**1. State of the art**

Celiac disease (CD) is an immune-mediated disorder triggered by gluten ingestion in genetically susceptible subjects. About 1% of the European and North American population are affected, but the number of CD cases currently undiagnosed is suspected to be far superior to known cases due to the prevalence of forms with nonspecific symptoms. An increasing incidence of CD has been observed in developing countries, possibly due to westernization of the local diet, changes in wheat production/preparation, and increasing simplicity of diagnostic techniques. The principal determinant of genetic susceptibility to CD is the major histocompatibility class II HLA molecules. The HLA-DQ2 haplotype is expressed in the majority of patients with CD, whereas the HLA-DQ8 haplotype is expressed only in a minority of patients. However, although the presence of the DQ2 and DQ8 haplotypes is a necessary condition, it is not sufficient for the development of CD. In point of fact, only 10% of people with a genetic predisposition goes on to develop CD.

Gluten is a protein complex rich in proline and glutamine and is found in wheat, rye, and barley. The term gluten refers to a group of prolamins of wheat (gliadin and glutenin). Other prolamins are found in rye (secalin) and barley (hordein) and are genetically similar to each other.

It is particularly interesting that maize, while containing prolamins, causes no mucosal damage in celiac patients, most likely because a different phylogenetic evolution of maize prolamins makes its consumption safe for celiac subjects and not toxic.

Gluten is poorly digested in the human intestine regardless of the presence of celiac disease. Its oligopeptides cross the intestinal mucosa and reach the submucosa where they are deamidated by transglutaminase type 2 (tTG2). Deamidation promotes high affinity binding with HLA DQ2 and DQ8 expressed on the surface of T lymphocytes. In celiac patients, this process triggers an inflammatory and immune-mediated response, typical of the disease. T lymphocytes recognize the HLA complex and release various cytokines including IL-15 and IFN-γ. These molecules induce the activation and clonal expansion of B cells which produce antibodies against gluten as well as autoantibodies against tTG2. Other cytokines stimulate fibroblasts and inflammatory cells to secrete matrix metalloproteinases with consequent tissue remodeling and further release of tTG2 in the extracellular compartment. At the same time, there is an increase in intraepithelial lymphocytes with cytolytic activity which determines epithelial damage.

The typical histological lesions of celiac disease are villous atrophy, intraepithelial lymphocytosis, and crypt hyperplasia. Villous atrophy consists of decreased villous height and alteration of normal crypt/villous ratio (3:1) until total disappearance of villi. Intraepithelial lymphocytosis is defined as a number of intraepithelial lymphocyte (IEL) greater than 30 per 100 enterocytes. Crypt hyperplasia is the extension of the regenerative epithelial crypts associated with changes in the presence of more than one mitosis per crypt.

These elementary lesions associated with celiac disease are identified through duodenal biopsies from endoscopic evaluation. Multiple biopsies of the duodenum (at least one biopsy of the bulb and four of the distal part of the duodenum) are required to make a diagnosis as elementary lesions are not exclusive and frequently may be patchy [1].

In children, adding biopsies of the bulb increases diagnostic reliability, owing to the fact that in 10% of pediatric patients, villous atrophy is exclusively located in the duodenal bulb [2].

Histological changes can be classified according to the Marsh classification which identifies three entities: (1) type 1 or infiltrative lesions (normal villous and crypt architecture, normal villous/crypt ratio, and an increased number of intraepithelial lymphocytes); (2) type 2 or hyperplastic lesion (normal villous architecture, hyperplasia of the glandular element with an increased number of mitoses, and increased intraepithelial lymphocytes); and (3) type 3 or destructive lesion (varying degrees of villous atrophy associated with hyperplasia of the glandular crypt and increased intraepithelial lymphocytes). Oberhuber et al. [3] proposed a different classification dividing the Marsh type 3 lesion into three subgroups according to the severity of villous atrophy: (3a) mild villous atrophy and pathological increase of IELs; (3b) moderate villous atrophy and pathological increase of IELs; and (3c) total villous atrophy and pathological increase of IELs.

Diagnosis of CD is based not only on histology but also on the presence of specific serological markers which should be performed in patients on a glutencontaining diet.

