*3.4.3 Reduction of estrogen effects*

Women who are taking medications such as birth control pills and hormonal replacement therapy have episodes of headache and estrogen seems to make it worse. Ask your doctor to reduce the dose or to prescribe alternate therapy [52].


**6. Liquor shunting operations (LSO)**

To correct persistent disorders of CSF circulation when it is impossible to use etiotropic treatment of decompensated hydrocephalus, LSO are used. The CSF shunting system is known to be an artificial analogue designed to compensate for disorders of CSF circulation, while its adequate functioning is determined by individual biomechanical parameters of the CSS.

Clinical and neuroimaging criteria, as well as their relationship with quantitative indicators of cerebrovascular circulation and cerebrovascular conjugation, determine the effectiveness of surgical treatment of hydrocephalus in children. Their importance while planning neurosurgical intervention is often underestimated. Solving these important tasks involves studying the disease aspects and taking into account how individual characteristics of the patient manifest—to develop a pathogenetically sound diagnostic system and personalize the hydrocephalus surgical treatment tactics.

In this regard, it is relevant to objectively evaluate these indicators and develop a system of minimally invasive monitoring of the viscoelastic properties of the CSS within the preoperative planning structure and to assess the effectiveness of hydrocephalus surgical treatment, taking into account changes in fluid dynamics.

Liquor anastomosis can be performed using shunts of various systems. The proximal part of the shunt is located in the cavity of the lateral ventricle, then the catheter passes through the brain substance, the soft and hard meninges, and bone and is connected to the pump. The pump is fixed to the bones of the skull and located directly under the skin. The pump valve regulates the pressure of the CSF at a predetermined level and allows it to pass in one direction only—from the cranial cavity to the extracerebral cavities. The distal part of the shunt is attached to the pump; it passes under the skin in the soft tissues of the neck and then, depending on the type of bypass surgery, plunges into the right atrium, transverse sinus, abdominal, pleural cavities, etc. (**Figure 5**).

Treatment of children with hydrocephalus involves various LSO. The removal of the CSF is carried out using implantable valve systems into the peritoneal cavity, with the inexpediency of classical methods, extracranial removal of CSF into the bloodstream (right atrium, jugular vein, sinuses of the dura mater, etc.) is used [28].

Indications for the CSF shunting operations with permanently implanted valve systems are persistent violations of CSF resorption, limiting the ability to normalize CSF circulation within the CSF system;

When choosing the parameters of the throughput of the CSF shunting system, they proceed from the results of measuring the biomechanical properties of the CSS and CSF circulation during surgery.

*CSF Bypass Surgery in Children with Hydrocephalus: Modern Possibilities, Prospects… DOI: http://dx.doi.org/10.5772/intechopen.110871*

#### **Figure 5.**

*Types of CSF bypass surgery. A—Scheme of ventriculoperitoneostomy. B—Scheme of lumboperitoneostomy. C—Scheme of ventriculoatriostomy. D—Scheme of ventriculosynustransverzostomy. 1—Ventricular catheter; 2—Bypass system valve; 3—Peritoneal catheter; 4—Lumbar catheter; 5—Atrial catheter; 6—Sinus catheter.*

Types of LSO:


**LOW BACK PAIN PATHOGENESIS AND TREATMENT**

Edited by **Yoshihito Sakai**

**INTECHOPEN.COM**

http://dx.doi.org/10.5772/2681 Edited by Yoshihito Sakai

#### **Contributors**

Yoshihito Sakai, Michael Ogbonnia Egwu, Afolabi O. Olakunle, Michal Filip, Petr Linzer, Jakub Strnad, Eyal Itshayek, Yair Barzilay, Amir Hasharoni, Leon Kaplan, José E. Cohen, Joshua E. Schroeder, S. Samuel Bederman, Vu H. Le, Jan Schroeder, Klaus Mattes, Leonardo Fonseca Rodrigues, Paula Voloch, Flavio Cavallari, Antoine Nachanakian, Antonios Georges El Helou, Moussa Alaywan, Wayne Hoskins, Hsi-Kai Tsou, Ting-Hsien Kao, John Peniston, Simone Ho

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2.1. Overview of simplified PIC-FDTD approach for the analysis of e-beam-induced THz radiation

The PIC-FDTD method has been widely used to study underlying physical mechanism of the Smith-Purcell superradiance [8–10]. To save computational time and memory, we have used simplified version of PIC-FDTD method [17, 18]. In our simplified model, the electron-bunch is treated as one negatively charged particle, the movement of the particle is restricted only in two-dimensional (2D) (x-y) plane, and only transverse electric (TE) mode, with Ex, Ey, and Hz fields, has been analyzed. Figure 1 shows schematic representation of the analyzed 2D system and definitions of dimensions of the graded grating, where Λ, s, d, and Δd are period, width, depth of the grooves, and depth variation, respectively.

Figure 1. Schematic representation of the analyzed 2D system and definitions of dimensions of the graded grating.

In the FDTD method, the time-dependent EM field propagating in 2D system is simulated using Yee's algorithm [19, 20] to solve the following Maxwell's equations (in the vacuum):

$$\nabla \times \mathbf{E}(\mathbf{x}, y, t) = -\frac{\partial \mathbf{B}(\mathbf{x}, y, t)}{\partial t} \tag{2}$$

CHZLX i þ

CHZLY i þ

1 2 ; j þ 1 2

1 2 ; j þ 1 2

� �

quency dependence of dielectric permittivity of metal can be expressed as follows:

χ ωð Þ¼

εrð Þ¼ ω 1 þ

DðÞ¼ t ε0ε∞Eð Þþ t ε0

field E(t) by the convolution:

Figure 2. 2D uniform rectangular Yee's grid for TE mode.

recursive manner.

� �

¼ Δt μ i þ 1

¼ Δt μ i þ 1

Figure 2 shows a typical Yee's 2D uniform rectangular grid for TE mode. Ex and Ey components are located at the middle of the edge of each grid, and Hz component is located at the center of the grids. The time evolution of EM fields is updated in a leapfrog manner. In order to model an open system, we have employed perfectly matched layer (PML)-absorbing conditions [21].

The dielectric properties of metals are strongly dispersive; therefore, we utilized recursive convolution (RC) approach [20] to model metallic grating. By adopting Drude model, fre-

> ω2 p

where ωp and Γ are the plasma frequency and collision frequency of metal, respectively. In a linear dispersive medium, the time-domain electric flux density D(t) is related to the electric

> ðt τ¼0

Since the Fourier-transformed electric susceptibility χ(τ) of Drude type of dispersion satisfies the condition for a recursive computation, the convolution in Eq. (15) can be solved in a

ω2 p

2 ; j þ 1 2 � �

2 ; j þ 1 2 � � 1

Electron Beam-Induced Directional Terahertz Radiation from Metamaterials

1

ωð Þ jΓ � ω ¼ 1 þ χ ωð Þ (13)

ωð Þ jΓ � ω (14)

Eð Þ t � τ χ τð Þdτ (15)

Δx (11)

117

http://dx.doi.org/10.5772/intechopen.80648

Δy (12)

$$\nabla \times \mathbf{H}(\mathbf{x}, y, t) = \varepsilon\_0 \frac{\partial \mathbf{E}(\mathbf{x}, y, t)}{\partial t} + \mathbf{J}(\mathbf{x}, y, t) \tag{3}$$

where E, H, and B are the electric and magnetic fields and magnetic flux density of EM wave, J is the current density, and ε0 and μ0 are the dielectric permittivity and the magnetic permeability in vacuum, respectively. In Yee's algorithm, these differential equations are discretized using centered finite-difference expressions for the space and time derivatives, and we have the following set of equations for TE mode in 2D space:

$$E\_x^{\pi} \left( i + \frac{1}{2}, j \right) = \mathbb{C}\_{\text{EX}} \left( i + \frac{1}{2}, j \right) E\_x^{\pi - 1} \left( i + \frac{1}{2}, j \right) + \mathbb{C}\_{\text{EX} \text{Y}} \left( i + \frac{1}{2}, j \right) \left\{ H\_z^{\pi - \frac{1}{2}} \left( i + \frac{1}{2}, j + \frac{1}{2} \right) - H\_z^{\pi - \frac{1}{2}} \left( i + \frac{1}{2}, j - \frac{1}{2} \right) \right\} \tag{4}$$

