**Clinical Application of One-Step Diagnosis for Ectopic Pregnancy by HCG Ratio: Hemoperitoneum Versus Venous Serum**

Yu-dong Wang, Wei-wei Cheng and Xiao-ping Wan *International Peace Maternal and Child Health hospital, Shanghai Jiaotong University China*

#### **1. Introduction**

136 Ectopic Pregnancy – Modern Diagnosis and Management

Tuomivaara L, Kauppila A. (1988). Radical or Conservative Surgery for Ectopic Pregnancy.

Udigwe GO, Umeonunihu OS, Mbachu II. (2010) Ectopic Pregnancy: A Five Year Review Of

Varma R, Gupta J. (2009). Tubal Ectopic Pregnancy. *Clinical Evidence.* Vol 04. Pp 1406. ISSN

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160-165. ISSN 1115 - 2613

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A Follow-Up Study of Fertility of 323 Patients. *Fertility and Sterility*. Vol 50. (1988).

Cases At Nnamdi Azikiwe University Teaching Hospital (NAUTH), Nnewi, Nigeria. *Nigerian Journal of Medicine.* Vol 51. No 4. (October-December 2010). Pp

> Suspected ectopic pregnancy (SEP) means a woman whose hemoperitoneum and pregnancy test are positive but the gestational sac is uncertain, which is finally diagnosed as an ectopic pregnancy (EP) or a hemoperitoneum with intrauterine pregnancy (hIUP). For emergency physicians, it is mostly important to differentiate EPs rapidly from hIUPs of which the vast majority can be managed without surgery. The combination of transvaginal ultrasound and serum HCG determination seem to be reliable for the early diagnosis of EP (Kaplan et al., 1996; Mol et al., 1998.). However, in most of the emergency rooms (especially on the night shift) in the general hospital, transvaginal ultrasound is often unavailable or instead of transabdominal ultrasound operated by a nonprofessional gynecologist in developing countries, which limits the prompt and accurate diagnosis of EP. Besides, the serial transvaignal ultrasound and HCG quantity result in a lot of workload for the gynecologist and additional medical costs for the patients (Condous et al., 2005.).

> A serum: cerebrospinal fluid (CSF) HCG ratio less than 40 is an accurate indication of the presence of brain metastases of gestational trophoblastic tumor, and may have considerable predictive value. However, false-negative serum: CSF HCG ratio (greater than 40) frequently occur in patients with proven brain deposits, and the cerebrospinal fluid puncture or lumbar puncture is difficult to perform for the gynecologist (Bakri et al., 2000.). Magnetic resonance imaging head scan, hence, is now preferred as the most sensitive and safe technology available for brain metastases of gestational trophoblastic tumor.

> Culdocentesis is the transvaginal passage of a needle into the posterior cul-de-sac in order to determine whether free blood is present in the abdomen. It is a simple procedure to determine whether there is intraperitoneal hemorrhage. It has been used less frequently in recent years because many gynecologists think it useless for the diagnosis of EP. In the light of the idea that serum: CSF HCG ratio is indication of the presence of brain metastases, making use of the simple operation of culdocentesis, we have proved that HCG ratio of hemoperitoneum versus venous serum (Rp/v-HCG) of EPs is apparently different from that of hIUPs (Wang, et al., 2010.). Hence, in order to provide a single-visit method for predicting EP from SEP, we want to prospectively further assess the diagnostic value of the Rp/v-HCG for early EP. Furthermore, we want to discuss the availability of Rp/v-HCG for rare EP such as abdominal pregnancy et cetera.

Clinical Application of One-Step Diagnosis for

SEPs) and hIUP group (51 cases, 17.1 percent of SEPs).

**Group EP**

miscarriage treatment (progesterone).

between the two groups.

the final diagnosis of the EPs.

were reported.

\*P<0.001 vs hIUP

respectively (Figure 2).

**2.5 Results**

Ectopic Pregnancy by HCG Ratio: Hemoperitoneum Versus Venous Serum 139

independent sample wilcoxon test or chi-squared test was used to compare variables

The diagnostic performance of Rp/v-HCG for active tubal hemorrhage was expressed using a scatter diagram. The one-step diagnostic value of the Rp/v-HCG for EP was evaluated in terms of the sensitivity, specificity, positive predictive value (PPV) and negative predictive value (NPV) with 95% confidence intervals (CI). The simple kappa coefficient of Rp/v-HCG test was also given for the 2×2 table to assess how the prediction of Rp/v-HCG agreed with

Significance was defined as p-values less than 0.05 for all the tests and two sided P-values

A total of 299 SEPs (average age, 33.1 years; range, 19-42 years) were enrolled and followed to the final diagnosis, which were finally divided into EP group (248 cases, 82.9 percent of

Table 1 shows a statistically significant difference (P < 0.001) between the EP group and the hIUP group in terms of the Rp/v-HCG (18.1 ± 40.75 and 0.72 ± 0.29, respectively) and the conservative treatment (23.0 % and 90.2 %, respectively). The culdocentesis before surgery was performed successfully for 255 SEPs except thirteen patients who rejected the culdocentesis, the success rate of the culdocentesis was 89.2 % (255/ 286), the success rate of the "first-time-right" was 76.9 % (220/ 286), even though the peritoneal fluid depth by ultrasound was only 8-12 mm (Figure 1). No complications of culdocentesis were recorded in this study. Of all the hIUPs, 90.2 percent of patients (46/ 51) were cured relying on the hemostatic therapy (Reptilase) instead of the surgical intervention (laparoscopy). 77.8 percent of patients (14/ 18) who desire to fertility succeeded to continue pregnancy with

(n=248)

EP: ectopic pregnancy; hIUP: hemoperitoneum or hematocolpos with intrauterine pregnancy; Rp/v-HCG: HCG ratio of peritoneal serum versus venous serum; PFD: peritoneal fluid depth by ultrasound.

We further confirmed the same cut-off value of the Rp/v-HCG (Rp/v-HCG = 1.0) as the previous results. At this point, the sensitivity and specificity was 98.5% and 100%,

The SEPs were predicted as EP group and hIUP group according to the Rp/v-HCG cut-off value. The final diagnosis versus the "predicted" diagnosis for suspected EPs were represented in Table 2. When the protocol was tested prospectively on the 299 SEPs, The overall sensitivity of Rp/v-HCG in the diagnosis of ectopic pregnancy was 98.4 % with a specificity of 100 %, a PPV of 100 % and an NPV of 93 %, whilst the likelihood ratio of a

Table 1. Comparison of managements between hIUP guoup and EP group.

Rp/v-HCG 18.1±40.75 0.72±0.29 *P* < 0.001 Successful culdocentesis 89.2 % (215/241) 88.9 % (40/45) *P* > 0.05 PFD (mm) 39±24 41±22 *P* > 0.05 Non-surgical treatment 23.0 % (57/248) 90.2 % (46/51) *P* < 0.001

**hIUP**

(n=51) *P value*


**5. Evidence for implantable cardioverter defibrillator device**

The evidence that supports ICD indication in patients with LVAD is very limited, and current guidelines are based primarily on the consensus of experts and observational studies [13].

A meta-analysis by Vakil et al. showed that ICD therapy was associated with an absolute risk reduction of 16% and a relative risk reduction of 39% in all-cause mortality at a 7-month follow-up. The number of patients who needed to treat to avoid an outcome was six subjects [11]. Nevertheless, there is not any statistical significance in the continuous-flow LVAD subgroup (34% of the total population). The ICD cohort showed a mortality up to 14% vs. 25% in the non-ICD group (and an absolute risk reduction of 11% and a 24% relative risk (p = 0.17). The lack of significant results was

#### *Implantable Cardioverter-Defibrillator Use in Patients with Left Ventricular Assist Devices DOI: http://dx.doi.org/10.5772/intechopen.109396*

due to the small sample size due to the better long-term results and hemodynamic stability with new continuous-flow assistance [13] with less dependence on native cardiac activity than pulsatile pumps [28].

Rorris et al. did not find any difference in all-cause mortality events, cardiovascular mortality, or right heart failure between LVAD patients with and without an ICD. Although, the study finds important differences in baseline patient characteristics between European and United States populations [29].

A subanalysis of the INTERMACS Registry that included of 2209 patients with an ICD and 2209 patients without one concluded that the presence of ICD was not related to reduced mortality, among patients with a continuous-flow LVAD. The presence of an ICD was associated with increased mortality risk and unexpected death during device support because of the result of propensity score matching, which resulted in an ICD group that had decreased prevalence of certain VD risk factors (as beta-blocker or amiodarone use, prior to VD, or chronic HF) [28].

