*Article* **Huaier Polysaccharide Interrupts PRV Infection via Reducing Virus Adsorption and Entry**

**Changchao Huan 1,2,3 , Jingting Yao 1,2,3, Weiyin Xu 1,2,3, Wei Zhang 1,2,3, Ziyan Zhou 1,2,3, Haochun Pan 1,2,3 and Song Gao 1,2,3,\***

**Abstract:** A pseudorabies virus (PRV) novel virulent variant outbreak occurred in China in 2011. However, little is known about PRV prevention and treatment. Huaier polysaccharide has been used to treat some solid cancers, although its antiviral activity has not been reported. Our study confirmed that the polysaccharide can effectively inhibit infection of PRV XJ5 in PK15 cells. It acted in a dose-dependent manner when blocking virus adsorption and entry into PK15 cells. Moreover, it suppressed PRV replication in PK15 cells. In addition, the results suggest that Huaier polysaccharide plays a role in treating PRV XJ5 infection by directly inactivating PRV XJ5. In conclusion, Huaier polysaccharide might be a novel therapeutic agent for preventing and controlling PRV infection.

**Keywords:** Huaier polysaccharide; pseudorabies virus; antiviral; infection

### **1. Introduction**

Pseudorabies virus (PRV) has been regarded as one of the major causative agents for fatal losses in the swine industry worldwide [1,2]. PRV is a double-stranded linear DNA and enveloped virus that belongs to the subfamily alphaherpesvirinae of the family Herpesviridae [3,4]. PRV can infect various species of mammals, such as swine, wild boars [5], ruminants (e.g., goat, sheep, and cattle) [6,7], carnivores (e.g., hunting dogs, minks, and foxes) [8,9], and rodents. Swine are the unique natural host and reservoir of PRV [10].  Pregnant sows infected with the virus exhibit abortions, stillbirths, and mummified fetuses and are often infertile, with a high rate of rebelliousness [11]. The Bartha-K61 strain is still one of the most widely used live virus vaccines to confront PRV infections worldwide [4]. Pseudorabies (PR) incidence was first reported among cats in 1947 in China; thereafter, PR incidence was reported in other species, particularly in the pig industry [12]. Before 2011, the Bartha-K61 vaccine could prevent and control PR in China; however, the emergence of several variant strains led to the new pseudorabies epidemic among immunized swine [13]. PRV variants exhibit high sequence divergence compared with classical PRV strains [14]. The Chinese triple-gene-deleted (gE/gI/TK) vaccine and TK/gG-deleted vaccine have been extensively used to prevent PR in the Chinese pig population. However, the protection efficacy of the two vaccines has not been reported [3]. More importantly, PRV could infect humans, and it was isolated from an acute human encephalitis case [15–17]. Therefore, identifying new preventive and therapeutic measures for controlling PR, in addition to vaccines, is imperative.

**Citation:** Huan, C.; Yao, J.; Xu, W.; Zhang, W.; Zhou, Z.; Pan, H.; Gao, S. Huaier Polysaccharide Interrupts PRV Infection via Reducing Virus Adsorption and Entry. *Viruses* **2022**, *14*, 745. https://doi.org/10.3390/ v14040745

Academic Editors: Yan-Dong Tang and Xiangdong Li

Received: 17 February 2022 Accepted: 29 March 2022 Published: 1 April 2022

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**Copyright:** © 2022 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 application of traditional Chinese medicine to treat diseases can be traced back to 200 Anno Domini (AD) [18]. Growing evidence suggests that the traditional Chinese medicine offers numerous compounds having antiviral activities [19]. Trametes robiniophila murr (Huaier), as a traditional Chinese medicine, has been used to treat many diseases for more than one thousand years [20]. Huaier extract can regulate DNA-dependent transcription and the cellular response to hypoxia during breast cancer development and progression [21]; it can also enhance the host immunity and induce apoptosis in breast cancer cells [22]. In addition, studies have confirmed that Huaier granule exhibits good safety in clinical antitumor therapies [23]. In particular, it was considered as a promising adjuvant for the treatment of breast cancer when used in combination with conventional treatment [24]. Huaier polysaccharide also exhibits excellent safety, therapeutic efficacy, and minimal side effects in the clinical treatment of lung cancer, liver cancer, and other solid tumors [25]. However, the effect of Huaier polysaccharide on PRV infection has not been investigated. In this study, we evaluated the mechanism of Huaier polysaccharide in PRV infection; our findings suggested that Huaier polysaccharide inhibits PRV XJ5 adsorption, entry, and replication and thus can dampen PRV infection.

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

### *2.1. Cells and Viruses*

Pig kidney (PK15) cells and African green monkey kidney (Vero) cells were stored at the Yangzhou University Infectious Diseases Laboratory and grown in monolayers at 37 ◦C under 5% CO2 conditions. PK15 cells and Vero cells were cultured in Dulbecco's modified Eagle medium (DMEM) supplemented with 5% and 6% fetal bovine serum (FBS; Lonsera, Uruguay), 100 units/mL penicillin, 100 µg/mL streptomycin sulfate, and fungizone.

PRV XJ5, PRV NT, and PRV Ra were stored at the Yangzhou University Infectious Diseases Laboratory. We used 0.1 multiplicity of infection (MOI) of PRV-infected PK15 cells in all experiments.

### *2.2. Reagents and Antibodies*

In all subsequent experiments, Huaier polysaccharide (Yangling Ciyuan Biotechnology Co., Ltd., Xian, China) was diluted with PBS to prepare stock solutions of 50 mg/mL and stored at −20 ◦C. The antibodies for PRV gB were generated by immunization of mice with purified recombinant gB in our laboratory. Actin Ab—T0022 was procured from Affinity Bioscience (Beijing, China). FITC-conjugated goat anti-pig IgG antibody combining PRV-positive sera was purchased from Sigma-Aldrich (St. Louis, MO, USA). DAPI (#C1006) was purchased from Beyotime Biotechnology (Shanghai, China).

### *2.3. Cell-Based Infectivity Assays*

### 2.3.1. Cells Viability Assay

Cell viability was evaluated with Enhanced Cell Counting Kit-8 (CCK-8) assays, according to the manufacturer's instructions (Beyotime Biotechnology, Shanghai, China). For cell viability assays, cells were seeded at 5000 per well into 96-well plates. On the next day, the medium was changed to DMEM/5% FBS supplemented with different concentrations of Huaier polysaccharide for 24 and 36 h. CCK-8 (10 µL) was then added to each well, and the cells were incubated for 1 h at 37 ◦C. The absorbance was detected at 450 nm with a microplate reader (Bio-rad, Hercules, CA, USA).

### 2.3.2. General Effect of Huaier Polysaccharide on PRV Infection

Huaier polysaccharide was added at 37 ◦C for 24 h to verify its effect on PRV infection. DMEM containing 5% FBS was used to grow the PK15 cells in a 37 ◦C/5% CO2 incubator. The PK15 cells were seeded in a 6-well plate, with a density of 5 × 105 cells per well. When the cells grew to approximately 8.5 × 105 , the PK15 cells were infected with PRV XJ5 (MOI = 0.1) for 1 h. At 1 h post infection (h.p.i.), DMEM was removed, and the cells were washed with PBS. The cells were incubated with different concentrations (25, 50, 100, or

200 µg/mL) of Huaier polysaccharide in 2% FBS DMEM (2% DMEM). On the next day, the cells were collected to determine PRV XJ5 protein expression through Western blotting and indirect Immunofluorescent Assay (IFA), intracellular viral DNA copies were analyzed by qRT-PCR after 24 h at 37 ◦C, and cell supernatants were used to measure the virus titer through TCID50 assay.

### 2.3.3. Exploration of Huaier Polysaccharide's Effect on PRV Adsorption and Entry

Huaier polysaccharide was added at 4 ◦C for 1 h and at 37 ◦C for 1 h to verify its effect on PRV adsorption and entry. The PK15 cells were cultured using 1 mL of DMEM without FBS to dilute Huaier polysaccharide to 25, 50, 100, 200 µg/mL and then infected with PRV XJ5 (MOI = 0.1) at 4 ◦C for 1 h. Thereafter, the cells were washed thrice with cold PBS and incubated in 2% DMEM containing appropriate concentrations of Huaier polysaccharide for 1 h at 37 ◦C. Then, cells were washed with citric acid to remove extracellular virus and again washed with PBS. Adding 2 mL 2% DMEM, intracellular viral proteins were detected through Western blotting and IFA, and the contained viruses' cell supernatants were used to measure virus titers by using the TCID50 assay at 24 h.p.i. Intracellular viral DNA copies were analyzed by qRT-PCR after 1 h at 37 ◦C.

### 2.3.4. General Effect of Huaier Polysaccharide on PRV Adsorption

Huaier polysaccharide was added at 4 ◦C for 1 h to verify its effect on PRV adsorption. The PK15 cells were digested with 0.25% trypsin and diluted with DMEM containing 5% FBS, dripped onto a 6-well plate at a concentration of 5 × 105 cells/well in a 37 ◦C/5% CO2 incubator. When the cells grew to approximately 70–80%, the cells were treated with different concentrations of Huaier polysaccharide and infected with PRV XJ5 (MOI = 0.1) at 4 ◦C for 1 h. The cells were cleaned thrice with cold PBS and maintained in 2% DMEM for 24 h. Intracellular viral proteins were detected through Western blotting and IFA. Cell supernatants were used to measure virus titers through TCID50 assay. Viral DNA copies of adsorption were analyzed by qRT-PCR after 1 h at 4 ◦C.

### 2.3.5. Exploration of Huaier Polysaccharide's Effect on PRV Entry

Huaier polysaccharide was added at 37 ◦C for 1 h to verify its effect on PRV entry. The PK15 cells were infected with PRV XJ5 (MOI = 0.1) at 4 ◦C for 1 h without Huaier polysaccharide. The infected cells were then washed with cold PBS three times and cultured in 2% DMEM containing different concentrations of Huaier polysaccharide at 37 ◦C for 1 h. The cells were washed thrice with citric acid and PBS. Then, cells were cultured in 2% DMEM without Huaier polysaccharide. Intracellular viral proteins were detected through Western blotting and IFA after 24 h at 37 ◦C. Cell supernatants were used to measure the virus titer through TCID50 assay. Intracellular viral DNA copies were analyzed by qRT-PCR after 1 h at 37 ◦C. The above experiments included three independent experiments.

### 2.3.6. Effect of Huaier Polysaccharide on PRV Replication

Huaier polysaccharide was added at 37 ◦C for 3 h or 5 h to verify its effect on PRV replication. When the PK15 cells grew to approximately 70–80%, the cells were incubated with PRV XJ5 (MOI = 0.1) for 1 h at 37 ◦C and under 5% CO2. After the cells were washed thrice with PBS, the cells were incubated with 2% DMEM containing 25, 50, 100, and 200 µg/mL Huaier polysaccharide. At 4 h.p.i. and 6 h.p.i., the cells were collected to determine PRV-related protein expression through Western blotting and viral DNA copies were analyzed by qRT-PCR. The above experiments included three independent experiments.