Anti-tTG2 is circulating, gluten-dependent, autoantibodies that target transglutaminase 2, the principal self-antigen involved in pathogenesis of CD. IgA anti-tTG2 has high sensitivity (97%) and specificity (91%) and is deemed the single most

**55**

*The Emerging Role of the Autophagy Process in Children with Celiac Disease: Current Status…*

reliable test for detection of CD in primary care in cases of clinical suspicion or as a screening test in relatives of celiac patients or in people with an increased risk of developing CD. In comparison with the anti-endomysial antibody, the anti-tTG2 IgA assay has greater sensitivity and reproducibility. It is important to remember that IgA deficiency is more common among celiac patients than in the general population; therefore, in cases of low serum IgA levels, IgG class anti-tTG2 should be evaluated. Anti-endomysial antibodies (EMA) are directed against the intermyofibril substance of smooth muscle, which may correspond to either a reticulin-like structure or a surface component of smooth muscle fibrils. These are detected by indirect immunofluorescence on monkey esophagus cells and on human umbilical cord cells as a substrate. The EMA assay specificity is high (100%), but it is also IgAbased and the EMA IgG assay is not widely available. Anti-endomysial antibodies are considered a confirmatory assay and should be used only in cases of borderline

Testing for antibodies directed against native gliadin is no longer recommended. However, antibodies against synthetic deamidated IgG class gliadin peptides (anti-

Histological evaluation and serological markers are important for diagnosis but also for testing efficacy of alternative therapies for celiac disease, as mentioned below. Currently, the only effective treatment for celiac disease is a strict gluten-free diet (GFD). The aim of dietary regimen is recovery of intestinal damage (usually within 24 months), disappearance of serological markers, and resolution of symptoms, when present. Moreover, a GFD improves nutritional parameters including

Celiac patients should avoid all products containing wheat, barley, and rye for life. Complete elimination of gluten is very difficult, especially due to contamina-

Strict avoidance of gluten is demanding especially in Mediterranean countries

The definition "gluten-free" is reserved for foods having less than 20 parts per million of gluten. The lowest quantity of gluten known to be responsible for mucosal damage ranges from 10 to 50 mg per day. A gluten intake of less than 10 mg per

Nevertheless, some patients may be more sensitive than others are to gluten

The gluten-free diet has numerous difficulties; a significant lifestyle change is required by patients, and it may be challenging especially in Western countries

Furthermore, gluten-free products are more expensive [4] and are known to

Hypothetical gluten exposure in restaurants may also be a source of anxiety for

It is extremely important that patients know potential hidden sources of gluten and obtain precise information about gluten-free substitute and their fiber and nutrient content. Celiac patients should have high-fiber diets and frequently need supplementation of iron, folic acid, vitamin B12, and vitamin D. It may be very

Serological markers are used to assess adhesion to gluten-free diet and its efficacy. First of all, in a patient with persistent symptoms, despite a gluten-free diet, it is mandatory to verify strictly compliance to GFD and in particular to investigate

exposure. Therefore, compliance to GFD should be strict and lifelong.

useful to refer patients to a dietitian at the time of diagnosis.

where gluten ingestion in normal diet is high as well as in adolescence and in asymptomatic children diagnosed by screening. Therefore, CD subjects should be monitored annually for adherence to the GFD. Verification of the disappearance of

*DOI: http://dx.doi.org/10.5772/intechopen.80692*

positive or possibly false positive results for anti-tTG2.

DPG) have a diagnostic role in cases of IgA deficiency.

the specific antibodies is important during follow-up.

body mass index and bone mineral density.

tion of other foods with traces of gluten.

day is unlikely to cause mucosal damage.

where gluten is contained in a lot of foods.

have poor palatability and high fat content.

celiac patients [5].

### *The Emerging Role of the Autophagy Process in Children with Celiac Disease: Current Status… DOI: http://dx.doi.org/10.5772/intechopen.80692*

reliable test for detection of CD in primary care in cases of clinical suspicion or as a screening test in relatives of celiac patients or in people with an increased risk of developing CD. In comparison with the anti-endomysial antibody, the anti-tTG2 IgA assay has greater sensitivity and reproducibility. It is important to remember that IgA deficiency is more common among celiac patients than in the general population; therefore, in cases of low serum IgA levels, IgG class anti-tTG2 should be evaluated.

Anti-endomysial antibodies (EMA) are directed against the intermyofibril substance of smooth muscle, which may correspond to either a reticulin-like structure or a surface component of smooth muscle fibrils. These are detected by indirect immunofluorescence on monkey esophagus cells and on human umbilical cord cells as a substrate. The EMA assay specificity is high (100%), but it is also IgAbased and the EMA IgG assay is not widely available. Anti-endomysial antibodies are considered a confirmatory assay and should be used only in cases of borderline positive or possibly false positive results for anti-tTG2.

Testing for antibodies directed against native gliadin is no longer recommended. However, antibodies against synthetic deamidated IgG class gliadin peptides (anti-DPG) have a diagnostic role in cases of IgA deficiency.

Histological evaluation and serological markers are important for diagnosis but also for testing efficacy of alternative therapies for celiac disease, as mentioned below.

Currently, the only effective treatment for celiac disease is a strict gluten-free diet (GFD). The aim of dietary regimen is recovery of intestinal damage (usually within 24 months), disappearance of serological markers, and resolution of symptoms, when present. Moreover, a GFD improves nutritional parameters including body mass index and bone mineral density.

