2. Block-type HTRs and calculation methodologies

## 2.1. Block-type HTRs and spatial separation levels

## 2.1.1. Block-type HTRs

1. Introduction

98 Recent Improvements of Power Plants Management and Technology

During the mid-1950s to the mid-1970s, some different types of Th/U MOX fuels, for example (Th,U)O2 or (Th,U)C2, were tested and used as fuels in high-temperature gas-cooled reactors (HTRs), like AVR and THTR in Germany [1] and Fort St. Vrain in the USA [2]. Three main reasons inspired them to demonstrate Th-U fuel cycle at that time. First, compared with kwon uranium, thorium is three times more abundant in nature. Second, Th-232 has an attractive potential for breeding to fissile U-233 efficiently in thermal neutron spectrum. U-233 is also considered as the best compared with other two common fissile isotopes, U-235 and Pu-239, in epithermal or thermal spectrum from neutronic point of view because the number of fission neutrons per neutron absorbed is 10–20% higher than that of U-235 and Pu-239. Finally, uranium resources were believed to be insufficient to support the development of nuclear

Besides HTRs, thorium has been an interesting nuclear fuel for various reactor applications [3], such as molten-salt reactors (MSRs) and water-cooled reactors.Especially, combined with molten-salt fuel in MSRs, thorium was used as a necessary composition of the "standard" fuel aiming to converse and even breed Th-232 to U-233 from the 1970s to mid-1980s. In past 20 years, the potential of thorium has been extended to radioactive waste management and plutonium incineration [4]. In this application, Th-232 is considered as a better fertile isotope than U-238 because of a larger net destruction of plutonium, when weapon-grade or reactorgrade plutonium is burned in various nuclear reactors. Furthermore, thorium-fueled reactors

Combined with the commercial purpose and potential application scale, light-water reactors (LWRs) are a natural choice from the reactor point of view in recent years because of a large amount of LWRs all over the world. The seed-and-blanket (S&B) concept has been reexamined for LWR application by the MIT group [5, 6]. The concepts originate from S&B configuration and were developed for the advanced water breeder application (AWBA) program and tested in the light water breeder reactor (LWBR) at Shippingport from 1977 to 1982 [7]. Further work on thorium-fueled LWRs has been pursued by Radkowsky and Galperin [8]. The MIT group proposed the micro-heterogeneous fuel assemblies and the whole assembly seed-and-blanket (WASB) concept. Moreover, compared with the past research, the recent MIT work is all based

Because of the burnup limit of LWRs (usually 50 GWd/tHM), some research showed that the potential of thorium is limited in LWRs, and HTRs are a better choice for thorium-based fuel for higher burnup and harder neutron spectrum. Recently, the concept of S&B fuel blockshas been introducedto the U-battery [9], a small long-life HTR, and a commercial-level GT-MHR [10], as well as advanced high-temperature reactors (AHTRs) [11] with low-pressure liquid-salt (Flibe) as coolant, which enables the design of a high-power (e.g., 2400–4000 MWth), high-temperature (850–950C) reactor with fully passive safety capability and the economic production of electricity

The past studies have shown the distribution of thorium and uranium fuels in space is a very important factor for the performance of thorium-fueled reactors and have proposed some

industries on a large scale at the early period of nuclear energy development.

generate less long-lived radioactive wastes than uranium-fueled ones.

on low-enriched uranium for proliferation resistance.

orhydrogen.

Modular block-type HTRs [12] are one kind of inherently safe reactors, which passively remove decay heat by natural convection, conduction, and radiation from the reactor core and keep the fuel intact. As mentioned in Section 1, the block-type HTRs are a better choice for thorium-based fuel for higher burnup and harder neutron spectrum. Moreover, an advantage of block-type HTRs over pebble-bed HTRs is that the former provides multi-level and fixed spatial distribution of thorium/uranium fuels in the reactor cores.The reactor core of the block-type HTRs investigated, as shown in Figure 1(a), is comprised of an annular fuel zone, inner reflectors, and outer reflectors. The annular fuel zone is comprised of 1980 fuel blocks, as shown in Figure 1(b). The fuel blocks are stacked firmly against each other in columns that form an annulus between an inner and an outer reflector, both of which consist of rings of unfueled graphite blocks. The annular core configuration ensures higher thermal power and inherent safety under most accidents and transient conditions. Each fuel block includes 210 fuel channels, 108 coolant channels, and 6 fixed burnable poison channels which are filled with

Figure 1. Thorium-fueled HTR and fuel block, (a) Reactor core and (b) Fuel block. Does the query aim to use second style for the book?

graphite in the flowing calculations.The cylindrical fuel compacts are stacked inside channels drilled into hexagonal graphite blocks. Other geometrical parameters ofthe fuel blocks are listed in Table 1.

The most prominent feature of the block-type HTRs is use of tristructural-isotropic (TRISO) particles, which contain five layers from inside to outside: fuel kernel, porous carbon buffer, inner pyrolytic carbon (IPyC), silicon carbide (SiC), and outer pyrolytic carbon (OPyC). The porous carbon buffer layer is provided to protect the dense PyC from fission recoil damage and to provide void volume to limit the fission gas pressure. The dense PyC has good irradiation stability and capability to remain intact to perform fission production retention under severe exposure conditions. Sandwiched between the two PyC layers, the SiC layer provides metallic fission production retention and mechanical strength. TRISO fuel particles are blended and bonded together with a graphite matrix to form fuel compacts. Figure 2 illustrates how the TRISO particles are packaged into the annular core.

## 2.1.2. Definition of multiscale spatial separation

When using thorium in HTRs, two important factors influence nuclear performance. One is the thorium content (the mass ratio of Th-232 to all heavy metal isotopes), meaning the mixed proportion of thorium and uranium. The other is the spatial separation level of thorium and uranium, meaning how thorium and uranium are to be mixed. According to the level of spatial separation, four levels are in a block-type HTR: (1) No separation (Th/U MOX level): with Th/U MOX fuel, the thorium and uranium are mixed in each fuel kernel as a form of (Th,U)O2, as shown in Figure 2(a). Thorium and uranium do not separate in the macrolevel, (2) TRISO-level separation (SBT level): UO2 and ThO2 are made into different TRISO fuel particles (UO2 TRISO and ThO2 TRISO) separately, but the two kinds of TRISO fuel particles are mixed into the same fuel compact, as shown in Figure 2(b), (3) Channel-level separation (SBU level): each fuel channel has only one kind of fuel compacts (UO2 fuel compacts or ThO2 fuel compacts), but a fuel block has both UO2 fuel channels and ThO2 fuel channels, as shown in Figure 2(c), and (4) Block-level separation (WASB level): each fuel block only has a kind of fuel (UO2 or ThO2), but the core has both UO2 fuel blocks and ThO2 fuel blocks, as shown in Figure 2(d).

## 2.2. Calculation and evaluation methods

## 2.2.1. Neutronic calculation method

To only analyze the influence of spatial separation, the other parameters are kept the same including the fuel block geometry, as listed in Table 1, and the fuel shuffling scheme, as shown in Figure 3. A detailed full-core 3D transport calculation in one step will require significant

Table 1. Basic geometrical parameters of fuel blocks in the HTR.

Analysis of the Spatial Separation Effects of Thorium/Uranium Fuels in Block‐Type HTRs http://dx.doi.org/10.5772/intechopen.68671 101

Figure 2. Four levels of spatial separation of thorium/uranium in block-type HTRs.

graphite in the flowing calculations.The cylindrical fuel compacts are stacked inside channels drilled into hexagonal graphite blocks. Other geometrical parameters ofthe fuel blocks are

The most prominent feature of the block-type HTRs is use of tristructural-isotropic (TRISO) particles, which contain five layers from inside to outside: fuel kernel, porous carbon buffer, inner pyrolytic carbon (IPyC), silicon carbide (SiC), and outer pyrolytic carbon (OPyC). The porous carbon buffer layer is provided to protect the dense PyC from fission recoil damage and to provide void volume to limit the fission gas pressure. The dense PyC has good irradiation stability and capability to remain intact to perform fission production retention under severe exposure conditions. Sandwiched between the two PyC layers, the SiC layer provides metallic fission production retention and mechanical strength. TRISO fuel particles are blended and bonded together with a graphite matrix to form fuel compacts. Figure 2 illustrates how the

When using thorium in HTRs, two important factors influence nuclear performance. One is the thorium content (the mass ratio of Th-232 to all heavy metal isotopes), meaning the mixed proportion of thorium and uranium. The other is the spatial separation level of thorium and uranium, meaning how thorium and uranium are to be mixed. According to the level of spatial separation, four levels are in a block-type HTR: (1) No separation (Th/U MOX level): with Th/U MOX fuel, the thorium and uranium are mixed in each fuel kernel as a form of (Th,U)O2, as shown in Figure 2(a). Thorium and uranium do not separate in the macrolevel, (2) TRISO-level separation (SBT level): UO2 and ThO2 are made into different TRISO fuel particles (UO2 TRISO and ThO2 TRISO) separately, but the two kinds of TRISO fuel particles are mixed into the same fuel compact, as shown in Figure 2(b), (3) Channel-level separation (SBU level): each fuel channel has only one kind of fuel compacts (UO2 fuel compacts or ThO2 fuel compacts), but a fuel block has both UO2 fuel channels and ThO2 fuel channels, as shown in Figure 2(c), and (4) Block-level separation (WASB level): each fuel block only has a kind of fuel (UO2 or ThO2), but

the core has both UO2 fuel blocks and ThO2 fuel blocks, as shown in Figure 2(d).

To only analyze the influence of spatial separation, the other parameters are kept the same including the fuel block geometry, as listed in Table 1, and the fuel shuffling scheme, as shown in Figure 3. A detailed full-core 3D transport calculation in one step will require significant

Values 36 79.3 1.27/210 1.588/102, 1.27/6 500 100/35/35/40 1.05/1.9/3.2/

Diameter/number of coolant channels [cm/]

Diameter of kernels [μm]

Thickness of TRISO layers [μm]

Density of TRISO layers [g/cm3 ]

1.9

listed in Table 1.

TRISO particles are packaged into the annular core.

100 Recent Improvements of Power Plants Management and Technology

2.1.2. Definition of multiscale spatial separation

2.2. Calculation and evaluation methods

Height of block [cm]

Table 1. Basic geometrical parameters of fuel blocks in the HTR.

Diameter/ number of fuel channels [cm/]

2.2.1. Neutronic calculation method

Parameters Width

across flat [cm]

Figure 3. Reactor core calculation model for 1/6th core.

memory and a central processing unit (CPU) time as utilities in producing calculations or even in laboratories for design purposes. Therefore, a two-step calculation scheme is typical: (1) a detailed calculation at the assembly level with reflective boundary conditions, which gives homogenized cross-sections for the assemblies, condensed to a certain number of groups (lattice calculation step) and (2) a second calculation at the core level with homogenized properties in each assembly and usually small number of groups (full-core calculation step).

In this chapter, the traditional two-step calculation scheme is constructed based on the DRAGON V4 code system [13], as shown in Figure 4. An attractive feature of the DRAGON code is its ability to treat particle fuel in a graphite matrix in a full-assembly calculation. It provides the possibility to define a stochastic mixture of spherical micro-structures that can be distributed inside composite mixtures of the current macro-geometry using the Hebert doubleheterogeneity model [14] or Sanchez-Pogroming double-heterogeneity model [15].