Kutyfa et al. demonstrated that neither implant ICD before nor after LVAD reached significant survival benefit in a 191-patient study after 23 months of follow-up [30].

Younes et al. designed a 1444 patients study included in a waitlist HF bridged to transplant with LVAD. These authors suggested that the presence of ICD was not associated with lower mortality, cardiovascular or global mortality, or delisting although arrhythmic death was more common in the non-ICD group compared with ICD [12, 31].

A 94-patient study about the use of ICD after continuous-flow LVAD implant showed that only patients with VD before LVAD placement had any benefit [19]. Therefore, it is reasonable to not implant ICD in LVAD patients without previous VD [20].

Alvarez et al. [3] studied 487 patients, mostly with ICDS, 79.6%. The presence of ICD before LVAD was not related to a significant benefit in terms of mortality. However, ICD patients before LVAD presented complications such as episodes of shocks (31%), ventricular lead dysfunction (4.6%), and 2% of infections associated with ICD [3, 32].

The high rates of inappropriate shocks and infection events may decrease the benefits of the ICD indication [5]. Indeed, ICD shocks are associated with worse long-term outcomes and poorer quality of life and can negatively affect mental status [33]. Patients experience inappropriate shocks due to supraventricular tachycardias or electromagnetic interference; for that reason; benefit of appropriate shocks for prolonged but hemodynamically critical VD remains unclear [12].

Infection is a frequent complication in the LVAD population (i.e., driveline infection or device-related sepsis) that can occur in up to 20% of patients. Malnutrition and high comorbidity including diabetes, surgical technique, and quality of percutaneous lead care are important risk factors for infection. Aggressive management often is needed including long-term antibiotics, device exchange, or even urgent transplants [4]. Therefore, infection treatment could be more complex in the presence of both devices (LVAD and ICD).

Riaz et al. described a cohort of 215 ICD-LVAD patients and six (2.8%) developed ICD infections. Three patients had pocket infections related to device generator exchange, and three patients had ICD lead-related endocarditis due to prior LVADrelated infections. In all cases, ICD was removed along with antibiotics. Three patients with a history of previous LVAD infections received longer antimicrobial therapy, and one patient had their LVAD exchanged [32].

Finally, at the last 2019 EACTS Expert Consensus on long-term mechanical circulatory support [34] indications are: (i) patients with LVAD who develop postoperative ventricular dysrhythmias associated with hemodynamic collapse, ICD implantation is

#### **Table 1.**

*Summary of current guidelines about the use of implantable cardioverter defibrillator devices in the LVAD population.*

recommended (IC); (ii) patients who have an ICD implanted before LVAD, it should be kept activated for prevention of adverse effects due to right ventricular dysfunction, but its programming should be very conservative (IIaC); (iii) primary prevention is not recommended in patients without VD before LVAD (IIIC).

On the other hand, the 2022 ESC Guidelines for the management of patients with ventricular dysrhythmias and the prevention of sudden cardiac death [35] recommends: ICD implantation should be considered in LVAD recipients with symptomatic sustained VD (IIaB) **Table 1**.


*Article Micractinium tetrahymenae* **(Trebouxiophyceae, Chlorophyta), a New Endosymbiont Isolated from Ciliates**

#### **Thomas Pröschold 1,\*, Gianna Pitsch 2 and Tatyana Darienko 3**

Received: 28 April 2020; Accepted: 13 May 2020; Published: 15 May 2020

**Abstract:** Endosymbiosis between coccoid green algae and ciliates are widely distributed and occur in various phylogenetic lineages among the Ciliophora. Most mixotrophic ciliates live in symbiosis with different species and genera of the so-called *Chlorella* clade (Trebouxiophyceae). The mixotrophic ciliates can be differentiated into two groups: (i) obligate, which always live in symbiosis with such green algae and are rarely algae-free and (ii) facultative, which formed under certain circumstances such as in anoxic environments an association with algae. A case of the facultative endosymbiosis is found in the recently described species of *Tetrahymena*, *T. utriculariae*, which lives in the bladder traps of the carnivorous aquatic plant *Utricularia reflexa*. The green endosymbiont of this ciliate belonged to the genus *Micractinium*. We characterized the isolated algal strain using an integrative approach and compared it to all described species of this genus. The phylogenetic analyses using complex evolutionary secondary structure-based models revealed that this endosymbiont represents a new species of *Micractinium*, *M. tetrahymenae* sp. nov., which was further confirmed by the ITS2/CBC approach.

**Keywords:** *Micractinium tetrahymenae*; Tetrahymena; *Utricularia*; facultative endosymbiosis; ciliate-algae symbiosis


**2. Entropy Force of Schwarzschild Black Holes**

Let us turn to our example, the Schwarzschild black hole, which we chose for demonstration because of its simplicity and cleanness compared to Kerr or charged Nordstrom black holes. Black holes are known to carry entropy [7–12].  This came as a surprise, as it implies that the horizon possesses a temperature and therefore must be considered as a macrosystem, which occupies a large number of states. Microscopically, this puzzle has not been resolved until today, even though a large number of attempts have been put forward to elucidate the internal structure of the horizon (see [13–17] and several others). Such considerations were based on the Bekenstein–Hawking entropy and the Hawking radiation of a black hole [11], which is attributed to its finite entropy and thus finite temperature. It implies the existence of a thermodynamic for the black hole horizon with the implication that the horizon physics involves a very large number of states that can be occupied. Jacobson [15] extended this concept to horizons in general in order to develop a thermodynamics of gravitational horizons from which he found that Einstein's gravitational field equations formally play the role of equations of state. This concept was reviewed and extended subsequently by Padmanabhan [16] to speculate about the general importance of horizon physics in general relativity and cosmology, suggesting that all the physics is holographically contained in the physics of horizons.

Schwarzschild black holes are in the first place classical objects. However, their entropy includes the quantum nature of matter at the horizon (cf., e.g., [13]), which is induced by the sharpness of the horizon and indicates that black holes are not purely classical. Let us ask what the entropy force related to the presence of the horizon would be.


*2.5. Subcellular Localization and Expression Patterns of OsCAF1*

OsCAF1 was localized in the chloroplasts, which was predicted using the TargetP website (http://www.cbs.dtu.dk/services/TargetP/). To determine the actual subcellular localization of OsCAF1, we fused the OsCAF1 full-length cDNA with GFP driven by the 2× CaMV 35S promoter and transiently transfected in rice protoplasts. The results showed that the green fluorescent signals of OsCAF1–GFP co-localized with chloroplast autofluorescence in transformed rice protoplasts (Figure 6A). The assays indicated that OsCAF1 was localized in the rice chloroplast.

The qRT-PCR assays were used to investigate the expression patterns of OsCAF1 in different tissues at the three leaves stage. According to our results, OsCAF1 was highly expressed in green tissue, particularly in the leaves, suggesting that the OsCAF1 mainly functions in green tissue (Figure 6B).

**Figure 6.** Subcellular localization and expression patterns of OsCAF1. (**A**) Subcellular localization of OsCAF1 in rice protoplasts. (**B**) Expression analysis of OsCAF1 in different tissues. The tissues include roots (R), stems (S), and leaves (L). The values in the figures represent the means ± SE (*n* = 3). \*\* indicate *p* < 0.01.


**1. Introduction**

Polyoxoniobates (PONbs), as a unique branch of polyoxometalates (POMs), have drawn widespread attention in the past few decades due to their diverse structures and multiple applications in catalysis, nuclear-waste treatment, and virology [1,2]. Nevertheless, compared with other POM members, such as polyoxotungstates, polyoxomolybdates, and polyoxovanadates, the development of PONbs is relatively slow due to the lack of soluble Nb precursors, and their low reactivity and narrow working pH range [3]. Recently, great progress has been made in isopolyoxoniobates and some large clusters, such as {Nb27O76}, {Nb32O96}, {Nb52O150}, {Nb81O225}, {Nb114O316}, and the highest nuclearity {Nb288O768(OH)48(CO3)12} have been reported [4–7]. In 2002, the first Keggin-type PONb {(Ti2O2)SiNb12O40} was successfully synthesized by Nyman et al., marking the beginning of heteropolyoxoniobate chemistry [8]. After that, a series of heteropolyoxoniobates were reported and the Keggin-type {XNb12O40} n− (X = Si, Ge, P) are the most extensively studied [9,10].