$$E\_y^{\mathrm{ul}}\left(i,j+\frac{1}{2}\right) = \mathbb{C}\_{\mathrm{EY}}\left(i,j+\frac{1}{2}\right)E\_y^{\mathrm{u-1}}\left(i,j+\frac{1}{2}\right) + \mathbb{C}\_{\mathrm{EYX}}\left(i,j+\frac{1}{2}\right)\left\{H\_z^{\mathrm{u-\frac{1}{2}}}\left(i+\frac{1}{2},j+\frac{1}{2}\right) - H\_z^{\mathrm{u-\frac{1}{2}}}\left(i-\frac{1}{2},j+\frac{1}{2}\right)\right\},\tag{5}$$

$$H\_z^{n+\frac{1}{2}}\left(i+\frac{1}{2},j+\frac{1}{2}\right) = H\_z^{n-\frac{1}{2}}\left(i+\frac{1}{2},j+\frac{1}{2}\right) - \mathcal{C}\_{\text{HELX}}\left(i+\frac{1}{2},j+\frac{1}{2}\right)\left\{E\_y^n\left(i+1,j+\frac{1}{2}\right) - E\_y^n\left(i,j+\frac{1}{2}\right)\right\}$$

$$+C\_{HZLI}\left(i+\frac{1}{2},j+\frac{1}{2}\right)\left\{E\_x^n\left(i+\frac{1}{2},j+1\right) - E\_x^n\left(i+\frac{1}{2},j\right)\right\}\tag{6}$$

where superscript n is for the time step and (i, j)=(iΔx, jΔy) for the spatial position. The coefficients in Eqs. (4)–(6) are as follows:

$$\mathbf{C}\_{EX}\left(\mathbf{i}+\frac{1}{2},\mathbf{j}\right) = \frac{\mathbf{1}-\frac{\sigma\left(\mathbf{i}+\frac{1}{2}j\right)\Delta t}{2\epsilon\left(\mathbf{i}+\frac{1}{2}j\right)}}{\mathbf{1}+\frac{\sigma\left(\mathbf{i}+\frac{1}{2}j\right)\Delta t}{2\epsilon\left(\mathbf{i}+\frac{1}{2}j\right)}}\tag{7}$$

$$\mathbf{C}\_{\text{EXLY}}\left(\mathbf{i}+\frac{1}{2},\mathbf{j}\right) = \frac{\frac{\Delta t}{\epsilon\left(\mathbf{i}+\frac{1}{2}j\right)}}{1+\frac{\sigma\left(\mathbf{i}+\frac{1}{2}j\right)\Delta t}{2\epsilon\left(\mathbf{i}+\frac{1}{2}j\right)}}\frac{1}{\Delta y} \tag{8}$$

$$\mathbf{C}\_{EY}\left(\mathbf{i},\mathbf{j}+\frac{1}{2}\right) = \frac{\mathbf{1} - \frac{\sigma\left(\mathbf{i},\mathbf{j}+\frac{1}{2}\right)\Delta t}{2\epsilon\left(\mathbf{i},\mathbf{j}+\frac{1}{2}\right)}}{\mathbf{1} + \frac{\sigma\left(\mathbf{i},\mathbf{j}+\frac{1}{2}\right)\Delta t}{2\epsilon\left(\mathbf{i},\mathbf{j}+\frac{1}{2}\right)}}\tag{9}$$

$$\mathbf{C}\_{EYLX}\left(\mathbf{i},\mathbf{j}+\frac{1}{2}\right) = \frac{\frac{\Delta t}{\epsilon\left(\mathbf{i},\mathbf{j}+\frac{1}{2}\right)}}{1+\frac{\sigma\left(\mathbf{i},\mathbf{j}+\frac{1}{2}\right)\Delta t}{2\epsilon\left(\mathbf{i},\mathbf{j}+\frac{1}{2}\right)}}\frac{1}{\Delta \mathbf{x}}\tag{10}$$

Electron Beam-Induced Directional Terahertz Radiation from Metamaterials http://dx.doi.org/10.5772/intechopen.80648 117

$$\mathbf{C}\_{\rm HZZ} \left( \mathbf{i} + \frac{1}{2}, j + \frac{1}{2} \right) = \frac{\Delta t}{\mu \left( \mathbf{i} + \frac{1}{2}, j + \frac{1}{2} \right)} \frac{1}{\Delta \mathbf{x}} \tag{11}$$

$$\mathbf{C}\_{HZLY}\left(\mathbf{i}+\frac{1}{2},j+\frac{1}{2}\right) = \frac{\Delta t}{\mu\left(\mathbf{i}+\frac{1}{2},j+\frac{1}{2}\right)}\frac{1}{\Delta y} \tag{12}$$

Figure 2 shows a typical Yee's 2D uniform rectangular grid for TE mode. Ex and Ey components are located at the middle of the edge of each grid, and Hz component is located at the center of the grids. The time evolution of EM fields is updated in a leapfrog manner. In order to model an open system, we have employed perfectly matched layer (PML)-absorbing conditions [21].

The dielectric properties of metals are strongly dispersive; therefore, we utilized recursive convolution (RC) approach [20] to model metallic grating. By adopting Drude model, frequency dependence of dielectric permittivity of metal can be expressed as follows:

$$\varepsilon\_r(\omega) = 1 + \frac{\omega\_p^2}{\omega(j\Gamma - \omega)} = 1 + \chi(\omega) \tag{13}$$

$$\chi(\omega) = \frac{\omega\_p^2}{\omega(\text{j}\Gamma - \omega)}\tag{14}$$

where ωp and Γ are the plasma frequency and collision frequency of metal, respectively. In a linear dispersive medium, the time-domain electric flux density D(t) is related to the electric field E(t) by the convolution:

$$\mathbf{D}(t) = \varepsilon\_0 \varepsilon\_\approx \mathbf{E}(t) + \varepsilon\_0 \int\_{\tau=0}^t \mathbf{E}(t-\tau)\chi(\tau)d\tau \tag{15}$$

Since the Fourier-transformed electric susceptibility χ(τ) of Drude type of dispersion satisfies the condition for a recursive computation, the convolution in Eq. (15) can be solved in a recursive manner.

Figure 2. 2D uniform rectangular Yee's grid for TE mode.

In the FDTD method, the time-dependent EM field propagating in 2D system is simulated using Yee's algorithm [19, 20] to solve the following Maxwell's equations (in the vacuum):

where E, H, and B are the electric and magnetic fields and magnetic flux density of EM wave, J is the current density, and ε0 and μ0 are the dielectric permittivity and the magnetic permeability in vacuum, respectively. In Yee's algorithm, these differential equations are discretized using centered finite-difference expressions for the space and time derivatives, and we have

þ CEXLY i þ

þ CEYLX i; j þ

� CHZLX i þ

where superscript n is for the time step and (i, j)=(iΔx, jΔy) for the spatial position. The

¼

¼

¼

¼

En x i þ 1 2 ; j þ 1

1 2 ; j

1 2 ; j

1 2

1 2  ∂Bð Þ x; y; t

∂Eð Þ x; y; t

1 2 ; j

1 2

> 1 2 ; j þ 1 2

1 � σ iþ1 2 ð Þ;j Δt 2ε iþ1 2 ð Þ;j

1 þ σ iþ1 2 ð Þ;j Δt 2ε iþ1 2 ð Þ;j

Δt ε iþ1 2 ð Þ;j 1 þ σ iþ1 2 ð Þ;j Δt 2ε iþ1 2 ð Þ;j

 � σ i;jþ1 ð Þ2 Δt ε i;jþ1 ð Þ2 þ σ i;jþ1 ð Þ2 Δt ε i;jþ1 ð Þ2

Δt ε i;jþ1 ð Þ2 1 þ σ i;jþ1 ð Þ2 Δt 2ε i;jþ1 ð Þ2

Hn�1 2 z i þ 1 2 ; j þ 1 2

Hn�1 2 z i þ 1 2 ; j þ 1 2

En

� En x i þ 1 2 ; j

1

1

y i þ 1; j þ

∂t (2)

� Hn�1 2 z i þ 1 2 ; j � 1 2

� Hn�1 2 z i � 1 2 ; j þ 1 2

> � En y i; j þ 1 2

Δy (8)

Δx (10)

1 2

(4)

(5)

(6)

(7)

(9)

∂t þ Jð Þ x; y; t (3)

∇ � Eð Þ¼� x; y; t

∇ � Hð Þ¼ x; y; t ε0

1 2

1 2 ; j þ 1 2

CEX i þ

CEXLY i þ

CEY i; j þ

CEYLX i; j þ

the following set of equations for TE mode in 2D space:

En�1 x i þ 1 2 ; j

En�1 y i; j þ

¼ CEX i þ

116 Metamaterials and Metasurfaces

¼ CEY i; j þ

1 2 ; j

1 2

> ¼ Hn�1 2 z i þ 1 2 ; j þ 1 2

þCHZLY i þ

coefficients in Eqs. (4)–(6) are as follows:

En x i þ 1 2 ; j

En y i; j þ 1 2

> Hnþ1 2 z i þ 1 2 ; j þ 1 2

In the PIC-FDTD method, time-dependent Maxwell's equations are coupled with the equation of motion of relativistic charged particles driven by the inertia and the Lorentz force and solved in a leapfrog manner similar to the main FDTD algorithm. In our simplified version, we assume the electron-bunch as one negatively charged particle with the following Gaussian spatial charge distribution:

$$m\_{\epsilon}(\mathbf{x}, y, t) = N\_0 \exp\left\{-\frac{(\mathbf{x} - \mathbf{x}\_0(t))^2 + \left(y - y\_0(t)\right)^2}{2\sigma^2}\right\} \tag{16}$$

$$
\sigma = \frac{w}{2\sqrt{2\ln(2)}}\tag{17}
$$

Ex5 ¼ ð Þ 1 � α Ex1 þ αEx2 (20)

Electron Beam-Induced Directional Terahertz Radiation from Metamaterials

http://dx.doi.org/10.5772/intechopen.80648

119

Ex6 ¼ ð Þ 1 � α Ex3 þ αEx4 (21)

Ex ¼ 1 � β Ex5 þ βEx6 (22)

Jð Þ¼� x; y; t neð Þ x; y; t ev x0; y0; t (23)

In order to include the movement of the electron-bunch in the FDTD formalism, a current

Figure 4 schematically summarizes our simplified PIC-FDTD simulation scheme. The solution of the time-dependent Maxwell's equations gives spatial counter maps of EM fields and their time evolution. The solution of the equation of motion of relativistic electron-bunch gives its trajectory, and the continuity equation gives the current and charge densities required for

In Figure 1, the analyzed 2D system and definitions of dimensions of the graded grating are schematically shown. In Table 1, parameters used in this study are summarized. The graded grating was assumed to be consisted of Ag, and the Drude model was adopted in order to model the dispersion characters of its dielectric function and solved by using RC scheme as discussed above. The plasma frequency (ωp) and the collision frequency (Γ) of Ag were set to

Maxwell's equations. The flowchart of our PIC-FDTD simulation is shown in Figure 5.

source term is added to Ampere's law:

2.2. Analyzed models and parameters

Figure 4. Schematic representation of simplified PIC-FDTD simulation scheme.

where N0 is the central electron density of the bunch and w is the half width of the bunch. The coordinate (x0, y0) represents the center of electron-bunch, and its movement (trajectory) is updated by solving following equation of motion:

$$\frac{\partial \mathbf{P}(\mathbf{x}\_0, y\_0, t)}{\partial t} = -n\_t e \left\{ \mathbf{E}(\mathbf{x}\_0, y\_0, t) + \mathbf{v}(\mathbf{x}\_0, y\_0, t) \times \mathbf{B}(\mathbf{x}\_0, y\_0, t) \right\} \tag{18}$$

$$P(\mathbf{x}\_0, y\_0, t) = \frac{m\_\epsilon \sigma(\mathbf{x}\_0, y\_0, t)}{\sqrt{1 - \left|\sigma(\mathbf{x}\_0, y\_0, t)\right|^2/c^2}}\tag{19}$$

where P is the momentum, e is the electron charge, v is the speed of the electron-bunch, and me is the electron mass. The movement of the electron-bunch is assumed to be in a continuous space, and the coordinate (x0, y0) of the center position of it is not necessarily on Yee's discrete FDTD grid points. Therefore, electric field and magnetic flux density on the electron-bunch to solve Eq. (18) should be interpolated from those at the nearest grid points. We used linear interpolation as schematically shown in Figure 3, in which Ex component is given as follows:

Figure 3. Schematic representation of the linear interpolation for Ex components at the center position (x0, y0) of the electron-bunch.

Electron Beam-Induced Directional Terahertz Radiation from Metamaterials http://dx.doi.org/10.5772/intechopen.80648 119

$$E\_{\rm x5} = (1 - a)E\_{\rm x1} + aE\_{\rm x2} \tag{20}$$

$$E\_{x6} = (1 - \alpha)E\_{x3} + \alpha E\_{x4} \tag{21}$$

$$E\_x = (1 - \beta)E\_{x5} + \beta E\_{x6} \tag{22}$$

In order to include the movement of the electron-bunch in the FDTD formalism, a current source term is added to Ampere's law:

$$J(\mathbf{x}, y, t) = -n\_e(\mathbf{x}, y, t) \text{ev}\left(\mathbf{x}\_0, y\_0, t\right) \tag{23}$$

Figure 4 schematically summarizes our simplified PIC-FDTD simulation scheme. The solution of the time-dependent Maxwell's equations gives spatial counter maps of EM fields and their time evolution. The solution of the equation of motion of relativistic electron-bunch gives its trajectory, and the continuity equation gives the current and charge densities required for Maxwell's equations. The flowchart of our PIC-FDTD simulation is shown in Figure 5.

#### 2.2. Analyzed models and parameters

In the PIC-FDTD method, time-dependent Maxwell's equations are coupled with the equation of motion of relativistic charged particles driven by the inertia and the Lorentz force and solved in a leapfrog manner similar to the main FDTD algorithm. In our simplified version, we assume the electron-bunch as one negatively charged particle with the following Gaussian

neð Þ¼ x; y; t N0exp � ð Þ x � x0ð Þt 2 þ y � y0ð Þt � �2

σ ¼ w 2 ffiffiffiffiffiffiffiffiffiffiffiffiffi

P x0; y0; t � � ¼ mev x0; y0; t � �

where P is the momentum, e is the electron charge, v is the speed of the electron-bunch, and me is the electron mass. The movement of the electron-bunch is assumed to be in a continuous space, and the coordinate (x0, y0) of the center position of it is not necessarily on Yee's discrete FDTD grid points. Therefore, electric field and magnetic flux density on the electron-bunch to solve Eq. (18) should be interpolated from those at the nearest grid points. We used linear interpolation as schematically shown in Figure 3, in which Ex component is given as follows:

Figure 3. Schematic representation of the linear interpolation for Ex components at the center position (x0, y0) of the

where N0 is the central electron density of the bunch and w is the half width of the bunch. The coordinate (x0, y0) represents the center of electron-bunch, and its movement (trajectory) is

2σ2 ( )

∂t ¼ �nee E x0; y0; t � � þ v x0; y0; t � � � B x0; y0; t � � � � (18)

� 2 =c2

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 � v x0; y0; t � � � � �

2lnð Þ2 p (17)

q (19)

(16)

spatial charge distribution:

118 Metamaterials and Metasurfaces

electron-bunch.

updated by solving following equation of motion:

∂P x0; y0; t � �

In Figure 1, the analyzed 2D system and definitions of dimensions of the graded grating are schematically shown. In Table 1, parameters used in this study are summarized. The graded grating was assumed to be consisted of Ag, and the Drude model was adopted in order to model the dispersion characters of its dielectric function and solved by using RC scheme as discussed above. The plasma frequency (ωp) and the collision frequency (Γ) of Ag were set to

Figure 4. Schematic representation of simplified PIC-FDTD simulation scheme.

A 20-μm-wide (w) bunched electron-bunch with Gaussian charge distribution (Eqs. (16) and (17)) was sent 20 μm (w) above the grating at the relativistic speed. The maximum current

acceleration energy of the electron-bunch is 30 keV, which is comparable to the recent experi-

In the e-beam-induced radiations from conventional periodic grating, there are two mechanisms. One is the so-called Smith-Purcell radiation emitted while the e-beam is passing over the grating. The radiation angle and its frequency satisfy Eq. (1). The other is the scattering of surface waves at both ends of the grating long after the e-beam moved away from the grating. These long-lived surface waves can propagate back and forth on the grating surface and can be emitted repeatedly even long after the e-beam has moved away from the grating as long as the surface waves can live. The frequency of the scattered surface waves is determined by the intersection of the dispersion curves of the surface wave and the beam line. Here, we are interested in the second mechanism long after the e-beam has moved away from the gratings, but the groove depths are gradually graded, and, therefore, the dispersion curves of the

Figure 6(a) and (b) shows snapshot contour maps of the Hz field long after the e-beam has moved away from the graded grating of GG[100, 168, 2] and GG[100, 168, 2], respectively. In both cases, directional radiations are obtained only from the shallowest end of the graded grating, in backward direction from GG[100, 168, 2] and forward direction from GG[100, 168, 2], respectively. These directional radiation characteristics cannot be expected from a conventional

surface waves induced by an e-beam cannot be uniquely determined.

periodic grating and might be unique in the graded grating considered here.