In step (a) in Figure 4, a 2D fuel block is modeled including the structure of the TRISO particle. The method of characteristics (MOC) and 295-group cross-section library (http://www. polymtl.ca/merlin/libraries.htm) are used to solve the transport equation. Then, the energy groups of the cross-sections are condensed to 26 groups during the homogenization of the fuel block. In step (b), a 1D annular core is modeled, comprising a homogenized fuel zone and two reflector zones. The homogenized cross-sections of the fuel block generated in step (a) are used for the fuel zone in this step, and the cross-sections of the graphite generated in step (a) are used for the reflectors of the 1D reactor model. The 1D transport calculations are executed by the discrete ordinate (SN) method. Only the reflectors are homogenized to generate the Analysis of the Spatial Separation Effects of Thorium/Uranium Fuels in Block‐Type HTRs http://dx.doi.org/10.5772/intechopen.68671 103

Figure 4. A schematic diagram of the two-step calculation scheme.

cross-sections of the reflector for the following full-core calculations. In step (c), the 2D full-core calculations are executed by the interface current (IC) method. The cross-sections of fuel blocks in this step come from the step (a), while the cross-sections of reflectors come from step (b).

## 2.2.2. Fuel cost analysis model

memory and a central processing unit (CPU) time as utilities in producing calculations or even in laboratories for design purposes. Therefore, a two-step calculation scheme is typical: (1) a detailed calculation at the assembly level with reflective boundary conditions, which gives homogenized cross-sections for the assemblies, condensed to a certain number of groups (lattice calculation step) and (2) a second calculation at the core level with homogenized properties in each assembly and usually small number of groups (full-core calculation step). In this chapter, the traditional two-step calculation scheme is constructed based on the DRAGON V4 code system [13], as shown in Figure 4. An attractive feature of the DRAGON code is its ability to treat particle fuel in a graphite matrix in a full-assembly calculation. It provides the possibility to define a stochastic mixture of spherical micro-structures that can be distributed inside composite mixtures of the current macro-geometry using the Hebert double-

Figure 3. Reactor core calculation model for 1/6th core.

102 Recent Improvements of Power Plants Management and Technology

heterogeneity model [14] or Sanchez-Pogroming double-heterogeneity model [15].

In step (a) in Figure 4, a 2D fuel block is modeled including the structure of the TRISO particle. The method of characteristics (MOC) and 295-group cross-section library (http://www. polymtl.ca/merlin/libraries.htm) are used to solve the transport equation. Then, the energy groups of the cross-sections are condensed to 26 groups during the homogenization of the fuel block. In step (b), a 1D annular core is modeled, comprising a homogenized fuel zone and two reflector zones. The homogenized cross-sections of the fuel block generated in step (a) are used for the fuel zone in this step, and the cross-sections of the graphite generated in step (a) are used for the reflectors of the 1D reactor model. The 1D transport calculations are executed by the discrete ordinate (SN) method. Only the reflectors are homogenized to generate the

An evaluation criterion must be in the comparison of different spatial separationlevels. Usually, the fuel cycle cost is one of the criteria. To make a fair comparison, the adoption of a standardized methodology for fuel cycle cost calculations is prerequisite. Therefore, the levelized lifetime cost methodology is used in this study. The levelized lifetime cost methodology was developed by the Organization for Economic Cooperation and Development (OECD) [16], which uses an internationally accepted investment appraisal methodology to analyze the fuel cycle cost.

The cash flow for fuel cycle material and services commences before the reactor starts to generate electricity and continues well after the reactor ceases operation. The exact timing of payments for natural uranium purchase, conversion, enrichment, fabrication, spent fuel storage, and disposal depends on the associated lead and lag times for the fuel cycle components. To calculate the overall fuel cycle cost, the magnitude of each component cost and the appropriate time that it occurs must be identified. Fuel quantities are obtained from reactor neutronic calculations as described in Section 2.2.1. These quantities of materials and services are adjusted to allow for process losses in the various component stages of the nuclear fuel cycle and then multiplied by the unit costs to obtain the component costs. Finally, the total fuel cycle cost is gotten by discounting these component costs to their present values in a specified base year (usually the commission date of reactor), as shown in Figure 5. The levelized lifetime cost methodology provides costs per unit of electricity generated which are the ratios of lifetime expenses to total expected output, expressed in terms of the present value equivalent. This method derives economic merits by comparing their respective average levelized lifetime costs.

The reactor data and fuel cycle cost data for the HTR are shown in Tables 2 and 3, respectively. Table 2 gives the information about the reactor including the power, lifetime, cycle length, and back-end options. Table 3 gives the unit price and lead or lag time for natural uranium

Figure 5. Time flow of nuclear fuel cycle cost with direct disposal option.

Table 2. Reactor operation data for the HTR.

Table 3. Fuel cycle cost data for the HTR.

purchase, thorium purchase, conversion, and enrichment. The price of natural uranium, conversion, and enrichment is the average price of spot market from 2010 to 2015 (http://www. uxc.com/), respectively: 120.9 \$/kg U, 8.75 \$/kg U, and 126.5 \$/SWU. The fabrication cost of 777 \$/kg HM for HTR fuel blocks comes from the Oak Ridge National Laboratory (ORNL)'s report [17]. Others are the same as the OECD's report [16]. Although different fuel separation levels would likely affect unit price related to fabrication and, in particular, storage, and disposal, their fraction in total fuel cycle cost is small, as mentioned in Section 3.4. Moreover, the sensitivity analysis shows that a 50% variation of the price of fabrication, storage, or disposal will lead to a no-more-than 5% variation of fuel cycle cost [18]. Thus, even if different fuel separation levels have a different price of fabrication, storage, and disposal, the analysis in this chapter is still valid.


**6. Stationary Green tensor construction: radiation conditions**

In this case let us construct the originals of the basic function but only over *ξ* by constant frequency:

$$\Phi\_{0m}(\mathfrak{x}, \alpha) = F\_{\xi}^{-1}\left[\left.f\_{0m}(\xi, \alpha)\right\vert\right]$$

which, in accordance with its definition (14), satisfies the equation:

$$\left(c\_m^2||\xi||^2 - \alpha^2\right)f\_{0m} = \mathbf{1} \tag{15}$$

Using property (12) for derivatives from here, we get Helmholtz equation for fundamental solution (accurate within a factor *c*�2 *m* ):

$$\left(\Delta + k\_m^2\right)\Phi\_{0m} + c\_m^{-2}\delta(\varkappa) = \mathbf{0}, \quad k\_m = \frac{\alpha}{c\_m} \tag{16}$$

*Generalized and Fundamental Solutions of Motion Equations of Two-Component Biot's Medium DOI: http://dx.doi.org/10.5772/intechopen.92064*

Fundamental solutions of Helmholtz equation, which satisfy Sommerfeld conditions of radiation:

$$\begin{aligned} \text{at } r &\to \infty \\\\ \Phi\_{0m}'(r) - ik\_m \Phi\_{0m}(r) &= O\left(r^{-1}\right), \qquad N = 3, \\\\ \Phi\_{0m}'(r) - ik\_m \Phi\_{0m}(r) &= O\left(r^{-1/2}\right), \quad N = 2. \end{aligned}$$

are well known [10]. They are unique. Using them, we obtain:

for *N* ¼ 3

*for j* ¼ 1, … , *N k* ¼ *N* þ 1, … , 2*N*

*j*þ*N* � *ρ*22*δk*

ð Þ �*iξk*�*N η*1 *f* 21 þ *η*2 *f* 22 þ *η*3 *f* 23

*f*03

ð Þ �*iξk*�*N ς*1*f*21 þ *ς*2*f*22 þ *ς*3 ½ *f*23��

*ρ*11*δk*

*m*, *q*1 ¼ *Qρ*12 � ð Þ *λ* þ *μ ρ*12, *q*2 ¼ *ρ*11*R* � *Qρ*12,

3 *α*2*υ*31*υ*32

3*υ*12 *α*2*υ*31*υ*32

> 3*υ*12 *α*2*υ*31*υ*32

3*υ*12 *α*2*υ*31*υ*32

*j*þ*N* þ *ρ*12*δk*

*j*

*f*03

*j* � *Q j* ð Þ ¼ 1, 2

ð Þ *d*1*bs*3 þ *d*2*d*33 ;

*q*1*b f* 3 þ *q*2*d*33 ;

ð Þ *d*1*d*33 þ *d*2*b*3*s* ;

*f*0*m* ¼ 1 (15)

(16)

*cm*

*q*1*d*33 þ *q*2*b*3*s*

*j*

*f*23 � 1 *α*2

þ

*Uk*

*Uk*

, *υlm* ¼ *c*

*D*1 ¼ 1 *α*2*υ*12

*β j* ¼ �ð Þ1 ð Þ *j*þ1 *D*1*с*2

*γ j* ¼ �ð Þ1 *j*þ1 *D*1*с*2

*η j* ¼ �ð Þ1 *j*þ1 *D*1*с*2

*ς j* ¼ �ð Þ1 *j*þ1 *D*1*с*2

constant frequency:

**28**

*bfj* ¼ *ρ*22*υfj*, *bsj* ¼ *ρ*11*υjs:*

*j* ¼ �*iξ j*

> þ 1 *α*2

*j*þ*N* ¼ �*iξ j*

> � *μ α*2 *δk j*þ*N*k k*ξ* 2

*where the next constants have been introduced as:*

2 *l* � *c* 2

*j α*2*υ*3*j*

*j α*2*υ*3*j*

*j α*2*υ*3*j*

*j α*2*υ*3*j*

*d*1 ¼ ð Þ *λ* þ *μ ρ*22 � *Qρ*12, *d*2 ¼ *Qρ*22 � *Rρ*12, *d*3*j* ¼ *ρ*12*с*2

, *β*3 ¼ � *с*2

, *γ*3 ¼ � *D*1*с*2

, *η*3 ¼ � *с*2

, *ς*3 ¼ � *с*2

This form is very convenient for constructing originals of Green tensor.

In this case let us construct the originals of the basic function but only over *ξ* by

*ξ f* 0*m*ð Þ *ξ*, *ω*

*m* ):

*m δ*ð Þ¼ *x* 0, *km* ¼ *ω*

**6. Stationary Green tensor construction: radiation conditions**

Φ0*m*ð Þ¼ *x*,*ω F*�1

*c* 2

fundamental solution (accurate within a factor *c*�2

*Δ* þ *k*2 *m* Φ0*m* þ *c*

which, in accordance with its definition (14), satisfies the equation:

*m*k k*ξ* 2 � *ω*2

Using property (12) for derivatives from here, we get Helmholtz equation for

�2

*d*1*bsj* þ *d*2*d*3*j*

*q*1*bfj* þ *q*2*d*3*j*

*d jd*3*j* þ *d*2*bjs*

*q*1*d*3*j* þ *q*2*b*ð Þ 4�*j s*

*ρ*12*δk*

*Mathematical Theorems - Boundary Value Problems and Approximations*

$$\Phi\_{0m} = \frac{1}{4\pi c^2} e^{ik\_m r}, \quad k\_m = \frac{\alpha}{c\_m};$$

for *N* ¼ 2

$$
\Phi\_{0m} = \frac{i}{4c^2} H\_0^{(1)}(k\_m r),
$$

where *H*ð Þ1 *j* ð Þ *kmr* is the cylindrical Hankel function of the first kind:

for *N* ¼ 1

$$\phi\_{0m} = \frac{\sin k\_m |\boldsymbol{\chi}|}{2k\_m c\_m^2}.$$

These functions (subject to factor *e*�*iωt* ) describe harmonic waves which move from the point *x* = 0 to infinity and decay at infinity.

The last property is true only for *N* = 2,3. In the case *N* = 1, all fundamental solutions of Eq. (16):

$$
\left(\frac{d^2}{d\mathfrak{x}^2} + k\_m^2\right)\Phi\_{0m} + c\_m^{-2}\delta(\mathfrak{x}) = \mathbf{0},
$$

do not decay at infinity.

From Theorem 1, the next theorem follows.