In the periodic table, Nb and V are neighbors with similar ionic radius and electronegativity, and their hydrolysis and condensation can be performed under alkaline

**Citation:** Li, X.; Zhen, N.; Liu, C.; Zhang, D.; Dong, J.; Chi, Y.; Hu, C. Controllable Assembly of Vanadium-Containing Polyoxoniobate-Based Materials and Their Electrocatalytic Activity for Selective Benzyl Alcohol Oxidation. *Molecules* **2022**, *27*, 2862. https:// doi.org/10.3390/molecules27092862

Academic Editor: Xiaobing Cui

Received: 14 April 2022 Accepted: 29 April 2022 Published: 30 April 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**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/).

conditions. Inspired by these similarities, in 2011, we synthesized the first Keggin-type vanadium-containing PONb {VNb12O40(VO)2} stabilized by Cu complex units [11]. Since then, a series of vanadium-containing Keggin-type PONbs and their derivatives have been reported, including {XNb12O40(VO)2} (X = Si, Ge, P, V), {XNb12O40(VO)4} (X = As, V), {PNb10V2O40(VO)4}, {XNb12O40(VO)6} (X = P, V), {VNb14O42L2} (L = CO3 2−, NO3 −), {XNb8V4O40(VO)4} (X = P, V, As), {AsNb9V3O40(VO)4}, {TeNb9V2O37}, and {TeNb9V3O39}, where the introduced V acts as central, capping, or/and substituted atoms [12–23]. Notably, most of the clusters were modified by metal-complex units. The use of the metal-complex unit not only contributes to the isolation of novel Keggin-type PONbs, but can also link the discrete PONb clusters into extended structures. In general, most transition metals tend to hydrolyze rapidly into precipitation under alkaline conditions, and thereby the coexistence of transition metal ions with basic PONbs is a challenge [3]. As the Cu ion can tolerate the alkaline synthesis conditions combining with its Jahn–Teller effect, Cu-complexes are the dominated metal organic units in the synthesis of PONb-based hybrids [24–28]. In contrast, Ni-complexes were seldom used and the extended structure based on V-containing PONb hybrids and a Ni-complex is rare.

Compared with other POM members, the catalytic properties of PONbs are not extensively explored. Due to their Brønsted basicity, PONbs have been used to promote the hydrolysis of chemical warfare agents [29,30]. The introduction of V endows basic PONb clusters with interesting redox properties. For example, a double-anion cluster {PNb12O40(VO)2(V4O12)2} was successfully prepared in our group, which can effectively promote the basic hydrolysis of the nerve agent simulant and the oxidative decontamination of the sulfur mustard simulant [31]. Then, we found that the organic-inorganic hybrids based on {PNb12O40(VO)2} were active for the selective oxidation of benzyl-alkanes to ketone [14]. Our investigation indicates that the V atoms of {V5Nb23O80} and {V6Nb23O81} play a key role in the selective oxidation of the sulfur mustard simulant [32]. Owing to their fast and reversible electron transfer behavior, POMs are also a kind of promising electrocatalyst [33–35]. Recently, the covalent triazine framework immobilized {PMo10V2O40} shows excellent activities in the electrocatalytic oxidation of benzyl alcohols and ethylbenzene [36,37]. However, the electrocatalytic activity of vanadium-containing PONbs is nearly unexplored.

Herein, we report the controllable synthesis and structural characterization of two vanadium-containing Keggin-type PONbs: [Ni(en)2]5[PNb12O40(VO)5](OH)5·18H2O (**1**) and [Ni(en)3]5[PNb12O40(VO)2]·17H2O (**2**, en = ethylenediamine) (Scheme 1). Compound **1** contains a Keggin-type PONb capped by five vanadyl groups, which was further connected by [Ni(en)2] 2+ units into a three-dimensional (3D) organic-inorganic framework. Compound **2** is a di-capped discrete vanadoniobate cluster with a [Ni(en)3] 2+ unit as count cations. Interestingly, **1** and **2** as electrode materials can catalyze the selective oxidation of benzyl alcohol to benzaldehyde under alkaline additive free conditions and compound **1** is more active than **2**. The control experiments show that both the capped V atom and the basic PONb cluster contribute to the enhancement of electrocatalytic activity.

**Scheme 1.** Controllable synthesis of **1** and **2**.


Preface

Blood is a type of connective tissue in fluid form. Formed elements suspended in the plasma fluid circulate throughout the body within the cardiovascular system. This book examines both the fluid and cellular components of this fascinating liquid.

Following an introductory chapter, the book begins with a section dedicated to novel developments and updates on various topics in hemodynamics.

A classical area of physiology, namely hemodynamics, explains the physical laws that govern the flow of blood in the vessels. The hemodynamic response continuously monitors and adjusts to conditions in the body and its environment. Understanding the interaction between different blood flow variables helps to better interpret their implications in various physiopathological conditions. Future research is expected to focus mainly on the relations between hemodynamics and biological processes with active cellular responses.

Chapter 2, "Hemodynamic Perspectives in Anemia", discusses hemodynamic perspectives in anemia patients in critical condition. Emphasizing the transfusion threshold and significance of oxygen delivery and consumption, it shares new modalities to assess volume status and presents the algorithm guiding resuscitation.

Chapter 3, "Four-Dimensional Flow Magnetic Resonance Imaging and Applications in Cardiology", discusses data acquisition and pre-processing in four-dimensional flow magnetic resonance imaging (4D flow MRI) and its cardiologic applications. It gives insight into the use of 4D flow MRI in congenital heart disease, mitral regurgitation, atrial fibrillation, and different aortic pathologies like stenosis, coarctation, and bicuspid valve disease.

Chapter 4, "Cardiovascular Changes during Robot-Assisted Pelvic Surgery", elaborates cardiovascular complications of robot-assisted laparoscopic pelvic surgery. It highlights the underlying pathophysiology and the importance of perioperative monitoring.

Chapter 5, "Hemodynamic Alterations in Multiple Sclerosis", presents the cervical and cerebral changes and possible mechanisms of altered perfusion in multiple sclerosis. It also shares methods for the evaluation of perfusion and the clinical implications of these alterations.

Finally, Chapter 6, "The Shear Stress/KLF2/Nrf2/ARE Pathway: A Hemodynamic Defense against Oxidative Stress", discusses the importance of hemodynamic laminar shear stress in oxidative homeostasis and how to overcome oxidative stress through hemodynamics by the induced shear stress/Krupple-like factor2/Nrf2/ARE pathway.

The second section of the book shares novel developments in thalassemia.

The thalassemias are related to red blood cells. Among other hemoglobinopathies, they represent a major group. Abnormal hemoglobin formation is the result of inherited disorders of hemoglobin synthesis. The two main categories of the disease are alpha and beta-thalassemia, which are then divided into further subcategories. Some patients with mild forms of the disease might even go unnoticed and present with only mild anemia and iron deficiency problems. However, other more severe forms can even result in death. Complications related to compromised immunity and cardiovascular issues require a cautious clinical approach in thalassemia.

Chapter 7, "An Early Diagnosis of Thalassemia: A Boon to a Healthy Society", shares diagnostic strategies and screening methods for thalassemia with emphasis on cost comparison and point-of-care testing.

Chapter 8, "Pulmonary Hypertension in Thalassemia Patients", reviews in detail pulmonary hypertension, which is an important cause of morbidity and mortality. This progressive condition is one of the most common cardiac complications. The chapter discusses every aspect from etiology to treatment and recommendations.

Finally, Chapter 9, "Challenges of Hepatitis C Virus Treatment in Thalassemia", discusses the approach to thalassemia patients with hepatitis C infection. Thalassemia patients are especially predisposed to multi-transfusion-acquired hepatitis C virus. The chapter presents novel treatments and pharmacokinetic considerations.

> **Aise Seda Artis** Western Balkans University, Tirana, Albania

Section 1 Introduction

#### **Chapter 1**

## Introductory Chapter: Fascinating Blood

*Aise Seda Artis*

#### **1. Introduction**

*"The blood jet is poetry and there is no stopping it."*

*Sylvia Plath, 'Ariel'.*

Ancient people were aware of blood's importance and fascinated by its mystery. According to the belief, Medusa had two kinds of blood circulating through her vessels: lethal blood on her left side, and life-giving blood on her right side. Later the humoral pathology theory of Hippocrates proposed the human body as a vessel for four liquids: yellow bile, black bile, white phlegm, and red blood. Each corresponds to one of the four classical elements – fire, earth, water, and air and one of the traditional four temperaments – sanguine, choleric, phlegmatic, and melancholic. Later, Galen proposed that blood was made in the liver from food and drink carried from the digestive tract. An ideal balance among the four humors was the key to good health [1]. Inspecting blood samples from patients and determining the relative amounts of each humor was the method for the diagnosis of an imbalance. Bloodletting treatments were common practice, and described in detail by Avicenna in his "Canon of Medicine". This theory shaped the practice in Greek, Roman, and Islamic philosophy and medicine for many centuries until the nineteenth century [2].