### 2.3.7. Effect of Huaier Polysaccharide on PRV XJ5

PRV XJ5 (MOI = 0.1) was pretreated with different concentrations of Huaier polysaccharide (25, 50, 100, and 200 µg/mL) for 1 h at 37 ◦C. Then, the cells were washed thrice with PBS. We co-incubated PRV XJ5 with cells as described above. At 24 h.p.i, the cells were collected to analyzed the expression of PRV-related proteins through Western blotting and

viral DNA copies were analyzed by qRT-PCR. PRV XJ5 (MOI = 0.1) was pretreated with different concentrations of Huaier polysaccharide (100 or 200 µg/mL) for 1 h at 37 ◦C with 100 µL. A transmission electron microscope was used to determine the real destruction of the virions. The above experiments included three independent experiments.

### 2.3.8. Western Blotting

Cell lysis buffer (Beyotime Biotechnology, Shanghai, China) was used to lyse the cells. The lysed cells were placed in a 1.5 mL EP tube (Eppendorf Micro Test Tubes), to which phosphorylated protease inhibitor and phenylmethanesulfonyl fluoride (PMSF) were added. The concentration of cell lysate protein was determined according to the manufacturer's instructions for the BCA protein quantification kit. Western blotting was performed following the previously described methods [26,27]. The membranes were incubated with PRV gB or actin primary antibodies at 4 ◦C overnight. On the next day, the membranes were incubated with goat anti-rat secondary antibody (Beyotime Biotechnology, Shanghai, China) at room temperature for 2 h.

### 2.3.9. Virus Titer Assays

The TCID50 assay was used to evaluate virus titers. After trypsinization of Vero cells, these cells were diluted with DMEM containing 6% FBS and added dropwise to a 96-well plate at a concentration of 2 × 103 cells/well. Then, the cells were placed in a 37 ◦C/5% CO2 incubator until the cells adhered to the wall. After the monolayer was in the logarithmic growth phase (around 16 h), cells were washed three times with PBS, absorbing the remaining liquid. The cells were inoculated with serially diluted viruses (10−1–10−7 fold) for 1 h at 37 ◦C and eight replicates for each concentration were prepared. Then, 250 µL of maintenance medium was added to each well. At 72 h.p.i., we observed the CPE. Finally, CPE were counted to calculate the TCID50 by using the Reed–Muench method.

### 2.3.10. Indirect Immunofluorescent Assay

After the PK15 cells were infected with PRV for 24 h, the supernatant was discarded, and the cells were washed thrice with PBS. Then, 4% paraformaldehyde that could cover the cell surface was added, and the cells were fixed at 37 ◦C for 15 min. Thereafter, 0.1% TritonX-100 was used to penetrate the cells for 10 min, and the cells were washed thrice with PBS. The cells were incubated with 5% BSA blocking solution at 37 ◦C for 2 h or 4 ◦C overnight. The primary antibody PRV pig-positive serum was diluted to 1:200 and incubated at 37 ◦C for 2 h, washed three times with PBST, and incubated with FITCconjugated goat anti-porcine IgG antibody (Sigma-Aldrich, St. Louis, MO, USA) at 37 ◦C for 1 h; finally, the cells were stained with DAPI for 5 min. The cells were observed under a fluorescence microscope (LAICA, DMi8) with 488nm. All the images were captured at 100× magnification. The fluorescence density of FITC was calculated by Image J (LOCI, Madison, WI, USA).

### 2.3.11. DNA Extraction and qRT-PCR

Briefly, we extracted DNA for each sample; 10% 92 µL SDS and 8 µL Proteinase K were added to samples and incubated at 58 ◦C for 1 h, followed by adding 600 µL phenol:chloroform (1:1, *v*/*v*) to each sample and vortexing, followed by centrifugation for 15 min. Then, 400 µL supernatant was collected and mixed with 800 µL anhydrous ethanol, and kept at −20 ◦C for 30 min. All samples were centrifuged at 4 ◦C for 15 min, and the precipitate was washed with anhydrous ethanol. The DNA was dissolved by ddH2O and incubated at 37 ◦C for 30 min. Primers used for qRT-PCR are as follows: gB94-F: 5 0 -ACAAGTTCAAGGCCCACATCTAC-30 , gB94-R: 50 -GTCCGTGAAGCGGTTCGTGAT-30 .

### 2.3.12. Electron Microscopy

First, we took a small amount of virus liquid or virus containing Huaier polysaccharide (100 or 200 µg/mL) droplets on the copper mesh and used filter paper to absorb excess virus solution, added 2% phosphotungstic acid dropwise on the copper mesh, used filter paper to absorb excess dye, placed the sample in a drying oven, left it to dry, and used a transmission electron microscope (Tecnai 12; Philips, Eindhoven, The Netherlands) to observe it.

### 2.3.13. Flow Cytometry Assay

For apoptosis assays, PK15 cells were seeded at 1.2 × 106 per well into 6-well plates. On the next day, the medium was changed to 2% DMEM supplemented with Huaier polysaccharide for 24 h. According to the manufacturer's instructions, PI staining was performed with a Cell Apoptosis Kit with PI (Beyotime Biotechnology, Shanghai, China). The percentage of apoptosis cells was measured by flow cytometry on a CytoFLEX instrument (Beckman Coulter, Inc. Brea, CA, USA).

### 2.3.14. Statistical Analysis

All the experiments were independently repeated at least three times, and all data are presented as the mean ± SD based on three independent experiments. The data were analyzed using GraphPad Prism software (GraphPad Software, SanDiego, CA, USA). One-way ANOVA, as well as Duncan's multiple range test, was utilized to analyze differences between groups. At a *p* value of <0.05, the differences were considered to be statistically significant.

### **3. Results**

### *3.1. Huaier Polysaccharide Has No Inhibitory Effect on PK15 Cells' Growth and Apoptosis*

According to a previous study [22], results showed that the vitality of breast cancer cells is more significantly inhibited by Huaier aqueous extract. To explore the effect of Huaier polysaccharide on PK15 cells, we checked the cells' growth using the Enhanced Cell Counting Kit-8. Figure 1A,B reveal that Huaier polysaccharide had no effect on PK15 cells' growth at 24 h.p.i and 36 h.p.i. The results show that cell viability is not affected by Huaier polysaccharide (25, 50, 100, and 200 µg/mL). In addition, we found that Huaier polysaccharide (200 µg/mL) could not induce apoptosis in PK15 cells (Figure 1C). *Viruses* **2022**, *13*, x FOR PEER REVIEW 6 of 15

**Figure 1.** Huaier polysaccharide has no inhibitory effect on PK15 cells' growth and apoptosis. (**A**,**B**)

of PK15 cells treated or not with Huaier polysaccharide (200 mg/mL) was checked by flow cytometry. Significance was analyzed using the one-tailed Student's *t*-test. Data are shown as mean ± SD

Figure 1 reveals that Huaier polysaccharide had no effect on PK15 cells' growth. To investigate the role of Huaier polysaccharides in preventing PRV XJ5 infection, PK15 cells were treated as described in Section 2.3.2. PRV XJ5 (MOI = 0.1) infection resulted in an obvious cytopathic effect (CPE) in the PK15 cells (Figure 2A), which could be inhibited by Huaier polysaccharide, especially at the concentrations of 100 and 200 μg/mL. The antiviral effect of Huaier polysaccharide against PRV XJ5 was further demonstrated through Western blot analysis. gB is a protein that is essential for PRV replication [28]. Thus, we assessed the change in gB expression. The results indicated that the PRV gB protein expression level was reduced after Huaier polysaccharide treatment, with an inhibition rate of 73–94%, at 100 and 200 μg/mL concentrations (Figure 2B,C). The supernatant of the infected PK15 cells was collected to determine the viral titer in terms of the 50% tissue culture infective dose (TCID50). As expected, TCID50 analysis showed that the Huaier polysaccharide treatment reduced the production of virions; 200 μg/mL Huaier polysaccharide displayed the inhibition rate of 99.9% (Figure 2D). Furthermore, the immunofluorescent assay (IFA) confirmed that Huaier polysaccharide treatment inhibited PRV XJ5 infection in a dose-dependent manner, with the inhibition rate of 13% (25 μg/mL)–99.6% (200 μg/mL) (Figure 2E). qRT-PCR analysis indicated that Huaier polysaccharide decreased the viral DNA copies of PRV XJ5 (Figure 2F). In addition, we explored the effect of Huaier polysaccharide on PRV NT and PRV Ra by qRT-PCR. qRT-PCR analysis revealed that Huaier polysaccharide decreased the viral DNA copies of PRV NT (Figure 2G) and PRV Ra (Figure 2H). The purpose of the infective assay experiment was to emphasize that

**Figure 1.** *Cont.*

based on three independent experiments. "ns" is not significant.

*3.2. Huaier Polysaccharide Inhibis PRV XJ5 Infection in PK15 Cells*

**Figure 1.** Huaier polysaccharide has no inhibitory effect on PK15 cells' growth and apoptosis. (**A**,**B**) PK15 cells were pretreated with different concentrations of Huaier polysaccharide at 37 °C for 24 h or 36 h. Cell viability of PK15 cells was assessed with CCK-8 cell counting assays. (**C**) The apoptosis of PK15 cells treated or not with Huaier polysaccharide (200 mg/mL) was checked by flow cytometry. Significance was analyzed using the one-tailed Student's *t*-test. Data are shown as mean ± SD based on three independent experiments. "ns" is not significant. **Figure 1.** Huaier polysaccharide has no inhibitory effect on PK15 cells' growth and apoptosis. (**A**,**B**) PK15 cells were pretreated with different concentrations of Huaier polysaccharide at 37 ◦C for 24 h or 36 h. Cell viability of PK15 cells was assessed with CCK-8 cell counting assays. (**C**) The apoptosis of PK15 cells treated or not with Huaier polysaccharide (200 mg/mL) was checked by flow cytometry. Significance was analyzed using the one-tailed Student's *t*-test. Data are shown as mean ± SD based on three independent experiments. "ns" is not significant.