Celiac patients should avoid all products containing wheat, barley, and rye for life. Complete elimination of gluten is very difficult, especially due to contamination of other foods with traces of gluten.

Strict avoidance of gluten is demanding especially in Mediterranean countries where gluten ingestion in normal diet is high as well as in adolescence and in asymptomatic children diagnosed by screening. Therefore, CD subjects should be monitored annually for adherence to the GFD. Verification of the disappearance of the specific antibodies is important during follow-up.

The definition "gluten-free" is reserved for foods having less than 20 parts per million of gluten. The lowest quantity of gluten known to be responsible for mucosal damage ranges from 10 to 50 mg per day. A gluten intake of less than 10 mg per day is unlikely to cause mucosal damage.

Nevertheless, some patients may be more sensitive than others are to gluten exposure. Therefore, compliance to GFD should be strict and lifelong.

The gluten-free diet has numerous difficulties; a significant lifestyle change is required by patients, and it may be challenging especially in Western countries where gluten is contained in a lot of foods.

Furthermore, gluten-free products are more expensive [4] and are known to have poor palatability and high fat content.

Hypothetical gluten exposure in restaurants may also be a source of anxiety for celiac patients [5].

It is extremely important that patients know potential hidden sources of gluten and obtain precise information about gluten-free substitute and their fiber and nutrient content. Celiac patients should have high-fiber diets and frequently need supplementation of iron, folic acid, vitamin B12, and vitamin D. It may be very useful to refer patients to a dietitian at the time of diagnosis.

Serological markers are used to assess adhesion to gluten-free diet and its efficacy. First of all, in a patient with persistent symptoms, despite a gluten-free diet, it is mandatory to verify strictly compliance to GFD and in particular to investigate

*Celiac Disease - From the Bench to the Clinic*

genetically similar to each other.

Gluten is a protein complex rich in proline and glutamine and is found in wheat, rye, and barley. The term gluten refers to a group of prolamins of wheat (gliadin and glutenin). Other prolamins are found in rye (secalin) and barley (hordein) and are

It is particularly interesting that maize, while containing prolamins, causes no mucosal damage in celiac patients, most likely because a different phylogenetic evolution of maize prolamins makes its consumption safe for celiac subjects and not toxic. Gluten is poorly digested in the human intestine regardless of the presence of celiac disease. Its oligopeptides cross the intestinal mucosa and reach the submucosa where they are deamidated by transglutaminase type 2 (tTG2). Deamidation promotes high affinity binding with HLA DQ2 and DQ8 expressed on the surface of T lymphocytes. In celiac patients, this process triggers an inflammatory and immune-mediated response, typical of the disease. T lymphocytes recognize the HLA complex and release various cytokines including IL-15 and IFN-γ. These molecules induce the activation and clonal expansion of B cells which produce antibodies against gluten as well as autoantibodies against tTG2. Other cytokines stimulate fibroblasts and inflammatory cells to secrete matrix metalloproteinases with consequent tissue remodeling and further release of tTG2 in the extracellular compartment. At the same time, there is an increase in intraepithelial lymphocytes

The typical histological lesions of celiac disease are villous atrophy, intraepithelial lymphocytosis, and crypt hyperplasia. Villous atrophy consists of decreased villous height and alteration of normal crypt/villous ratio (3:1) until total disappearance of villi. Intraepithelial lymphocytosis is defined as a number of intraepithelial lymphocyte (IEL) greater than 30 per 100 enterocytes. Crypt hyperplasia is the extension of the regenerative epithelial crypts associated with changes in the

These elementary lesions associated with celiac disease are identified through duodenal biopsies from endoscopic evaluation. Multiple biopsies of the duodenum (at least one biopsy of the bulb and four of the distal part of the duodenum) are required to make a diagnosis as elementary lesions are not exclusive and frequently

In children, adding biopsies of the bulb increases diagnostic reliability, owing to the fact that in 10% of pediatric patients, villous atrophy is exclusively located in the

Histological changes can be classified according to the Marsh classification which identifies three entities: (1) type 1 or infiltrative lesions (normal villous and crypt architecture, normal villous/crypt ratio, and an increased number of intraepithelial lymphocytes); (2) type 2 or hyperplastic lesion (normal villous architecture, hyperplasia of the glandular element with an increased number of mitoses, and increased intraepithelial lymphocytes); and (3) type 3 or destructive lesion (varying degrees of villous atrophy associated with hyperplasia of the glandular crypt and increased intraepithelial lymphocytes). Oberhuber et al. [3] proposed a different classification dividing the Marsh type 3 lesion into three subgroups according to the severity of villous atrophy: (3a) mild villous atrophy and pathological increase of IELs; (3b) moderate villous atrophy and pathological increase of IELs; and (3c)

Diagnosis of CD is based not only on histology but also on the presence of specific serological markers which should be performed in patients on a gluten-

Anti-tTG2 is circulating, gluten-dependent, autoantibodies that target transglutaminase 2, the principal self-antigen involved in pathogenesis of CD. IgA anti-tTG2 has high sensitivity (97%) and specificity (91%) and is deemed the single most

with cytolytic activity which determines epithelial damage.

presence of more than one mitosis per crypt.

total villous atrophy and pathological increase of IELs.

may be patchy [1].

duodenal bulb [2].

containing diet.