In today's view, blood is a type of connective tissue in fluid form. Formed elements suspended in the plasma fluid circulate throughout the body within the cardiovascular system. While the primary function is to transport oxygen, nutrients, and other substances; its specific functions also include defense, distribution of heat, and maintenance of homeostasis throughout the body.

#### **2. Hemodynamics**

Hemodynamics is the study of the mechanical and physiologic properties controlling blood pressure and flow through the body, "the physical study of flowing blood and of all the solid structures (such as arteries) through which it flows" [3]. This classical area of physiology emphasizes the fluid and solid mechanics of the cardiovascular system, concerning the distribution of pressures and flows in the circulatory system. Control of the circulatory system is through the homeostatic mechanisms of autoregulation. Many biological processes, physical factors influence blood flow (and vice versa). In addition to systemic hemodynamic alterations, microvascular alterations are frequently observed in critically ill patients. The hemodynamic response continuously monitors and

adjusts to conditions in the body and its environment. Some parameters have been defined to quantify blood flow and its relationship with systemic circulatory changes. There is a constant development of the instrumentation and the techniques together with increasing capabilities for numerical computation. Complex and extensive factors influence hemodynamics. Understanding the interactions between different blood flow variables help to better interpret their implications in variable physiopathological conditions. Also, the help of improved imaging techniques is undeniable. Future research is expected to focus mainly on the interactions between hemodynamics and biological processes involving active cellular responses [4].

#### **3. Hemorheology**

The study of blood flow is called hemodynamics, and the study of the properties of the blood flow is called hemorheology. Blood is a non-Newtonian shear-thinning fluid and therefore is most efficiently studied using rheology rather than hydrodynamics [5]. The blood flow properties include blood viscosity which depends on plasma viscosity, hematocrit, red blood cell (RBC) aggregation, and RBC deformability [6]. The RBCs have a unique ability to deform and pass through small capillaries before rapidly recovering their initial shape. Under most flow conditions RBCs behave like fluid drops [7]. Due to the liquid-like behavior of RBCs under shear stress, blood can also be considered as a liquid-liquid emulsion. White blood cells and platelets can also affect blood rheology but, under normal conditions, RBCs represent most of the cellular components and make the biggest contribution to blood viscosity [8].

Hemorheological alterations occur in a wide range of physiological and pathophysiological conditions. In many diseases, the deformability of RBCs is impaired as a result of defects in cell membrane skeletal architecture, RBC aging, and mechanical damage [9–11]. Adverse hemorheological alterations may decrease tissue perfusion. Since control of blood flow is directly related to the metabolic conditions of the tissue, the perfusion change can be compensated by controlling the vascular geometry (i.e., diameter) component of flow resistance.

#### **4. Thalassemia**

RBCs show rheological abnormalities, also when thalassemia is present. Currently seen most frequently in the tropical belt, thalassemias remain a serious global health problem. Thalassemias are a group of inherited microcytic, hemolytic anemias characterized by defective hemoglobin synthesis. Alteration of the cell membrane may result from the interaction between the defective hemoglobin chain and the membrane cytoskeleton [12]. However, other changes are caused by hemoglobin denaturation [13]. Previous works suggest that the decreased RBC deformability is probably due to microcytosis that is present even in thalassemia carriers [14]. Recent work also suggests the presence of additional but yet unknown causes [15]. Thalassemia results from unbalanced hemoglobin synthesis caused by decreased production of at least one globin polypeptide chain. Symptoms and signs result from anemia, hemolysis, splenomegaly, bone marrow hyperplasia, and if there have been multiple transfusions, iron overload. Endothelial injury, splenomegaly, and transfusion-related hemodynamic alterations play an important role in the altered hemodynamics of thalassemia [16–18].

### **5. Conclusion**

For future research, the concepts of hemodynamics and hemorheology will retain their importance with their basis in the understanding of fluid and solid mechanics. A better understanding of the biological processes involving active cellular responses provided by advanced techniques is the key.

To serve this purpose, the first section of the present book is dedicated to present novel developments and updates on various topics in the frame of hemodynamics:

The second section of this book is a thalassemia update. Concisely, this section gives an update and novel developments in thalassemia. Four chapters present an outline of B-thalassemia, the early diagnostic tools, and strategies in thalassemia, together with the approaches for the obstacles of pulmonary hypertension and Hepatitis C virus infection.

The chapters of this book may not seem to be in complete harmony. However, in the present era of fast communications, we aimed to provide some novelties in the field. This work serves an audience from different backgrounds providing a review on a variety of selected topics with the purpose of an update.

#### **Acknowledgements**

I would like to thank Prof Talip Asil for his kind effort in reviewing one of the chapters. I would also like to appreciate Author Service Manager Ms. Marica Novakovic and Commissioning Editor Ms. Ana Simcic for their constant help.

*Blood - Updates on Hemodynamics and Thalassemia*

#### **Author details**

Aise Seda Artis1,2

1 Istanbul Medeniyet University, Istanbul, Turkey

2 Vistula University, Warsaw, Poland

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

*Introductory Chapter: Fascinating Blood DOI: http://dx.doi.org/10.5772/intechopen.102119*

#### **References**

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**Acknowledgements**

This chapter is based upon work from COST Action CA15127 ("Resilient communication ser‐ vices protecting end user applications from disaster‐based failures: RECODIS") supported by COST (European Cooperation in Science and Technology). This work has received funding from the People Program (Marie Curie Actions) of the European Union's Seventh Framework Program (FP7/2007–2013) under REA Grant Agreement n° 630853.


**The Role of Exercise in Chemotherapy-Induced Peripheral Neuropathy**

Karen Y. Wonders and Brittany Stout

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/62839

#### **Abstract**

[16] Kan P, Schmidt MH. Minimally invasive thoracoscopic approach for anterior decom‐ pression and stabilization of metastatic spine disease. Neurosurg Focus. 2008;25:E8.

[17] Mobbs RJ, Sivabalan P, Li J. Technique, challenges and indications for percutaneous pedicle screw fixation. J Clin Neurosci. 2011;18:741–749. DOI: 10.1016/j.jocn.

[18] Leithner A, Radl R, Gruber G, Hochegger M, Leithner K, Welkerling H, et al. Predictive value of seven preoperative prognostic scoring systems for spinal metastases. Eur Spine

2010.09.019.

434 Neurooncology - Newer Developments

J. 2008;17:1488–1495.

Chemotherapy-induced peripheral neuropathy (CIPN) is the most common neurologi‐ cal side effect of chemotherapy and is characterized by damage to the nervous system that is a direct result of the medications associated with chemotherapy. Often, this damage to the central nervous system pain pathways results in neuropathic pain described as burning, paroxysmal, stabbing, or elective shock-like and accompanied by pins-andneedles sensations and itching. The presence and severity of neuropathic pain is often shown to be associated with impairments in walking, general activities, sleep, work, mood, enjoyment of life, and relationships with others. Treatment of neuropathic pain due to CIPN often requires a multidisciplinary approach due to the broad variety of symp‐ toms and their negative impact on quality of life. To provide treatment strategies that are effective for patients, they should include a combination of pharmacological agents and exercise rehabilitation. Exercise rehabilitation programs should be designed in order to help patients familiarize themselves to changes in physical functioning. The goals of the program should target three main areas: maximize functional capacities, prolong or maintain independent function, and improve quality of life.

**Keywords:** Cancer, Exercise, Neuropathy, Chemotherapy, Rehabilitation


**1. Introduction**

Five-level inverters are power electronic converters that play important roles in applications of mechanical-electrical systems, transportation, power quality management, renewable energy conversion system, and motor drives [1–4]. In the design of five-level inverters, di fferent topologies have been evolved, including the diode-clamped [5–9], flying capacitor [10–13], cascaded H bridge [14–16], and T type topologies [17–20]. A new single-phase five-level T-type inverter can reduce the harmonic components compared with that of the traditional full-bridge three-level PWM inverter under the same conditions of DC voltage source and switching frequency [18]. In [19] the DC-DC boost converter is connected to a five-level inverter and PI control is used, to control the inverter with much less total harmonic distortion (THD) and near unity power factor. To enhance the input voltage, three PV strings in cascade and parallel configurations with the five-level inverter are found in [19]. To maintain the power factor at near unity, the inverters in [19] and [20] use a proportional–integral (PI) current control scheme. The main solutions for the small-scale rooftop PV applications are proposed in [20]. That paper presents a comparison of four multilevel converters based on the T-type topology.

