also, on average they start insulin treatment before the classical diabetes type 2 patients.

Thus, we are planning to deepen into genetic typing, in order to see if it may help us to understand the etiopathogenesis of these patients, and why they do not have the expected response to the drug treatment.

As stated above, these patients surprisingly had a genotype that does not agree with their phenotype. This was what allowed us as clinicians to begin to understand these facts and to find an explanation (albeit partial) of the poor outcome of each patient.

What are the issues that the clinician should consider for further study of certain patients?

In the last 15 to 20 years, clinicians have been concerned with grasping the increasing complexity of this disease, with a gradual worldwide increase of its prevalence that has turned it into a pandemic disease. The latest evidence shows that, despite correcting their lifestyle, we cannot always achieve good metabolic control in patients in complex

There is a population, which is probably formed by most of our patients, with clinical features where their phenotype is a good reflection of their genotype; but we are finding with increasingly frequency clinical cases that are difficulty to classify with the current

In these cases, a high percentage of patients had severe difficulties with their metabolic control. It is precisely here where we need to carry out a proper genetic diagnosis, and eventually an immunologic one, to allow us a broader view of their pathology. Several clinical observations and systematic studies have shown that classical type 1 diabetes, whether in children, late onset in adults, or individuals over 65, can coexist in the same individual with "classic" type 2 diabetes where insulin secretion deficiency and insulin resistance are detected simultaneously (Serrano Rios, 2009). This group of patients is usually referred to a diabetes specialist because the primary care physician cannot decide about or control them. Once reached this stage and after correcting the variables that affect proper metabolic control, such as nutritional plan and regular physical activity, we can see that many of these patients keep having a poor metabolic control. These patients are usually overweight and / or obese with a very erratic response to anti-diabetic drugs alone or in

Complying with the algorithms, we almost always end up giving insulin to our patients, but in many cases this is probably done too late. This was analyzed by many authors that described as final: "therapeutic inertia". They are usually described as patients with a poor adherence to the treatment plan. Also, on average they start insulin treatment before the

Thus, we are planning to deepen into genetic typing, in order to see if it may help us to understand the etiopathogenesis of these patients, and why they do not have the expected

As stated above, these patients surprisingly had a genotype that does not agree with their phenotype. This was what allowed us as clinicians to begin to understand these facts and to

What are the issues that the clinician should consider for further study of certain patients? a. Obese patients showing good response to insulin during intercurrence: many of these patients had an intercurrent disease, and with the temporary insulin treatment they achieved a good control (especially in early stages of diagnosis) that may be explained by an improvement in glucotoxicity and / or moderate insulinopenia. In these patients the insulin will be removed based on these myths: (1) Insulin is "ineffective"; (2) Insulin injection increases cardiovascular diseases and hyperinsulinemia; and (3) Insulin causes weight gain. The reluctance we see in these patients insulin is based on misguided or questionable in view of the genetic results

b. Poor response to insulin sensitizers: in particular thiazolidinedione but also biguanides. c. Poor response to secretagogues: it is usually attributed to glucotoxicity, but how much

find an explanation (albeit partial) of the poor outcome of each patient.

we are finding and the matching clinical trials.

influence does drug response have?

**5. Importance of genetics for the clinician**

combination, both between them and with insulin.

classical diabetes type 2 patients.

response to the drug treatment.

clinical situations.

criteria.

Already, Nolan and Murphy (2001) posed an approach to the phenotypic and metabolic characterization of insulin-resistant patients, impaired glucose tolerance, or type 2 diabetes, and the use of glutamic acid decarboxylase antibodies (GADA), genetic markers, and models to estimate the insulin-resistance should be considered. These authors discuss the utility of using genetic markers based on population studies for type 2 diabetes mellitus. In what it has to do with the poor response to treatment, we must remember that both therapeutic inefficiency and drug toxicity, which have been seen in some individuals, have been frequently observed. Due to the presence of some drug metabolizing enzymes, drugs can participate as inhibitors or inducers of these enzymes, thereby their variation in activity between individuals. This variability in enzyme activity may reflect the existence of mutations in their genes.