#### *3.2. Huaier Polysaccharide Inhibis PRV XJ5 Infection in PK15 Cells 3.2. Huaier Polysaccharide Inhibis PRV XJ5 Infection in PK15 Cells*

Figure 1 reveals that Huaier polysaccharide had no effect on PK15 cells' growth. To investigate the role of Huaier polysaccharides in preventing PRV XJ5 infection, PK15 cells were treated as described in Section 2.3.2. PRV XJ5 (MOI = 0.1) infection resulted in an obvious cytopathic effect (CPE) in the PK15 cells (Figure 2A), which could be inhibited by Huaier polysaccharide, especially at the concentrations of 100 and 200 μg/mL. The antiviral effect of Huaier polysaccharide against PRV XJ5 was further demonstrated through Western blot analysis. gB is a protein that is essential for PRV replication [28]. Thus, we assessed the change in gB expression. The results indicated that the PRV gB protein expression level was reduced after Huaier polysaccharide treatment, with an inhibition rate of 73–94%, at 100 and 200 μg/mL concentrations (Figure 2B,C). The supernatant of the infected PK15 cells was collected to determine the viral titer in terms of the 50% tissue culture infective dose (TCID50). As expected, TCID50 analysis showed that the Huaier polysaccharide treatment reduced the production of virions; 200 μg/mL Huaier polysaccharide displayed the inhibition rate of 99.9% (Figure 2D). Furthermore, the immunofluorescent assay (IFA) confirmed that Huaier polysaccharide treatment inhibited PRV XJ5 infection in a dose-dependent manner, with the inhibition rate of 13% (25 μg/mL)–99.6% (200 μg/mL) (Figure 2E). qRT-PCR analysis indicated that Huaier polysaccharide decreased the viral DNA copies of PRV XJ5 (Figure 2F). In addition, we explored the effect of Huaier polysaccharide on PRV NT and PRV Ra by qRT-PCR. qRT-PCR analysis revealed that Huaier polysaccharide decreased the viral DNA copies of PRV NT (Figure 2G) and PRV Ra (Figure 2H). The purpose of the infective assay experiment was to emphasize that Figure 1 reveals that Huaier polysaccharide had no effect on PK15 cells' growth. To investigate the role of Huaier polysaccharides in preventing PRV XJ5 infection, PK15 cells were treated as described in Section 2.3.2. PRV XJ5 (MOI = 0.1) infection resulted in an obvious cytopathic effect (CPE) in the PK15 cells (Figure 2A), which could be inhibited by Huaier polysaccharide, especially at the concentrations of 100 and 200 µg/mL. The antiviral effect of Huaier polysaccharide against PRV XJ5 was further demonstrated through Western blot analysis. gB is a protein that is essential for PRV replication [28]. Thus, we assessed the change in gB expression. The results indicated that the PRV gB protein expression level was reduced after Huaier polysaccharide treatment, with an inhibition rate of 73–94%, at 100 and 200 µg/mL concentrations (Figure 2B,C). The supernatant of the infected PK15 cells was collected to determine the viral titer in terms of the 50% tissue culture infective dose (TCID50). As expected, TCID50 analysis showed that the Huaier polysaccharide treatment reduced the production of virions; 200 µg/mL Huaier polysaccharide displayed the inhibition rate of 99.9% (Figure 2D). Furthermore, the immunofluorescent assay (IFA) confirmed that Huaier polysaccharide treatment inhibited PRV XJ5 infection in a dose-dependent manner, with the inhibition rate of 13% (25 µg/mL)–99.6% (200 µg/mL) (Figure 2E). qRT-PCR analysis indicated that Huaier polysaccharide decreased the viral DNA copies of PRV XJ5 (Figure 2F). In addition, we explored the effect of Huaier polysaccharide on PRV NT and PRV Ra by qRT-PCR. qRT-PCR analysis revealed that Huaier polysaccharide decreased the viral DNA copies of PRV NT (Figure 2G) and PRV Ra (Figure 2H). The purpose of the infective assay experiment was to emphasize that Huaier polysaccharide has a significant role in the whole process of PRV XJ5 infection of PK15 cells.

PK15 cells.

Huaier polysaccharide has a significant role in the whole process of PRV XJ5 infection of

**Figure 2.** Huaier polysaccharide inhibits PRV XJ5 infection in PK15 cells. (**A**) Infected cells treated with 25, 50, 100, or 200 μg/mL Huaier polysaccharide for 12 or 24 h, showing changes in cell morphology. (**B**) gB and actin protein expression was determined through Western blot assay. (**C**) The relative intensity of intracellular gB to that of actin. Data are presented as means from three independent statistical experiments. The relative intensities of protein were quantified using Image J. Significance was analyzed using a one-tailed Student's *t*-test. (**D**) The viral titers were evaluated through 50% tissue culture infective dose (TCID50), and (**E**) immunofluorescent assay (IFA) for internalized virus was performed. (**F**–**H**) PRV gB were assessed with qRT-PCR analysis in PK15 cells treated with Huaier polysaccharide (25, 50, 100, and 200 μg/mL) at 24 h.p.i. \*\*\* *p* = 0.0003, \*\*\*\* *p* < 0.0001. Data are shown as mean ± SD based on three independent experiments. **Figure 2.** Huaier polysaccharide inhibits PRV XJ5 infection in PK15 cells. (**A**) Infected cells treated with 25, 50, 100, or 200 µg/mL Huaier polysaccharide for 12 or 24 h, showing changes in cell morphology. (**B**) gB and actin protein expression was determined through Western blot assay. (**C**) The relative intensity of intracellular gB to that of actin. Data are presented as means from three independent statistical experiments. The relative intensities of protein were quantified using Image J. Significance was analyzed using a one-tailed Student's *t*-test. (**D**) The viral titers were evaluated through 50% tissue culture infective dose (TCID50), and (**E**) immunofluorescent assay (IFA) for internalized virus was performed. (**F**–**H**) PRV gB were assessed with qRT-PCR analysis in PK15 cells treated with Huaier polysaccharide (25, 50, 100, and 200 µg/mL) at 24 h.p.i. \*\*\* *p* = 0.0003, \*\*\*\* *p* < 0.0001. Data are shown as mean ± SD based on three independent experiments.

### *3.3. Huaier Polysaccharide Decreased the Adsorption and Entry of PRV XJ5* The PRV life cycle comprises adsorption, entry, viral DNA replication, virion mor-*3.3. Huaier Polysaccharide Decreased the Adsorption and Entry of PRV XJ5*

phogenesis, and viral egress [12,26,27]. In order to further explore the role of Huaier polysaccharides in these processes of PRV XJ5 infected PK15 cells, we firstly studied the effect of Huaier polysaccharide on virus adsorption and entry. The PK15 cells were infected with PRV XJ5 (MOI = 0.1) according to the method described in Section 2.3.3. gB protein was reduced, especially in the presence of 50, 100, and 200 μg/mL Huaier polysaccharide, with inhibition rates of 51%, 75%, and 87%, respectively (Figure 3A,B). Simultaneously, the supernatant was collected, and the viral titer was determined at 24 h.p.i. The results indicated that the PRV XJ5 viral titer was decreased significantly in the cells treated with Huaier polysaccharide (Figure 3C). Furthermore, the IFA demonstrated that Huaier polysaccharide decreased the numbers of cells infected with PRV XJ5 by approximately 48– 99.1% (Figure 3D). In addition, we collected cells to quantify the viral DNA copies by qRT-PCR after cells were washed with citric acid and PBS to remove uninternalized virus. qRT-The PRV life cycle comprises adsorption, entry, viral DNA replication, virion morphogenesis, and viral egress [12,26,27]. In order to further explore the role of Huaier polysaccharides in these processes of PRV XJ5 infected PK15 cells, we firstly studied the effect of Huaier polysaccharide on virus adsorption and entry. The PK15 cells were infected with PRV XJ5 (MOI = 0.1) according to the method described in Section 2.3.3. gB protein was reduced, especially in the presence of 50, 100, and 200 µg/mL Huaier polysaccharide, with inhibition rates of 51%, 75%, and 87%, respectively (Figure 3A,B). Simultaneously, the supernatant was collected, and the viral titer was determined at 24 h.p.i. The results indicated that the PRV XJ5 viral titer was decreased significantly in the cells treated with Huaier polysaccharide (Figure 3C). Furthermore, the IFA demonstrated that Huaier polysaccharide decreased the numbers of cells infected with PRV XJ5 by approximately 48–99.1% (Figure 3D). In addition, we collected cells to quantify the viral DNA copies by qRT-PCR after cells were washed with citric acid and PBS to remove uninternalized virus. qRT-PCR analysis indicated that Huaier polysaccharide decreased viral adsorption and entry in a dose-dependent manner (Figure 3E).

PCR analysis indicated that Huaier polysaccharide decreased viral adsorption and entry

in a dose-dependent manner (Figure 3E).

**Figure 3.** Huaier polysaccharide reduced PRV XJ5 adsorption and entry. The cells were treated according to the method described in Section 2.3.3. (**A**) Western blot showing changes in gB and actin expression. (**B**) The intensity band ratio of intracellular gB to actin. Data are presented as means from three independent statistical experiments. The intensities of protein bands were quantified using Image J. Significance was analyzed using one-tailed Student's *t*-test. \*\*\*\* *p* < 0.0001. (**C**) The viral titers were evaluated through TCID50 assay. (**D**) The numbers of cells infected with PRV were observed through IFA. (**E**) The virus DNA copies were observed through qRT-PCR after cells were washed with citric acid and PBS to remove uninternalized virus. \*\* *p* = 0.003, \*\*\*\* *p* < 0.0001. Data are shown as mean ± SD based on three independent experiments. **Figure 3.** Huaier polysaccharide reduced PRV XJ5 adsorption and entry. The cells were treated according to the method described in Section 2.3.3. (**A**) Western blot showing changes in gB and actin expression. (**B**) The intensity band ratio of intracellular gB to actin. Data are presented as means from three independent statistical experiments. The intensities of protein bands were quantified using Image J. Significance was analyzed using one-tailed Student's *t*-test. \*\*\*\* *p* < 0.0001. (**C**) The viral titers were evaluated through TCID50 assay. (**D**) The numbers of cells infected with PRV were observed through IFA. (**E**) The virus DNA copies were observed through qRT-PCR after cells were washed with citric acid and PBS to remove uninternalized virus. \*\* *p* = 0.003, \*\*\*\* *p* < 0.0001. Data are shown as mean ± SD based on three independent experiments.