The switching loss is very important to evaluate the performance of the inverter, especially when multilevel inverter operates at a high frequency. Several studies on switching loss reduction have been introduced in recent years [21–26]. The complete analytical calculation of the switching loss is proposed in [23] for the basic inverters. The switching losses of the IGBT depend on switching frequency, load current, input DC voltage, and characteristics of switches are presented in [24]. The paper [24] shows that the total switching losses of the inverter on a control voltage period are proportional to switching frequency, load current, and DC voltage supply. The switching frequency depends on the carrier frequency and the modulation method. Note that the switching frequency is opposite to the total harmonic distortion (THD) of the output voltage. So that, lower carrier frequencies based switching loss reduction can increase THD value. Therefore, a new technique for switching loss reduction without THD increment is needed to be solved. As a result, the switching energy of the switches when the switches operate is turned on (Ec(on)) or turned off (Ec(off)) mode, are determined by current and voltage across the switch (*IC* and *VCE*) [25].

The average switching loss in the switch (*PS*) during each period *Ts* is calculated as Equation (1) [25].

$$P\_S = \frac{1}{6} \left( V\_{CE} I\_s \frac{t\_{\rm c(on)} + t\_{\rm c(off)}}{T\_s} \right) - \frac{1}{3} \left( V\_{out} I\_s \frac{t\_{\rm c(on)} + t\_{\rm c(off)}}{T\_s} \right) \tag{1}$$

where:

> *fs*—switching frequency

*VCE*—voltage across the switch when the switch is turned off *Von*—voltage across the switch when the switch is turned on *Is*—current through the switch when the switch is turned on *tc(on)*—turn-on cross-over interval *tc(o*ff*)*—turn-off cross-over interval

From Equation (1), it can be seen that to reduce switching losses it needs to reduce switching frequency (*fs*). Or for reduction switching loss, it needs to choose a switching state based on *IC* and *VCE* of phase to have the smallest value in the three-phase. As a result, *fs*, *IC* and *VCE* are three basic elements that affect to reduce switching loss. A new space vector modulation strategy with two PI regulators is used in both DC voltage and load voltage sides for controlling the PWM parameters. So, the non-switching state can be controlled by these parameters to generate pulses as found in [26]. The switching losses are reduced by reducing either switching frequency or instantaneous current and voltage values at the time of switching in [26]. Since using two PI regulators, the control technique is very complex and hard to control for the system.

A reduced switching loss PWM strategy to eliminate common mode voltage in multilevel inverters is presented in [27]. This PWM method has increased switching times for the phase with the smallest load current by comparing the three-phase load current to eliminate common mode voltage. Simulation and experimental results in [27] are performed based on the standard models with the collector-emitter voltage of the IGBTs equaled. Therefore, for application to other models, which the voltage crossed IGBTs is not the same, as if the 5L-HBT2I, its effect of loss reduction may not be very high. The two modified space vector modulation strategies were proposed in [28] for the reduction of the qZSI number of switch commutations at high current level with shorter periods during the fundamental cycle, i.e., reducing the switching loss, simplifying the generation of the gate signals by utilizing only three reference signals, and achieving a single switch commutation at a time were also presented in [28].

This paper proposes a new modulation technique to reduce the number of switch commutations for switching losses reduction. There is no switching on the phase which the control voltage has the smallest displacement to top or bottom of the carrier, and the absolute of the load current being the first or second large.  The paper is organized as follows: in Section 2, the topology, operating principles, and circuit analysis of the three-phase 5L-HBT2I are presented. Section 3 presents switching loss calculation for 5L-HBT2I. Section 4 presents the proposed PWM scheme. Simulation and experimental results are shown in Section 5. Finally, the result is summarized in Section 6.

#### **2. Three-Phase Five-Level H-Bridge T-Type Inverter Topology**

Figure 1 shows the three-phase 5L-HBT2I. As shown in Figure 1a, the 5L-HBT2I consists of three DC sources (*U*a, *U*b, *U*c), six capacitors (*C*a1, *C*b1, *C*c1, *C*a2, *C*b2, and *C*c2), and three T-type H-bridge circuits.

**Figure 1.** Five-level T-type H-bridge inverter topologies. (**a**) Three-phase inverter and (**b**) One phase module.

Define *TSxi* is status of the *i*th switch on phase *x* (*x* = a, b, c); where *i* is the index of switches (1 to 5), with conditions:

$$T\_{\text{Sxi}} = \begin{cases} \ 0 \text{ if } \text{Sxi} \text{ off} \\ \ 1 \text{ if } \text{Sxi} \text{ or} \end{cases} \tag{2}$$

$$T\_{\text{Sx5}} + T\_{\text{Sx4}} = 1\tag{3}$$

$$T\_{\rm Sx1} + T\_{\rm Sx2} + T\_{\rm Sx3} = 1\tag{4}$$

Figure 1b shows a structure of phase *x*, where a leg of 5L-HBT2I is built from two single-phase inverters: two-level and three-level T-type.

From Equations (3) and (4), the pole voltage of two-level ( *Ux2-cx*) and three-level T type inverter (*Ux3-cx*) are determined:

$$
\Delta I\_{\rm x2-cx} = (2T\_{\rm Sx5} - 1)\frac{V\_{\rm dc}}{2} \tag{5}
$$

$$\mathcal{U}\_{\rm x3-cx} = \left(2T\_{\rm Sx3} + T\_{\rm Sx2} - 1\right) \frac{V\_{dc}}{2} \tag{6}$$

Hence, the voltage from phase to pole (Uxg) is determined as

$$V\_{\rm x\%} = \mathcal{U}\mathbf{1}\_{\rm x3-cx} - \mathcal{U}\mathbf{1}\_{\rm x2-cx} = \left(2T\_{\rm Sx3} + T\_{\rm Sx2} - 2T\_{\rm Sx5}\right)\frac{V\_{\rm dc}}{2} \tag{7}$$

Set *TSx* is status of phase *x*:

$$T\_{\rm Sx} = 2T\_{\rm Sx3} + T\_{\rm Sx2} - 2T\_{\rm Sx5} \tag{8}$$

So, the phase to pole voltages is given as Equation (9).

$$
\begin{bmatrix} V\_{\text{ag}} \\ V\_{\text{bg}} \\ V\_{\text{cg}} \end{bmatrix} = \frac{V\_{\text{dc}}}{2} \begin{bmatrix} T\_{\text{Sa}} \\ T\_{\text{Sb}} \\ T\_{\text{Sc}} \end{bmatrix} \tag{9}
$$

The output phase and line-to-line voltages of this inverter is given as Equations (10) and (11).

$$
\begin{bmatrix} V\_{an} \\ V\_{bn} \\ V\_{cn} \end{bmatrix} = \frac{1}{3} \begin{bmatrix} 2 & -1 & -1 \\ -1 & 2 & -1 \\ -1 & -1 & 2 \end{bmatrix} \begin{bmatrix} V\_{a\circ} \\ V\_{b\circ} \\ V\_{c\circ} \end{bmatrix} \tag{10}
$$

$$
\begin{bmatrix} V\_{ab} \\ V\_{hc} \\ V\_{ca} \end{bmatrix} = \begin{bmatrix} 1 & -1 & 0 \\ 0 & 1 & -1 \\ -1 & 0 & 1 \end{bmatrix} \begin{bmatrix} V\_{an} \\ V\_{bn} \\ V\_{cn} \end{bmatrix} \tag{11}
$$

As a result, the third order harmonic does not appear in the output phase voltage ( *Vxn*), while it appears in both pole voltage ( *Vxg*) and line-to-line voltage. Therefore, the proposed algorithm has o ffset the function at the third order harmonic, which will not a ffect the third order harmonic magnitude of the load. From Equation (8) to Equation (11), the values of *Vxg* can be determined in Table 1. As shown in Table 1, the pole voltage *Vxg* has five levels including two positive, two negative, and one zero.