#### **6. Conclusion: What is happening?**

The above mentioned points will lead us to review the different mechanisms that may have taken place in the evolutionary processes leading to the current status of this disease. We will consider some possible situations.

a. Researchers are considering the way natural selection is currently operating in humans. The concept of "the survival of the strongest individual" perhaps is no longer valid in the 21st century. Quintana Murci et al. (2007), at the Pasteur Institute (Paris), have looked for answers regarding the mechanisms of human evolution by comparing whole genomes of different populations. They analyzed more than 2.8 million genetic markers in different populations from different ethnic groups collected in the HAPMAP project. They found that 582 genes were subject to "strong selective pressures" during the last 60,000 to 10,000 years. Some of these genes are strongly associated to external features (e.g.: hair, skin color); others are to the response to pathogenic agents or drugs; and others to diseases with different incidences between populations, like diabetes, obesity, or hypertension. Barreiro pointed out that "it is the first time that it can be demonstrated, concerning the whole genome that natural selection participates in the differentiation of the populations" This work is not only useful to satisfy our curiosity, but also to aid in the identification of genes implied in different diseases (Barreiro et al., 2005; 2008).

Well defined since the XV century, clinical knowledge on diabetes gradually increased, and in the end two major distinct types of this pathology were described (1 and 2). In order to understand the current increase of chronic diseases, it is necessary to consider the important relationship between human feeding and human evolution. The regular offer of food that seemed to help human evolution so greatly in the past is also generating a great amount of diseases and their corresponding incapacities (like hemiplegics, aphasia, amputations, etc.). This fact is a true evolutionary paradox (Insua & Fuks, 2003).

Initially, we must consider the importance of the neutralization of positive selective pressure introduced by the availability of nutrients as consequence of human civilization. A good

Diabetes Type 1 and 2: What is Behind a Classification? 297

the lack of information, or misinterpretation, of the importance of the genetic components of the disease. But this disregarding could be considered also as having iatrogenic elements: we improve the current patient's quality of life, but on the other hand we hamper that of future persons. This process implies the emergence of currently unknown entities. New discoveries have allowed life extension for affected people, with the subsequent appearance of new pathological complications that were not seen before simply because affected

b. Are we witnessing a new type of diabetes, called "double o hybrid" by some authors? We believe that the phenomenon we are watching is simply another expression of the multifactorial nature of this disease. When we analyze populations with an ethnic mixture or of different ethnic origins, we begin to get a glimpse of the products of genetic admixture. This leads us to find a higher proportion of problematic patients that are difficult to classify because, when examining their phenotype, they are affected by certain genes that are masked by others. Hence, we can see families where, according to traditional classification, both entities (type 1 and type 2) coexist. This fusion would be associated with a new and intermediate phenotype (Tuomi, 2005). There are a few studies identifying patients where both type of diabetes overlap (Libman &. Becker, 2003; Pozzilli & Guglielmi, 2009); moreover, Pozzilli and Gugliemi (2007) place this entity in the middle of the double "rainbow" (made up of type 1 and type 2 diabetes). The "accelerator hypothesis" is a theory that shares this vision. It is a singular, unifying concept, which states that type 1 and type 2 diabetes are the same insulin-resistance disorder set against different genetic backgrounds. This hypothesis does not deny the role of autoimmunity, only its primacy in the process. It distinguishes type 1 and 2 diabetes only by tempo, the faster tempo reflecting the (inevitably) earlier presentation in the more

Recognition that susceptibility arises through the combination of multiple genetic pathways influencing hazardous factors in a nonlinear manner suggests that a 'decanalization' process contributes to the epidemic nature of common genetic diseases. The evolution of the human genome, combined with a marked environmental and cultural perturbation in the past two generations, might lead to the uncovering of cryptic genetic variations that are a major

This would be also favored by others processes such as an increase of life expectancy and fertility of affected individuals, the globalization phenomena, and increased admixture of different ethnic groups when compared with the past. The last phenomenon is clearly seen

Regardless of all the arguments presented in this chapter, we think that it is extremely important to introduce the genetic risk profile into the present diabetes classification criteria. This will clearly improve our capability of distinguishing between different types of