, and the

121

density at the center of the electron-bunch was assumed to be 1.0 106 A/m2

Grating period (Λ) 170 μm Groove width (s) 60 μm

Number of grooves (N) 35

Groove depth (d) Variable parameter

Electron Beam-Induced Directional Terahertz Radiation from Metamaterials

http://dx.doi.org/10.5772/intechopen.80648

Plasma frequency of Ag (ωp) 2.2 103 THz Collision frequency of Ag (Γ) 5.4 THz Electron-bunch energy 30 keV Half width of electron-bunch (w) 20 μm Bunch-grating distance (w) 20 μm

mental condition by Urata et al. [5].

Table 1. Parameters used in this study.

3. Results and discussions

Figure 5. Flowchart of our PIC-FDTD scheme.

be 2.2 103 and 5.4 THz, respectively. The grating period (Λ) and the groove width (s) are 170 and 60 μm, respectively. The number of grooves of the grating (N) is 35. The groove depth (d) is gradually made deeper or shallower. Here, we denote each graded grating using grating parameters as GG[ds, dd, Δd], where ds and dd are the shallowest and the deepest groove depths, respectively, and Δd is the difference in depths between two consecutive grooves (all values are in μm). The space increment for the FDTD grids chosen here is Δx = Δy = 10 μm. The time increment is set to be Δt = 23 fs, which is sufficiently small to satisfy the condition for the stabilization of the FDTD algorithm.

Table 1. Parameters used in this study.

A 20-μm-wide (w) bunched electron-bunch with Gaussian charge distribution (Eqs. (16) and (17)) was sent 20 μm (w) above the grating at the relativistic speed. The maximum current density at the center of the electron-bunch was assumed to be 1.0 106 A/m2 , and the acceleration energy of the electron-bunch is 30 keV, which is comparable to the recent experimental condition by Urata et al. [5].

### 3. Results and discussions

be 2.2 103 and 5.4 THz, respectively. The grating period (Λ) and the groove width (s) are 170 and 60 μm, respectively. The number of grooves of the grating (N) is 35. The groove depth (d) is gradually made deeper or shallower. Here, we denote each graded grating using grating parameters as GG[ds, dd, Δd], where ds and dd are the shallowest and the deepest groove depths, respectively, and Δd is the difference in depths between two consecutive grooves (all values are in μm). The space increment for the FDTD grids chosen here is Δx = Δy = 10 μm. The time increment is set to be Δt = 23 fs, which is sufficiently small to satisfy the condition for the

stabilization of the FDTD algorithm.

Figure 5. Flowchart of our PIC-FDTD scheme.

120 Metamaterials and Metasurfaces

In the e-beam-induced radiations from conventional periodic grating, there are two mechanisms. One is the so-called Smith-Purcell radiation emitted while the e-beam is passing over the grating. The radiation angle and its frequency satisfy Eq. (1). The other is the scattering of surface waves at both ends of the grating long after the e-beam moved away from the grating. These long-lived surface waves can propagate back and forth on the grating surface and can be emitted repeatedly even long after the e-beam has moved away from the grating as long as the surface waves can live. The frequency of the scattered surface waves is determined by the intersection of the dispersion curves of the surface wave and the beam line. Here, we are interested in the second mechanism long after the e-beam has moved away from the gratings, but the groove depths are gradually graded, and, therefore, the dispersion curves of the surface waves induced by an e-beam cannot be uniquely determined.

Figure 6(a) and (b) shows snapshot contour maps of the Hz field long after the e-beam has moved away from the graded grating of GG[100, 168, 2] and GG[100, 168, 2], respectively. In both cases, directional radiations are obtained only from the shallowest end of the graded grating, in backward direction from GG[100, 168, 2] and forward direction from GG[100, 168, 2], respectively. These directional radiation characteristics cannot be expected from a conventional periodic grating and might be unique in the graded grating considered here.

Figure 6. Snapshot contour map of Hz field long after the e-beam moved over (a) GG[100, 168, 2] and (b) GG[100, 168, 2].

As discussed by Gan et al. [16], the dispersion relations of the surface waves on these graded gratings are different at each location on the grating, and thus the frequencies of the e-beaminduced surface waves should also be different at different locations. These surface modes with different frequency components originated from different locations on the graded gratings can propagate toward the side with shallower groove depth due to the cutoff nature as reported by Gan et al. [16], which may give a mechanism of the directional radiation obtained only from the shallow end of the graded grating.

Figure 7(a) shows the time-domain Hz field amplitude from GG[100, 168, 2] monitored at probe P indicated in Figure 6(a). After around 400 ps, successive pulse train with exponentially decaying magnitude can be seen. Magnified figure in the inset of Figure 7(a) indicates that each pulse train has duration of tens of ps and seems to be composed by the beating between several frequency components. Figure 7(b) shows the Fourier-transformed spectra of the far-field radiation from GG[100, 168, 2] monitored at probe P and from GG[100, 168, 2] monitored at probe Q. Both spectra have relatively wideband spectra and multiple sharp peaks, which cannot be expected from a conventional SPR in a periodic grating. The beating response seen in

time-domain response in Figure 7(a) should be attributed to these multiple sharp peaks. These two spectra from GG[100, 168, 2] and GG[100, 168, 2] are quite similar. The geometric parameters of these two graded gratings are identical except the groove depth variation Δd is opposite in sign; therefore, e-beam-induced surface modes are almost identical in both graded gratings, and only radiation direction was switched by making groove depth variation Δd opposite.

Figure 7. (a) Time-domain Hz field amplitude from GG[100, 168, 2] monitored at probe P. (b) Fourier-transformed spectra of the far-field radiation from GG[100, 168, 2] monitored at probe P (red solid line) and from GG[100, 168, 2] monitored

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at probe Q (blue-dotted line).

In order to clarify the nature of the surface modes, we have also investigated near fields on the different locations on the graded gratings. Figure 8 shows Fourier-transformed

Figure 7. (a) Time-domain Hz field amplitude from GG[100, 168, 2] monitored at probe P. (b) Fourier-transformed spectra of the far-field radiation from GG[100, 168, 2] monitored at probe P (red solid line) and from GG[100, 168, 2] monitored at probe Q (blue-dotted line).

As discussed by Gan et al. [16], the dispersion relations of the surface waves on these graded gratings are different at each location on the grating, and thus the frequencies of the e-beaminduced surface waves should also be different at different locations. These surface modes with different frequency components originated from different locations on the graded gratings can propagate toward the side with shallower groove depth due to the cutoff nature as reported by Gan et al. [16], which may give a mechanism of the directional radiation obtained

Figure 6. Snapshot contour map of Hz field long after the e-beam moved over (a) GG[100, 168, 2] and (b) GG[100, 168, 2].

Figure 7(a) shows the time-domain Hz field amplitude from GG[100, 168, 2] monitored at probe P indicated in Figure 6(a). After around 400 ps, successive pulse train with exponentially decaying magnitude can be seen. Magnified figure in the inset of Figure 7(a) indicates that each pulse train has duration of tens of ps and seems to be composed by the beating between several frequency components. Figure 7(b) shows the Fourier-transformed spectra of the far-field radiation from GG[100, 168, 2] monitored at probe P and from GG[100, 168, 2] monitored at probe Q. Both spectra have relatively wideband spectra and multiple sharp peaks, which cannot be expected from a conventional SPR in a periodic grating. The beating response seen in

only from the shallow end of the graded grating.

122 Metamaterials and Metasurfaces

time-domain response in Figure 7(a) should be attributed to these multiple sharp peaks. These two spectra from GG[100, 168, 2] and GG[100, 168, 2] are quite similar. The geometric parameters of these two graded gratings are identical except the groove depth variation Δd is opposite in sign; therefore, e-beam-induced surface modes are almost identical in both graded gratings, and only radiation direction was switched by making groove depth variation Δd opposite.