**Table 1.** Switching state of five-level H-bridge T-type inverter (5L-HBT2I) for phase-*x* index.

#### **3. Switching Loss Calculation for 5L-HBT2I**

The switching loss depends on the load current and collector-emitter voltage of the power switches and the number of commutations during the entire fundamental cycle [24,25]. Therefore, the switching losses of the 5L-HBT2I will be calculated based on the switching losses of the power switches of each phase, where phase *x* consists of five switches: *Sx*1–*Sx*5, *x* = a, b, c.

Figure 1b and Table 1 can be seen that

$$V\_{CE1} = V\_{CE2} = V\_{CE3} = V\_{C2}/2 = V\_{C2}/2 = V\_{\&}/2\tag{12}$$

where *VCE,i* is the voltage across switch *Sxi* when *Sxi* is turned-off (*i* = 1, 2, 3, 4, 5).

And the current through switches, *is* is determined as

$$\dot{i}\_{\rm si} = \left| \dot{i}\_{\rm Lx}(\theta) \right| \qquad \text{where } \theta \text{ is phase angle, } \propto a \text{, } b \text{, } c \tag{13}$$

In Equation (13), *iSi* and *iLx* are current through switch *Sxi* when *Sxi* is turned-on (*i* = 1, 2, 3, 4, 5) and the load current over phase *x* (*x* = a, b, c), respectively.

Hence, the average value of the local (per control voltage cycle) switching loss over switches *Sx*1–*Sx*5 (for instance, for phase-a) can be calculated as [27]

$$P\_{S1} = \frac{1}{2\pi} (t\_{\varepsilon(on)} + t\_{\varepsilon(off)}) \int\_0^{2\pi} \left( \frac{V\_{CE1}}{6} - \frac{V\_{on}}{3} \right) i\_{s1} d\theta = \frac{1}{2\pi} (t\_{\varepsilon(on)} + t\_{\varepsilon(off)}) \left( \frac{V\_{dc}}{12} - \frac{V\_{on}}{3} \right) \int\_0^{2\pi} i\_{s1} d\theta \quad (14)$$

Similarly, we have

$$P\_{S2} = \frac{1}{2\pi} (t\_{c(on)} + t\_{c(off)}) \left(\frac{V\_{dc}}{12} - \frac{V\_{on}}{3}\right) \int\_0^{2\pi} i\_{s2} d\theta \tag{15}$$

$$P\_{S3} = \frac{1}{2\pi} (t\_{c(on)} + t\_{c(off)}) \left(\frac{V\_{dc}}{12} - \frac{V\_{on}}{3}\right) \int\_0^{2\pi} i\_{s3} d\theta \tag{16}$$

$$P\_{\rm S4} = \frac{1}{2\pi} (t\_{c(on)} + t\_{c(off)}) \left(\frac{V\_{dc}}{6} - \frac{V\_{on}}{3}\right) \int\_{0}^{2\pi} i\_{s4} d\theta \tag{17}$$

$$P\_{S5} = \frac{1}{2\pi} (t\_{c(on)} + t\_{c(off)}) \left(\frac{V\_{dc}}{6} - \frac{V\_{on}}{3}\right) \int\_0^{2\pi} i\_{s5} d\theta \tag{18}$$

where *PSi* is an average value of the local (per carrier cycle) switching loss over the switch (*i* = 1, 2, 3, 4, 5). *Von,i is* voltage across switch *Sxi* in turned-on state.

Equations (14)–(18) can show that switching loss decreases if the switching is on the phase, which has a small load current. Due to the decrement of the number of commutations on two-level inverter switches (*Sx*5 or *Sx*4), the switching loss will be smaller when compared with three-level T-type inverter switches (*Sx*1 or *Sx*2 or *Sx*3).

As a result, the proposed technique helps to reduce the switching loss by reducing the number of commutations on the phase, which has the absolute of the load current are first or second large in three-phase and by reducing the number of commutations on two level inverter.

#### **4. Proposed Algorithm**

#### *4.1. Principle of the Proposed Algorithm*

The switching loss depends on the current through power switches, the voltage across the switch, and the number of commutations in the period of control voltage is shown in Equations (14)–(18). Since the switching loss can be decreased by reducing switching frequency of *Sx*5 and *Sx*4 and reducing the number of commutations on the phase, which has the absolute of the load current is high or medium in comparison to another phase. Therefore, in the first stage, the new control voltages are determined with a non-switching state on the phase, which has the smallest displacement to top or bottom peak (of the carrier) and the absolute of the load current being the first or second largest. In addition, in the second stage, the control voltages that have been determined in the previous stage, are divided into the control voltage for the two-level inverter and three-level T-type inverter for reducing switch turn-on/turn-off on the two-level inverter.

The first stage:

It is defined that *vx* is the initial control voltage phase *x* (*x* = a, b, c) and *vrx* is control voltage that it is determined as the new control voltage by adding voffset into *vx* from first stage of proposed algorithm. The maximum ampplitude of carrier is selected by 1. Due to the 5-level inverter, threshold comparison of the carrier is 0, 1, 2, 3 and 4. The initial control voltage of phase *vx* is determined as Equation (19).

$$v\_x = m \frac{4}{\sqrt{3}} \cos(\omega t + \theta\_{0x}) + 2\tag{19}$$

where *vx*, *m*, ω and θ*0x* are the initial control voltage of phase *x*, modulation index, angular velocity, and initial phase angle, respectively.

The error of *vx* and *Lx* are determined:

$$L\_{\mathbf{x}} = \begin{cases} \begin{array}{c} \int \text{int}(\upsilon\_{\mathbf{x}}) \text{ if } \inf(\upsilon\_{\mathbf{x}}) < 4 \\ \text{int}(\upsilon\_{\mathbf{x}} - 1) \end{array}; \ H\_{\mathbf{x}} = L\_{\mathbf{x}} + 1 \end{cases} \tag{20}$$

$$e\_{\mathbf{x}} = \upsilon\_{\mathbf{x}} - L\_{\mathbf{x}} \tag{21}$$

Call *IxABS* is the absolute of current across phase *x*, then

$$\dot{\mathbf{u}}\_{\mathbf{x},\mathbf{A}\mathbf{S}} = \left| \dot{\mathbf{u}}\_{\mathbf{L}\mathbf{x}}(\theta) \right| \tag{22}$$

where θ is phase angle, *ILx* is the load current of phase *x* (*x* = a, b, c).

The maximum, minimum, medium of error (*emax*, *emin*, *emed*) and the maximum and medium of absolute of load current (*Imax*, *Imed*) are defined:

$$\mathfrak{e}\_{\max} = \mathsf{max}(\mathfrak{e}\_{\mathfrak{a}\prime} \ \mathfrak{e}\_{\mathfrak{b}\prime} \mathfrak{e}\_{\mathfrak{c}}), \ \mathfrak{e}\_{\min} = \min(\mathfrak{e}\_{\mathfrak{a}\prime} \ \mathfrak{e}\_{\mathfrak{b}\prime} \mathfrak{e}\_{\mathfrak{c}}), \ \mathfrak{e}\_{\max} = \mathsf{med}(\mathfrak{e}\_{\mathfrak{a}\prime} \ \mathfrak{e}\_{\mathfrak{b}\prime} \mathfrak{e}\_{\mathfrak{c}}) \tag{23}$$

$$i\_{\text{max}} = \max(i\_{a\text{ABS}\_{\prime}}, i\_{b\text{ABS}\_{\prime}}, i\_{c\text{ABS}}), \ i\_{\text{med}} = \text{med}(i\_{a\text{ABS}\_{\prime}}, i\_{b\text{ABS}\_{\prime}}, i\_{c\text{ABS}}) \tag{24}$$

Case 1: When the *ixABS* is the largest and (*ex* = *emin*) or (*ex* = *emax*), the none switching phase is *x* and the offset voltage (*vo*ff*set*) is determined through the value ex as Equation (25)

$$
v\_{offset} = \begin{bmatrix} -\mathbf{e}\_x \text{ if } \mathbf{e}\_x = \mathbf{e}\_{min} \\ 1 - \mathbf{e}\_x \text{ if } \mathbf{e}\_x = \mathbf{e}\_{max} \end{bmatrix} . \tag{25}$$

Case 2: When *iaABS* is the largest and *ea* equal the *emed*, for reducing error of output voltages, the offset voltage will be not equal to *ea*. In this case, another phase has the absolute of the load current as medium (assuming it is phase b) and the error (*eb*) of *vb* and *Lb* fix the maximum or minimum. Then, the offset voltage is calculated following *ibABS* and *eb* as Equation (26)

$$v\_{offset} = \begin{array}{l} 1 - c\_b \text{ if } (c\_b = c\_{max}) \text{ and } (i\_{bABS} = i\_{mcd})\\ -c\_b \text{ if } (c\_b = c\_{min}) \text{ and } (i\_{bABS} = i\_{mcd}) \end{array} \tag{26}$$

Thus, the offset values can be determined as *ixABS* and *ex* in Table 2.