**Theorem 2.** *The components of Green tensor of Biot's equations at stationary oscillations with frequency ω, which satisfy the radiation conditions, have the form:*

$$\begin{aligned} \text{for } j = \overline{1, N}, \qquad k = \overline{1, N}, \\ U\_j^k(\mathbf{x}, \boldsymbol{\alpha}) &= -\boldsymbol{\alpha}^{-2} \sum\_{m=1}^3 \beta\_m \frac{\partial^2 \Phi\_{0m}}{\partial \mathbf{x}\_j \partial \mathbf{x}\_k} + \frac{1}{\alpha\_2} \left(\rho\_{12} \boldsymbol{\delta}\_{j+N}^k - \rho\_{22} \boldsymbol{\delta}\_j^k \right) \Phi\_{03}, \\\\ U\_{j+N}^k(\mathbf{x}, \boldsymbol{\alpha}) &= -\boldsymbol{\alpha}^{-2} \sum\_{m=1}^3 \gamma\_m \frac{\partial^2 \Phi\_{0m}}{\partial \mathbf{x}\_j \partial \mathbf{x}\_k} + \\\\ &\quad + \frac{\mu \boldsymbol{\delta}\_{j+N}^k}{\alpha\_2 \boldsymbol{\alpha}^2} \left(\boldsymbol{\varepsilon}\_3^{-2} \boldsymbol{\delta}(\mathbf{x}) + k\_3^2 \boldsymbol{\Phi}\_{0m} \right) - \frac{\rho\_{11} \boldsymbol{\delta}\_{j+N}^k + \rho\_{12} \boldsymbol{\delta}\_j^k}{\alpha\_2} \boldsymbol{\Phi}\_{03}; \end{aligned}$$

$$\begin{split} U^{k}\_{j}(\mathbf{x},\boldsymbol{\alpha}) &= -\boldsymbol{\alpha}^{-2} \sum\_{m=1}^{3} \eta\_{m} \frac{\partial^{2} \Phi\_{0m}}{\partial \mathbf{x}\_{j} \partial \mathbf{x}\_{k}} + \frac{1}{\alpha\_{2}} \left(\rho\_{12} \boldsymbol{\delta}^{k}\_{j+N} - \rho\_{22} \boldsymbol{\delta}^{k}\_{j}\right) \boldsymbol{\Phi}\_{03} \\ U^{k}\_{j+N}(\mathbf{x},\boldsymbol{\alpha}) &= -\boldsymbol{\alpha}^{-2} \sum\_{m=1}^{3} \xi\_{m} \frac{\partial^{2} \Phi\_{0m}}{\partial \mathbf{x}\_{j} \partial \mathbf{x}\_{k}} + \\ &\quad + \frac{\mu}{\alpha\_{2} \boldsymbol{\alpha}^{2}} \left(\boldsymbol{\varepsilon}\_{3}^{-2} \boldsymbol{\delta}(\mathbf{x}) + k\_{3}^{2} \boldsymbol{\Phi}\_{0m}\right) \boldsymbol{\delta}^{k}\_{j+N} - \frac{1}{\alpha\_{2}} \left(\rho\_{11} \boldsymbol{\delta}^{k}\_{j+N} + \rho\_{12} \boldsymbol{\delta}^{k}\_{j}\right) \boldsymbol{\Phi}\_{03} \end{split}$$

The obtained solutions allow us to study the dynamics of porous water- and gassaturated media at the action of periodic sources of disturbances of a sufficiently arbitrary form. In particular, they are applicable in the case of actions of certain forces on surfaces, for example, cracks, in porous media that can be simulated by

*Generalized and Fundamental Solutions of Motion Equations of Two-Component Biot's Medium*

There is another interesting feature of the Green tensor of the Biot's equations, which contains, as one of the terms, the delta-function that complicates the application of this tensor for solving boundary value problems based on analogues of Green formulas for elliptic systems of equations or the boundary element method. Here, when constructing the model, the viscosity of the liquid is not taken into account, which, apparently, leads to the presence of such terms, and it requires

simple and double layers on the crack surface.

*DOI: http://dx.doi.org/10.5772/intechopen.92064*

improvement of this model taking into account a viscosity.

originals of the basic functions in an initial space-time:

They are originals of the classic wave equation:

*∂*2 *∂t*2 � *c* 2 *m*Δ

satisfy the radiation conditions have the following form [10]:

**Φ**0*m*ð Þ¼ *x*, *t*

**Φ**0*m*ð Þ¼ *x*, *t*

*simple layer on the sound cone r* ¼ *cmt*, *r* ¼ k k*x* .

It is easy to show that the next lemma is true.

*conditions are representable in the following form:*

**31**

**Ф**0*m*ð Þ¼ *x*, *t*

**8. Green tensor of Biot's equations by non-stationary motion**

**Φ**0*m*ð Þ¼ *x*, *t F*�1 *f* 0*m*ð Þ *ξ*, *ω* � � ¼ *F*�1 *c*

To construct the non-stationary Green tensor, at first we also construct the

Depending on the dimension of a space, solutions of this wave equation that

*δ t* � *r cm*

*H ct* ð Þ � *r* ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi *c*2

1 4*πc*2 *mr*

1 2*πcm*

> 1 2

*H t*ð Þ*δ*ð Þ\$ *x*

Here *H t*ð Þ is the Heaviside function, and singular function *δ*ð Þ *t* � *r=cm* is the

Using regularization of the general function *ω*�1in the space of distribution [10]:

and the properties of Fourier transform of generalized functions convolution:

*h* ¼ *f* ∗ *g* \$ *h* ¼ *f* � *g*

**Lemma.** *The originals of the primitives of the basic functions satisfying the radiation*

1 �*i*ð Þ *ω* þ *i*0

2

� �**Φ**0*m* ¼ *δ*ð Þ*t δ*ð Þ *x* (18)

*m*k k*ξ* 2 � *ω*2 � ��1 � �

� �, *N* ¼ 3; (19)

*mt*2 � *r*2 p , *N* ¼ 2; (20)

*H c*ð Þ *mt* � j j *x* , *N* ¼ 1*:* (21)

where

*for N* ¼ 1

$$\frac{d^2\Phi\_{0m}}{d\boldsymbol{\chi}^2} = \frac{1}{2c\_m^2 k\_m} \left( k\_m \, ^2(\sin k\_m |\boldsymbol{\chi}|) - 2k\_m \delta(\boldsymbol{\chi}) \right);$$

*for N* ¼ 2

$$\frac{\partial^2 \Phi\_{0m}}{\partial \mathbf{x}\_j \partial \mathbf{x}\_k} = -\frac{i}{4c\_m^2} \left( 0.5k\_m^2 (H\_0(k\_m r) - H\_2(k\_m r))r\_{,j}r\_{,k} + k H\_1^1(k\_m r)r\_{,jk} \right);$$

*for N* ¼ 3

$$\frac{\partial \Phi\_{0m}}{\partial \mathbf{x}\_{j} \partial \mathbf{x}\_{k}} = \frac{1}{4\pi r c\_{m}^{2}} e^{ikr} \left\{ r, \, \_{j} r, \_{k} \left( \left( ik\_{m} - \frac{1}{r} \right)^{2} + \frac{1}{r^{2}} \right) + r, \, \_{jk} \left( ik\_{m} - \frac{1}{r} \right) \right\};$$

$$k\_{m} = \frac{\alpha r}{c\_{m}}, r = ||\mathbf{x}||, \quad r, \, \_{j} = \frac{\mathbf{x}\_{j}}{r}, \quad r, \, \_{\vec{\eta}} = \frac{1}{r} \left( \delta\_{\vec{\eta}} - \frac{\boldsymbol{\varkappa}\_{i} \boldsymbol{\varkappa}\_{j}}{r^{2}} \right).$$

*Proof*. By using originals of basic functions, property (12) of derivatives, we can obtain from formulas for *Uk j* in Theorem 1 the originals of all addends, besides that which contain factor k k*ξ* 2 . But using (16) we have:

$$-\Delta \Phi = \mathfrak{c}\_m^{-2} \delta(\mathfrak{x}) + k\_m^2 \Phi\_{0m} \quad \leftarrow \quad ||\xi||^2 f\_{0m} = \mathfrak{c}\_m^{-2} + k\_m^2 f\_{0m}$$

Then formulas of Theorem 2 follow from formulas of Theorem 1.

## **7. Generalized solutions by arbitrary periodic forces**

Under the action of arbitrary mass forces with frequency *ω* in Biot's medium, the solution for complex amplitudes has the form of a tensor functional convolution:

$$u\_j(\mathbf{x}, t) = U\_j^k(\mathbf{x}, a) \* F\_k(\mathbf{x}) e^{-i\alpha t}, j, k = \overline{1, 2N} \tag{17}$$

Note that mass forces may be different from the space of generalized vector function, singular and regular. Since Green tensor is singular and contains deltafunctions, this convolution is calculated on the rule of convolution in generalized function space. If a support of acting forces are bounded (contained in a ball of finite radius), then all convolutions exist. If supports are not bounded, then the existence conditions of convolutions in formula (17) requires some limitations on behavior of forces at infinity which depends on a type of mass forces and space dimension.

*Generalized and Fundamental Solutions of Motion Equations of Two-Component Biot's Medium DOI: http://dx.doi.org/10.5772/intechopen.92064*

The obtained solutions allow us to study the dynamics of porous water- and gassaturated media at the action of periodic sources of disturbances of a sufficiently arbitrary form. In particular, they are applicable in the case of actions of certain forces on surfaces, for example, cracks, in porous media that can be simulated by simple and double layers on the crack surface.

There is another interesting feature of the Green tensor of the Biot's equations, which contains, as one of the terms, the delta-function that complicates the application of this tensor for solving boundary value problems based on analogues of Green formulas for elliptic systems of equations or the boundary element method. Here, when constructing the model, the viscosity of the liquid is not taken into account, which, apparently, leads to the presence of such terms, and it requires improvement of this model taking into account a viscosity.


**4. CSR: a moral obligation**

Focusing on CSR from a moral viewpoint implies that managers have a duty/ obligation towards their stakeholders to act in a responsibly way. The moral duty to be socially responsible can be derived from religious or ethical principles of a moral philosophy. According to Kant's moral philosophy, these actions must be driven by a sense of duty to be morally valuable. To further discuss the CSR's moral perspective, it is imperative to explore the Kantian moral philosophy.

#### **4.1 CSR according to Kant's moral philosophy**

Morally speaking, CSR is an act of reciprocity according to which the firm has duty/obligation towards its stakeholders. Kant considers duty or doing what is right for its own sake as the foundation of morality. He argues that only actions that emanate from a sense of duty can be considered as having a moral worth. According to the Kantian moral philosophy, moral criteria are categorical imperatives. They are also unconditional, absolute and irrespective in consequences [38].

As a result, moral actions do not have to be justified by any reasons or theirs consequences except for their own sake. So, firms should simply show societal concerns because it is just the right thing to do and not because they would like to enhance their business fortunes or reputation. According to Kant, every human being has moral rights and everyone should be well treated and have the correlative duty to treat others in a good way.

Consequently, the responsibility to engage in CSR may lose its moral value if it is achieved because it brings beneficial returns or because society or governments require it. It must be driven by the sense of duty and must not be imposed by orders or legislations. Thus, enforcing CSR would be considered immoral since it would violate the moral rights of the decision maker to freely choose whether to consider societal issues and solve society's problems or not. Kant pinpoints the freedom of human beings and considers that everyone's existence as a rational and free person should be promoted. He defends the idea according to which humanity should be treated as an end and not as a means. Therefore, enforcing CSR may lead to its manipulation to achieve economic goals and self-interest motives and, consequently, CSR would shift from morality to immorality.

However, Kant's moral philosophy is criticized for being narrow and inadequate to deal with different issues morally [39]. According to Kant being ethical is following a set of absolute moral rules without alternatives for exceptions, neglecting moral emotions like sympathy.