### 3.3.1. Huaier Polysaccharide Attenuates PRV Adsorption 3.3.1. Huaier Polysaccharide Attenuates PRV Adsorption

This experiment emphasized PRV XJ5 adsorption. The adsorption of PRV occurred for 1 h at 4 °C. We performed the experiment to study virus adsorption, as described in Section 2.3.4. Figure 4A,B reveal that the Huaier polysaccharide treatment reduced PRV gB protein expression levels, with the inhibition rate of 86–99%, compared with those in untreated cells. To further assess the effect of Huaier polysaccharide on PRV XJ5 adsorption, inhibition of virus adsorption was observed through TCID50 assay in the cell supernatant (Figure 4C), and the IFA assay was used to observe the virus-infected cells (Figure 4D). In addition, we collected cells to quantify the viral DNA copies by qRT-PCR after cells were washed with PBS to remove unabsorbed virus. qRT-PCR analysis indicated that Huaier polysaccharide decreased viral adsorption (Figure 4E). The results indicated that Huaier polysaccharide attenuated virus adsorption by the PK15 cells. This experiment emphasized PRV XJ5 adsorption. The adsorption of PRV occurred for 1 h at 4 ◦C. We performed the experiment to study virus adsorption, as described in Section 2.3.4. Figure 4A,B reveal that the Huaier polysaccharide treatment reduced PRV gB protein expression levels, with the inhibition rate of 86–99%, compared with those in untreated cells. To further assess the effect of Huaier polysaccharide on PRV XJ5 adsorption, inhibition of virus adsorption was observed through TCID50 assay in the cell supernatant (Figure 4C), and the IFA assay was used to observe the virus-infected cells (Figure 4D). In addition, we collected cells to quantify the viral DNA copies by qRT-PCR after cells were washed with PBS to remove unabsorbed virus. qRT-PCR analysis indicated that Huaier polysaccharide decreased viral adsorption (Figure 4E). The results indicated that Huaier polysaccharide attenuated virus adsorption by the PK15 cells.

#### 3.3.2. Huaier Polysaccharide Influences PRV Entry into PK15 Cells 3.3.2. Huaier Polysaccharide Influences PRV Entry into PK15 Cells

This experiment explored separately the entry of PRV at 1 h and 37 °C. We performed the experiment to study PRV entry according to the method described in Section 2.3.5. Western blot analysis showed that Huaier polysaccharide decreased the expression of PRV gB, with the PRV entry inhibition rate being 13–47% (Figure 5A,B). The TCID50 assay revealed that the PRV XJ5 titers were decreased (Figure 5C). The cells infected with PRV were examined through IFA (Figure 5D). In addition, we collected cells to quantify the viral DNA copies by qRT-PCR after cells were washed with citric acid and PBS to remove uninternalized virus. qRT-PCR analysis indicated that Huaier polysaccharide decreased viral entry in a dose-dependent manner (Figure 5E). The results confirmed that Huaier polysaccharide influences PRV XJ5 entry. However, the inhibition rate of PRV entry by Huaier polysaccharide was lower than the observed inhibition rate of PRV adsorption. The results indicate that Huaier polysaccharide might have a prominent role in PRV ad-This experiment explored separately the entry of PRV at 1 h and 37 ◦C. We performed the experiment to study PRV entry according to the method described in Section 2.3.5. Western blot analysis showed that Huaier polysaccharide decreased the expression of PRV gB, with the PRV entry inhibition rate being 13–47% (Figure 5A,B). The TCID50 assay revealed that the PRV XJ5 titers were decreased (Figure 5C). The cells infected with PRV were examined through IFA (Figure 5D). In addition, we collected cells to quantify the viral DNA copies by qRT-PCR after cells were washed with citric acid and PBS to remove uninternalized virus. qRT-PCR analysis indicated that Huaier polysaccharide decreased viral entry in a dose-dependent manner (Figure 5E). The results confirmed that Huaier polysaccharide influences PRV XJ5 entry. However, the inhibition rate of PRV entry by Huaier polysaccharide was lower than the observed inhibition rate of PRV adsorption. The results indicate that Huaier polysaccharide might have a prominent role in PRV adsorption.

sorption.

**Figure 5.** Huaier polysaccharide influences entry of pseudorabies virus in PK15 cells. The PK15 cells were treated according to the method described in Section 2.3.5. (**A**) At 24 h.p.i, PRV gB and actin protein expression were quantified through Western blot assay. (**B**) The relative intensity of intracellular gB to that of actin. Data are presented as the mean value from three independent statistical experiments. The relative intensities of protein were quantified using Image J. Significance was analyzed using the one-tailed Student's *t*-test. (**C**) The viral titers were evaluated through TCID50 assay. (**D**) Immunofluorescence assay (IFA) for internalized virus was performed. (**E**) Intracellular viral DNA copies were analyzed by qRT-PCR after cells were washed with citric acid and PBS to remove uninternalized virus. \*\*\* *p* = 0.0001, \*\*\*\* *p* < 0.0001. Data are shown as mean ± SD based on three independent experiments. **Figure 5.** Huaier polysaccharide influences entry of pseudorabies virus in PK15 cells. The PK15 cells were treated according to the method described in Section 2.3.5. (**A**) At 24 h.p.i, PRV gB and actin protein expression were quantified through Western blot assay. (**B**) The relative intensity of intracellular gB to that of actin. Data are presented as the mean value from three independent statistical experiments. The relative intensities of protein were quantified using Image J. Significance was analyzed using the one-tailed Student's *t*-test. (**C**) The viral titers were evaluated through TCID50 assay. (**D**) Immunofluorescence assay (IFA) for internalized virus was performed. (**E**) Intracellular viral DNA copies were analyzed by qRT-PCR after cells were washed with citric acid and PBS to remove uninternalized virus. \*\*\* *p* = 0.0001, \*\*\*\* *p* < 0.0001. Data are shown as mean ± SD based on three independent experiments.

### *3.4. Huaier Polysaccharide Mildly Reduces PRV XJ5 Replication in PK15 Cells* The adsorption of PRV requires 1 h and occurs at 4 °C; entry of PRV requires 1 h and *3.4. Huaier Polysaccharide Mildly Reduces PRV XJ5 Replication in PK15 Cells*

occurs at 37 °C [29]. The life cycle of PRV is completed in approximately 6 h. Hence, we chose the time periods of 4 and 6 h to study PRV replication. The expression of virus protein gB and actin was analyzed through the Western blot assay at 4 and 6 h.p.i. The DNA copies were analyzed by qRT-PCR. The results indicated that Huaier polysaccharide has a slight effect on gB expression (Figure 6A–F), indicating that Huaier polysaccharide mildly affects virus replication. The adsorption of PRV requires 1 h and occurs at 4 ◦C; entry of PRV requires 1 h and occurs at 37 ◦C [29]. The life cycle of PRV is completed in approximately 6 h. Hence, we chose the time periods of 4 and 6 h to study PRV replication. The expression of virus protein gB and actin was analyzed through the Western blot assay at 4 and 6 h.p.i. The DNA copies were analyzed by qRT-PCR. The results indicated that Huaier polysaccharide has a slight effect on gB expression (Figure 6A–F), indicating that Huaier polysaccharide mildly affects virus replication.

**Figure 6.** Huaier polysaccharide affects PRV XJ5 replication in PK15 cells. The PK15 cells were treated according to the method described in Section 2.3.6. At 4 and 6 h.p.i., the cells were collected to evaluate the expression of PRV gB and actin proteins through Western blotting (**A**,**C**). (**B**,**D**) The relative intensity of intracellular gB to that of actin. The relative intensities of protein were quantified using Image J. (**E**,**F**) PRV viral DNA copies were analyzed by qRT-PCR at 4 and 6 h.p.i. Significance was analyzed using the one-tailed Student's *t*-test. NS, \* *p* = 0.0299, \*\* *p* = 0.0017, \*\*\* *p* = 0.0001, \*\*\*\* *p* < 0.0001. Data are shown as mean ± SD based on three independent experiments. **Figure 6.** Huaier polysaccharide affects PRV XJ5 replication in PK15 cells. The PK15 cells were treated according to the method described in Section 2.3.6. At 4 and 6 h.p.i., the cells were collected to evaluate the expression of PRV gB and actin proteins through Western blotting (**A**,**C**). (**B**,**D**) The relative intensity of intracellular gB to that of actin. The relative intensities of protein were quantified using Image J. (**E**,**F**) PRV viral DNA copies were analyzed by qRT-PCR at 4 and 6 h.p.i. Significance was analyzed using the one-tailed Student's *t*-test. NS, \* *p* = 0.0299, \*\* *p* = 0.0017, \*\*\* *p* = 0.0001, \*\*\*\* *p* < 0.0001. Data are shown as mean ± SD based on three independent experiments.

#### *3.5. Huaier Polysaccharide May Directly Inactivate PRV XJ5 3.5. Huaier Polysaccharide May Directly Inactivate PRV XJ5*

PRV XJ5 (MOI = 0.1) was pretreated with different concentrations of Huaier polysaccharide for 1 h at 37 °C, and the PK15 cells were infected for 24 h. The cells were collected to assess PRV gB expression through Western blotting. Figure 7A,B illustrate that Huaier polysaccharide reduced PRV gB expression. Figure 7C indicated that virus copies were reduced significantly. In addition, the transmission electron microscope experiment revealed that the PRV envelope was destroyed by Huaier polysaccharide (Figure 7D). These results indicate that Huaier polysaccharide may directly inactivate PRV XJ5. PRV XJ5 (MOI = 0.1) was pretreated with different concentrations of Huaier polysaccharide for 1 h at 37 ◦C, and the PK15 cells were infected for 24 h. The cells were collected to assess PRV gB expression through Western blotting. Figure 7A,B illustrate that Huaier polysaccharide reduced PRV gB expression. Figure 7C indicated that virus copies were reduced significantly. In addition, the transmission electron microscope experiment revealed that the PRV envelope was destroyed by Huaier polysaccharide (Figure 7D). These results indicate that Huaier polysaccharide may directly inactivate PRV XJ5.

**Figure 7.** Huaier polysaccharide may directly inactivate PRV XJ5. PRV XJ5 (MOI = 0.1) was treated according to the method described in Section 2.3.8. (**A**) PRV gB was analyzed through Western blotting. (**B**) The relative intensity of intracellular gB to that of actin. (**C**) PRV viral DNA copies were analyzed by qRT-PCR at 24 h.p.i (**D**) PRV particle morphology was observed by electron microscopy. The relative intensities of protein were quantified using Image J. Significance was analyzed using the one-tailed Student's *t*-test. \*\*\*\* *p* < 0.0001. Data are shown as mean ± SD based on three independent experiments. **Figure 7.** Huaier polysaccharide may directly inactivate PRV XJ5. PRV XJ5 (MOI = 0.1) was treated according to the method described in Section 2.3.8. (**A**) PRV gB was analyzed through Western blotting. (**B**) The relative intensity of intracellular gB to that of actin. (**C**) PRV viral DNA copies were analyzed by qRT-PCR at 24 h.p.i (**D**) PRV particle morphology was observed by electron microscopy. The relative intensities of protein were quantified using Image J. Significance was analyzed using the one-tailed Student's *t*-test. \*\*\*\* *p* < 0.0001. Data are shown as mean ± SD based on three independent experiments.