**Table 2.** The offset voltage of the 5L-HBT2I.

*NA*: Not applicable.

If the matrixes from Equation (27) to Equation (31) are defined, the offset voltage will be calculated as Equation (32).

> ⎧⎪⎪⎪⎪⎨⎪⎪⎪⎪⎩

⎧⎪⎪⎪⎨⎪⎪⎪⎩

$$\begin{aligned} \begin{bmatrix} I\_{\text{max}} \end{bmatrix} &= \begin{bmatrix} a\_{\text{max}} & b\_{\text{max}} & c\_{\text{max}} \end{bmatrix} \\ \mathbf{x}\_{\text{max}} &= \begin{bmatrix} 1 \text{ if } i\_{\text{x}ABSS} = i\_{\text{max}} \\ 0 \text{ else} \end{bmatrix} \end{aligned} \tag{27}$$

$$\begin{cases} \begin{array}{cc} \begin{bmatrix} I\_{mcd} \end{bmatrix} = \begin{bmatrix} a\_{mcd} & b\_{mcd} & c\_{mcd} \end{bmatrix} \end{array} \end{cases} \right] $$

$$\begin{array}{c} \begin{array}{c} \begin{array}{c} \text{1} \ i \ i\_{xABS} = i\_{mcd} \end{array} \end{array} \end{cases} \begin{array}{c} \begin{array}{c} \text{1} \ i \ i\_{xABS} = i\_{mcd} \end{array} \end{array} \tag{28}$$

$$\begin{cases} \begin{array}{|c|c|} \hline \begin{Bmatrix} E\_{\text{max}} \end{Bmatrix} = \begin{Bmatrix} \mathcal{c}\_{\text{argmax}} & \mathcal{c}\_{\text{bmax}} \end{Bmatrix} \\\\ \mathcal{c}\_{\text{xmax}} = \begin{bmatrix} 1 \text{ if } \mathcal{c}\_{\text{x}} = \mathcal{c}\_{\text{max}} \\\ 0 \text{ else} \end{bmatrix} \end{cases} \end{cases} \tag{29}$$

$$\begin{cases} \begin{array}{cc} \begin{array}{c} \begin{array}{c} \begin{array}{c} \begin{array}{c} \varepsilon\_{\text{mcd}} \end{array} \end{array} \end{array} \end{cases} \begin{array}{c} \begin{array}{c} \varepsilon\_{\text{bmd}} \end{array} \end{array} \begin{array}{c} \begin{array}{c} \varepsilon\_{\text{cmd}} \end{array} \end{array} \right] \end{cases} \end{cases}$$

$$\varepsilon\_{\text{xmcd}} = \begin{bmatrix} \begin{array}{c} 1 \ if \ e\_{\text{x}} = e\_{\text{mcd}} \\ 0 \text{ else} \end{array} \end{bmatrix} \tag{30}$$

$$\begin{aligned} \begin{bmatrix} E\_{\text{min}} \end{bmatrix} &= \begin{bmatrix} \mathfrak{e}\_{\text{amin}} & \mathfrak{e}\_{l \text{min}} \, \mathfrak{e}\_{\text{cmin}} \end{bmatrix} \\ \begin{array}{l} \mathfrak{e}\_{\text{x} \text{min}} = \begin{bmatrix} 1 \; \text{if } \mathfrak{e}\_{\text{x}} = \mathfrak{e}\_{\text{min}} \\ 0 \; \text{else} \end{bmatrix} \end{aligned} \tag{31}$$

$$\boldsymbol{w}\_{offset} = \begin{bmatrix} \left[I\_{\max}\right] \left[E\_{\max}\right]^T \left(1 - \varepsilon\_{\max}\right) - \left[I\_{\max}\right] \left[E\_{\min}\right]^T \boldsymbol{e}\_{\min} \ \boldsymbol{i} \ \boldsymbol{f} \ \left[I\_{\max}\right] \left[E\_{\max}\right]^T = \boldsymbol{0} \\\ \left[I\_{\max}\right] \left[E\_{\max}\right]^T \left(1 - \varepsilon\_{\max}\right) - \left[I\_{\max}\right] \left[E\_{\min}\right]^T \boldsymbol{e}\_{\min} \ \boldsymbol{e} \ \boldsymbol{else} \end{bmatrix} \tag{32}$$

The new control voltage *vrx* is determined

$$
\upsilon\_{rx} = \upsilon\_x + \upsilon\_{offset} \tag{33}
$$

Since matrixes [*Imax*], [*Imed*], [*Emax*], [*Emed*] and [*Emin*] have "0" and "1" values, which can be determined by simple comparison commands lead to the calculation of the offset voltage easy and quick. The new control voltage (*vrx*) is the old control voltage (*vx*) add the offset voltage. The new control voltages (*vrx*) on the phase which the absolute of the load current are first or the second large in three-phase and *ex* equal *emax* or *emin* will be shifted to the top or bottom peak of the carrier.

Figure 2 shows the shift of the control voltages according to the conditions of the proposed algorithm. As shown in Figure 2a, when (*iaABS* = *imax*) and (*ea* = *emin*), the offset voltage is <sup>−</sup>*ea*. This offset voltage is added to the original control voltages so the new control voltages will shift down to the new positions. The new position of the control voltage of phase-a will be *La*. Therefore, there will be no switching on the phase-a when (*iaABS* = *imax*) *and* (*ea* = *emin*) as shown in Figure 2b. Similarly, the switching state on the phase-b is off if (*IaABS* ≥ *IbABS* ≥ *IcABS*), (*ea* = *emed*) *and* (*eb* = *emin* or *emax*), as shown in Figure 2c or 2d.

**Figure 2.** Offset voltages under the proposed algorithm. (**a**) (*iaABS* = *imax*) *and* (*ea* = *emin*); (**b**) (*iaABS* = *imax*)*and* (*ea* = *emax*); (**c**) (*iaABS* ≥ *ibABS* ≥ *icABS*), (*ea* = *emed*) *and* (*eb* = *emin*); (**d**) (*iaABS* ≥ *ibABS* ≥ *icABS*), (*ea* = *emed*) *and* (*eb* = *emax*).

The second stage:

In the second stage, the control voltages that were created in the previous stage will be divided into the control voltage for the two-level inverter and three-level T-type inverter. Since the two-level inverter is operated in six-step mode, its control voltage can be calculated as

$$
v\_{\mathbf{x},2l} = \begin{bmatrix} 1 \ if \ v\_{rx} \ge 2 \\ & 0 \ els\varepsilon \end{bmatrix} \tag{34}$$

In addition, from Equation (7), it is easy to determine the control voltages for three-level T type, which are:

$$
v\_{x,\ \mathcal{U}} = v\_{rx} - 2v\_{x,\mathcal{U}}\tag{35}$$

where *vrx* is the control voltage, created form first stage; *vx*,2*l* and *vx*,3*l* are the control voltages for two-level inverter and T-type inverter on phase *x*.

#### *4.2. Flow Chart*

Figure 3 shows a flow chart of the proposed algorithm using simple commands such as subtraction, and comparison on the program. The comparison of the phase currents can be done by comparing hardware circuits that do not require the use of expensive sensors. Thus, calculation time of the algorithm is low and suitable for closed-loop control or other control methods.

For example, assuming that control voltages *va*, *vb*, and *vc* are 1.12 V, 0.64 V and 3.24 V, respectively, from Equation (22), the error of *vx* and *Lx* are *ea* = 0.12, *eb* = 0.64, and *ec* = 0.24. From Equation (24), *emin* = 0.12, *emax* = 0.64, *emid* = 0.24.

Assuming that *IaABS* > *IbABS* > *IcABS*, from Equations (27) and (28), [*Imax*] = [100], [*Imid*]=[010]. From Equations (30)–(32), [*Emax*] = [010], [*Emed*]=[001], [*Emin*]=[100]. From Equations (22)–(32), the offset voltage is *vo f f det* = −*emin* = −0.12. Then, new control voltages are *vra* = *va* − *emin* = 1 V, *vrb* = *vb* − *emin* = 0.52 V, *vrc* = *vc* − *emin* = 3.12 V.