#### **4.2 Moral CSR**

As a moral duty, CSR should be accepted as an ethical obligation rather than any other consideration. This perspective is based on values that highlight the right thing to do or the obligation to create a good society. Therefore, the intrinsic motives enhance the CSR behavior as long as managers perceive CSR as a moral duty they should fulfill [40].

Besides the economic and legal responsibilities established by Caroll 1979, firms have an ethical responsibility by doing what is moral, just and fair and philanthropic to benefit society by voluntary, educational, social and cultural projects. However, managers do not carefully consider the consequences of an action before taking decisions (whether it is good or not); rather, their values, gut feelings and affective reactions are also involved to shape their moral judgments [41].

Moral psychologists have focused on the role of reasoning (cognition) when facing social dilemmas [42]. In fact, managers' responses to moral and ethical issues depend on their individual characteristics in interpreting and dealing with societal problems whenever cognition is involved. Kohlgerb [42] considers reasoning as the principle foundation of a moral judgment. When investigating social behavior, Crilly et al. [43] explore four types of reasoning drawing on Kohlberg's [42] and Carroll's [3] studies such as: economic, legal, moral and reputation-based reasoning.

However, moral reasoning differs from other forms of reasoning since it is guided by moral rules and knowledge that have been stored in the memory as moral schemas [44]. Prior research highlights that moral reasoning influences significantly ethical decisions [45] and decreases cheating [46]. A study conducted by Crilly et al. [43] reveals a positive and significant association between CSR behavior and moral reasoning. In fact, managers who respect moral rules and ethical principles are more likely to act in a responsible way. A moral decision is a response to a moral dilemma according to which a response choice is required for a situation to which moral rules are attached [44]. Furthermore, Jones [47] argue that an ethical decision emanates from an emotional component that is essential to admit a moral issue. Moral decisions are stimulated by moral affect including shame and sympathy [43].


*2.1. Credit Default Prediction Models*

In the field of corporate credit default prediction, statistical methods are first employed. Date back to the work of Beaver [21], the univariate discriminant model was used for default prediction, and the results demonstrate that the univariate linear model can utilize financial information to forecast default effectively. The multivariate discriminant model was firstly used by Altman [22] to construct the famous Z-score model, and the result shows that its default predictive power is significantly better than that of single variable analysis. The logit regression model, which can transform the dependent variable of corporate default into a continuous one by logistic function, was more rational than the multivariate discriminant model for default prediction [23]. Nonetheless, it requires that there is no linear functional relationship among the predictor variables, which may cause a multicollinearity problem [24]. To alleviate this problem, Serrano-Cinca and Gutiérrez-Nieto [25] proposed partial least square discriminant analysis (PLS-DA) for default prediction, which is not affected by multi-collinearity. Using classical statistical methods, researchers can identify the determinants most relevant to default prediction, which can help test default theories and guide regulations of credit markets.

A significant strand of literature has found that intelligent models in credit default prediction models are efficient in predicting corporate defaulting [20,26–28]. Without the strict assumptions of the traditional statistical models (e.g., independence and normality among predictor variables), intelligent techniques can automatically derive knowledge from training data [28–30]. In addition, the intelligent methods permit non-linear decision boundaries (e.g., neural networks and SVM with non-linear kernels), which provide better model flexibility and predictive performance. In general, relative to statistic models, the corporate default prediction performance of intelligent techniques is better. For instance, Kim et al. [20] found that the neural network model outperforms logit regression. Similarly, Lahmiri [31] documented that SVM is significantly more accurate than a linear discriminant analysis classifier.

A trend in recent literature is adopting ensemble learning, which has achieved notable success in real-world applications. Differently from the mechanisms of conventional machine learning methods (such as SVM), which consist of a single estimator, ensemble learning methods combine a number of base estimators to get better generalization ability and robustness. In the work of Moscatelli et al. [27], ensemble models, including random forest and gradient boosted trees, were applied to predict corporate defaults, and the results showed that ensemble models perform better than models with a single estimator. Compared with neural networks, the ensemble model named AdaBoost had better default prediction performance in both cross-validation and test set estimation of the prediction error [32].

Among the commonly used ensemble models, the decision-tree-based XGBoost recently spread rapidly and is widely utilized in the field of credit default risk assessment [10,33,34], achieving satisfactory prediction results with its strong learning ability. For instance, in the study of Wang et al. [35], the XGBoost model was used to predict the default risk of the Chinese credit bond market, and the results show that the XGBoost model can accurately predict the default cases. For the personal credit risk evaluation, Li et al. [36] compared XGBoost to logistic regression, decision tree, and random forest. Based on the

dataset from the Lending Club Platform, the XGBoost model has better performance in both feature selection and classification.

#### *2.2. Techniques for Solving the Class-Imbalance Problem*

While previous studies could effectively predict corporate default by intelligent methods, an important problem that cannot be ignored is the class-imbalance in the default database. In the real world, the default class includes a small number of data points, and the non-default class includes a large number of data points. After ignoring the classimbalance problem, the learning algorithms or constructed models for default prediction can be overwhelmed by the majority non-default class and ignore the minority default class [7]. As the primary purpose of the default predicting model is to identify default corporates among all the corporates, the class-imbalance problem cannot be ignored.

To overcome the limitation of the class-imbalance problem, various imbalance processing approaches have been proposed. Such approaches can be generally divided into three categories: data-level methods, algorithmic-level methods, and hybrid methods [14].

Data-level methods focus on processing the imbalanced dataset before the model's construction. As the stage of data preprocessing and the stage of model training can be independent, the data preprocessing methods resample the imbalanced training dataset before training the model. To create a balanced dataset, the original imbalanced dataset can be resampled by (1) oversampling the minority class, (2) under-sampling the majority class, or (3) a hybrid of the two methods [6]. A widely used data-level method is the synthetic minority over-sampling technique (SMOTE) [9]. SMOTE generates new artificial minority cases by inserting them between existing minority cases and their neighbors. In credit default prediction tasks, after preprocessing the imbalanced dataset with SMOTE, the model based on the processed balanced training dataset can perform better [10,37]. The simplest but most effective under-sampling method is random under-sampling (RUS) [38], which involves the random elimination of majority class samples and helps improve the performance of assessing credit risk [39]. Moreover, hybrid data preprocessing methods, which combine the oversampling and undersample methods, were suggested to be helpful by recent studies [14].

Algorithmic-level methods involve modifying existing learning algorithms or proposing novel ones to directly solve the class-imbalance problem of the dataset; such algorithms usually outperform previously existing algorithms [6]. Commonly used approaches in the literature include (1) the cost-sensitive method, (2) the threshold method, and (3) one-class learning. The most commonly used is the cost-sensitive method, which deals to the nature of class imbalance by defining different misclassification costs for different classes [14]. The threshold method focuses on setting different threshold values for different classes in the model learning stage [13]. The main idea of the one-class method is to train the classifier from a training set that contains only the minority class [12].

Recently, hybrid methods have gained more popularity in learning from imbalanced datasets because of their superior performance [6]. The main idea of hybrid methods is that ensemble methods, or individual classifiers, are coupled with data or algorithm-level approaches [16], such as balanced random forests, which apply a random under-sampling strategy to the majority class to create a balanced class dataset before training an ensemble classifier with decision trees as base models [11]. SMOTEBoost combines the SMOTE oversampling approach and a rule-based learner, which is a boosting procedure [40]. Similarly, RUSBoost, which combines the random under-sampling approach with a boosting procedure, performs simpler, faster, and less complexly than SMOTEBoost during the model training [15]. Moreover, several studies combined the cost-sensitive method with boosting models where different classes are assigned different misclassification costs [41].

In summary, previous literature on class imbalance learning has proposed various methods, and hybrid methods have better performance. However, previous studies on hybrid methods mainly focus on combining ensemble learners with data-level methods, and hybridization of ensemble models with algorithm-level approaches has rarely been

considered. Compared with the data-level methods, the algorithmic-level methods may be more suitable to be combined with ensemble models for the class imbalance in credit default data. The main two reasons are: (1) First, the data-level methods can alter the shape of the original data, which may impact the efficiency of the model. The oversampling strategy may increase the possibility of overfitting during the model learning process, and the undersampling strategy might eliminate some valuable data present in the majority class [16]. (2) Second, relative to data-level methods, algorithm-level methods are more straightforward and efficient in computation, making them more appropriate for big-data streams [14].

Thus, in this paper, we propose a novel algorithm that combines the algorithm-level methods and the popular ensemble model XGBoost. The main reason to select XGBoost is the superior performance of XGBoost in the credit default prediction task [17]. As for the selection of algorithm-level methods, we selected the commonly used cost-sensitive methods to combine with XGBoost. This is because the cost-sensitive method is widespread in financial management, where businesses are usually driven by profit but not accuracy [6]. Moreover, we added the threshold method into the new model, where a more rational threshold is set to classify the samples into two groups. Details of modification will be explained in the next section.


**3.1. NORM and TE-NORM at the landfill**

Many industries produce wastes that might contain natural radionuclides, and most of these wastes end up at landfills, either hazardous or otherwise. The majority of TE-NORM sources waste arise from industrial processes. Most of the wastes obtained are produced in very large amounts with low activity. Improper disposal, recycling, and reuse of TE-NORM have led to circumstances resulting in contamination and unnecessary public exposures.

Disposal of TE-NORM in piles or stacks can lead to contamination of groundwater and airborne releases of radioactive particulates and radon. Improper use and/or disposal of the TE-NORM used for soil conditioning or fill around homes can lead to accumulation of radon gas in homes, direct exposure to individuals, and contamination of soil and of the crops growing in the soil. Reuse of TE-NORM-contaminated materials, such as in concrete aggregate, ceramic industry, and red stone can lead to increased radiation risks to members of the public in a variety of ways.

The main radionuclides daughter found in the uranium series in industrial TE-NORM are 238U, 234U, 230Th, 226Ra, and 222Rn, while the thorium series are 232Th, 228Ra, and 220Rn. In addition, 40K should be characterized. Radium226 is used as a monitor to show the relative activity and volume among the TE-NORM sectors. It was found that Radium226 is in equilibrium with its progeny, but Radium228 is not and their activity appears to be about three times greater than Radium228.


*Article* **Artificial Neural Network Solution for a Fractional-Order Human Skull Model Using a Hybrid Cuckoo Search Algorithm**

**Waseem1,\*, Sabir Ali 2, Shahzad Khattak 2,3, Asad Ullah 4,5, Muhammad Ayaz 6, Fuad A. Awwad 7 and Emad A. A. Ismail 7**

**Abstract:** In this study, a new fractional-order model for human skull heat conduction is tackled by using a neural network, and the results were further modified by using the hybrid cuckoo search algorithm. In order to understand the temperature distribution, we introduced memory effects into our model by using fractional time derivatives. The objective function was constructed in such a way that the *L*2−error remained at a minimum. The fractional order equation was then calculated by using the proposed biogeography-based hybrid cuckoo search (BHCS) algorithm to approximate the solution. When compared to earlier simulations based on integer-order models, this method enabled us to examine the fractional-order (FO) cases, as well as the integer order. The results are presented in the form of figures and tables for the different case studies. The results obtained for the various parameters were validated numerically against the available literature, where our proposed methodology showed better performance when compared to the least squares method (LSM).

**Keywords:** boundary value problems; fractional derivatives; heat conduction; BHCS algorithm; Cuckoo search; numerical method; human head

#### **1. Introduction**

The use of electronic devices is increasing day by day. One reason behind this is the advancement of technology and its applications in various sectors. This advancement in technological equipment has some side effects, especially when it crosses some limit in its use. Some of the devices and systems are Bluetooth, mobile phones, and other headphone-like devices. These devices produce thermal waves that pass through the skin and enter the human head, damaging various tissues, including the brain. The use of these electronic devices produces brain damage and other neural disorders, as explained in the references [1–3]. Furthermore, the analysis of the effects of the thermal and nonthermal waves are numerically and experimentally analyzed by Bernardi et al. [4]. The flow symmetry of heat is widely analyzed by many researchers due to its experimental and theoretical applications [5]. The energy transfer from the electronic object to the human head follows the one-sided symmetry in the skull. The facial, brain, and skull symmetries are well explained by Ratajczak et al. [6].