The effects of genetic traits in diabetes had been studied for decades, but few consistent risk factors have been well established. Currently, most of large scale studies on candidate genes do not combine the analysis of both types of diabetes. Establishing the association between genotype and phenotype would allow a deeper insight into the pathogenesis of the disease. Screening of associated anomalies and the possibility of anticipating future outcomes would

While for many countries, especially in Latin-America, individual genetic diagnosis can be very expensive to implement, we must realize that we are facing a multifactorial disease.

in Latin America and mainly in the Uruguayan population as it was stated above.

individuals passed away before their onset.

susceptible genotype (Wilkin, 2009).

diabetes or specific presentations.

be consequently improved.

source of disease susceptibility (Gibson, 2009).

example of the relationship between nutritional factors, diabetes, and population genetics is Szathmary's hypothesis (Marrodán, 2000) for explaining the high incidence of diabetes in several Amerindian populations (USA and Canada), either in reservations or in those adapted to western life.

Diabetes is a genetic-based disease whose manifestation is partly favored by excessive carbohydrate consumption. Possibly, several individuals with a specific genotype would produce insulin faster when faced with higher glucose levels than others; and they would also store this glucose as glycogen or fat more efficiently. This genotype would have been positively selected in a nutritional environment where periods of abundant or shortage of foods oscillate in a critical form. But this capacity for a faster answer to carbohydrate stimulus has a biological cost when food intake is constant. Under this situation, genes increasing insulin production are no longer beneficial to the individual because their carriers become obese, exhausting the physiological capacity of the pancreas, and leading to the subsequent development of diabetes (Marrodán, 2000; Harris, 2002). Variations in diabetes or obesity genes imply that adaptation to fasting was also an important selective agent. Quintana-Murci et al. (2007) pointed out that insulin-regulating genes have been positively selected. Thus, for instance, the ENPP1 gene has a mutation protecting against obesity and type II diabetes. This variant is present in 90% of non-African individuals and it is almost absent in African ones.

The susceptible genotype may have been selected in these populations because unusually frequent fasting periods may have taken place during the initial colonization of 'new worlds'. The abovementioned non-insulin dependent diabetes mellitus has shown a strong genetic component that may include a 'thrifty' genotype(s) (Neel 1962; Zimmet et al., 1990).

The 'thrifty' genotype(s) may have once allowed founding populations to survive both 'feast' and 'famine' conditions for several generations. Individuals carrying these genes would have had an increased efficiency for energy extraction (nutrition) from environmental scarce resources. During times of abundance those individuals with this predisposition would store more energy than those lacking it. When the progress of human civilization assured continuous fat-rich and fiber-poor diets, and a sedentary lifestyle, the 'thrifty' genotype(s) became disadvantageous, leading to obesity, increased insulin resistance, beta cell misbalance, and finally diabetes (Wendorf, 1991; 1992).

What was a selective advantage in past environments is currently, for most people in industrialized countries, an undesired condition. The result is obesity, diabetes, and the metabolic syndrome. For many years, diabetes was considered as a lethal or near-fatal disease by death simply by complications or by difficulties in the reproductive stages, both for men and women. More recently —the use of insulin is a landmark in this subject reproductive problems and some of their related complications have been solved.

In conclusion, evolutionary or Darwinian medicine considers that many contemporary diseases are associated to incompatibility between current human lifestyles and environments, and those under which human biology was shaped. As the observed difference between the incremental rates of both civilization and evolution is so great, most human evolutionary changes took place when our ancestors were gatherer-hunters. Thus, many characteristics and conducts that had adaptive value in the past may currently have non-adaptive value. Medicine has always tried to improve and look for the patient's cure. It really improved people's health, but in this process populational issues that are beyond the epidemiologic point of view were overlooked. This medical conduct may be explained by

example of the relationship between nutritional factors, diabetes, and population genetics is Szathmary's hypothesis (Marrodán, 2000) for explaining the high incidence of diabetes in several Amerindian populations (USA and Canada), either in reservations or in those