#### **4. Discussion 4. Discussion**

Huaier has been used as a traditional Chinese herbal medicine for the treatment of various diseases for thousands of years. In clinical treatment, Huaier polysaccharide has demonstrated a promising auxiliary effect in the treatment of breast cancer, liver cancer, and gastric cancer [30]. Increasing evidence suggests that Huaier polysaccharide can inhibit cell proliferation [31,32], cause cell cycle arrest [33,34], and induce apoptosis [35,36] in cancer cells. In a study, the bi-directional solid fermentation product extract of Huaier with Radix Isatidis (TIF) could upregulate the expression of p53 and caspase-3 in both SK-BR-3 and MDA-MB-231 cell lines [37]. In another study, researchers found that Huaier polysaccharide could inhibit proliferation and promote apoptosis by increasing miR-26b-5p expression in pulmonary cancer cells [38]. Additionally, Huaier polysaccharide extract was found to impair genes related to cell division, the cell cycle, cell cycle phases, and DNA repair [39]. Moreover, in vitro assays confirmed that Huaier polysaccharide could markedly increase the persistence of γ-H2A.X foci and interfere with the homologous recombination pathway [39]. Huaier has been used as a traditional Chinese herbal medicine for the treatment of various diseases for thousands of years. In clinical treatment, Huaier polysaccharide has demonstrated a promising auxiliary effect in the treatment of breast cancer, liver cancer, and gastric cancer [30]. Increasing evidence suggests that Huaier polysaccharide can inhibit cell proliferation [31,32], cause cell cycle arrest [33,34], and induce apoptosis [35,36] in cancer cells. In a study, the bi-directional solid fermentation product extract of Huaier with Radix Isatidis (TIF) could upregulate the expression of p53 and caspase-3 in both SK-BR-3 and MDA-MB-231 cell lines [37]. In another study, researchers found that Huaier polysaccharide could inhibit proliferation and promote apoptosis by increasing miR-26b-5p expression in pulmonary cancer cells [38]. Additionally, Huaier polysaccharide extract was found to impair genes related to cell division, the cell cycle, cell cycle phases, and DNA repair [39]. Moreover, in vitro assays confirmed that Huaier polysaccharide could markedly increase the persistence of γ-H2A.X foci and interfere with the homologous recombination pathway [39].

The present study focused on determining the effect of Huaier polysaccharide on virus infection and confirmed that Huaier polysaccharide can affect multiple life cycle stages of PRV XJ5 virus to exert its antiviral effects. PK15 cells are generally used in in vitro PRV research [40]. Huaier polysaccharide mainly affects the adsorption of PRV XJ5 on PK15 cells, and the effect is dose-dependent. The results of qRT-PCR further illustrated this phenomenon. In a study by Zhang et al., the number of successfully invading/migrating cells and the wound closure rate established through the transwell assay and scratch assay, respectively, were reported to be decreased significantly by Huaier polysaccharide, which proved the anti-metastasis effect of Huaier polysaccharide [20]. Thus, we speculate that Huaier polysaccharide inhibits PRV adsorption through its anti-metastasis action; however, the confirmation of this assumption warrants further study. In addition, we revealed that Huaier polysaccharide inhibited PRV entry into PK15 cells by qRT-PCR. The present study focused on determining the effect of Huaier polysaccharide on virus infection and confirmed that Huaier polysaccharide can affect multiple life cycle stages of PRV XJ5 virus to exert its antiviral effects. PK15 cells are generally used in in vitro PRV research [40]. Huaier polysaccharide mainly affects the adsorption of PRV XJ5 on PK15 cells, and the effect is dose-dependent. The results of qRT-PCR further illustrated this phenomenon. In a study by Zhang et al., the number of successfully invading/migrating cells and the wound closure rate established through the transwell assay and scratch assay, respectively, were reported to be decreased significantly by Huaier polysaccharide, which proved the anti-metastasis effect of Huaier polysaccharide [20]. Thus, we speculate that Huaier polysaccharide inhibits PRV adsorption through its anti-metastasis action; however, the confirmation of this assumption warrants further study. In addition, we revealed that Huaier polysaccharide inhibited PRV entry into PK15 cells by qRT-PCR. Moreover, we

found that Huaier polysaccharide prevents virus infection, possibly by binding to a certain receptor on the cell surface, and it protects the cells probably by directly inactivating the virus. The polysaccharide might exert a weak effect on PRV XJ5 replication.

Studies have been focusing on one of the main pathways of programmed cell death after viral infection [41]. The host cell can destroy virus-infected cells through apoptosis, thereby preventing virus infection [42]. Huaier polysaccharide plays a central role in activating the caspase-3 signaling pathway for apoptosis induction [43]. The Huaier polysaccharide component SP1 (a type of purified Huaier polysaccharide) could increase the proportion of Bax/Bcl-2 through the MTDH signaling pathway, which could be another potential mechanism of Huaier in apoptosis induction in breast cancer cells [22]. Moreover, 18β-glycyrrhetinic acid inhibits apoptosis of the cells infected with rotavirus SA11 to decrease rotavirus SA11 infection by Fas (CD95) and FasL (CD178). Similarly, Huaier polysaccharide may depend on Fas (CD95) and FasL (CD178) to regulate apoptosis to inhibit PRV infection [44]. We aim to investigate this assumption in our future studies.

### **5. Conclusions**

In this study, we revealed that Huaier polysaccharide acts against PRV in PK15 cells by blocking PRV adsorption and entry. Hence, Huaier polysaccharide could be further developed as an antiviral agent against PRV infection. Although some studies have investigated the molecular mechanisms, pharmacokinetic and pharmacodynamic models should be developed for an in-depth understanding of the mechanism.

**Author Contributions:** S.G. and C.H. conceived study, designed the experiments, and analyzed the data. J.Y., W.Z., W.X. and H.P. performed the experiments and analyzed the data. C.H. and J.Y. wrote the manuscript. S.G., C.H., J.Y. and Z.Z. supervised the experiments and edited the manuscript. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the National Natural Science Foundation of China (31902253), the Natural Science Foundation of Jiangsu Province (BK20180921), the Individual Technology Research and Development of Modern Agricultural Industry of Jiangsu Province (CX(19)3024), the China Postdoctoral Science Foundation (2018M632399), the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD), and the earmarked fund for Jiangsu Agricultural Industry Technology System, and the Top-level Talents support Program of Yangzhou University.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

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

### **References**


**3. Electromagnetic compatibility for implantable medical device**

### **3.1 EMI shield**

The EMI shield is designed to decrease the electromagnetic (EM) wave transmission using a shield to increase the reflection or absorption of EM wave incident at the interfaces between different mediums. As shown in **Figure 5**, the electric and magnetic fields of EM waves are perpendicular to each component and the EM

*Electromagnetic Compatibility Issues in Medical Devices DOI: http://dx.doi.org/10.5772/intechopen.99694*

**Figure 5.**

*Time-varying EM waves and the propagation, transmission, and reflection of the EM waves in different mediums.*

propagation direction, which can be expressed as phasor form [23], according to Eqs. (1) and (2). Where γ, α, β are the propagation, attenuation, phase constants of the medium, respectively; E0 and H0 are the amplitude of the electric and magnetic fields.

$$\mathbf{E} = \hat{\mathbf{a}}\_{\text{Y}} \mathbf{E}\_{0} \mathbf{e}^{-\text{yr}} = \hat{\mathbf{a}}\_{\text{Y}} \mathbf{E}\_{0} \mathbf{e}^{-\text{oz}} \mathbf{e}^{-\text{j0z}} \tag{1}$$

$$\mathbf{H} = \hat{\mathbf{a}}\_{\text{\textquotedblleft}} \mathbf{H}\_{0} \mathbf{e}^{-\text{\textquotedblleft}\mathbf{z}} = \hat{\mathbf{a}}\_{\text{\textquotedblleft}\mathbf{H}} \mathbf{e}^{-\text{\textquotedblleft}\mathbf{z}} \mathbf{e}^{-\text{\textquotedblleft}\mathbf{z}} \tag{2}$$

The EM wave propagates at the interface of two different mediums that induce reflection due to impedance mismatching. The reflection coefficient (R12) and transmission coefficient (T12) at the interface between two mediums can be determined, according to Eqs. (3) and (4). Ei, Er, η1, η2 represent incident, reflected electric fields, impedances in Medium 1 and Medium 2, respectively. The impedance in the medium can be defined by a ratio of electric field and magnetic field, which is related to the permittivity (ε), permeability (μ), and conductivity (σ), according to Eq. (5).

$$\mathbf{R\_{12}} = \frac{\mathbf{E\_r}}{\mathbf{E\_i}} = \frac{\eta\_2 - \eta\_1}{\eta\_2 + \eta\_1} \tag{3}$$

$$\mathbf{T\_{12}} = \frac{\mathbf{E\_t}}{\mathbf{E\_i}} = \frac{2\eta\_2}{\eta\_2 + \eta\_1} \tag{4}$$

$$\eta = \frac{|\mathbf{E}|}{|\mathbf{H}|} = \sqrt{\frac{\text{joļņ}}{\sigma + \text{joē}}} \tag{5}$$

The time-domain electric field can be rewritten as Eq. (6), according to Eq. (1).

$$\mathbf{E} = \hat{\mathbf{a}}\_{\mathbf{y}} \mathbf{E}\_{0} \mathbf{e}^{-\text{yr}} = \hat{\mathbf{a}}\_{\mathbf{y}} \mathbf{E}\_{0} \mathbf{e}^{-\text{oz}} \cos \left( \alpha \mathbf{t} - \beta \mathbf{z} \right) \tag{6}$$

When the EM wave propagates in the conductive shield (loss medium) at a time of zero, the expression between the distance and amplitude of the electric field can be obtained, according to (7).

$$\mathbf{E} = \hat{\mathbf{a}}\_{\text{y}} \mathbf{E}\_{0} \mathbf{e}^{-\alpha \mathbf{z}} \cos \left( \beta \mathbf{z} \right) \tag{7}$$

**Figure 6** demonstrates the EM wave propagation in the conductive shield. The skin depth (δ) can be defined as that penetration distance at which the intensity of

**Figure 6.** *Schematic of skin depth of EM waves using the shield.*

the electric field attenuates to 1/e of the original incident wave intensity. According to the Eqs. (8) and (9), the skin depth (δ) is the reciprocal of attenuation constant (α), which is related to the EM operating frequency, permeability (μ), and conductivity (σ) in the medium [10].

$$\frac{\mathbf{E}\_0}{\mathbf{e}} = \mathbf{E}\_0 \mathbf{e}^{-\alpha \mathbf{8}} \tag{8}$$

$$\delta = \frac{1}{\alpha} = \frac{1}{\sqrt{\pi f \mu \sigma}} \tag{9}$$

Thus, conductivity and permeability in shielding design play an important role in EM wave absorption enhancement, thus increasing the overall EMI shielding effectiveness.