In order to clarify the nature of the surface modes, we have also investigated near fields on the different locations on the graded gratings. Figure 8 shows Fourier-transformed

Figure 8. Fourier-transformed spectra of near-field (surface wave) Hz monitored at several positions 10 μm above each groove with depth of d = 160, 150, 140, 130, 120, 110, or 100 μm, along with that of the far-field radiation monitored at the probe P in GG[100, 168, 2] (from top to bottom). Markers A, B, and C refer to the peaks at 0.314, 0.329, and 0.347 THz, respectively.

In order to reveal from where each mode originate in the graded grating, we excited the system with quasi-monochromatic EM pulse and monitored long enough until the initial pulse damped and only long-lived surface modes survive. Figure 9 shows spatial distributions of Hz fields for quasi-monochromatic long-lived surface modes of 0.314 (A), 0.329 (B), and 0.347 (C) THz. It can be seen that each surface modes originate at different locations of the graded grating and that higher-frequency modes originate at shallower grooves. This also supports that a superposition of the surface modes with different frequencies originated at different locations on the graded grating results in the directional and wideband far-field radiation with

Figure 9. Snapshot contour map of Hz fields long after the exciting quasi-monochromatic electromagnetic pulse has been damped when the frequencies of the mode are 0.314 (A), 0.329 (B), and 0.347 (C) THz in GG[100, 168, 2]. Each mode and

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its name (A, B, C) correspond to the peaks in the far-field radiation spectrum in Figure 8.

The fact that the dispersion characters and frequency of the e-beam-induced surface mode is quite sensitive to the local environment of the grooves suggests that one can design the radiation frequency of the directional radiation from graded gratings by appropriately choosing groove parameters of the grating. Figure 10 shows the Fourier-transformed spectra of the far-field radiation from graded gratings with different groove parameters: GG[100, 304, 6], GG[100, 236, 4], GG[100, 168, 2], GG[168, 236, 2], GG[50, 186, 4], and GG[50, 118, 2]. Roughly speaking, the deepest and shallowest grooves determine the lowest and highest frequencies of the radiation, respectively. This can be confirmed by comparing spectra for GG[100, 304, 6], GG[100, 236, 4], and GG[100, 168, 2], for example. The highest frequency of these radiations is almost the same 0.40 THz and determined by their common shallowest groove depth ds of 100 μm. The concept of spoof SPPs may be promising for developing THz

multiple sharp peaks.

radiation sources.

spectra of the near-field (surface wave) Hz field monitored just above each groove with d = 160, 150, 140, 130, 120, 110, or 100 μm, along with that of the far-field radiation monitored at the probe P, all in GG[100, 168, 2]. It can be seen that more peaks appear on the higher-frequency side of the spectra for monitoring above the shallower grooves. This is because the frequency of the surface waves and their cutoff frequency are lower at deeper grooves, and more surface modes can be supported above the shallower grooves. The spectrum monitored at the left end groove of the grating (d = 100 μm) is almost identical to the far-field radiation spectrum, which also supports that the directional and wideband far-field radiation with multiple sharp peaks was obtained as a superposition of all of the surface modes with different frequencies originated at different locations on the graded grating.

Figure 9. Snapshot contour map of Hz fields long after the exciting quasi-monochromatic electromagnetic pulse has been damped when the frequencies of the mode are 0.314 (A), 0.329 (B), and 0.347 (C) THz in GG[100, 168, 2]. Each mode and its name (A, B, C) correspond to the peaks in the far-field radiation spectrum in Figure 8.

In order to reveal from where each mode originate in the graded grating, we excited the system with quasi-monochromatic EM pulse and monitored long enough until the initial pulse damped and only long-lived surface modes survive. Figure 9 shows spatial distributions of Hz fields for quasi-monochromatic long-lived surface modes of 0.314 (A), 0.329 (B), and 0.347 (C) THz. It can be seen that each surface modes originate at different locations of the graded grating and that higher-frequency modes originate at shallower grooves. This also supports that a superposition of the surface modes with different frequencies originated at different locations on the graded grating results in the directional and wideband far-field radiation with multiple sharp peaks.

The fact that the dispersion characters and frequency of the e-beam-induced surface mode is quite sensitive to the local environment of the grooves suggests that one can design the radiation frequency of the directional radiation from graded gratings by appropriately choosing groove parameters of the grating. Figure 10 shows the Fourier-transformed spectra of the far-field radiation from graded gratings with different groove parameters: GG[100, 304, 6], GG[100, 236, 4], GG[100, 168, 2], GG[168, 236, 2], GG[50, 186, 4], and GG[50, 118, 2]. Roughly speaking, the deepest and shallowest grooves determine the lowest and highest frequencies of the radiation, respectively. This can be confirmed by comparing spectra for GG[100, 304, 6], GG[100, 236, 4], and GG[100, 168, 2], for example. The highest frequency of these radiations is almost the same 0.40 THz and determined by their common shallowest groove depth ds of 100 μm. The concept of spoof SPPs may be promising for developing THz radiation sources.

spectra of the near-field (surface wave) Hz field monitored just above each groove with d = 160, 150, 140, 130, 120, 110, or 100 μm, along with that of the far-field radiation monitored at the probe P, all in GG[100, 168, 2]. It can be seen that more peaks appear on the higher-frequency side of the spectra for monitoring above the shallower grooves. This is because the frequency of the surface waves and their cutoff frequency are lower at deeper grooves, and more surface modes can be supported above the shallower grooves. The spectrum monitored at the left end groove of the grating (d = 100 μm) is almost identical to the far-field radiation spectrum, which also supports that the directional and wideband far-field radiation with multiple sharp peaks was obtained as a superposition of all of the surface modes with different frequencies originated at different locations on

Figure 8. Fourier-transformed spectra of near-field (surface wave) Hz monitored at several positions 10 μm above each groove with depth of d = 160, 150, 140, 130, 120, 110, or 100 μm, along with that of the far-field radiation monitored at the probe P in GG[100, 168, 2] (from top to bottom). Markers A, B, and C refer to the peaks at 0.314, 0.329, and 0.347 THz,

the graded grating.

respectively.

124 Metamaterials and Metasurfaces

side of the grating with shallower grooves. The direction of these radiations can be switched backward or forward by making the groove depth deeper or shallower. The spectra of these directional radiations are wideband and contain multiple sharp peaks. The deepest and the shallowest groove depths determine the lowest and the highest frequency of the radiation band, respectively. These unique radiation characteristics cannot be explained by the conventional Smith-Purcell radiation and should be attributed to the spoof SPP that originates from different locations on the graded grating. The unique e-beam-induced radiation from metamaterials based on spoof SPP's concept may open a way for a development of novel types

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This work is partly supported from Okasan-Kato Foundation. The presented works have been carried out with graduate students who formerly belonged and currently belong to our

Department of Electrical and Electronic Engineering, Graduate School of Engineering,

[1] Tonouchi M. Cutting-edge terahertz technology. Nature Photonics. 2007;1:97-105. DOI:

[2] Hangyo M. Development and future prospects of terahertz technology. Japanese Journal

[3] Matsui T. A brief review on metamaterial-based vacuum electronics for terahertz and microwave science and technology. Journal of Infrared, Millimeter and Terahertz Waves.

of Applied Physics. 2015;54:120101. DOI: 10.7567/JJAP.54.120101

2017;38:1140-1161. DOI: 10.1007/s10762-017-0387-9

of THz radiation sources.

Acknowledgments

Conflict of interest

Author details

Tatsunosuke Matsui

References

Mie University, Tsu, Japan

10.1038/nphoton.2007.3

There is no conflict of interest.

research group, Okajima, Omura, and Yoshida.

Address all correspondence to<EMAIL_ADDRESS>
Figure 10. Fourier-transformed spectra of the far-field radiation from graded gratings with different groove parameters: GG[100, 304, 6], GG[100, 236, 4], GG[100, 168, 2], GG[168, 236, 2], GG[50, 186, 4], and GG[50, 118, 2] (from top to bottom).

## 4. Conclusions

We have numerically analyzed the e-beam-induced directional THz radiation from metallic grating structures with graded depths. We used a simplified PIC-FDTD method for numerical analysis to save computational time and memory, and the detailed description of our method is given here. In our simplified model, the electron-bunch is treated as one negatively charged particle with Gaussian charge distribution, and its movement is restricted only in 2D space, and only TE mode, with Ex, Ey, and Hz fields, has been analyzed.