Diabetes is a genetic-based disease whose manifestation is partly favored by excessive carbohydrate consumption. Possibly, several individuals with a specific genotype would produce insulin faster when faced with higher glucose levels than others; and they would also store this glucose as glycogen or fat more efficiently. This genotype would have been positively selected in a nutritional environment where periods of abundant or shortage of foods oscillate in a critical form. But this capacity for a faster answer to carbohydrate stimulus has a biological cost when food intake is constant. Under this situation, genes increasing insulin production are no longer beneficial to the individual because their carriers become obese, exhausting the physiological capacity of the pancreas, and leading to the subsequent development of diabetes (Marrodán, 2000; Harris, 2002). Variations in diabetes or obesity genes imply that adaptation to fasting was also an important selective agent. Quintana-Murci et al. (2007) pointed out that insulin-regulating genes have been positively selected. Thus, for instance, the ENPP1 gene has a mutation protecting against obesity and type II diabetes. This variant is present in 90% of non-African individuals and it is almost

The susceptible genotype may have been selected in these populations because unusually frequent fasting periods may have taken place during the initial colonization of 'new worlds'. The abovementioned non-insulin dependent diabetes mellitus has shown a strong genetic component that may include a 'thrifty' genotype(s) (Neel 1962; Zimmet et al., 1990). The 'thrifty' genotype(s) may have once allowed founding populations to survive both 'feast' and 'famine' conditions for several generations. Individuals carrying these genes would have had an increased efficiency for energy extraction (nutrition) from environmental scarce resources. During times of abundance those individuals with this predisposition would store more energy than those lacking it. When the progress of human civilization assured continuous fat-rich and fiber-poor diets, and a sedentary lifestyle, the 'thrifty' genotype(s) became disadvantageous, leading to obesity, increased insulin resistance, beta cell

What was a selective advantage in past environments is currently, for most people in industrialized countries, an undesired condition. The result is obesity, diabetes, and the metabolic syndrome. For many years, diabetes was considered as a lethal or near-fatal disease by death simply by complications or by difficulties in the reproductive stages, both for men and women. More recently —the use of insulin is a landmark in this subject—

In conclusion, evolutionary or Darwinian medicine considers that many contemporary diseases are associated to incompatibility between current human lifestyles and environments, and those under which human biology was shaped. As the observed difference between the incremental rates of both civilization and evolution is so great, most human evolutionary changes took place when our ancestors were gatherer-hunters. Thus, many characteristics and conducts that had adaptive value in the past may currently have non-adaptive value. Medicine has always tried to improve and look for the patient's cure. It really improved people's health, but in this process populational issues that are beyond the epidemiologic point of view were overlooked. This medical conduct may be explained by

reproductive problems and some of their related complications have been solved.

adapted to western life.

absent in African ones.

misbalance, and finally diabetes (Wendorf, 1991; 1992).

the lack of information, or misinterpretation, of the importance of the genetic components of the disease. But this disregarding could be considered also as having iatrogenic elements: we improve the current patient's quality of life, but on the other hand we hamper that of future persons. This process implies the emergence of currently unknown entities. New discoveries have allowed life extension for affected people, with the subsequent appearance of new pathological complications that were not seen before simply because affected individuals passed away before their onset.

b. Are we witnessing a new type of diabetes, called "double o hybrid" by some authors? We believe that the phenomenon we are watching is simply another expression of the multifactorial nature of this disease. When we analyze populations with an ethnic mixture or of different ethnic origins, we begin to get a glimpse of the products of genetic admixture. This leads us to find a higher proportion of problematic patients that are difficult to classify because, when examining their phenotype, they are affected by certain genes that are masked by others. Hence, we can see families where, according to traditional classification, both entities (type 1 and type 2) coexist. This fusion would be associated with a new and intermediate phenotype (Tuomi, 2005). There are a few studies identifying patients where both type of diabetes overlap (Libman &. Becker, 2003; Pozzilli & Guglielmi, 2009); moreover, Pozzilli and Gugliemi (2007) place this entity in the middle of the double "rainbow" (made up of type 1 and type 2 diabetes).

The "accelerator hypothesis" is a theory that shares this vision. It is a singular, unifying concept, which states that type 1 and type 2 diabetes are the same insulin-resistance disorder set against different genetic backgrounds. This hypothesis does not deny the role of autoimmunity, only its primacy in the process. It distinguishes type 1 and 2 diabetes only by tempo, the faster tempo reflecting the (inevitably) earlier presentation in the more susceptible genotype (Wilkin, 2009).