However, the implantable medical device is not a fully closed system that must require the openings of the shield to interact with external equipment such as body sensing devices for signal transmit or receive. In some cases, the external controlled magnetic fields or electrical signals can be utilized to externally modulate the stimulation protocol of implantable medical devices according to patients' clinical requirements. So, the selective filtering of EMI waves is important for implantable medical devices to classify the noise and external signals. Thus, the EMI filter was provided in the following subsection to promote the EMC applications in implantable medical devices.

#### **3.2 EMI filter**

The filter implementation is also a strategy for EMI elimination in medical devices [24–27]. For example, the typical ranges of P, R, T waves in ECG are 20 to 40 Hz, 18 to 50 Hz, and 0 to 10 Hz [28], as shown in **Table 2**.

Filtering can be divided into active and passive modes. Active filters consist of several operational amplifiers and passive elements such as capacitors and resistors. [29–32]. The active filters are applied in wide applications owing to excellent filter performance. However, the active filters need a power source to sustain the

*Electromagnetic Compatibility Issues in Medical Devices DOI: http://dx.doi.org/10.5772/intechopen.99694*

**Table 2.**

*Significant frequency bandwidth of ECG waveform [28].*

**Figure 7.** *Filter implementation for removing the time-varying electric and magnetic fields.*

operations. Moreover, the upper frequency of active filters may be limited. Thus, the active filter is not suitable for EMI filtering in implantable medical devices. The active filter can perform programmatical filtering for the received signals, thus separating the signal from noise. However, programmatical computation requires a high-cost and complex circuit with larger power consumption to sustain the processing functions. Because the implantable devices aim to sustain life, such devices are not expected to remove or insert frequently because of extremely high costs for device failure.

Moreover, it is not easy to replace it if the devices fail due to the high risk of surgery. The concern regarding the surgery risk, which makes battery life issues more important. Owing to the battery requirements of implantable medical devices, the minimization of filters' power is crucial to prolong the implantable device lifespan.

The capacitor-based passive filter is frequently used for most high-frequency noise in the surrounding ambient for the filter design regarding implantable medical devices. Capacitors can filter EMI noise utilizing absorption and smoothing of electromagnetic noise. The high-frequency noise attenuates as quickly as charging and discharging the capacitor-based filter. Absorbing such EMI noise to the ground will neutralize or prevent specific frequencies from passing through the circuit, as shown in **Figure 7**.

The discoidal capacitor and feedthrough capacitor array were commonly utilized in the practical applications of medical devices, which deliver high-density performance with low-volume packaging [33–35], as shown in **Figure 8**.

The circular-shaped discoidal capacitor is one of the most common constructions for feed-through-style EMI filters. Circular capacitors outside and inside diameters serve as connection points for the case and the lead and serve as the capacitor poles. Moreover, several discoidal capacitors can be assembled to integrate as a capacitor array on a single piece of ceramic [36]. Such assembly offers the highest filter performance within the limited physical dimension. Thus, the feedthrough

**Figure 8.** *The feedthrough capacitor array and discoidal capacitor for the implantable medical device.*

capacitor array provides the merits of the miniature dimension and lightweight within a high-density implantable device [37].

However, a feedthrough filter will have a double impact on battery life. First, a minimal amount of current always flows between the plates of the charging capacitor. Since one capacitor is processing the signal and the other capacitor is grounded, the leakage current will drain the battery over time. A strong dielectric with an appropriate thickness can resist this current flow, thereby significantly reducing battery consumption. Besides, filter design in implantable medical devices is to minimize the loss of expected signals. The filter's insertion loss implies how much a signal will be lost or reduced for each frequency. An excellent filter requires a lower insertion loss for signal frequencies and a higher insertion loss for noise frequencies. Some energy in the expected signal will attenuate in internal resistance and inductance of the filter, which implies that the implantable battery needs optimize in the power design. Thus, an optimized design can suppress the energy loss. The less power dissipated in the battery, which extends battery life and improves effectiveness.


*White Maize Tortillas Fortified with Brown Algae* Macrocystis pyrifera *DOI: http://dx.doi.org/10.5772/intechopen.105162*

*standard deviation (mean ± SD). T10, T20, T30 = tortilla with 10, 20 or 30% of seaweed, T0 = control.*

#### **Table 1.**

*Chemical composition of tortillas with different concentrations of seaweed.*

(4.49%) was similar to the control sample from reference [28] (4.65%), the addition of seaweed resulted in lower protein values (4.75–5.27%.) than the addition of *J. curcas* flour (6.52–10.85%) [28]. In other, the protein content from hand-made white tortillas has been reported to be between 7.5 and 9.6% [35], the protein content of the tortillas from this study was lower. As seaweeds are not considered to have an elevated lipid content [33], it was not expected to observe a high increase in the lipid fraction. The lipid content in all tortillas from this study was lower than the one reported in other studies [28, 35], with lipid values ranging between 1.87 and 3.95%. The differences in the lipid content can be related to the variety of the used maize as well as to the nixtamalization conditions, as lipids from the kernel can be solubilized during the alkaline treatment or during the steeping time [35]. The fiber content of all samples was higher than the reported in [28] (0.8–1.98%) while the fiber content of T30 was similar to the one reported in Ref. [35] (15.72%).

With an increment in ash content, the increase in minerals would be expected, specially as seaweeds can contain between 10 and 20 times the mineral amount when compared to land plants since seaweeds gather them from the seawater [36]. All the analyzed minerals (Na, Ca, P, K, and Mg) increased significantly (p < 0.05) with an increment in seaweed (**Table 2**). The most notorious increase in minerals was Na, which increased almost 100 times when T0 and T30 were compared, followed by K, which augmented 16 times, Mg went from 85 to 380 mg/100 g, Ca was almost triplicated when comparing the same samples (T0 and T30), and P barely increased from 315 (T0) to 360 mg/100 g (T30), however it was also significant. The mineral composition of seaweeds is influenced by the environmental conditions, their age and their capability to absorb inorganic substances from the environment. Due to the polysaccharides in their cell walls, brown seaweeds (like *M. pyrifera*) present higher affinity to absorb calcium, magnesium, sodium, and potassium salts due to the presence of alginic acid, alginate, and alginic acid salt [36]. The Ca content of all samples was higher than the content of white maize tortillas (155.5 mg/100 g) [35]. The recommended dietary allowance (RDA) for women and men between 18 and 50 years old for Ca is 1000 mg [37], amount that could be covered with 130 g of T30. The RDA of P is 700 mg [37] value that could be covered with 200 g of T30, with 50–70 g of T30 covers the RDA of K (2600–3400 mg [37]) while the RDA of Mg (310–420 mg [37]) could be covered with 80–110 g of T30. While the Chronic Disease Risk Reduction Level (CDRR) of Na is 2300 [37], dose that is not overpassed with 200 g of T30, which is the amount of tortilla needed to cover all the minerals.

The increase in seaweed concentration in *masa*s led to a significant increase in the differences (ΔE) between T0 and T10, T20, and T30. Additionally, the seaweed

*All results are expressed as mg/100 g. Different letters in the same row represents significant differences (p < 0.05). Results are expressed as mean (n = 3) and standard deviation (mean ± SD). T10, T20, T30 = tortilla with 10, 20 or 30% of seaweed. T0 = control.*

#### **Table 2.**

*Mineral content of tortillas with different concentrations of seaweed.*

*Different letters in the same row represents significant differences (p < 0.05). Results are expressed as mean (n = 3) and standard deviation (mean ± SD). M10, M20, M30 = masa with 10, 20 or 30% of seaweed. M0 = control.*

#### **Table 3.**

*Color of masas with different concentrations of seaweed.*

affected all the color parameters analyzed (**Table 3**) on *masa*s. The lightness (L\*) of T0 decreased to half its value in T30. The negative values of a\* are indicative of greener tonalities [6], it could be seen that the increase in seaweed concentration led to an increase of this tonalities. The b\* values also decreased when the concentration of algae was augmented, which means that the *masa* was less yellow and started to have more blue tonalities. On the contrary, the seaweed lead to a significant increase in hue values, changing from 90.5 to 99.7, while chroma was higher in the control sample and showed no differences between samples T10, T20 and T30. Similarly, the addition of muicle led to a variation in L\*, a\* and b\* parameters [6]. The authors reported a decrease in lightness and in b\* values, indicative that color tended to display increasingly blue tonalities, while an increase in a\*, related to an increase in red tonalities, was also observed [6]. While the addition of *J. curcas* flour to *masa* led to increase in L\* and a\*, while there were no changes in b\* [28].

The analyzed color parameters of tortillas were also significantly modified with the incorporation of seaweed (**Table 4**). Similarly, to the *masa*s, there was a bigger difference (ΔE) between T0 and T30. Additionally, the lightness (L\*) presented a similar behavior to the one observed in *masa*s, with the value from T0 decreasing to almost half its value in T30. With the progressive incorporation of seaweed, the a\* changed from positive values to negative ones, meaning that the samples became greener as a result of incorporation the algae. Despite the addition of seaweed, the values of b\* remained positive, and while there was no significant difference between T20 and T30, this values were significantly smaller that T0 and T10. Chroma decreased with the increase of seaweed and went from 23.8 (T0) to 18.2 (T30), while T30 presented the highest hue values (95.4), followed by T20, and T0 showed the lowest values (84.3).

*White Maize Tortillas Fortified with Brown Algae* Macrocystis pyrifera *DOI: http://dx.doi.org/10.5772/intechopen.105162*

*Different letters in the same row represents significant differences (p < 0.05). Results are expressed as mean (n = 3) and standard deviation (SD = ±). T10, 20, 30 = tortilla with 10, 20 or 30% of seaweed. TC = control.*

#### **Table 4.**

*Color of tortillas with different concentrations of seaweed.*

However all the hue values could be described as yellowish-green. Tortillas fortified with white bean flour showed reddish color, with the value of a\* in the positive range, while b \* values had a clear tendency to yellow [14].

The antioxidant capacity and TPC of *masa*s were significantly affected by the seaweed concentration (**Figures 1** and **2**). M0 presented the lowest values in the three assays, similarly to the effect of incorporating muicle extracts [6]. The highest values of both FRAP and TPC were obtained for M30. The TPC showed a linear trend with higher concentrations of seaweed. The TPC increased 5 times between M0 and M30, while the FRAP value from M30 increased more than twice when compared with M0. The TPC of all samples was higher than the value reported for hand-made tortillas from white maize (~75 mg GAE/100 g) [35]; while the TPC of T0 was similar to the one reported in [38] (~160 mg GAE/100 g). The highest percentage of inhibition of ABTS was obtained for M20 (90%), while the lowest value was 70% for M0. The incorporation of different varieties of beans to wheat tortillas also led to the increase in antioxidant capacity when compared to their control samples [39].