Our results show unique directional THz radiation from graded gratings. By passing pulsed (bunched) e-beam along the grating surface, directional THz radiations are obtained from one side of the grating with shallower grooves. The direction of these radiations can be switched backward or forward by making the groove depth deeper or shallower. The spectra of these directional radiations are wideband and contain multiple sharp peaks. The deepest and the shallowest groove depths determine the lowest and the highest frequency of the radiation band, respectively. These unique radiation characteristics cannot be explained by the conventional Smith-Purcell radiation and should be attributed to the spoof SPP that originates from different locations on the graded grating. The unique e-beam-induced radiation from metamaterials based on spoof SPP's concept may open a way for a development of novel types of THz radiation sources.


*Laboratory Tests*

*Object of tests.* The tests were carried out with the use of the one-cylinder two stroke crosshead supercharged diesel engine, which is an element of the test stand adapted to investigations on emission exhaust gas components (Figure 4). The Wimmer MRU/2D analyzer with measuring accuracy of ≤±5% and a resolution of 1 ppm was used to measure the composition of the exhaust gases.

To supply the engine during the tests in question, the marine diesel oil (MDO) and its mixtures with rape oil esters (RME) of the following proportions were prepared:

The MDO had a density of 831 kg/m3 and the RME of 883 kg/m3. As a result of the mixing, the biofuel had a density of 839 kg/m3 in the first case and 840 kg/m3 in the second case.

*Test program.* The tests were carried out within the broad range of the engine's loading, namely: 40%, 50%, 60%, 70%, and 80% M/Mn (set torque of engine M/nominal torque of engine Mn) and for a constant rotational speed of the engine, set at 220 rpm. At a given rotational speed and successively set loads, measurements of the engine's exhaust gas content during combusting by the engine were realized: The MDO alone, and the two above specified mixtures (i.e., 15% of RME in MDO, and 20% of RME in MDO). The results obtained from the tests during the supply of the engine with the MDO alone was assumed as the reference point for determination of the influence of combustion of the MDO/RME mixtures on the engine's exhaust gas content.

**Figure 4.** Test stand: (**a**) block diagram: 1—L-22 diesel engine, 2—water brake, 3—torsiometer, 4—gauge for crankshaft position marking and rotational speed measuring, 5—combustion pressure transducer, 6—injection pressure transducer, 7—computer, 8—exhaust gas analyzer, 9—analog/digital converter; (**b**) engine L22-view.

*Test results and their analysis.* The selected tests results are presented in Figures 5 and 6. On the basis of the exhaust gas analysis, it can be stated that combustion of MDO with 15% addition of RME caused, on average, a drop of the NOx content by 35% (for higher engine loads—70% and 80% M/Mn) and that during combusting of the MDO with the 20% addition of RME, the drop, on average, exceeded 57% (for higher engine loads—70% and 80% M/Mn), as shown in Figure 5.

**Figure 5.** NOx content in exhaust gas as a function of the engine load for different kinds of fuel at a constant rotational speed *n* = 220 rpm.

**Figure 6.** CO2 content in exhaust gas as a function of the engine load for different kinds of fuel at a constant rotational speed *n* = 220 rpm.

It can also be noted that the combustion of MDO with the 15% and 20% addition of RME, especially for higher engine loads (70% and 80% M/Mn), causes a clear drop in CO2. This drop is exceeded by 33% in the combustion of MDO with the 15% addition of RME and exceeded by 57% in the combustion of MDO with the 20% addition of RME (Figure 6).

### **4. Change of Fuel Injection Parameters-Change Advance Angles of Fuel Injection**

The possibility of reducing NOx emission by changing the fuel injection parameters has been noted [9]. The fundamental parameter for an injection system is the advance angle of fuel injection. You can expect that change of the advance angle of fuel injection affects the composition of exhaust gases, including toxic component emissions. This thesis is confirmed by the research carried out by the author, described in follow section.


Author details

Alberto Di Giuseppe1,2,3\*, Federico Giovagnoli4 , Saverio Di Giuseppe5 and Diana Ronconi5

1 Department of Plastic Surgery, University of Padova, Italy

\*Address all correspondence to<EMAIL_ADDRESS>
© 2019 The Author(s). Licensee IntechOpen. This chapteris distributed underthe terms oftheCreative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


**2. Materials and Methods**

#### *2.1. Preparation of the Polysaccharides*

The dried sea cucumbers, *H. leucospilota* (80–130 mm, 22–47 g), were purchased from the Market Property Development Co., Ltd. (Haikou, China). Professor Yongqin Feng of Hainan University confirmed the species of the sea cucumber sample.

The polysaccharides were extracted from the *H. leucospilota* sample according to a previously reported method with slight modifications [15]. The dried sea cucumber body wall powder was mixed with sodium acetate buffer, papain, EDTA solution, and cysteine. The mixture was centrifuged (4500× *g*, 15 min, 4 ◦C), and a chlorohexadecyl pyridinium (CPC) solution was added to the clear supernatant. After 12 h, the mixture was centrifuged (4500× *g*, 15 min, 4 ◦C), and the precipitated polysaccharides were redissolved in NaCl: ethanol (100:15, *v*/*v*) solution with 95% ethanol. The sediments were collected after centrifugation (3500× *g*, 15 min, 4 ◦C) and were reconstituted with distilled water. After decolorization and deproteinization, the polysaccharides were dialyzed with distilled water for 72 h. The HLP with extremely low protein content (0.26%) was obtained by concentration and lyophilization.

#### *2.2. In-Vitro Fermentation of HLP*

#### 2.2.1. Preparation of Human Intestinal Microbiota

Fecal inocula were collected from eight healthy volunteers who had not taken any antibiotics within three months (male: female = 1:1, average age 20–30 years). Equal amounts of feces from each person were pooled. Samples of 50 g were diluted with 200 mL of Dulbecco's phosphate-buffered saline (10%, D-PBS), which was followed by homogenization. The mixture was filtered through four-layer nylon gauze, and the obtained filtrate was collected.

#### 2.2.2. In-Vitro Fermentation Procedure

The polysaccharides solution, fermentation medium solution, and fecal solution were added to each ampoule tube. The sealed ampoule tubes were incubated in a shaker (250 rpm, 37 ◦C) for 6, 12, 24, and 48 h. After incubation, the anaerobic tubes were placed in an ice water bath for 10 min for termination. After centrifugation (8000× *g*, 10 min), the supernatant was transferred and stored at −20 ◦C before analysis.

2.2.3. Determination of Total Sugar, Reducing Sugar, and Free Monosaccharides in the Fermented Products

The total sugar contents were determined by the phenol sulfuric acid method with glucose as the standard. The dinitrosalicylic acid (DNS) method was utilized to determine the reducing sugar contents [18]. The free monosaccharides were determined by gas chromatography (GC) according to the methods of a previous study [19].

#### 2.2.4. Determination of pH and SCFA Content

The fermentation supernatant pH levels were measured with an MP511 Lab pH Meter (Sanxin Apparatus, Shanghai, China).

Anhydrous ethanol and the fermentation supernatants (or SCFAs standard solutions) were added to tubes and mixed. The mixtures were supplemented with concentrated sulfuric acid and n-hexane. The upper organic phase was used to determine the concentrations of SCFAs. SCFAs analysis was performed by an Agilent 6890A GC equipped with a flame ionization detector (FID) and HP-FFAP column (30 m × 0.32 mm × 0.25 μm, Agilent Technologies, Santa Clara, CA, USA).

#### *2.3. In Vivo Fermentation of HLP*

Thirty-two male Kunming mice were purchased from the Tianqin Biotechnology Co., Ltd. (Changsha, China), Certificate Number: SCXK (Xiang) 2014−0011. The mice were housed under controlled environmental conditions at a temperature of 23 ± 1 ◦C and a 12/12 h light/dark cycle with ad libitum water and food. All procedures were performed according to the Guidelines of the Care and Use of Laboratory Animals. The experiments were approved by the Animal Experimentation Ethics Committee of Hainan Medical University.

The mice were randomly divided into four groups and received intragastric administrations once every day: low-dose (HLP-L, 50 mg/kg body weight) group; medium-dose (HLP-M, 100 mg/kg body weight) group; high-dose (HLP-H, 200 mg/kg body weight) group; and an equal volume of distilled water as the normal group (ND). The health of the mice was recorded daily for 28 days. Fecal samples from each group were collected after gavage every fortnight. Finally, the mice were sacrificed by cervical dislocation after anesthesia with chloral hydrate. The liver and small intestine tissues were taken under sterile conditions and transferred to a −80 ◦C refrigerator for preservation.