**Citation:** Waseem; Ali, S.; Khattak, S.; Ullah, A.; Ayaz, M.; Awwad, F.A.; Ismail, E.A.A. Artificial Neural Network Solution for a Fractional-Order Human Skull Model Using a Hybrid Cuckoo Search Algorithm. *Symmetry* **2023**, *15*, 1722. https://doi.org/10.3390/ sym15091722

Academic Editors: Francisco Martínez González, Mohammed K. A. Kaabar and Junesang Choi

Received: 12 July 2023 Revised: 26 August 2023 Accepted: 5 September 2023 Published: 8 September 2023

**Copyright:** © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

The analysis of heat in a human head became famous after the work of Flesch [7]. In this work, Flesch used a differential equation for the analysis of heat. This work was further examined by Gray [8] in 1980, which provides a theoretical approach to heat transfer analysis in terms of the human head. The human skull produces more heat on the outer layer than the center. On the other hand, when the surrounding temperature is reduced, the heat production is more peripheral to the skull. Simply put, the temperature outside and the radial distance from the skull's center affect how much heat is produced inside the human skull. Anderson and Arthurs [9] used the complementary extremum approach to analyze this famous problem. Makinde [10] analyzed the human skull problem by using the non-perturbation approach. Raja et al. [11] implemented the stochastic approach to study the human skull problem. Abdelhakem and Youssri [12] analyzed the Lane-Emden and Bratu equations by using the spectral Legendre's algorithm. Youssri et al. [13] used the wavelets approach for a solution of the Lane–Emden equations. A more brief analysis using the numerical approaches to the solution of D.Eqs. can be found in the literature [14,15].

The methodology and the model modifications are both points of interest to researchers. In recent years, the use of fractional derivatives in differential equations has been widely implemented [16,17]. The applications of fractional derivatives are well explained by Podlubny [18]. The use of fractional derivatives in the field of differential equations is explained by Aleksandrovich et al. [19]. Wang [20] studied the febrifuge effect for analyzing the fractional-order human skull problem. The concept of Caputo-type derivatives was introduced by Kumar et al. Kumar et al. [21] for use in differential equations. At the same time, the concept of Caputo-type derivatives for delay-type differential equations was introduced by Odibat et al. [22]. The concept of fractional derivatives in applications can be found in ecology [23,24], psychology [25], chemistry [26], epidemiology [27–30], and physics [31]. Yavuz and Sene [32] examined how various parameters affect fractional-order second-grade fluid flow. Hammouch et al. [33] numerically simulated a fractional chaotic system with changing order. Yavuz [34] studied the classic and generalized Mittag-Leffler kernels used in the fractional derivative definition in the European option pricing model.

The applications of fractional derivatives are not limited to a single definition. The solution to Cauchy and Dirichlet problems are studied by Avci et al. [35] by using the Caputo-Fabrizio derivative definition. Erturk et al. [36] developed a unique Caputo fractional derivative for the corneal shape model of the human eye. The recent literature shows the application of fractional calculus, which can be found in the following references [37–39].

The following is the integer-order model for temperature distribution in the human skull:

$$\begin{array}{l} T''(r) + \frac{2T'(r)}{r} + \lambda.exp(-mT) = 0, \\ T'(0) = 0, \ T'(1) = \mathcal{N}\_B(1 - T). \end{array} \tag{1}$$

Here, *T*, *r*, *NB*, *m*, and *λ* denote the temperature, radial distance, Biot number, metabolic thermogenesis slope, and thermogenesis heat production, respectively.

We introduce the Riemann–Liouville definition of the fractional-order derivative of the function ∈ *Cd* −1 below [18]:

$$D\_t^{\mu} \mathbb{S}(t) = \begin{cases} \frac{d^{\gamma} \mathbb{S}(t)}{d\mathbb{S}^{\gamma}}, & \mu = \gamma \in \mathbb{Z},\\ \frac{1}{\gamma(\gamma - \mu)} \int\_0^t (t - \sigma)^{\gamma - \mu - 1} \mathbb{S}^{\gamma}(\sigma) d\sigma, & \gamma - 1 < \mu < \gamma, \gamma \in \mathbb{Z}. \end{cases} \tag{2}$$

In light of Equation (2), the suggested classical BVP (1) is transformed into a fractionalorder generalized form:

$$\begin{array}{ll} \frac{2}{r} \, ^c D\_0^\nu T(r) + ^c D\_0^\mu T(r) + \lambda .exp(-mT) = 0, \\ \qquad T'(0) = 0, \; \, T'(1) = \mathcal{N}\_B(1 - T). \end{array} \tag{3}$$

Here, *r* ∈ [0.1, 1] and the derivatives of the function *T*(*r*) with fractional orders 0 < *ν* ≤ 1 and 1 < *μ* ≤ 2, are represented by the symbols *cDν* 0 and *cDμ* 0 respectively.

The graphical abstract of the proposed methodology is given in Figure 1, whereas the structure of the neural network is presented in Figure 2.

**Figure 1.** Graphical abstract of the given model.

**Figure 2.** Graphical presentation of the ANN structure for the given model.

#### *Our Contribution*

The primary objective of this research study is to develop an approximate solution for a fractional-order human head heat conduction model by using the BHCS algorithm. More specifically, we summarize our contributions as follows:

In this article, the proposed methodology of BHCS is discussed in Section 2, and the numerical step-up and various proposed cases (with graphs and tables) are presented in Section 3 and are discussed in detail. At the end, a conclusion is provided in Section 4 of the article.

#### **2. The Proposed Methodology**

The approximate solution (*T*ˆ(*r*)) of the fractional-order model for temperature in the human head by using feed-forward neural networks with the help of an exponential function is given as

$$\hat{T}(r) = \sum\_{i=1}^{m} \alpha\_i e^{\omega\_i r + \beta\_i} \,\,\,\,\,\,\tag{4}$$

$$\frac{d^\mu \hat{T}(r)}{dr^\mu} = \sum\_{i=1}^m \alpha\_i r^{-\mu} e^{\beta\_i} E\_{1,1-\mu}(\omega\_i r),\tag{5}$$

$$\frac{d^\nu \hat{T}(r)}{dr^\nu} = \sum\_{i=1}^m \alpha\_i r^{-\nu} e^{\theta\_i} E\_{1,1-\nu}(\omega\_i r) \tag{6}$$

where *αi*, *ωi* and *βi* are the weights given as *α* = [*α*1, *α*2, ... , *αm*], *ω* = [*ω*1, *ω*2, ... , *ωm*], *β* = [*β*1, *β*2, ... , *βm*], and *m* represents the number of neurons. Moreover, *dνT*ˆ(*r*) *drν* and *dμT*ˆ(*r*) *drμ* are the fractional derivatives of the series solution.

#### *2.1. Fitness Function*

In the fitness function, we compute the absolute error and make an optimization process to minimize the error , *i.e.,* when → 0, then *T*ˆ(*r*) → *T*(*r*).

The fitness function for the transformed equations is given as

$$
\mathfrak{e} = \mathfrak{e}\_1 + \mathfrak{e}\_2.\tag{7}
$$

where 1 represents the mean squared error for a given differential equation (DE), and 2 represents the conditions on it. Therefore, we have

$$\varepsilon\_{1} = \frac{1}{k} \sum\_{k=1}^{K} \left( \frac{2}{r\_{k}} \, ^{c}D\_{0}^{\nu} \hat{T}\_{k} + ^{c}D\_{0}^{\mu} \hat{T}\_{k} + \lambda.exp(-m\hat{T}\_{k}) \right)^{2},\tag{8}$$

and

$$\varepsilon\_{2} = \frac{1}{2} \left( (\hat{T}\_{0}')^{2} + (\hat{T}\_{1}' - \text{N}\_{B}(1 - \hat{T}))^{2} \right), \tag{9}$$

where *h* = *u k* , *T*ˆ *k* = *T*ˆ(*rk*), and *rk* = *kh*.

#### *2.2. Cuckoo Search (CS) Technique*

The cuckoo search (CS) algorithm follows the breeding behavior of the cuckoo bird [41]. In this algorithm, other birds give their eggs to others' nearest nests. When the host bird finds it, she adopts two methods: either to remove the eggs or to find a new nearest nest to lay their own eggs. In this process, the host bird's eggs indicate a solution, and the cuckoo bird's eggs display a fresh potential resolution [42].

This procedure is explained in [43]:

We assume, *yi* = *yi*1, *yi*2, *yi*3, ... , *yiD* as *i th* egg positions. The egg is defined as a solution, and Lévy flights update the new solution *ynew i* as follows:

$$y\_i^{new} = y\_i^{old} + a(y\_l - x\_\mathcal{g}) \oplus \text{Levy}(\mathcal{g}),\tag{10}$$

$$y\_i^{new} = y\_i^{old} + \frac{0.01u}{|v|^{\frac{1}{\beta}}}(y\_i - y\_{\mathcal{S}})\_\prime \tag{11}$$

where ⊕ is the entry-wise product, *β* indicates the Lévy flight exponent, *α* > 0 is the cuckoo's step size, *xg* is the optimal sample, and *u* and *v* are random numbers. Furthermore,

$$v \sim N(0, \sigma\_v^2), \qquad u \sim N(0, \sigma\_u^2), \tag{12}$$

$$\sigma\_{\rm u} = \left[ \frac{\sin \frac{\pi \beta}{2} \cdot \Gamma(1+\beta)}{2^{\frac{\beta-1}{2}} \beta \cdot \Gamma(\frac{1+\beta}{2})} \right]^{\frac{1}{\beta}}, \qquad \sigma\_{\rm v} = 1. \tag{13}$$

Here, the function *σu* is controlled by the parameter *β* and the Γ function. In CS, the discovered nests are replaced using a discovery operator that takes the probability *pa* into account. Thus, we have the updated solution given as follows:

$$y\_{ij}^{\text{new}} = \begin{cases} y\_{ij}^{\text{old}} + \text{rand} \cdot (y\_{r1}j(k) - y\_{r2}j(k)) & \text{if } P > p\_{a\nu} \\ y\_{ij}^{\text{old}}(k) & \text{else}. \end{cases} \tag{14}$$

Here, *y*new *ij* represents the *j*th component of the *i*th solution *y*new *i* , *yr*1,*j* is the *j*th element of the solution *yr*1, and *yr*2,*j* is *j*th element of the solution *yr*2. Moreover, *r*1 and *r*2 are two distinct integers within in [1, *NP*], where *NP* denotes the size of the population, and *pa* is the discovery denoting probability.

#### *2.3. Biogeography-Based Optimization*

An evolutionary biogeography-based optimization method (BBO) was motivated by several traits of animals found on islands. In BBO, NP habitats (solutions) are used to randomly initialize the population. Each generation ranks the population from best to worst.

Here, we define *λ*ˆ and *μ*ˆ as the particular habitat's immigration and emigration rates, as given in [44]:

$$\begin{cases} \hat{\lambda}\_i = I \left( 1 - \frac{\mathcal{S}\_i}{N\mathcal{P}} \right), \\ \hat{\mu}\_i = E \frac{\mathcal{S}\_i}{N\mathcal{P}}. \end{cases} \tag{15}$$

where *E* = *I* = 1 are the immigration rates, *s*ˆ*i* is a species of a certain population, which is defined as {*s*ˆ*i* = *NP* − *i*}, *i* ∈ *N*. The changing parameter updates the corresponding solution, and BBO also utilizes the mutation operator to update the solution accordingly.