**54**

the possibility of inadvertent gluten exposure. Second, it is important to exclude other causes of persistent symptoms. It is necessary to underline the hypothetic presence of alternative diagnosis (i.e., lactose or fructose intolerance, irritable bowel syndrome, microscopic colitis, pancreatic insufficiency, and small intestinal bacterial overgrowth). Another reason for the recurrence of clinical manifestations is refractory celiac disease, whereby CD patients present symptoms of malabsorption and villous atrophy despite a GFD for more than 12 months. In the primary form, there is no initial response to a diet, while in the secondary one, a relapse occurs after an initial response to a GFD. Patients with refractory CD are at risk of developing enteropathy-associated T cell lymphomas.


*2.1. CHOC*

The CHOC Neonatal Intensive Care Unit (NICU) is a level IV, 104-bed NICU with a Surgical NICU, Small Baby Unit, Neuro NICU and Cardiac NICU within a free-standing Children's hospital that also has a Pediatric Residency and Neonatal Fellowship program. Participation in Simulating Success was intended to enhance positive team behaviors during neonatal resuscitation that impact patient outcomes. The SMART aims were to (1) increase staff participation in at least one multidisciplinary simulation team

training in the NICU from baseline of 0% to a target of 75% by June 2019; and (2) to improve patient safety through simulation exercises as demonstrated by a decrease in LSTs identified from a baseline of 4.5 per simulation to one over a period of six months, from January to June 2019.

LSTs are improvement goals identified during simulation exercises that have an impact on delivery of optimal care to the patient [14,16,17]. In situ simulations can help identify these knowledge gaps and reinforce positive team behaviors [18]. Knowledge gaps were further categorized as cognitive, technical, or behavioral. The CHOC instructor team used these debriefings to help identify LSTs. The CAPE Real-Time Debriefing Evaluation (DART) tool was used to assess the e ffectiveness of the debriefer(s) and participation of the learners during debriefing (Appendix A). Using the DART tool, a goal ratio of trainee responses to instructor questions plus statements is ideally >3:1. Participants were also asked to submit post-simulation surveys which included 13 questions related to understanding scenario learning objectives, duration and realism of the simulation, facilitators' ability to encourage participation and knowledge base, participants' confidence and psychological safety (Appendix A). The purpose of these were twofold: (1) to ideally increase the value of the program for trainees; and (2) to generate continuous data collection and share it with the Patient Safety Committee and hospital administration to engender support. The data was collected electronically via a QR code and entered into Research Electronic Data Capture (REDCap)—an existing data collection platform used by the hospital.


2.2.2. Q347A and Q990A Act Synergistically to Reduce the Transport of Calcein-AM

All three double mutant combinations and the triple mutant (Qtriple) were generated. Their ability to transport Calcein-AM showed pronounced and unexpected differences. A simple additive effect of Q347A and Q990A would predict a functionality of the Q347/990A double mutant to be 57% (the level of functionality of the Q990A mutant multiplied by the level of functionality of the Q347A mutant; 90/100 × 63/100 = 57/100). The observed activity of the Q347/990A mutant was reduced to 8.8% of the wild-type transporter suggesting a synergistic effect of the combined mutations and the importance of these two hydrogen bond donors for the efficient efflux of Calcein-AM. However, it is clearly not essential that these two glutamines are present because the 8.8 ± 1.87% (mean ± SEM) level of activity remains statistically higher than the Walker B mutant E556/1201Q (1.3 ± 0.59%) which is unable to hydrolyze ATP, indicating that the Q347/990A mutant retains measurable function.

**Figure 3.** Functionality of glutamine to alanine mutants for the transport of Calcein-AM. Live HEK293T cells transiently expressing equivalent amounts of wild-type (wt) and mutant ABCB1 were challenged with Calcein-AM. Functionality was measured as the ratio of Calcein accumulation (Calcein-AM only becomes fluorescent once it is de-esterified in the cytosol) between the ABCB1 expressing and untransfected cells within the population. This was normalized to 100% for wild-type ABCB1 for the bar graph shown. The mean ± SEM was plotted using GraphPad Prism version 8; sample number was ≥3. Selected statistical analysis (ratio of paired Student's *t*-test, two-tailed) performed on the raw data is shown with *p* values: \* <0.05, \*\* <0.01. The full pairwise comparison of the data is given in Appendix A Table A1.