Recognition that susceptibility arises through the combination of multiple genetic pathways influencing hazardous factors in a nonlinear manner suggests that a 'decanalization' process contributes to the epidemic nature of common genetic diseases. The evolution of the human genome, combined with a marked environmental and cultural perturbation in the past two generations, might lead to the uncovering of cryptic genetic variations that are a major source of disease susceptibility (Gibson, 2009).

This would be also favored by others processes such as an increase of life expectancy and fertility of affected individuals, the globalization phenomena, and increased admixture of different ethnic groups when compared with the past. The last phenomenon is clearly seen in Latin America and mainly in the Uruguayan population as it was stated above.

Regardless of all the arguments presented in this chapter, we think that it is extremely important to introduce the genetic risk profile into the present diabetes classification criteria. This will clearly improve our capability of distinguishing between different types of diabetes or specific presentations.

The effects of genetic traits in diabetes had been studied for decades, but few consistent risk factors have been well established. Currently, most of large scale studies on candidate genes do not combine the analysis of both types of diabetes. Establishing the association between genotype and phenotype would allow a deeper insight into the pathogenesis of the disease. Screening of associated anomalies and the possibility of anticipating future outcomes would be consequently improved.

While for many countries, especially in Latin-America, individual genetic diagnosis can be very expensive to implement, we must realize that we are facing a multifactorial disease.

Diabetes Type 1 and 2: What is Behind a Classification? 299

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#### **7. Acknowledgment**

This chapter could not have been written without the valuable collaboration of graduate and postgraduate students that are part of our research group (in alphabetic list): Br. Matías Fabregat, B.S. Joaquina Farías, MSc. Mariana Fernández, B.S. Ana Laura Reyes, Br. Jorge Souto, MSc. Pilar Zorrilla.

#### **8. References**

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Although we are aware that understanding the pathogenesis of hyperglycemia or the basis for an effective treatment may be deemed as more important than knowing the type of diabetes we are dealing with, we are currently persuaded that the distinguishing between different types or presentation forms of diabetes based on genetic information is an

This chapter could not have been written without the valuable collaboration of graduate and postgraduate students that are part of our research group (in alphabetic list): Br. Matías Fabregat, B.S. Joaquina Farías, MSc. Mariana Fernández, B.S. Ana Laura Reyes, Br. Jorge

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**15**

*Italy*

**The Enlarging List of Phenotypic**

 **Clinical Identification of Families**

**at Risk for Type 1 Diabetes**

Elena Matteucci and Ottavio Giampietro *Department of Internal Medicine, University of Pisa*

**Characteristics That Might Allow the**

Type 1 diabetes is a chronic metabolic disease whose aetiology and pathogenesis remain not completely understood. Current criteria for the diagnosis of diabetes are: 1) haemoglobin A1c ≥ 6.5% (assayed using a method that is certified by the National Glycohemoglobin Standardization Program, NGSP, and standardised or traceable to the Diabetes Control and Complications Trial, DCCT, reference assay), 2) fasting plasma glucose (FPG) ≥ 126 mg/dl, 3) 2-hour plasma glucose ≥ 200 mg/dl during an oral glucose tolerance test (OGTT, 75 g), 4) a random plasma glucose ≥ 200 mg/dl (American Diabetes Association, 2011). The classification of diabetes includes: type 1 diabetes, type 2 diabetes, other specific types of diabetes due to other causes, and gestational diabetes mellitus. Type 2 diabetes, which is usually associated with obesity and older age, results from insulin resistance and progressive failure of pancreatic beta-cell function. Type 1 diabetes, which has usually an abrupt onset in younger people, is an organ-specific autoimmune disease characterised by absolute insulin deficiency resulting from beta-cell destruction. However, autoimmunity may not be the primary cause: environmental triggers are believed to precipitate type 1 diabetes in genetically susceptible individuals (van Belle et al., 2011). The overall incidence of type 1 diabetes is increasing; the majority of the increase is observed in the youngest age group, which also appeared to be the heaviest (Evertsen et al., 2009). Indeed, the accelerator hypothesis (Wilkin, 2009) suggests that type 1 and type 2 diabetes are the same disorder of insulin resistance set against different genetic backgrounds. Three processes could variably accelerate the loss of beta cells through apoptosis: constitution, insulin resistance, and autoimmunity. None of these accelerators leads to diabetes without excess weight, which causes an increase in insulin resistance and, thus, the weakening of glucose control. In turn, the glucotoxicity accelerates beta-cell apoptosis directly and by inducing beta-cell immunogens and autoimmunity in genetically predisposed subjects. Insulitis is commonly observed in recent-onset type 1 diabetes, but it does not uniformly affect all insulincontaining islets (differences in islet function?). It has been suggested that under increased insulin demand (puberty, adolescence, high sugar intake, etc.) a population of islets may be more prone to dysfunction or death, thereby attracting antigen presenting cells and