#### *2.4. Liver Antioxidant Activity Assay*

The mouse liver tissues were added to ice-cold physiological saline, homogenized, and centrifuged (4 ◦C, 3000× *g* and 10 min). The malondialdehyde (MDA) contents and superoxide dismutase (SOD) and glutathione peroxidase (GSH-Px) activities in the liver were measured with the corresponding kits (Jiancheng, Nanjing, China).

### *2.5. Histological Examinations*

The ileum and liver samples were fixed in 10% neutral buffered formalin solution for histopathological processing. After dehydration, the fixed tissues were embedded in paraffin and were sectioned and dyed with hematoxylin-eosin (H&E). The stained areas were viewed with an optical microscope (Nikon Eclipse, Tokyo, Japan).

#### *2.6. Statistical Analysis*

The results were presented as the means ± standard deviation (SD). The data were analyzed using one-way analysis of variance (ANOVA) using SPSS 25.0 software (SPSS Inc., Chicago, IL, USA) and compared using Duncan's test. *p* < 0.05 was considered to be significantly different.

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

#### *3.1. Changes in Total Sugar, Reducing Sugar, and Free Monosaccharide Contents during In-Vitro Fermentation*

The enzymes that are encoded by the human microbiota cleave the glycosidic bonds of carbohydrates to fermentable saccharides [20]. The breakdown of glycosidic bonds leads to the release of some terminal, reducing sugars of the polysaccharides. Hence, the total sugar and reducing sugar contents are useful to evaluate the fermentation extent of polysaccharides [21]. As illustrated in Table 1, the initial total sugar concentration was 1.099 mg/mL. After six hours of fermentation, the total sugar concentration decreased by 56.77% to 0.475 mg/mL, and the rate of decrease was faster than that afterward. The total sugar concentration was 0.218 mg/mL at the end of fermentation, which decreased by 0.881 mg/mL from the initial concentration. However, despite being widely used in many reported studies, the phenol-sulfuric method is not specific enough to determine the residual carbohydrate contents from in-vitro fermentation. Consequently, the total sugar contents that were determined at 0 h were not consistent with the original amount of HLP in the culture medium.

**Table 1.** Changes in total sugar, reducing sugar and free monosaccharide contents for in-vitro fermentation.

Values are the means ± SD of three replicates. Data that are followed by different letters in the same column are significantly different (*p* < 0.05).

> Meanwhile, the concentration of reducing sugar was initially 0.432 mg/mL, and it increased to 0.833 mg/mL after three hours, which was followed by a sharp drop to 0.274 mg/mL at six hours. These changes occurred because the generation rate of reducing sugar was faster than its consumption rate at the beginning of fermentation. Thus, the total sugar concentrations showed a declining trend throughout the fermentation process, while the reducing sugar concentrations increased and then followed by a decrease. Similar changes were observed in a study of the in-vitro fermentation of polysaccharides from *Sargassum thunbergii* [21]. The free monosaccharide contents in the fermented products reflect the hierarchy of polysaccharide utilization [22]. As shown in Table 1, free monosaccharides were detected after three hours of fermentation (the fucose, xylose, and galactosamine concentrations were 0.174, 0.063, and 0.017 mg/mL, respectively). The results showed that HLP was degraded into free monosaccharides by the gut microbiota combined with reducing sugar variations. The degradation rate was lower than the monosaccharide utilization rate in the first three hours. Furthermore, fucose was not detected after 24 h of fermentation, while xylose and galactosamine were not detected after 48 h of fermentation. The disappearance of free monosaccharides occurred because the gut microbiota rapidly utilized them. This result was in accordance with the changing trend reported in another study of *Oudemansiella radicata* polysaccharides [19]. Interestingly, the fucose concentrations were higher than those of xylose and galactosamine from 3 h to 12 h, and fucose disappeared earlier, which was different from xylose and galactosamine. It has been reported that the constituent monosaccharides and spatial structures significantly influence the fermentability of polysaccharides [23]. Fucose was consumed on the branches with a residual content of xylose, and then, galactosamine in the backbone was consumed [14]. In addition, diverse fecal bacteria prefer to utilize different monosaccharides that are liberated from polysaccharides [24]. Thus, it was speculated that fucose might be linked

to the side chain in the HLP structure and be more prone to be utilized or degraded by the microbiota [14,21].

#### *3.2. Changes in pH Values and SCFA Contents during In-Vitro Fermentation*

The variations in pH values of the fermented products reflected the fermentation surroundings and are summarized in Table 2. The pH value in the human colon is approximately 5–7, and this slight acidity is due to some acidic metabolites (such as SCFAs) that are produced by intestinal microorganisms. The initial pH value of the HLP fermentation system exhibited slight acidity at 6.87 (0 h). Thereafter, a rapid and significant pH decrease (to 4.49) was observed during HLP fermentation from 0 h to 12 h (*p* < 0.05), which indicated that some acid metabolites were produced during fermentation. Many other studies have also reported that the pH values of fermentation solutions declined with the extension of fermentation time [25]. However, the pH values of the fermented products exhibited an increasing trend after 24 h, which were similar to the results reported by Gao et al. [26]. Presumably, this might be due to the production of some alkaline metabolites in the culture medium. A weakly acidic environment has been proven to promote the proliferation of beneficial bacteria in the intestinal tract and inhibit the growth of harmful bacterial [27]. Thus, HLP promotes gut health by maintaining acidic environments.

**Table 2.** Changes in pH and SCFAs in fermented cultures that were supplemented with HLP at different times during in vitro fermentation.

Values are the means ± SD of three replicates. Data that are followed by different letters on the same line are significantly different (*p* < 0.05).

SCFAs, such as acetic acid, propionic acid, and butyric acid, which are produced during fermentation, play an indispensable role in sustaining human health [28]. Nevertheless, it is difficult to determine the SCFA contents that are generated in vivo, as over 95% of SCFAs are rapidly absorbed and metabolized by the host. The SCFA concentrations in fecal samples are greatly affected by the intestinal transport times and cannot accurately reflect the proximal colon environment [29]. Hence, combining in-vitro and in-vivo fermentation methods more accurately describes the actual fermentation behavior of polysaccharides. The total SCFAs concentration increased with fermentation time (Table 2). After 48 h of fermentation, the total SCFAs content increased by 111.13 mmol/L. The SCFA amounts are related to the microbial compositions, substrate sources, and intestinal action times [30]. Therefore, the variety of SCFAs and their concentrations during fermentation are generally used to determine polysaccharide fermentability.

Acetic acid is usually converted from pyruvate and is utilized by the liver, muscles, and peripheral tissues through blood circulation and is the most abundant SCFA in the colon [31]. As histone deacetylase inhibitors, propionic and butyric acids participate in the immune regulation process [32]. Among the various SCFAs, the acetic acid, propionic acid, and butyric acid contents were comparably higher and changed more distinctly. The acetic acid concentrations showed a continuously increasing trend from the initial 12 h period and decreased gradually from 12 to 24 h. Nevertheless, the propionic acid and butyric acid contents increased gradually throughout the entire process. This result was probably explained by the acetate CoA-transferase route, namely the gut bacteria further metabolized acetate to butyrate via butyryl-CoA [33]. It is noteworthy that the acetic acid

concentration reached its peak value at 12 h, which was consistent with the trend of pH values. The fact that the pH of acetic acid is lower than that of other SCFAs at the same concentrations contributes to this phenomenon. Additionally, the butyric acid concentration was evidently high because the weakly acidic environment was conducive to the metabolism and reproduction of butyrate-producing bacteria. The growth of pH-sensitive pathogens and certain carcinogenic saprophytes (such as *Clostridium* and *Enterobacteriaceae*) was effectively inhibited [29]. In addition, Chen et al. also found that the isobutyric acid and isovaleric acid levels were relatively lower, which resulted from few intestinal bacteria producing isobutyrate and isovalerate [4,19]. HLP may be degraded and utilized by the gut microbiota during in-vitro fermentation, which produced abundant SCFAs.

### *3.3. Changes in pH Values and SCFA Contents in Mouse Feces*

The intestinal microenvironment is a complex ecological and reaction system. The appropriately decreased pH values in the intestine contributed to the growth of probiotics and inhibition of pathogens [34]. The fecal pH value is generally used as an indicator to respond to intestinal health. Based on seven days of oral administration, significant differences in pH values appeared among the different groups (Figure 1). In particular, the fecal pH values of the HLP-H and HLP-M groups were obviously lower than those of the HLP-L and ND groups. This result suggested that the intake of HLP decreased pH in the mouse intestine and that a high-dose intake had a greater influence on pH. The colon and fecal SCFA contents are closely associated with human health.