**2021**, , x FOR PEER REVIEW 4 of 16


**6. Conclusions**

The picture we have attempted to draw in the present review moves from the important role specific mitochondrial dehydrogenases play in cell metabolism. Under conditions in which metabolic reprogramming occurs (i.e. cancer, diabetes, obesity), cells move away from efficient mitochondrial bioenergetics and come to rely on glycolysis for ATP generation purposes. This metabolic shift has the unintended consequence of increasing reactive oxygen species production, which further disrupt cell metabolism and activate genes and oncogenes through specific signaling pathways and nuclear transcription factors (HIF-1α, MAPKs, PI3K). Current and future lines of research aim at better understanding the signaling and metabolic routes connecting mitochondria to cell functions in the attempt to possibly recondition metabolism and energy production of target cell and mitochondria.

[9] McKenna MC, Ferreira GC. The glutamate/ GABA-glutamine cycle. In: Enzyme Complexes Important for the Glutamate-Glutamine Cycle. Springer Int; 2016. pp. 59-98 [10] Tretter L, Adam-Vizi V. Alpha-ketoglutarate dehydrogenase: A target and generator of oxidative stress. Philosophical Transactions of the Royal Society B: Biological Sciences.

Physiology and Pathology of Mitochondrial Dehydrogenases

http://dx.doi.org/10.5772/intechopen.76403

135

[11] Panov A, Scarpa A. Independent modulation of the activity of alpha-ketoglutarate dehy-

[12] McLain AL, Szweda PA, Szweda LI. α-Ketoglutarate dehydrogenase: A mitochondrial

[13] McLain AL, Cormier PJ, Kinter M, Szweda LI. Glutathionylation of α-ketoglutarate dehydrogenase: The chemical nature and relative susceptibility of the cofactor lipoic

[14] Applegate MA, Humphries KM, Szweda LI. Reversible inhibition of alpha-ketoglutarate dehydrogenase by hydrogen peroxide: Glutathionylation and protection of lipoic acid.

[15] Tadhg PB, McMurry J. The Organic Chemistry of Biological Pathways. Roberts and Co.

[16] Oyedotun KS, Lemire BD. The quaternary structure of the Saccharomyces cerevisiae succinate dehydrogenase. Homology modeling, cofactor docking, and molecular dynamics

[17] Yankovskaya V, Horsefield R, Törnroth S, Luna-Chavez C, Miyoshi H, Léger C, Byrne B, Cecchini G, Iwata S. Architecture of succinate dehydrogenase and reactive oxygen spe-

[18] Horsefield R, Yankovskaya V, Sexton G, Whittingham W, Shiomi K, Omura S, Byrne B, Cecchini G, Iwata S. Structural and computational analysis of the quinone-binding site of complex II (succinate-ubiquinone oxidoreductase): A mechanism of electron transfer and proton conduction during ubiquinone reduction. The Journal of Biological

[19] Selak MA, Armour SM, MacKenzie ED, Boulahbel H, Watson DG, Mansfield KD, Pan Y, Simon MC, Thompson CB, Gottlieb E. Succinate links TCA cycle dysfunction to onco-

[20] Jaimes R. Functional response of the isolated, perfused normoxic heart to pyruvate dehydrogenase activation by dichloroacetate and pyruvate. Pflügers Archiv. 2015;**468**:131-142

[21] Ward PS, Thompson CB. Metabolic reprogramming: A cancer hallmark even Warburg

[22] Michelakis ED, Sutendra G, Dromparis P, Weber L, Haromy A, Niven E, Maguire C, Gammer TL, Mackey JR, Fulton D, Abdulkarim B, McMurtry MS, Petruk KC. Metabolic modulation of glioblastoma with dichloroacetate. Science Translational Medicine. 2010;

genesis by inhibiting HIF-alpha prolyl hydroxylase. Cancer Cell. 2005;**7**:77-85

simulation studies. The Journal of Biological Chemistry. 2004;**279**:9424-9431

drogenase complex by Ca2+ and Mg2+. Biochemistry. 1996;**16**:427-432

acid to modification. Free Radical Biology & Medicine. 2013;**61**:161-169

redox sensor. Free Radical Research. 2011;**45**:29-36

2005;**360**:2335-2345

Biochemistry. 2008;**47**:473-478

Publishers; 2005. pp. 189-190

Chemistry. 2006;**281**:7309-7316

**2**:31ra34

cies generation. Science. 2003;**229**:700-704

did not anticipate. Cancer Cell. 2012;**21**:297-308


**4.6 The overall rating**

As alluded at the beginning, the five key components of a mini-grid rating which have been distilled into two profile categories – the "Regulatory framework effectiveness and economic profile" and the "flexibility and performance profile" – will be summarized and combined to produce a final, overall mini-grid rating. The two aforementioned profiles that were created as an intermediate step are the base to attain the final, overall SRMP mini-grid rating.