**1. Introduction**

Noviembre

http://www.congresoaladchile2010.com/pdfs/trabajos\_modalidad\_poster.pdf


**Acknowledgements**

The authors are greatly indebted to **Late Professor (Dr.) Ashok Panagariya**, a *Neuroscientist of International acclaim*, whose piercing insight and vision had been and will remain *The Fountainhead* of the ongoing work on *Modelling of Human Mind*.


**Table 1.** *Cont*.

### **Table 2.** Groups of less liquid cryptocurrencies.

1.15 × Fluz Fluz

Bitdeal 1.16 × 2.49 ×

6.53 ×

**Table 2.** *Cont*.

It can be observed that the most important coins in the cryptocurrency markets, such as Bitcoin, Ethereum, Monero, BitcoinCash, IOTA, Tether, EOS, Ethereum Classic, Stellar, Stratis, Dash and Cardano remain the most popular across investor trading preferences even in bearish periods, despite their large price decreases. In this highest liquidity group, the Amihud's illiquidity ratio takes values from 9.09 × 10−28 (most liquid) to 5.66 × 10−12 (least liquid in this group). The number of active traders of these currencies remains high as it costs less for investors and speculators to trade with these coins due to lower spreads as well as lower transaction costs. Investors believe that if the liquidity of a cryptocurrency is low, it is more difficult to make profit from it as it would be more time-consuming to find a preference matching with other traders willing to make the opposite move. This is why more liquid assets are found to be more preferable during distressed times and not only during flourishing periods that previous academic work has shown (Wei 2018).

On the other hand, less known virtual currencies such as the 808, Dix Asset, Sprouts and WeAreSatoshi appear to exhibit much lower levels of liquidity. More specifically, the Amihud's illiquidity ratio takes values from 1.95 × 10−6 to 0.017296 in this eighth group of currencies that stands for the least liquid digital coins. This provides evidence that investors do not prefer during bearish periods currencies that traditionally exhibit low market capitalization, as they are considered more costly to invest in.

Overall, our findings are partly in line with conventional methods for measuring liquidity, based on, such as, the market capitalization or the trading volume of digital currencies. As one can easily observe, the great majority of high-capitalization cryptocurrencies are found to be the most liquid ones according to the Amihud's illiquidity ratio. Moreover, lower-capitalization currencies are part of the lower-liquidity groups based on the categorization performed by Amihud's method. Liquidity examination based on trading volume brings about similar outcomes.

The results of our study are informative about the potential that investors have on substituting investments in high-capitalization cryptocurrencies with lower-capitalization ones during turbulent times when market values of Bitcoin are decreasing. Evidence reveals that there is little tendency of economic agents to invest in alternative digital currencies, but only in the best-known ones. It is remarkable that the most liquid currency during this bearish period, which leaves Bitcoin at the second place, has been the TrueUSD stablecoin that is tied to the US dollar. This is very informative about investors' preferences during distressed times. Notably, they do not abandon investments in the already unstable cryptocurrencies in order to invest in less known and probably more volatile ones, but they rather invest in a coin tied to the most prestigious international currency that carries a global legal tender. These findings reveal that economic units tend to diversify their portfolios and hold a mildly more risk-averse investment profile during crises rather than a more risky attitude.