**Figure 1.** Changes in pH values in the mouse feces among different groups. The different uppercase and lowercase letters around the points represent significant differences in various groups and times (day), respectively (*p* < 0.05).

When compared to the ND group, after HLP treatments for two and four weeks, the total SCFAs concentrations in the HLP-M and HLP-H groups increased significantly (*p* < 0.05, Figure 2). The HLP-H group increased most notably among all groups after four weeks, from 13.4 mmol/L to 20.67 mmol/L. The total SCFAs contents after four weeks were significantly higher than those after two weeks. This result was consistent with the changing trend of pH values in mouse feces and indicated the close relationship between the mouse fecal pH values and SCFA contents in the mouse colon. After four weeks of continuous gavage, both the HLP-M and HLP-H doses caused significant increases in the acetic acid and butyric acid concentrations in feces compared to the ND group (*p* < 0.05). In addition, the fecal isobutyric acid concentrations in the HLP-H group were significantly higher than those in the ND group after four weeks (*p* < 0.05). This result suggested that the intestinal environment of the medium-dose and high-dose HLP-treated mice was affected for four weeks.

**Figure 2.** Changes in total SCFAs (**a**), acetic acid (**b**), propionic acid (**c**), butyric acid (**d**), isobutyric acid (**e**), and isovaleric acid (**f**) contents in mouse feces. Values with different superscripts represent significant differences (*p* < 0.05).


**3. Results**

#### *3.1. Control-Pre and Control-Post Conditions*

There was no significant di fference in performance score between the control-pre (Median = 2.975) and control-post (Median = 3.075) conditions (Z = −1.430, *p* = 0.153). Similarly, there was no significant di fference in the coe fficient of variation of performance score between the control-pre and control-post conditions (Z = −1.382, *p* = 0.167). We assumed that there was no pronounced carry-over or fatigue effect that significantly a ffected performance over the course of the experiment.

#### *3.2. Free-Throw Accuracy*

There were no significant di fferences in free-throw performance score ( χ2(4) = 6.510, *p* = 0.089) or the coe fficient of variation of the performance score ( χ2(4) = 5.629, *p* = 0.131) between the conditions (control-pre, top, bottom or full). However, post hoc pairwise comparison showed that the free-throw performance scores of the top (Median = 3.1, Z = −2.357, *p* = 0.018) and full (Median = 3.15, Z = −2.112, *p* = 0.035) conditions were significantly larger than that of the control-pre condition (Median = 2.975), as shown in Tables 2 and 3.

**Table 2.** Descriptive statistics of the averaged and coe fficient of variation of the free-throw performance score.

\* significant difference (*p* < 0.05) compared to the control-pre condition by post hoc Wilcoxon signed-rank test.

**Table 3.** Probability values (*p*-value) of the average (upper right triangle) and coe fficient of variation (lower left triangle) of the free-throw performance score.

\* significant difference (*p* < 0.05) by post hoc Wilcoxon signed-rank test.

#### *3.3. Full-Body Joint Range of Motion (RoM)*

One-way ANOVA repeated measures showed that the variation in compression garments imposed significant e ffects on the ROM of head flexion (*p* = 0.014, partial η2 = 0.169), trunk lateral bending (*p* = 0.024, partial η2 = 0.152), left shoulder flexion (*p* = 0.041, partial η2 = 0.152), right shoulder rotation (*p* = 0.048, partial η2 = 0.128) and left knee flexion (*p* = 0.003, partial η2 = 0.212). Post hoc pairwise comparison showed that the top condition significantly reduced the head flexion (*p* = 0.037; d = 0.503; 1.346, 95% CI 0.376 to 2.315) and trunk lateral bending (*p* = 0.042; d = 0.487; 1.039, 95% CI 0.041 to 2.036) ROM compared with the control-pre condition (Table 4). Similarly, the full condition significantly reduced head flexion (*p* = 0.009; d = 0.650; 1.346, 95% CI 0.376 to 2.315) and trunk lateral bending (*p* = 0.028; d = 0.532; 1.446, 95% CI 0.173 to 2.718) ROM compared to the control-pre condition.

**Table 4.** Descriptive statistics and one-way ANOVA repeated measures outcome of the range of motion of head and trunk in di fferent compression garment conditions.

FL/EX: flexion/extension; \* significant difference (*p* < 0.05) using one-way ANOVA repeated measures; g Greenhouse–Geisser correction to adjust the lack of sphericity; a and A denote *p* < 0.05 and *p* < 0.0125 than the control-pre condition.

Compared to that of the bottom condition, both the top (*p* = 0.01; d = 0.642; 3.422, 95% CI 0.929 to 5.915) and full (*p* = 0.003; d = 0.778; 3.530, 95% CI 1.405 to 5.655) conditions significantly reduced the ROM of the left shoulder flexion, while the top condition had significantly larger right shoulder rotation compared with the control-pre (*p* = 0.013; d = 0.611; 38.316, 95% CI −8.98 to 67.65) and bottom (*p* = 0.041; d = 0.491; 23.028, 95% CI 1.08 to 44.976) conditions (Table 5). The control-pre condition had significantly larger left knee flexion ROM than the bottom (*p* = 0.026; d = 0.539; 2.605, 95% CI 0.345 to 4.864) and full (*p* = 0.002; d = 0.804; 2.908, 95% CI 1.214 to 4.602) conditions. Similarly, the top condition had a significantly larger left knee flexion ROM than the bottom (*p* = 0.044; d = 0.482; 2.047, 95% CI 0.059 to 4.035) and full (*p* = 0.018; d = 0.585; 2.351, 95% CI, 0.469 to 4.232) conditions (Table 6).

**Table 5.** Descriptive statistics and one-way ANOVA repeated measures outcome of the range of motion of the upper limb in different compression garment conditions.

FL/EX: flexion/extension; AB/AD: abduction/adduction; RA/UL: Radial/Ulnar deviation; \* significant difference (*p* < 0.05) using one-way ANOVA repeated measures; g Greenhouse–Geisser correction to adjust the lack of sphericity; a denotes *p* < 0.05 than the control-pre condition; b and B denote *p* < 0.05 and *p* < 0.0125 than the top condition; C denotes *p* < 0.0125 than the bottom condition.

**Table 6.** Descriptive statistics and one-way ANOVA repeated measures outcome of the range of motion of the lower limb in different compression garment conditions.

FL/EX: flexion/extension; AB/AD: abduction/adduction; EV/IV: eversion/inversion; PL/DO: plantarflexion/ dorsiflexion; \* significant difference (*p* < 0.05) using one-way ANOVA repeated measures; g Greenhouse–Geisser correction to adjust the lack of sphericity; a and A denote *p* < 0.05 and *p* < 0.0125 than the control-pre condition; b denotes *p* < 0.05 than the top condition.


*Article* **Success History-Based Adaptive Di**ff**erential Evolution Using Turning-Based Mutation**

#### **Xingping Sun, Linsheng Jiang, Yong Shen \*, Hongwei Kang \* and Qingyi Chen**

School of Software, Yunnan University, Kunming 650000, China<EMAIL_ADDRESS>(X.S<EMAIL_ADDRESS>(L.J<EMAIL_ADDRESS>(Q.C.)

**\*** Correspondence<EMAIL_ADDRESS>(Y.S<EMAIL_ADDRESS>(H.K.)

Received: 24 August 2020; Accepted: 7 September 2020; Published: 11 September 2020

**Abstract:** Single objective optimization algorithms are the foundation of establishing more complex methods, like constrained optimization, niching andmulti-objective algorithms. Therefore, improvements to single objective optimization algorithms are important because they can impact other domains as well. This paper proposes a method using turning-based mutation that is aimed to solve the problem of premature convergence of algorithms based on SHADE (Success-History based Adaptive Differential Evolution) in high dimensional search space. The proposed method is tested on the Single Objective Bound Constrained Numerical Optimization (CEC2020) benchmark sets in 5, 10, 15, and 20 dimensions for all SHADE, L-SHADE, and jSO algorithms. The effectiveness of the method is verified by population diversity measure and population clustering analysis. In addition, the new versions (Tb-SHADE, TbL-SHADE and Tb-jSO) using the proposed turning-based mutation get apparently better optimization results than the original algorithms (SHADE, L-SHADE, and jSO) as well as the advanced DISH and the jDE100 algorithms in 10, 15, and 20 dimensional functions, but only have advantages compared with the advanced j2020 algorithm in 5 dimensional functions.

**Keywords:** single objective optimization; differential evolution; success-history; premature convergence; turning-based mutation