The five factors of the SRMP mini-grid rating procedure are allocated to two categories – the 'regulatory framework effectiveness and economic profile' and the 'flexibility and performance profile'. These profiles are subsequently combined to receive a final, overall mini-grid rating. **Table 13** presents the results in the case of the Tsumkwe mini-grid.


7. FEM MATLAB model setup, formulation and implementation

In order to implement the conductor model in MATLAB environment, finite element analysis formulation was done as function of the physical state of power transmission line conductor. The models developed using finite element analysis can then be implemented in MATLAB. The FEM model enables the analysis of the dynamic behavior and response of power line conductor to the dynamic forces of wind [33]. Consider a power transmission line subjected to dynamic aeolian vibration as an assembly of thin strands having distributed mass and elasticity. The physical model can be represented used partial differential equations. Each strand in the transmission line experiences axial, bending and torsional loads from the wind [34, 35]. The accurate representation of each factor is critical in the determination of the dynamic behavior of power transmission lines [36, 37]. Euler-Bernoulli curved beam theory was used to formulate the finite element model of power transmission lines.

Consider a power transmission line experiencing a vertical force, curvature and an axial force has an axial displacement modeled in Eq. (49) as [21]:

$$u(\mathbf{x}, y) = u\_0(\mathbf{x}) + \frac{v}{R} - y\left(\theta\_\mathbf{x} + \frac{u(\mathbf{x})}{R}\right) \tag{49}$$

Where θx represents the rotation of the power line due to flexural effect, R represents the radius of rotation, y represents the distance from the axis of rotation to the centroidal axis of the conductor or transverse displacement, v represents tangential displacement and u xð Þ represents the axial displacement of the power lines. The shape function for power transmission lines having rotation, bending and axial motion components is modeled using discretization techniques and represented in Eqs. (50)–(52) as:

$$u(s) = b\_0 + b\_1 s \tag{50}$$

$$
\sigma(\mathbf{s}) = \mathbf{c}\_0 + \mathbf{c}\_1 \mathbf{S} + \mathbf{c}\_2 \mathbf{S}^2 + \mathbf{c}\_3 \mathbf{S}^3 \tag{51}
$$

$$\theta = \frac{dv(S)}{ds} = c\_1 + 2c\_2S + 3c\_3S^2 \tag{52}$$

The solution to the discretization of the models yields Eq. (53) to Eq. (59):

$$
\begin{bmatrix} u \\ v \\ \theta \end{bmatrix} = \begin{bmatrix} N\_1 & 0 & N\_2 & 0 & 0 & 0 \\ 0 & N\_3 & 0 & N\_4 & N\_5 & N\_6 \\ 0 & 0 & N\_4 & 0 & N\_5 & N\_6 \end{bmatrix} \begin{bmatrix} u\_1 \\ v\_1 \\ \theta\_1 \\ u\_2 \\ u\_3 \\ v\_2 \\ \theta\_2 \end{bmatrix} \tag{53}
$$

Where

$$N\_1 = \frac{1}{2}(1 - \zeta) \tag{54}$$

$$N\_2 = \frac{1}{2}(1+\zeta) \tag{55}$$

$$N\_3 = \frac{1}{4} \left( 2 - 3\zeta + \zeta^3 \right) \tag{56}$$

$$N\_4 = \frac{1}{4} \left( 1 - \zeta - \zeta^2 - \zeta^3 \right) \tag{57}$$

$$N\_5 = \frac{1}{4} \left( 2 + 3\zeta - \zeta^3 \right) \tag{58}$$

$$N\_{\theta} = \frac{1}{4} \left( 1 - \zeta + \zeta^2 + \zeta^3 \right) \tag{59}$$

The power line matrix model contains the strand stiffness K, mass matrix M and the load vector F. They are expressed in Eq. (60) as:

High Voltage Transmission Line Vibration: Using MATLAB to Implement the Finite Element Model of a Wind… 51 http://dx.doi.org/10.5772/intechopen.75186

$$\mathbf{N}[K] = \frac{1}{2} \left[ \mathbf{N}\_a{}^T (EA) \mathbf{N}\_a \ \delta \zeta + \frac{1}{2} \right] \mathbf{N}\_B{}^T (EI) \mathbf{N}\_B \ \delta \zeta + \frac{1}{2} \left[ \mathbf{N}\_B{}^T (T) \mathbf{N}\_{B,T} \ \delta \zeta \tag{60}$$