#### *2.4. Hybrid Cuckoo Search*

In order to further improve the best nests obtained from the CS, we applied BBO. Both exploration and exploitation were employed alternatively. By combining exploration and exploitation, the BBO-based heterogeneous cuckoo search (BHCS) method was designed as a hybrid meta-heuristic. The proposed BHCS algorithm comprises two primary steps: heterogeneous CS and biogeography-based discovery.

#### The Methodology of Heterogeneous CS

The first component of BHCS employs the Lévy flights and a quantum mechanismbased heterogeneous CS. Heterogeneous CS is based on quantum mechanics [42,45].

$$y\_i^{\text{new}} = \begin{cases} y\_i^{\text{old}} + \mathfrak{a} \cdot \left( y\_i - y\_\mathcal{g} \right) \oplus \text{Lévy}(\beta) & \frac{2}{3} < s\_r < 1, \\ \bar{y} + L \cdot \left( \bar{y} - y\_i^{\text{old}} \right) & \frac{1}{3} < s\_r \le \frac{2}{3}, \\ y\_i^{\text{old}} + \varepsilon \cdot \left( y\_\mathcal{g} - y\_i^{\text{old}} \right) & \text{else}. \end{cases} \tag{16}$$

Here, the terms *L* = ln ( 1 *η* ), = *δeη*, and *yg* refer to the iteration's best solution, *sr* is the number *η* ∈ [0, 1], and *y*¯ = 1 *NP* ∑*NP i*=1 *yi* is the average of the solutions. Equation (16) demonstrates that three equations are used in a heterogeneous cuckoo search to update the answers with the exact probabilities. The 1st equation is derived from the Lévy flights in the original CS, and the 2nd and 3rd equations are used to update the results by using the quantum-based algorithm. The search space is diversified by updating the solutions with heterogeneous rules, which move toward the actual global region.

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

In this section, we calculate four individual case studies and compute the results using our proposed BHCS as a global search technique. The case studies are shown in Table 1. A total of 100 independent runs were performed for each case study by taking the domain *r* ∈ [0.1, 1] with 0.1 step size.

**Table 1.** Different cases with the variation of fractional derivative parameters.

The formulation for these case studies is given below:

#### *3.1. Case Study 1*

For this case, the fitness function with the boundary conditions is given as

$$\varepsilon\_{1} = \frac{1}{11} \sum\_{k=1}^{11} \left( \frac{2}{r\_{k}} .^{c}D\_{0}^{1}\hat{T}\_{k} + ^{c}D\_{0}^{2}\hat{T}\_{k} + \lambda.exp(-m\hat{T}\_{k}) \right)^{2} . \tag{17}$$

$$\varepsilon\_2 = \frac{1}{2} \left( (\hat{T}\_0')^2 + (\hat{T}\_1' - \mathcal{N}\_B(1 - \hat{T}))^2 \right). \tag{18}$$

We considered the parameters *λ* = 1, *m* = 1, *Nb* = 1. By using BHCS, the best weights for this case are given in the following equation.

$$\mathcal{T}\_{\mathbf{c}\_{1}} = \begin{cases} 1.4025e^{( -0.2030r - 0.7130)} - 0.0856e^{( -1.4281r + 0.5922)} \\ \quad + 0.2617e^{( -0.0189r - 0.1831)} - 0.7062e^{( 0.5749r - 1.612)} \\ \quad - 2.4658e^{( -0.5143r - 1.7698)} + 1.7948e^{( -0.0388r - 0.7866)} \\ \quad - 0.1858e^{( -0.5612r - 0.5207)} + 0.7182e^{( -1.3911r - 1.2173)} \\ \quad + 0.9790e^{( 0.3547r - 2.6460)} - 0.0509e^{( -1.6107r - 1.0547)} \end{cases} \tag{19}$$

Here, Equation (19) is a series solution for case study 1.

#### *3.2. Case Study 2*

The fitness function for the current case study is formulated below:

$$\varepsilon\_{1} = \frac{1}{11} \sum\_{k=1}^{11} \left( \frac{2}{r\_{k}} .^{c}D\_{0}^{0.70} \hat{T}\_{k} + ^{c}D\_{0}^{1.70} \hat{T}\_{k} + \lambda.exp(-m\hat{T}\_{k}) \right)^{2} . \tag{20}$$

$$\varepsilon\_2 = \frac{1}{2} \left( (\hat{T}\_0')^2 + (\hat{T}\_1' - N\_B(1 - \hat{T}))^2 \right). \tag{21}$$

Here, we take the parameters *λ* = 1, *m* = 1, *Nb* = 1. The best weights for this case are given as

$$\hat{T}\_{c\_2} = \begin{cases} -0.7538e^{( -0.8125r + 0.7228)} + 1.3636e^{( -0.3377r - 0.4151)} \\ + 0.8281e^{( -0.2094r - 1.3968)} + 0.4684e^{( -0.4236r - 0.2732)} \\ + 0.9507e^{( -1.3841r - 1.4493)} + 1.1338e^{( -1.1852r - 0.9906)} \\ -0.6161e^{( -5.0000r - 4.1270)} - 0.1282e^{( -0.7593r - 1.3885)} \\ + 1.9087e^{( -0.3513r - 0.8274)} + 0.0553e^{( 0.1238r - 0.1236)} \end{cases} \tag{22}$$

Here, the above equation is the corresponding series solution for this special case 2. The absolute errors (AE) are presented in Table 2. The approximate solutions of the given fractional model, which were obtained by using the series solution of Equation (19), are illustrated in Figure 3. The best fitness values are evaluated by considering the above conditions, and the results are displayed in Figure 4.

**Table 2.** Minimum Absolute Errors ().

We analyzed the FO heat conduction model for the human head given in Equation (3) by using an interval of [0.1, 1]. Four different cases were considered by choosing varying values of *μ*, *ν* for the fixed parameters *λ* = 1, *Nb* = 1. The approximate solutions for both cases, 1 and 2, are presented in Figure 3. These graphs show that when we decrease the order of the fractional parameters from an integer order to a non-integer, the temperature profile jumps to 1.17 from 1.16. A decreasing trend is observed when *r* −→ 1. This trend is more sharp in the integer order when compared to the fractional order. The fitness of the functions is shown in Figure 4, where the red lines show the mean. Almost all the values are bounded by the box, and the distance from the mean positions is displayed on the vertical line.

**Figure 3.** Graphical representation of the solutions for (**a**) Case study 1 and (**b**) Case study 2.

**Figure 4.** Graphical representation of fitness functions for (**a**) Case study 1 and (**b**) Case study 2.

#### *3.3. Case Study 3*

In case 3, we considered *μ* = 1.80 and *ν* = 0.80 by choosing *λ* = 1, *m* = 1, *Nb* = 1. The fitness functions for this case are given by

$$\epsilon\_1 = \frac{1}{11} \sum\_{k=1}^{11} \left( \frac{2}{r\_k} .^{\circ}D\_0^{0.80} \hat{T}\_k + ^{\circ}D\_0^{1.80} \hat{T}\_k + \lambda.exp(-m\hat{T}\_k) \right)^2,\tag{23}$$

$$\epsilon\_2 = \frac{1}{2} \left( (\hat{T}\_0')^2 + (\hat{T}\_1' - N\_B(1 - \hat{T}))^2 \right). \tag{24}$$

The corresponding best weights are given below:

$$\hat{T}\_{\varepsilon\_3} = \begin{cases} 0.3527e^{(0.7055r - 2.1888)} - 1.1520e^{(-0.7899r - 1.8388)} \\ \quad + 1.4121e^{(-3.4830r - 1.8823)} + 1.3158e^{(-0.4966r - 0.9646)} \\ \quad + 0.1036e^{(0.3872r - 0.0793)} - 1.0951e^{(-0.9004r - 0.8300)} \\ \quad - 0.2317e^{(-3.6303r - 0.1507)} + 0.1977e^{(-1.2789r - 0.2822)} \\ \quad + 0.8166e^{(-0.0468r + 0.4276)} - 0.5767e^{(0.5119r - 0.9304)} . \end{cases} \tag{25}$$

#### *3.4. Case Study 4*

For this case study, we took *μ* = 1.90 and *ν* = 0.90. So, the corresponding fitness functions take the following form:

$$\varepsilon\_{1} = \frac{1}{11} \sum\_{k=1}^{11} \left( \frac{2}{r\_{k}} \prescript{c}{}{D\_{0}^{0.90}} \hat{\mathbf{T}}\_{k} + \prescript{c}{}{D\_{0}^{1.90}} \hat{\mathbf{T}}\_{k} + \lambda . exp(-m\hat{\mathbf{T}}\_{k}) \right)^{2} \tag{26}$$

$$\epsilon\_2 = \frac{1}{2}\left( (\hat{T}\_0')^2 + (\hat{T}\_1' - N\_B(1 - \hat{T}))^2 \right). \tag{27}$$

By choosing *λ* = 1, *m* = 1, *Nb* = 1, we have

$$
\hat{T}\_{c4} = \begin{cases}
+ 0.1558e^{(-1.3456r - 1.2083)} - 0.9332e^{(0.3765r - 0.7752)} \\
+ 1.3882e^{(-0.1069r + 0.1492)} - 0.3297e^{(-0.4075r - 1.2062)} \\
\end{cases} \tag{28}
$$

Here, *T*ˆ *c*3 and *T*ˆ *c*4 are the series solutions for cases 3 and 4. The AE are plotted in Table 2, whereas the approximate solutions are presented in Figure 5. The fitness values are given in Figure 6. The values of AE for all the case studies are presented in Table 2.

Similarly, in cases 3 and 4, when we increase the fractional parameters that nearly approach the integer, the solution profiles fall from 1.65 to 1.61. As a result, the suggested fractional-order graph, which takes into account the radial distance (*r*), Biot number (*NB*), metabolic thermogenesis slope parameter (*m*), and thermogenesis heat production parameter (*λ*), provides a more accurate representation of the distribution of temperature within the human skull.

The fitness functions for cases 3 and 4 are displayed in Figure 6. The horizontal red line shows the mean, and the red addition symbols show the positions of the results from this point. In both cases, the results are in the range of 10−5 and 10−4, respectively. This further recommends that the fitness functions remain as minimal as possible.

In Table 2, the results for the minimum values of the absolute error are displayed numerically. These cases are chosen in such a way that the deviations from the integer order to a fractional order are clearly visible as time varies. First, the decreasing trend from the integer order is observed for various fractional parameters. In the last two columns, the increasing trend towards the integer order is displayed. If we compare the results of the second case and the fourth, we see that the results initially go toward the worst and

then beat the integer order at *r* = 0.7. Similarly, the BHCS results are compared against the available literature in Table 3. In case 1, the results for the integer order are almost the same as the LSM. In cases 2, 3, and 4, the results of BHCS are nearer the integer-order solution when compared to LSM. This proves the validity and efficiency of our proposed method, BHCS.

**Table 3.** Comparison of the approximate solutions of the BHCS neural network using the least squares method (LSM) [40].

**Figure 5.** Graphical representation of the solutions for (**a**) Case study 3 and (**b**) Case study 4.

**Figure 6.** Graphical representation of fitness function for (**a**) Case study 3 and (**b**) Case study 4.

#### **4. Conclusions**

In this article, we discussed the distribution of temperature within the human skull by considering the fractional derivative. In order to solve the proposed model, we utilized the biogeography-based hybrid cuckoo search (BHCS) algorithm to then be used on the transformed fractional-order equation. The following are the main features obtained based on our analysis.