The texture of *masa*s and tortillas was significantly affected by the incorporation of seaweed (**Figures 3** and **4**, respectively). M0 showed the lowest values for hardness and adhesiveness when compared to M10, M20 and M30. The adhesiveness and hardness of the *masa* showed a similar trend, the highest value was obtained for M10,

#### **Figure 1.**

*Total phenolic content of masas with different concentrations of seaweed. Each value represent the results from mean and standard deviation. Different letters indicate significant differences.*

#### **Figure 2.**

*Antioxidant capacity (FRAP and ABTS) of masas with different concentrations of seaweed. Each value represent the results from mean and standard deviation. Different letters indicate significant differences.*

#### **Figure 3.**

*Texture profile analysis (TPA) of masas with different concentrations of seaweed. Each value represent the results from mean and standard deviation. Different letters indicate significant differences.*

and decreased with a higher concentration of seaweed. There was not a linear trend depending on the concentration of seaweed, which was similar to the effect of incorporating grasshopper (*S. purpuracens)* flour. However, the adhesiveness of tortillas with seaweed was higher than the ones with grasshopper flour (~0.10 - ~0.20 N) [18]. In the same study, the control sample showed higher hardness than *masa* with grasshopper flour [18], while in this study M0 showed the lowest values for both adhesiveness and hardness. The opposite behavior was observed in tortillas, were T0 required more applied force to puncture the tortilla. In the tortillas this trend was not observed, as T10 required the lowest force to get punctured while T20 and T30 showed no significant difference among them. Different concentrations of muicle did not affect the hardness of tortillas, which was lower (2.48–2.81 N) [6] than the one reported in this study (3.5–7.5 N).

*White Maize Tortillas Fortified with Brown Algae* Macrocystis pyrifera *DOI: http://dx.doi.org/10.5772/intechopen.105162*

**Figure 4.**

*Texture of tortillas with different concentrations of seaweed. Each value represent the results from mean and standard deviation. Different letters indicate significant differences.*


6. Conclusions

MCS is a widely used method in statistical physics to study thermodynamic, structural, or phase properties. It is based on random and probabilistic processes. The purpose of this chapter is to present the technique for general use in physics for the study of thin film deposition problems. The technique can be generalized to other fields of science: biology, economics, transportation, and social sciences.

We started by presenting general rules for numerical simulation methods. Metropolis algorithm has been considered as the basic algorithm. After, we presented the different steps for the realization of a MCS code. We chose the particle-particle model MCS (PP-MCS) to explain the different steps and procedures to be applied in the deposition of thin layers by PECVD processes. We have shown that this technique can be generalized to the particle-in-cell MCS (PIC-MCS) case or kinetic MCS (kMCS), as it can be joined with other modules to give hybrid models. It is important to know how to choose random configurations from the laws or probability distributions in the system.

A numerical application is presented for collisions in a SiH4/H2 gas mixture in the PECVD process. A preliminary work of determination of the chemical reactions between molecules and radicals is made. A choice of the simulation cell is made, and the definition of the probabilities of the collisions between peers is made. The Metropolis algorithm makes it possible to follow the various elastic and inelastic

How to Use the Monte Carlo Simulation Technique? Application: A Study of the Gas Phase… DOI: http://dx.doi.org/10.5772/intechopen.88559

collisions; it also makes it possible to make the statistics of the interactions with the surface. The results are compatible with [39, 51, 52].

Other questions may be asked to account for molecular ions, surface and volume kinetics, or thin film formation. The techniques and different models of the MCS (PP-MCS, MCS-PIC, kMCS) allow taking care of these questions.

The interconnection of the MCS with other models (MDS, hybrid model, fluid model, electromagnetic model, etc.) would allow answering more questions. The methods can be applied to other specialties than the physical sciences.


**Acknowledgements**

The work at Kyiv was funded by the Ministry of Education and Science of Ukraine (0119U100303). Financial support from the University of Vienna is also acknowledged.

**Author details**

Andriy Nadtochiy1

of Vienna, Austria

**153**

, Artem Podolian1

*Ultrasonic Processing of Si and SiGe for Photovoltaic Applications*

*DOI: http://dx.doi.org/10.5772/intechopen.96939*

\*Address all correspondence to<EMAIL_ADDRESS>
provided the original work is properly cited.

1 Faculty of Physics, Taras Shevchenko National University of Kyiv, Kyiv, Ukraine

2 Department of Electronic Properties of Materials, Faculty of Physics, University

© 2021 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

, Oleg Korotchenkov1 and Viktor Schlosser2

\*


*6.1. ICE's Oversight*

The GAO and DHS OIG reports illustrate another reason that ICE should have just one set of detention standards—one set comprised solely of evidence-based practices—and it is this. ICE is unable to get most of the facilities it uses to comply with one set of standards; it is at least five times as unlikely that it will ever achieve compliance when there are five different sets of expectations in the field. There are several reasons why this is the case.

First, ICE's standards for acceptable and unacceptable performance (ICE 2021a) do not adequately address conditions that detainees encounter. Both acceptable and unacceptable are highly subjective terms. Not all deficiencies are equal. Frequency and severity vary— and no objective benchmarks are provided.

Additionally, ICE monitors detention facilities by several means. It assigns on-site agency monitors to its largest facilities. Independent reviews and fairly thorough inspections are also conducted at some facilities every several years by the Office of Detention Oversight, an independent office within ICE but outside of ERO. ICE also contracts with the Nakamoto Group Inc. to inspect most facilities annually. Those inspections were suspended through much of 2020 due to the pandemic then resumed remotely. Both oversight agencies and Congressional committees have been critical of ICE's contract management including its continued use of Nakamoto, and its inability to achieve better results over time. Chief among their concerns, no matter how poorly facilities perform, both the on-site agency monitors and the Nakamoto Group report that they Meet Standards. The GAO and OIG have also issued reports about ICE's failed oversight of detention operators, the most recent of which were published by the DHS OIG in June 2018 (OIG 2018), and the GAO in August 2020 (GAO 2020).


**1. Introduction**

It is well known, due to stochastic variations in both supply and demand, that travel time almost always involves a measure of uncertainty. Recently, several empirical studies on the value of time and reliability revealed that travel time reliability plays an important role in the traveler's route choice decision-making process [1–3]. With these studies as a basis, the study of travel time variability (reliability) has gradually emerged as an important topic. In this context, travel time reliability pertains to the probability that a trip can be successfully completed within a specified time interval, reflecting the uncertainty in trip journey times [4, 5]. To model the characteristics of travel time reliability, the concept of TTB is commonly used. TTB is defined as the average travel time plus extra time (for a measure of the buffer time) such that the probability of completing the trip within the TTB is no less than a predefined reliability threshold α [6]. Earlier research applied the concept of effective travel time to capture the travel time reliability [7]. Recently, [6] further proposed a stochastic mean-excess traffic equilibrium model to represent both the reliability and unreliability aspects of travel time variability and travelers' route choice perception errors.

Generally speaking, uncertainties from both the demand and supply sides of a system directly lead to recurring variability and unreliability of travel times and

have an obvious impact on the traveler's route choice behavior. Supply-side sources refer to the capacity variations that can occur, due to several exogenous sources of uncertainty on the road sections or at-grade intersections concerned. These exogenous sources of uncertainty may take different forms, such as environmental conditions, traffic incidents, traffic management and control, work zones, and so on. Such stochastic link capacity degradations usually lead to non-recurrent congestion [8–10]. Demand-side sources are regarded as the travel demand fluctuations, which result from various endogenous sources. These endogenous sources can include temporal factors, special events, population characteristics, and traffic information among others. Travel demand variations usually lead to recurrent congestion [4, 11, 12].

Although considerable research exists on congestion pricing and travel time reliability, relatively little research combines the two, especially regarding travelers' risk attitudes and/or the valuation of reliable travel [19]. Some examples of research that do combine congestion pricing and travel time reliability are included here. Li et al. [20] proposed a reliability-based optimal toll design bi-level model. On the upper level, network performance is optimized from a road authority point of view including travel time reliability, while a dynamic user-equilibrium is achieved from the viewpoint of travelers on the lower level. Boyles et al. [19] proposed a first-best congestion pricing model considering network capacity uncertainty and user valuation of travel time reliability, while [18] investigated marginal cost pricing in a stochastic traffic network in which demand uncertainty is explicitly considered. By assuming that all travelers have complete information about the road traffic condition, [18] derived an analytical function of Stochastic Network-Marginal Cost Pricing (SN-MCP) for a risk-neutral case and risk-based SN-MCP (RSN-MCP) for a risk-based case under the assumptions of lognormal demand and constant VMR across all OD pairs. Gardner et al. [21] consider the uncertainty in long-term travel demand and in day-to-day network capacity, and discuss the benefit of responsive

In the above-mentioned studies, MCP is analysis in a stochastic network, which considers either link supply uncertainty (e.g., see [19]) or stochastic travel demand

researchers usually assume the commonly adopted Gumbel variate as the random error term and use the conventional logit-based Stochastic User Equilibrium (SUE) model. However, this approach may not reflect the travelers' perception of the random travel time exactly. Due to the variation of travel time, it is more rational to assume that the travelers' perception error is also dependent on the random perceived travel time [22]. Therefore, in order to explicitly consider both supply and demand aspects of a stochastic network and to reflect the travelers' perception error of the random travel time, this investigation extends [18] by (1) considering both the stochastic travel demand and link capacity degradation, and (2) incorporating

The remainder of the chapter is organized as follows. The next section introduces the assumptions used in the analysis and presents the variational inequality (VI) formulation for different stochastic models. It also discusses the stochastic travel times under different sources of uncertainty. Then, Section 3 and Section 4

(e.g., see [18]). In addition, to account for the travelers' perception error,

travelers' perception error into the first-best MCP analysis.

pricing and travel information.

*Reliability-Based Marginal Cost Pricing Problem DOI: http://dx.doi.org/10.5772/intechopen.92844*

**Figure 1.**

**51**

*Flow chart for the research process.*

Several stochastic traffic network (SN) modeling approaches have been proposed to represent such uncertainties. On the capacity side, [13] proposed a probabilistic approach using the concept of capacity reliability to model the uncertain characteristics of link capacities. Lo et al. [14] proposed the Probabilistic User Equilibrium (PUE) model, which takes the fact that the link capacities are subject to stochastic degradations into account. In subsequent research using the concept of Travel Time Budget (TTB), [10] further extended the PUE model to capture the route choice behaviors of travelers with heterogeneous risk aversions. On the demand side, [11] proposed a framework of the stochastic network model to represent the stochastic demand. Ref. [12] extended the TTB model and proposed a travel time reliability-based traffic assignment model to consider the effect of daily demand fluctuations. On both the demand and supply sides, [15] proposed a traffic assignment model, which considers the uncertainties of a traffic network due to adverse weather conditions. Sumalee et al. [16] proposed a stochastic network model with log-normal distributed origin–destination (OD) travel demands and link capacities. It should be noted that all of the above studies focused on the question of how to represent the travel time reliability in a traffic assignment model, but did not answer the question of how to improve the travel time reliability in a stochastic traffic network.