Where A represents the cross-sectional area of the power line, E represents the young modulus of the power line material, I represents polar moment of area, T represents the kinetic energy of the system. The matrix is modeled in Eq. (61).

$$[M] = \frac{1}{2} \left[ \dot{\boldsymbol{\mu}}^T \rho A \dot{\boldsymbol{\mu}} + \frac{1}{2} \right] \dot{\boldsymbol{g}}^T \rho A \dot{\boldsymbol{\psi}} \tag{61}$$

Where r represents the density of the power line material and Eq. (62) indicates external excitation.

$$
\delta W = \frac{1}{2} \int F \cdot \delta u \tag{62}
$$

The power line conductor model is constructed using Euler-Bernoulli theories and summarized in Eq. (63) as:

$$
\begin{bmatrix} M\_{11} & M\_{12} \\ M\_{21} & M\_{22} \end{bmatrix} \begin{pmatrix} \ddot{u} \\ \ddot{v} \end{pmatrix} + \begin{bmatrix} K\_{11} & K\_{12} \\ K\_{21} & K\_{22} \end{bmatrix} \begin{pmatrix} u \\ v \end{pmatrix} = \begin{pmatrix} F\_1 \\ F\_2 \end{pmatrix} \tag{63}
$$

The finite element analysis follows a step by step numerical computation in the MATLAB environment as documented in [38, 39]. The dynamic response analysis assumes continuous displacement, velocity and acceleration [40, 41]. The numerical integration technique utilized was based on Newmark integration method. The compact form of the high voltage transmission line model is expressed in Eqs. (64)–(69) as [18]:

$$[M]\{\ddot{y}\} + [\mathbb{C}]\{\dot{y}\} + [\mathbb{K}]\{y\} = [F] \tag{64}$$

$$\mathbb{E}\left[\overset{\wedge}{K}\right]\_{s+1} = [K]\_{s+1} + a\_3[m]\_{s+1} \tag{65}$$

$$\left[\stackrel{\wedge}{F}\right]\_{s,s+1} = \{F\}\_{s+1} + [m]\_{s+1} \left(a\{y\}\_s + a\{\dot{y}\}\_s + a\{\ddot{y}\}\_s\right) \tag{66}$$

$$a\_3 = \frac{2}{\chi \left(\Delta t\right)^2} \tag{67}$$

$$a\_4 = \frac{2}{\gamma \Delta t} \tag{68}$$

$$a\_5 = \frac{1}{\mathcal{V}} - 1\tag{69}$$

The initial conditions are expressed in Eq. (70) as:

$$\left[\ddot{y}\right]\_0 = \left[\mathcal{M}\right]^{-1}\left[F\right]\_0 - \left[\mathcal{K}\right]^{-1}\left[y\right]\_0\tag{70}$$

The acceleration vector is expressed in Eqs. (71)–(74) as:

$$\left[\ddot{y}\right]\_{s+1} = a\_3 \left( \{y\}\_{s+1} - \{y\}\_s \right) - a\_4 \{\dot{y}\} - a\_5 \{\ddot{y}\}\_s \tag{71}$$

$$\left[\ddot{y}\right]\_{s+1} = \left\{\ddot{y}\right\}\_{s} + a\_{2}\{\ddot{y}\}\_{s} = a\_{1}\{\ddot{y}\}\_{s+1} \tag{72}$$

$$a\_1 = a \Delta t \tag{73}$$

$$a\_2 = (1 - \alpha)\Delta t\tag{74}$$


*Assed Haddad, Civil Engineering Series Editor*

Published in London, UK © 2024 IntechOpen © Jarwis / iStock

New Research on Railway Engineering and Transportation

IntechOpen Series

Civil Engineering, Volume 3

New Research on

Railway Engineering and

Transportation

*Edited by Ali G. Hessami and Roderick Muttram*


**1. Introduction**

Trace elements such as Fluoride (F) are essential to animals and humans for normal health status. Fluorine is the ninth element on the periodic table. It has crustal abundance of 0.054%, which makes it the 24th most abundance element on the earth and most reactive member of the halogen family. It has an atomic weight of 18.9984. The physical and chemical properties of fluorine have been given in **Table 1**. Fluorine reacts with other elements to produce ionic compounds such as calcium fluoride (CaF), sodium fluoride (NaF), hydrogen fluoride (HF), aluminum fluoride (AlF), and many other compounds [1, 2]. In general, F-like elements causus only a source of local pollution [3]. The degree of toxicity, the scope of exploitation of the element, and its application and subsequent mobilization into the air, water, and soil are used to assess the environmental relevance of increased levels of these elements.