**Author Contributions:** Conceptualization, W. and S.A.; methodology, S.K.; software, W. and A.U.; validation, M.A., E.A.A.I., S.K., F.A.A. and A.U.; formal analysis, W. and E.A.A.I.; investigation, S.A.; resources, A.U.; data curation, W.; writing—original draft preparation, M.A.; visualization, A.U.; supervision, W.; review writing, E.A.A.I., F.A.A., W., S.A. and A.U.; funding, E.A.A.I. and F.A.A. All authors have read and agreed to the published version of the manuscript.

**Funding:** This project was funded by King Saud University, Riyadh, Saudi Arabia.

**Data Availability Statement:** No data are used in this study.

**Acknowledgments:** Researchers' supporting project number: (RSPD2023R1060), King Saud University, Riyadh, Saudi Arabia.

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

#### **References**

**Disclaimer/Publisher's Note:** The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.


Salmon Aquaculture *Edited by Qian Lu*

Published in London, United Kingdom

### *Supporting open minds since 2005*

Salmon Aquaculture http://dx.doi.org/10.5772/intechopen.95211 Edited by Qian Lu

#### Contributors

Renzo Pepe-Victoriano, Héctor Aravena-Ambrosetti, Piera Pepe-Vargas, James E. Barasa, Purity Nasimiyu Nasimiyu Mukhongo, Cynthia Chepkemoi Chepkemoi Ngetich, Paul Gümpel, Arnulf Hörtnagl, Torsten Bogatzky, Urs Dornbierer, Jose A. Gallardo, Margarita Rivera, Cristian Araneda, Anti Vasemägi, Alexander Dindial, Aslihan Katip

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[20] Holland et al. The micronucleus assay in human buccal cells as a tool for biomonitoring DNA damage: The HUMN project perspective on current status and knowledge gaps.

[21] Aiassa D, Mañas F, Bosch B, Gentile N, Bernardi N, Gorla N. Biomarcadores de daño genético en poblaciones humanas expuestas a plaguicidas. Acta Biológica Colombiana.

[22] Alavanja MC, Hoppin JA, Kamel F. Health effects of chronic pesticide exposure: Cancer

[23] Reffstrup TK, Larsen JC, Meyer O. Risk assessment of mixtures of pesticides. Current approaches and future strategies. Regulatory Toxicology and Pharmacology. 2010;56:174-192

[24] Lock EA, Bonventre JV. Biomarkers in translation; past, present and future. Toxicology.

[25] Mudry M, Carballo M. Genética Toxicológica. Buenos Aires, Argentina: Ed. De Los 4

[26] Hagmar L, Brogger A, Hansteen IL, Heim S, Hogstedt B, Knudsen L, et al. Cancer risk in ¨humans predicted by increased levels of chromosomal aberrations in lymphocytes: Nordic study group on the health risk of chromosome damage. Cancer Research. 1994;54:

[27] Hagmar L, Bonassi S, Stromberg U, Brogger A, Knudsen LE, Norppa H, Reuterwall C. Chromosomal aberrations in lymphocytes predict human cancer: A report from the European Study Group on Cytogenetic Biomarkers and Health (ESCH). Cancer Research. 1998;

[28] Albertini RJ, Anderson D, Douglas GR, Hagmar L, Hemminki K, Merlo F, et al. IPCS guidelines for the monitoring of genotoxic effects of carcinogens in humans. Mutation

and neurotoxicity. Annual Review of Public Health. 2004;25:155-197

334-339

Reserach. 656(1–2):93-108

2012;17(3):485-510

2008;245(3):163-166

Vientos; 2006

2919-2922

58:4117-4121

Research. 2000;463:111-172

Mutation Research. 2008c;659(1–2):93-108

[16] Bosch B, Mañas F, Gorla N, Aiassa D. Micronucleus test in post metamorphic Odontophrynus cordobae and Rhinella arenarum (Amphibia: Anura) for environmental monitoring. Journal of Toxicology and Environmental Health Sciences. 2011;3(6):154-163

[2] IARC International Agency for Research on Cancer 2015. Monographs on the evaluation

[4] Martínez-Valenzuela C, Gómez-Arroyo S. Riesgo genotóxico por exposición a plaguicidas en trabajadores agrícolas. Revista internacional de contaminación ambiental. 2007;23(4):185-200

[5] Bhalli JA, Khan QM, Haq MA, Khalid AM, Nasim A. Cytogenetic analysis of Pakistani individuals occupationally exposed to pesticides in a pesticide production industry. Muta-

[6] Alavanja M, Sandler D, McDonnell C, Lynch C, Pennybacker M, Zahm S, Mage D, Steen W, Wintersteen W, Blair A. Characteristics of pesticide use in a pesticide applicator cohort:

[7] Kohen R, Nyska A. Oxidation of biological systems: Oxidative stress phenomena, antioxidants, redox reactions, and methods for the quantification. Toxicology Pathology. 2002;

[8] Bolognesi C, Creus A, Ostrosky-Wegman P, Marcos R. Micronuclei and pesticide expo-

[9] Dearfield KL, McCarroll NE, Protzel A, Stack HF, Jackson MA, Waters MD. A survey of EPA/OPP and open literature on selected pesticide chemicals. II: Mutagenicity and carcinogenicity of selected chloroacetanilides and related compounds. Mutation Research.

[10] Ambulkar P, Ghosh S, Ingole I, Pal A. Genotoxic and cytotoxic effects of antibacterial drug, ciprofloxacin, on human lymphocytes in vitro. Nepal Medical College Journal. 2009;

[11] Gorla N, García Ovando H, Larripa I. Chromosomal aberrations in human lymphocytes exposed to enrofloxacin and ciprofloxacin. Toxicology Letters. 1999;104:43-48

[12] Mañas F, Gonzalez Cid M, Weyers A, Ugnia L, García Ovando H, Larripa I, et al. Evaluación De Genotoxicidad "In Vivo" Mediante El Ensayo Cometa Y De Micronúcleos

[13] Mañas F, Peralta L, Gorla N, Bosch B, Aiassa D. Aberraciones Cromosómicas En Trabajadores Rurales De La Provincia De Córdoba Expuestos A Plaguicidas. Journal of

[14] Mañas F, Peralta L, Raviolo J, García Ovando H, Weyers A, Ugnia L, et al. Genotoxicity of Ampa, environmental metabolite of glyphosate, assessed by the comet assay and cytoge-

[15] Mañas F, Peralta L, Raviolo J, García Ovando H, Weyers A, Ugnia L, et al. Genotoxicity and oxidative stress of glyphosate: In vivo and in vitro testing. Environ Toxicol

En Ratones Tratados Con Glifosato. Theoria. 2007. 2007;15:53-60

netic tests. Ecotoxicology and Environmental Safety. 2009a;72:834-837

of carcinogenic risks to humans: 112. World Health Organization

genesis. 2006;21(2):143-148

106 Genotoxicity - A Predictable Risk to Our Actual World

sure. Mutagenesis. 2011;26(1):19-26

Basic Applied Genetics. 2009;20(1):9-13

Pharmacol. 2009b:37-41

30(6):620-650

1999;443:183-221

11(3):147-151

[3] FAO. 2004. El estado de la inseguridad alimentaria en el mundo 2004. Roma

The agricultural health study. Environmental Research. 1997;80:172-179

[29] Bonassi C, Abbondandolo A, Camurri L, Dal Pra L, De Ferrari M, Degrassi F. Are chromosome aberrations in circulating lymphocytes predictive of a future Cancer onset in humans preliminary results of an Italian cohort. Study. Cancer Genetics and Cytogenetics. 1995;79(2):133-135

[42] Barbosa MC, Aiassa y D, Mañas YF. Evaluación de daño al ADN en leucocitos de sangre periférica humana expuestos al herbicida Glifosato. Revista Internacional de Contami-

Genotoxic Risk in Human Populations Exposed to Pesticides

http://dx.doi.org/10.5772/intechopen.77968

109

[43] Kocaman A, Topaktaş M. The in vitro genotoxic effects of a commercial formulation of αcypermethrin in human peripheral blood lymphocytes. Environmental and Molecular

[44] Rahman M, Mahboob M, Danadevi K, Banu B, Grover P. Assessment of genotoxic effects of chloropyrifos and acephate by the comet assay in mice leucocytes. Mutation Research.

[45] Vindas R, Ortiz F, Ramírez V, Cuenca P. Genotoxicidad de tres plaguicidas utilizados en la actividad bananera de Costa Rica. Revista de biologia tropical. 2004;52:197-205

[46] Bandyopadhyay U, Das D, Banerjee R. Reactive oxygen species: Oxidative damage and

[47] Martínez-Cayuela M. Toxicidad de xenobióticos mediada por radicales libres de oxígeno.

[48] Beuret C, Zirulnik F, Giménez M. Effect of the herbicide glyphosate on liver lipoperoxidation

[49] Gómez Miralles J, Bevilacqua S, Mañas F, Bosch B, Gentile N, Peralta L, Aiassa D. Los plaguicidas en Argentina: la genotoxicidad de los agroquímicos y la falta de prevención

[50] Gómez Miralles J, Bevilacqua V, Bevilacqua S. ¿Cuál es la normativa sobre agroquímicos en la República Argentina? Cap. 10. En Aiassa, D., B. Bosch y F. Mañas (comp). Plaguicidas a la

[51] Au WW, Badary OA, Heo MY. Cytogenetic assays for monitoring populations exposed to

[52] Bonassi S, Au WW. Biomarkers in molecular epidemiology studies for health risk predic-

[53] Landrigan PJ, Kimmel CA, Correa A, Eskenazi B. Children's health and the environment: Public health issues and challenges for risk assessment. Environmental Health Perspec-

[55] Bernardi et al. Assessment of the level of damage to the genetic material of children exposed to pesticides in the province of Córdoba. Archivos Argentinos de Pediatría. 2015;113(1):126-

[56] Neri M, Ugolini D, Bonassi S, Fucic A, Holland N, Knudsen LE, et al. Children's exposure to environmental pollutants and biomarkers of genetic damage II. Results of a compre-

hensive literature search and meta-analysis. Mutation Research. 2006;612(1):14-39

carta: daño genético y otros riesgos. Miguel Tréspidi Editores. 2012a. 216pp

environmental mutagens. Occupational Medicine. 2001;16(2):345-357

[54] Roberts JR, Karr CJ. Pesticide exposure in children. Pediatrics. 2012;130:6

in pregnant rats and their fetuses. Toxicology Reports. 2005;19:501-504

nación Ambiental. 2017;4(33):403-410

pathogenesis. Current Science. 1999;77:103-121

penal. Abeledo Perrot Córdoba. 2012;2:128-139

tion. Mutation Research. 2002;511(1):73-86

tives. 2004a;112(2):257-265

132 ISSN: 0325–0075

Mutagenesis. 2009;50(1):27-36

Ars Pharmaceutica. 1998;39:5-18

2002;516:139-147

[42] Barbosa MC, Aiassa y D, Mañas YF. Evaluación de daño al ADN en leucocitos de sangre periférica humana expuestos al herbicida Glifosato. Revista Internacional de Contaminación Ambiental. 2017;4(33):403-410

[29] Bonassi C, Abbondandolo A, Camurri L, Dal Pra L, De Ferrari M, Degrassi F. Are chromosome aberrations in circulating lymphocytes predictive of a future Cancer onset in humans preliminary results of an Italian cohort. Study. Cancer Genetics and Cytogenetics.

[30] Mitelman F, Mertens F, Johansson F. A breakpoint map of recurrent chromosomal

[31] Bonassi S, Znaor A, Ceppi M, Lando C, Chang WP, Holland N, et al. An increased micronucleus frequency in peripheral blood lymphocytes predicts the risk of cancer in

[32] Bonassi S, Znaor A, Ceppi M, Lando C, Chang WP, et al. An increased micronucleus frequency in peripheral blood lymphocytes predicts the risk of cancer in humans. Carci-

[33] Bonassi et al. The HUman MicroNucleus project on eXfoLiated buccal cells (HUMN(XL)): The role of life-style, host factors, occupational exposures, health status, and assay proto-

[34] Rojas E, López MC, Valverde M. Single cell gel electrophoresis assay: Methodology and

[35] Aiassa D, Mañas F, Bernardi N, Gentile N, Méndez Á, Roma D, Gorla N. Monitoreo de Genotoxicidad en personas expuestas a plaguicidas. Estudio preliminar en niños.