All the aforementioned studies discovered that travelers do indeed consider travel time variability as a risk in their route choice decisions. Nevertheless, the first-best marginal cost pricing (MCP) is commonly modeled via a deterministic approach, which assumes that both traffic supply and travel demand are known, and that the route travel times are deterministic [17]. Furthermore, travelers are assumed to know exactly the time on each available route and can always choose the least-cost routes for their trips. As indicated earlier, due to various sources of uncertainty coming from both supply-side and demand-side of road network, it is unreasonable to assume that travel times are deterministic and known perfectly by all the travelers. Though several traffic equilibrium models have been developed for environments characterized by uncertainty in the past decades, such models have not been adopted in the analysis of first-best MCP. Intuitively, the variability and unreliability of travel times caused by network uncertainties directly influence the traveler's route choice behavior, thereby negatively affecting the performance of MCP. However, there is little theoretical basis for this intuition. At least, it is not yet clear to what extent the stochastic demand and supply and the travelers' perception error affect the performance of MCP. In this context, the study of first-best MCP under an uncertain environment is a necessary and urgent theoretical task. In addition, this investigation is also practically relevant. As indicated by [18], the recent change in the Electronic Road Pricing (ERP) toll adjustment scheme in Singapore involves the consideration of the 85th-percetile traffic condition (speed) to reflect the variability of traffic conditions. This involves determining optimal tolls in a stochastic environment, where both demand and capacity are subject to uncertainty.

### *Reliability-Based Marginal Cost Pricing Problem DOI: http://dx.doi.org/10.5772/intechopen.92844*

have an obvious impact on the traveler's route choice behavior. Supply-side sources refer to the capacity variations that can occur, due to several exogenous sources of uncertainty on the road sections or at-grade intersections concerned. These exogenous sources of uncertainty may take different forms, such as environmental conditions, traffic incidents, traffic management and control, work zones, and so on. Such stochastic link capacity degradations usually lead to non-recurrent congestion [8–10]. Demand-side sources are regarded as the travel demand fluctuations, which result from various endogenous sources. These endogenous sources can include temporal factors, special events, population characteristics, and traffic information among others. Travel demand variations usually lead to recurrent congestion [4, 11, 12]. Several stochastic traffic network (SN) modeling approaches have been proposed to represent such uncertainties. On the capacity side, [13] proposed a probabilistic approach using the concept of capacity reliability to model the uncertain characteristics of link capacities. Lo et al. [14] proposed the Probabilistic User Equilibrium (PUE) model, which takes the fact that the link capacities are subject to stochastic degradations into account. In subsequent research using the concept of Travel Time Budget (TTB), [10] further extended the PUE model to capture the route choice behaviors of travelers with heterogeneous risk aversions. On the demand side, [11] proposed a framework of the stochastic network model to represent the stochastic demand. Ref. [12] extended the TTB model and proposed a travel time reliability-based traffic assignment model to consider the effect of daily demand fluctuations. On both the demand and supply sides, [15] proposed a traffic assignment model, which considers the uncertainties of a traffic network due to adverse weather conditions. Sumalee et al. [16] proposed a stochastic network model with log-normal distributed origin–destination (OD) travel demands and link capacities. It should be noted that all of the above studies focused on the question of how to represent the travel time reliability in a traffic assignment model, but did not answer the question of how to improve the travel time reliability

*Linear and Non-Linear Financial Econometrics - Theory and Practice*

All the aforementioned studies discovered that travelers do indeed consider travel time variability as a risk in their route choice decisions. Nevertheless, the first-best marginal cost pricing (MCP) is commonly modeled via a deterministic approach, which assumes that both traffic supply and travel demand are known, and that the route travel times are deterministic [17]. Furthermore, travelers are assumed to know exactly the time on each available route and can always choose the least-cost routes for their trips. As indicated earlier, due to various sources of uncertainty coming from both supply-side and demand-side of road network, it is unreasonable to assume that travel times are deterministic and known perfectly by all the travelers. Though several traffic equilibrium models have been developed for environments characterized by uncertainty in the past decades, such models have not been adopted in the analysis of first-best MCP. Intuitively, the variability and unreliability of travel times caused by network uncertainties directly influence the traveler's route choice behavior, thereby negatively affecting the performance of MCP. However, there is little theoretical basis for this intuition. At least, it is not yet clear to what extent the stochastic demand and supply and the travelers' perception error affect the performance of MCP. In this context, the study of first-best MCP under an uncertain environment is a necessary and urgent theoretical task. In addition, this investigation is also practically relevant. As indicated by [18], the recent change in the Electronic Road Pricing (ERP) toll adjustment scheme in Singapore involves the consideration of the 85th-percetile traffic condition (speed) to reflect the variability of traffic conditions. This involves determining optimal tolls in a stochastic environment, where both demand and capacity are subject to

in a stochastic traffic network.

uncertainty.

**50**

Although considerable research exists on congestion pricing and travel time reliability, relatively little research combines the two, especially regarding travelers' risk attitudes and/or the valuation of reliable travel [19]. Some examples of research that do combine congestion pricing and travel time reliability are included here. Li et al. [20] proposed a reliability-based optimal toll design bi-level model. On the upper level, network performance is optimized from a road authority point of view including travel time reliability, while a dynamic user-equilibrium is achieved from the viewpoint of travelers on the lower level. Boyles et al. [19] proposed a first-best congestion pricing model considering network capacity uncertainty and user valuation of travel time reliability, while [18] investigated marginal cost pricing in a stochastic traffic network in which demand uncertainty is explicitly considered. By assuming that all travelers have complete information about the road traffic condition, [18] derived an analytical function of Stochastic Network-Marginal Cost Pricing (SN-MCP) for a risk-neutral case and risk-based SN-MCP (RSN-MCP) for a risk-based case under the assumptions of lognormal demand and constant VMR across all OD pairs. Gardner et al. [21] consider the uncertainty in long-term travel demand and in day-to-day network capacity, and discuss the benefit of responsive pricing and travel information.

In the above-mentioned studies, MCP is analysis in a stochastic network, which considers either link supply uncertainty (e.g., see [19]) or stochastic travel demand (e.g., see [18]). In addition, to account for the travelers' perception error, researchers usually assume the commonly adopted Gumbel variate as the random error term and use the conventional logit-based Stochastic User Equilibrium (SUE) model. However, this approach may not reflect the travelers' perception of the random travel time exactly. Due to the variation of travel time, it is more rational to assume that the travelers' perception error is also dependent on the random perceived travel time [22]. Therefore, in order to explicitly consider both supply and demand aspects of a stochastic network and to reflect the travelers' perception error of the random travel time, this investigation extends [18] by (1) considering both the stochastic travel demand and link capacity degradation, and (2) incorporating travelers' perception error into the first-best MCP analysis.

The remainder of the chapter is organized as follows. The next section introduces the assumptions used in the analysis and presents the variational inequality (VI) formulation for different stochastic models. It also discusses the stochastic travel times under different sources of uncertainty. Then, Section 3 and Section 4

**Figure 1.** *Flow chart for the research process.*

derive the analytical function of SN-MCP for a risk-neutral case and RSN-MCP for a risk-based case in a stochastic network with both supply and demand uncertainty, respectively. In Section 5, the analysis for the PRSN-MCP is then described under different simplifications of network uncertainties. In Section 6, numerical examples with respect to a small-scale network and a medium-scale network (Sioux Falls network) are undertaken to demonstrate the effects of the proposed models. The final section contains some concluding remarks and recommends further research. The flow chart of the process applied in this chapter is presented in **Figure 1**.

~*ta* mean perceived travel time on link *a*

*Reliability-Based Marginal Cost Pricing Problem DOI: http://dx.doi.org/10.5772/intechopen.92844*

*a* free-flow travel time on link *a*∈ *A*

*ya* parameter, where *ya* ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

*εa Ta* j travelers' perception error on link *a*∈ *A*

*Ca* capacity of link *a*∈ *A*

A2. The route flow *F w*

ships among them

**53**

*t* variance of perceived travel time on link *a*∈ *A*

*T*~*T*~ total perceived travel time of the system, where *T*~*T*~ ¼ P

design capacity (upper bound) of link *a* ∈ *A* degree of worst-degraded capacity for link *a* ∈ *A*

p

closed-form formulation/calculation of the PRSN-MCP model.

opposed to the more commonly used normal distribution [18, 23].

dent random variable with a mean of *qw*and variance of *εw*

1 þ *VMR=va*

*N χ*, *ϖ*2 ð Þ perception error distribution of traveler, in this chapter *N χ*, *ϖ*2 ð Þ follows a normal distribution with predefined and deterministic mean *χ* and variance *ϖ*2

Before proceeding with the analysis, some assumptions are made to allow for the

A1. The travel demand *Qw* between each OD pair is assumed to be an indepen-

*r* , and link flow *Va* are also assumed to be independent

variance-to-mean ratio (*VMR*) of the random travel demand in which *VMRw* ¼

*q =qw*. Stochastic demand is further assumed to follow a lognormal distribution, which is a nonnegative, asymmetrical distribution. This has been adopted in the literature as a more realistic approximation of the stochastic travel demand, as

random variables that follow the same statistical distribution as OD demand. The

A3. The *VMRs* of travel demand are assumed to be the same for all OD pairs in

A4. The capacity degradation random variable *Ca* is independent of the traffic flow *va* on it and follows a uniform distribution with the design capacity *ca*of the link as its upper bound and the worst-degraded capacity as its lower bound (the

According to the Assumption A1 and A2, the OD travel demand, route flow *F w*

and link flow *Va* are random variables, which consequently induce the random route/link travel times. As such, we have the following flow conservation relation-

> *r*∈*Rw F w*

X *r*∈*Rw δw a*,*rF w*

where Eq. (1) is the travel demand conservation constraint, Eq. (2) is a definitional constraint that sums up all route flows that pass through a given link *a*,

*Qw* ¼ X

*w* ∈*W*

*F w*

*VMRs* of route flows are equal to those of the corresponding OD demand.

order to derive the closed-form formulation of the PRSN-MCP model.

lower bound would be a fraction *θa* of the design capacity).

*2.2.1 Stochastic network-system optimal (SN-SO) formulation*

*Va* ¼ X

**2.2 VI formulation for different stochastic network models**

*a*∈ *AVaT*~ *a*

*q* , while *VMRw* is the

*r* , *w* ∈*W* (1)

*r* ≥0, *w* ∈*W*,*r*∈*Rw* (3)

*r* , ∀*a*∈ *A* (2)

*r* ,

~*ε a*

*t* 0

*εw*