#### **Table 1.**

*The physical and chemical properties of fluorine.*


*2.3. Litterbag Experiment*

Foliar litters of the four dominant trees species in this alpine forest were studied using an in situ litterbag method [22]. In the fall of 2012, senesced needles or leaves of each tree species were collected on tarpaulins from 20 or more trees (15–20 cm in diameter) by shaking their limbs. Green or partly decomposed needles (leaves), twigs and bark were removed, and only newly shed foliar litter was air-dried at room temperature for two weeks. Litter samples (10 ± 0.05 g) were placed into nylon litterbags (20 × 25 cm in size with mesh sizes of 1.0 mm on the top and 0.5 mm on the bottom). A total of 1172 litterbags (2 litterbags × 6 replicates × 4 litter species × 2 snow plots × 12 sampling times + 5 litterbags × 4 litter species) were incubated in the deep and shallow snow plots on November 15 and 16, 2012. Litterbags in the same subplots were strung together and kept 2–5 cm apart. Five litterbags of each litter species were randomly collected to determine the losses during

sample establishment and the gravimetric water contents of these air-dried litter samples before field incubation.

**Figure 1.** Snow depth, temperature and freeze–thaw cycle. (**a**) Snow depths (±SE, *n* = 18) in deep and shallow snow plots on each sampling date. The samplings were scheduled at the ends of the snow formation, snow coverage and snowmelt stages during winter from 2012 to 2014 (only the snowmelt stages from 2014 to 2016) and at the end of the growing season (beginning of the snow formation stage). The differences between deep and shallow snow plots are significant (*p* < 0.05) on all sampling dates. (**b**) Daily temperatures (*n* = 6) at the litter surface during the four years of decomposition. Winter times including the snow formation, snow coverage and snowmelt stages are shaded. The dashed line is drawn at the zero value. (**c**) Mean temperatures (±SE, *n* = 6) at individual stages. The times between two adjacent sampling dates were defined as separate stages. (**d**) Freeze–thaw cycles (±SE, *n* = 6) at individual stages. The values were calculated by the quotients of the total number of freeze–thaw cycles and the number of days of certain stages. For panel c and d, the winters in 2015 and 2016 were not divided into snow formation, snow coverage and snowmelt stages. SF: snow formation stage, SC: snow coverage stage, SM: snowmelt stage, W: winter, and GS: growing season. \* *p* < 0.05, \*\* *p* < 0.01 and \*\*\* *p* < 0.001.

#### *2.4. Sampling and Analysis*

On each sampling date, snow depths were manually measured in triplicate in each deep and shallow snow plot (*n* = 18). Temperatures at the litter surface were recorded using data loggers (iButton DS1923-F5, Sunnyvale, CA, USA) placed in marked litterbags in deep and shallow snow plots (both *n* = 6). Based on hourly temperature data, a freeze–thaw cycle was defined as a transition above or below 0 ◦C for at least 3 h and then a transition back [25].

Two litterbags per subplot were randomly collected, carefully placed in separate plastic bags and returned to the laboratory. Roots, mosses and soils were carefully removed from the litter samples. One cleaned subsample was oven-dried at 105 ◦C for 48 h to measure the dry mass remaining and gravimetric water content in the decomposing litter. The remaining mass of decomposing litter was evaluated on a dry matter basis. Another subsample was air-dried, milled and used to extract the acid hydrolysable components using an acid hydrolysis method [26]. In our long-term study in this alpine forest, we also measured proximate fractions, elements, humic substances and microbial activities during

the decomposition of these foliar litters. In this study, we focused on the release pattern of acid hydrolysable components.

Here, the acid hydrolysable components were defined as the fraction that can be hydrolyzed by 2.5 mol/L H2SO4 [26]. These components were different with acid-soluble substances hydrolyzed by 72% H2SO4 as well as with dissolved organic carbon or hot-water extractable carbon, which are considered to be more labile with higher decomposability than acid hydrolysable components. In this study, the acid hydrolysable components include some polysaccharide, hemicellulose, cellulose and soluble lignin or phenols [6].

Specifically, a 0.10 g subsample was hydrolyzed by 2.5 mol/L H2SO4 at 105 ◦C for 30 min. The extracted acid hydrolysable components were diluted with deionized water, filtered through a 0.45 μm mesh and measured using a TOC analyzer (multi N/C 2100, Analytic Jena, Thüringen, Germany). Litter C and N contents were determined by elemental analyzer (Vario Max CN, Elementar, Germany) and were used to calculate litter C/N stoichiometry. Microbial biomass C content was measured using the chloroform fumigationincubation method [27]. At the same time, a 0.5 g subsample was oven-dried at 105 ◦C for 48 h to determine the gravimetric water content in the air-dried decomposing litter. The content of acid hydrolysable components was calculated based on the dry mass of decomposing litter.