[36] Gómez Arroyo S, Martinez Valenzuela C, Carbajal-López A, Martínez-Arroyo MC-S. R., Villalobos-Pietrini y S. Waliszewski, Riesgo genotóxico por la exposición ocupacional a plaguicidas en América Latina. Revista Internacional de Contaminación Ambiental. 2013;

[37] Bolognesi C. Review Genotoxicity of pesticides: A review of human biomonitoring stud-

[38] Ergene S, Çelik A, Çavaş T, Kaya F. Genotoxic biomonitoring study of population residing in pesticide contaminated regions in Göksu Delta: Micronucleus, chromosomal aberrations and sister chromatid exchanges. Environment International. 2007;33(7):877-885 [39] Pastor Benito S. Biomonitorización citogenética de cuatro poblaciones agrícolas europeas expuestas a plaguicidas mediante el ensayo de micronúcleos. Tesis doctoral. Universitat Autónoma de Barcelona. Disponible en; 2002 http://www.tdx.cat/bitstream/handle/10803/

[40] López SL, Aiassa D, Benítez-Leite S, Lajmanovich R, Mañas F, Poletta G, Sánchez N, Simoniello MF, Carrasco AE. Pesticides Used in South American GMO-Based Agriculture:

[41] Gentile N, Mañas F, Bosch B, Peralta L, Gorla N, Aiassa D. Micronucleus assay as a biomarker of genotoxicity in the occupational exposure to agrochemiclas in rural workers.

A Review of Their Effects on Humans and Animal Models. 2012 In James

Bulletin of Environmental Contamination and Toxicology. 2012;88(6):816-822

rearrangements in human neoplasia. Nature Genetics. 1997;15:417-474

humans. Carcinogenesis. 2007a;28(3):625-631

col. Mutation Research. 2011c;728(3):88-97

ies. Mutation Research. 2003;543(3):251-272

3858/spb1de5.pdf?sequence=1

applications. Journal of Chromatography B. 1999;722:225-254

Cuestiones de Población y Sociedad. 2014;4(4):73-84

nogenesis. 2007b;28(3):625-631

1995;79(2):133-135

108 Genotoxicity - A Predictable Risk to Our Actual World

29:159-180

[57] Grigg J. Particulate matter exposure in children: Relevance to chronic obstructive pulmonary disease. Proceedings of the American Thoracic Society. 2009;6(7):564-569

Martino-Roth MG, Montero Montoya R, Nersesyan A, Pastor-Benito S, Favero Salvadori DM, Shaposhnikova A, Stopper H, Thomas P, Torres-Bugarín O, Yadav AS, Zúñiga González G, Fenech M. The Human MicroNucleus project on eXfoLiated buccal cells (HUMN(XL)): The role of life-style, host factors, occupational exposures, health status,

Genotoxic Risk in Human Populations Exposed to Pesticides

http://dx.doi.org/10.5772/intechopen.77968

111

[72] Gentile N, Bernardi N, Bosch B, Mañas F, Aiassa D. Estudios de genotoxicidad en trabajadores rurales y familias. Revista Cubana de Investigaciones Biomédicas. 2016;35(3):228-239

[73] Ghosh P, Basu A, Singh KK, Giri AK. Evaluation of cell types for assessment of cytogenetic

[74] Suruda A, Schulte P, Boeniger M, Hayes RB, Livingston GT, Steenland K, et al. Cytogenetic effects of formaldehyde exposure in students of mortuary science. Cancer Epidemi-

[75] Benítez-Leite S, Macchi ML, Fernández V, Franco D, Ferro EA, Mojoli A, Cuevas F, Alfonso J, Sales L. Daño celular en una población infantil potencialmente expuesta a pesticidas.

[76] Castillo-Cadena J, Tenorio-Vieyra LE, Quintana-Carabia AI, García-Fabila MM, Ramírez-San Juan E. y Madrigal-Bujaidar E. Determination of DNA damage in floriculturists exposed to mixtures of pesticides. Journal of Biomedicine & Biotechnology. 2006. DOI 10.1155/ JBB/

[77] Gómez-Arroyo S, Martínez-Valenzuela C, Calvo-González S, Villalobos-Pietrini R, et al. Assessing the genotoxic risk for mexican children who are in residential proximity to agricultural areas with intense aerial pesticide applications. Revista internacional de contamin-

[78] Dulout FN, Pastori MC, Olivero OA, Gonzales CID, Loria D, Matos E, et al. Sisterchromatid exchanges and chromosomal aberrations in a population exposed to pesticides.

[79] Dulout FN, Pastori MC, González Cid M, Matos E, Von Guradze HN, Maderna CR, et al. Cytogenetic analysis in plant breeders. Mutation Research. 1987;189(4):381-386

[80] Dulout FN, López Camelo JS, Guradze HN. Analysis of sister chromatid exchanges (SCE)

[81] Simoniello MF, Kleinsorge EC, Carballo MA. Evaluación bioquímica de trabajadores

[82] Peralta P, Mañas F, Gentile N, Bosch B, Méndez A, Aiassa D. Evaluación del daño genético en pobladores de Marcos Juárez Expuestos a plaguicidas: estudio de un caso en Córdoba,

[83] Souza CJ. La problemática del uso de los agroquímicos y sus envases, su incidencia en la salud de los trabajadores, la población expuesta y el ambiente: Estudio colaborativo

Argentina. Rev Cient Psicol Ciencias Soc Human Ciencias Salud. 2011;2(1):7-26

multicéntrico. Ministerio de Salud de la Nación. Argentina: Buenos Aires; 2007

in human populations studies. Rev Brazil Genetics. 1992;15(1):169-182

rurales expuestos a pesticidas. Medicina (Buenos Aires). 2010;70(6):489-498

and assay protocol. Mutation Research. 2011;728(3):88-97

ology, Biomarkers & Prevention. 1993;2:453-460

Pediatria. 2010;37(2)

ación ambiental. 2013;29(3):217-225

Mutation Research. 1985;143:237-244

2006/97896

damage in arsenic exposed population. Molecular Cancer. 2008;7:45

Martino-Roth MG, Montero Montoya R, Nersesyan A, Pastor-Benito S, Favero Salvadori DM, Shaposhnikova A, Stopper H, Thomas P, Torres-Bugarín O, Yadav AS, Zúñiga González G, Fenech M. The Human MicroNucleus project on eXfoLiated buccal cells (HUMN(XL)): The role of life-style, host factors, occupational exposures, health status, and assay protocol. Mutation Research. 2011;728(3):88-97

[57] Grigg J. Particulate matter exposure in children: Relevance to chronic obstructive pulmonary disease. Proceedings of the American Thoracic Society. 2009;6(7):564-569

[58] WHO. Children's Health and the Environment in Europe: A Baseline Assessment. Copenhagen, Denmark: World Health Organization Regional Office for Europe; 2007

[60] Wild CP, Kleinjans J. Children and increased susceptibility to environmental carcinogens: Evidence or empathy? Cancer Epidemiology, Biomarkers & Prevention. 2003;12:1389-1394

[61] Gallo V, Khan A, Gonzales C, Phillips DH, Schoket B, Györffy E, et al. Validation of biomarkers for the study of environmental carcinogens: A review. Biomarkers. 2008;13:505-534

[62] Salameh PR, Baldi I, Brochard P, Raherison C, et al. Respiratory symptoms in children and exposure to pesticides. The European Respiratory Journal. 2003;22(3):507-512

[63] Salam MT, Li YF, Langholz B, Gilliland FD. Early-life environmental risk factors for asthma: Findings from the Children's health study. Environmental Health Perspectives.

[64] Alarcon WA, Calvert GM, Blondell JM, Mehler LN, Sievert J, Propeck M, Tibbetts DS, Becker A, Lackovic M, Soileau SB, Das R, Beckman J, Male DP, Thomsen CL, Stanbury M. Acute illnesses associated with pesticide exposure at schools. Journal of the American

[65] Bonassi S, Coskun E, Ceppi M, Lando C, Bolognesi C, et al. The HUman MicroNucleus project on eXfoLiated buccal cells (HUMN(XL)): The role of life-style, host factors, occupational exposures, health status, and assay protocol. Mutation Research. 2011a;728(3):88-97 [66] Bonassi S, El-Zein R, Bolognesi C, Fenech M. Micronuclei frequency in peripheral blood lymphocytes and cancer risk: Evidence from human studies. Mutagenesis. 2011b;26(1):93-100

[67] Coronas MV, Pereira TS, Rocha JA, Lemos AT, Fachel JM, et al. Genetic biomonitoring of an urban population exposed to mutagenic airborne pollutants. Environment Interna-

[68] Kashyap B, Reddy PS. Micronuclei assay of exfoliated oral buccal cells: Means to assess the nuclear abnormalities in different diseases. Journal of Cancer Research and Therapeu-

[69] Samanta S, Dey P. Micronucleus and its applications. Diagnostic Cytopathology. 2012;40:

[70] Ceppi M, Biasotti B, Fenech M, Bonassi S. Human population studies with the exfoliated buccal micronucleus assay: Statistical and epidemiological issues. Mutation Research.

[71] Bonassi S, Coskun E, Ceppi M, Lando C, Bolognesi C, Burgaz S, Holland N, Kirsh-Volders M, Knasmueller S, Zeiger E, Carnesoltas D, Cavallo D, da Silva J, de Andrade VM, Demircigil GC, Domínguez Odio A, Donmez-Altuntas H, Gattas G, Giri A, Giri S, Gómez-Meda B, Gómez-Arroyo S, Hadjidekova V, Haveric A, Kamboj M, Kurteshi K,

2004;112(6):760-765

110 Genotoxicity - A Predictable Risk to Our Actual World

Medical Association. 2005;294:455-465

tional. 2009;35(7):1023-1029

tics. 2012;8(2):184-191

2010;705(1):11-19

84-90

[59] European Respiratory Society (ERS). 2010 Annual Congress 22; Barcelona, Spain; 2010

[84] Holland N, Fucic A, Merlo DF, Sram R, Kirsch-Volders M. Micronuclei in neonates and children: effects of environmental, genetic, demographic and disease variables. Mutagen-

[85] Gajskia G, Gerića M, Oreščaninb V, Garaj-Vrhovaca. Cytogenetic status of healthy children assessed with the alkaline comet assay and the cytokinesis-block micronucleus

[86] Garry VF. Pesticides and children. Toxicology and Applied Pharmacology. 2004;198:152-163

esis. 2011;26(1):51-56

112 Genotoxicity - A Predictable Risk to Our Actual World

cytome assay. Mutation Research. 2013;750:55-62

## *Edited by Marcelo L. Larramendy and Sonia Soloneski*

This book is designed to provide an overview of the different genotoxicants and their effects on living organisms, including humans. The contributions made by the specialists in this field of research are gratefully acknowledged. We hope that the information presented in this book will meet the expectations and needs of all those interested in the different aspects of the genotoxicity field. The publication of this book is of great importance to those scientists, pharmacologists, physicians and veterinarians, as well as engineers, teachers, graduate students and administrators of environmental programmes, who make use of these investigations to understand both the basic and applied genotoxic aspects of known and new xenobiotics, and to guide them in their future investigations.

Published in London, UK © 2018 IntechOpen © danez / iStock

Genotoxicity - A Predictable Risk to Our Actual World

Genotoxicity

A Predictable Risk to Our Actual World

*Edited by Marcelo L. Larramendy*

*and Sonia Soloneski*