When *vra* = 1 V, switches S1, S3, and S5 are turned off while switches S2 and S4 are turned on. Thus, the phase-a switches will not be switched in one cycle *T*. Similarly, when *vrc* = 3.12 V, S1, S3, and S4 are turned off while S2 and S5 are switching. As a result, the phase-c switches will be switched in one cycle *T*. Therefore, the proposed algorithm can reduce the switching times of the switches.

**Figure 3.** The flow chart of the proposed scheme.

#### **5. Simulation and Experimental Results**

#### *5.1. Simulation Results*

Parameters used in simulation is shown in Table 3. Figure 4 shows the simulation results of the proposed algorithm when modulation index are 0.4 and 0.9, respectively. The waveforms from top to bottom in Figure 4 are three-phase absolute current, three-phase error (*ea, eb, ec*), maximum and minimum errors (*emax* and *emin*), the initial voltage (*vx*) and new control voltage (*Vrx*), control voltage of two-level inverter (*va*2*L*), and control voltage of three-level T-type inverter (*va*3*L*), the next waveforms are gating signals of *Sx*1 to *Sx*5 and the bottom is the pole voltage output. It can be seen that from *t*1 to *t*2, *iaABS* is maximum and *ea* hit maximum (*emax)*, then *vo*ff*set* will be 1 − *ea* lead to the control voltage of phase a move up to 3*V*; see Figure 4a and obtain 4V; see Figure 4b. As shown in Figure 4a, during a time interval of [*t*1 to *t*2], the control phase-a voltage is 4 *V*. As a result, the switching states on phase-a are (*S*5*a* = 0, *S*4*a* = 1, *S*3*a* = 1, *S*2*a* = 0 and *S*1*a* = 0) and its phase pole voltage is *Vag* = *Vdc* = 100 V. Similarly, in Figure 4b, the phase-a to pole voltage is *Vag* = *Vdc* 2 = 50 V when (*S*5*a* = 0, *S*4*a* = 1, *S*3*a* = 0, *S*2*a* = 1 and *S*1*a* = 0). From *t*3 to *t*4, *ibABS* is maximum, the *eb* is medium. Simultaneously, the absolute of phase a current load (*iaABS*) is medium and *ea* is emin as analyzed in the above section, the offset voltage is –ea and the new control voltage of phase a shift down 0 V (*m* = 0.9) and 1 V (*m* = 0.4), so there is no switching in phase-a. Similarly, the phase-b and phase-c in the situation have no switching.

**Table 3.** Parameters used in simulation.

#### **Figure 4.** *Cont.*

**Figure 4.** Control voltage generation, gating signals of Sa1 to Sa5 and the phase pole voltage in the proposed technique with (**<sup>a</sup>**,**<sup>c</sup>**) *m* = 0.4 and (**b**,**d**) *m* = 0.9.

To evaluate the efficiency of switching loss reduction, IGBT CM1000HA-24H module (Mitsubishi Electric., Tokyo, Japan) in PSIM's device database is used in the simulation. Figure 5 shows the conduction loss (*Pc-sinPWM*), switching loss (*Ps-sinPWM*) using sine PWM algorithm and conduction loss (*Pc-proposed*), switching loss (*PS-proposed*) using the proposed algorithm on a phase on changing carrier frequency. As a result, the proposed technique can reduce switching losses. The switching loss reduction value is maximized when *m* = 0.5, equivalent to 78% reduction. There is no significant difference in conduction loss (*Pc*) between the proposed algorithm and sinPWM algorithm, especially at low carrier frequencies. The difference in conduction loss is due to the difference in the high harmonic amplitude between the proposed algorithm and sinPWM algorithm. When the carrier frequency is not high enough (e.g., at *fc* = 5 kHz), the load phase voltage that applies the proposed technique has the high harmonic amplitude at some modulation index values. Therefore, the conduction loss in this case is greater than that in the sinPWM method as in Figure 5c,d. The harmonics spectrum of the proposed and sinPWM algorithms are presented in Figure 6. The harmonics with a large amplitude in the proposed technique focus around the carrier frequency, while they are around twice the carrier frequency in the sinPWM algorithm. The THD of the phase current in the two algorithms is slightly different, as seen in Figure 7.

**Figure 5.** *Cont.*

**Figure 5.** Power loss on a phase under sinPWM method and proposed algorithm at carrier frequency of (**a**) 20 kHz, (**b**) 15 kHz, (**c**) 10 kHz, and (**d**) 5 kHz.

**Figure 6.** Harmonics spectrum of phase voltage at *fs* = 20 kHz using (**a**) sinPWM method with *m* = 0.4, (**b**) proposed method with *m* = 0.4, (**c**) sinPWM method with *m* = 0.9, and (**d**) proposed method with *m* = 0.9.

**Figure 7.** Total harmonic distortion (THD) comparison between sinPWM method and proposed technique at *fs* = 20 kHz.

Figure 7 shows a comparison of THD values of the phase current between sinPWM method and the proposed technique. As shown in Figure 7, THD value of the phase voltage of 5L-HBT2I under the proposed algorithm is smaller than that with the sinPWM method at *fc* = 20 kHz. This can explain that the two-level inverter only operates in a six-step mode with rarely rapid changes of phase voltage on this inverter. As a result, the output harmonics have a small amplitude and conductive losses are also lower than sinPWM techniques, as shown in Figure 5.

Under the load of 40 Ω and 10 mH at the output frequency of 50 Hz, the calculated load power factor is 0.997. Table 4 shows the power factor (PF) and the power factor displacement (PFD) in simulation. As shown in Table 4, the simulated power factor of the inverter is lower than the calculated load power factor of 0.997. This is due to the harmonics distortion of load current and voltage.

**Table 4.** Simulated power factor and power factor displacement.

## *5.2. Experimental Results*

An experimental model based on the DSP TMS320F28335 microcontroller (Texas Instruments, Dallas, TX, US) is built in the laboratory to verify the effectiveness of the proposed control technique with the elements in Table 5. Figure 8 shows a laboratory prototype. The input voltage is 100 V. The output frequency is 50 Hz, while the switching frequency of the inverter circuit is 5 kHz. A three-phase inductive load of 40 Ω and 10 mH is used in the experiment.

**Table 5.** Elements used in experiment.

**Figure 8.** Experimental setup of the prototype.

Figure 9 shows the experimental result of the proposed algorithm when *m* = 0.9 and *m* = 0.4. In Figure 9, the waveforms from the top to the bottom are the gating control signals of the power switches SA5, SA3, SA2 and SA1, the pole voltage (*Vag*), the phase voltage that its harmonic spectrum is in Figure 10. The experimental result of the proposed algorithm in Figure 9 are under modulation index *m* = 0.4 (Figure 9a) and *m* = 0.9 (Figure 9b).

**Figure 9.** Experimental results at (**a**) *m* = 0.4 and (**b**) *m* = 0.9.

The experimental results are close to the simulation results. Figure 9a,b show the position "no switching" in the phase, which has the absolute of its load current hitting maximum or medium in three phases. The gating signal of SA5 is similar to that of SA4, that is the switch of the two-level inverter. This is similar to its waveform in the six-steps mode.

Figure 10 shows the experimental results of the load current fast Fourier transform (FFT) and its THD at *m* = 0.4 and 0.9. The experimental results are close to the simulation results. As shown in Figure 10, the THD of the load current with the proposed algorithm at *m* = 0.4 is bigger it at *m* = 0.9. Since the THD of the load current under the proposed algorithm is smaller than 5%, this complies in the standard IEC61000-4-30 Edition 2 Class A. The experimental results in Figure 10 show that the amplitude of lower harmonics is very small. That is one of the advantages of the proposed technique. The measured THD values in Figure 10 are close to the simulation results shown in Figure 7.

**Figure 10.** The load current fast Fourier transform (FFT) and its THD. (**a**) *m* = 0.4 and (**b**) *m* = 0.9.


**Suburethral Slingplasty Using a Self-Fashioned Mesh for Treating Urinary Incontinence and Anterior Vaginal Wall Prolapse**

Chi-Feng Su, Soo-Cheen Ng, Horng-Jyh Tsai and Gin-Den Chen *Kuang Tien General Hospital, Chung Shan Medical University/Hospital, Department of Obstetrics and Gynecology Taiwan*


**5. Conclusions**

The conducted research proved an essential influence of difficult geotechnical and environmental conditions of the power line tower foundation on the strain state in the tower legs. The testing of supporting structures of high-voltage power transmission lines by means of optical FBG systems provided a lot of essential information about the real values of strains and stresses occurring in the legs

of the analyzed towers of overhead power transmission lines. This is of particular importance in the case of lines which have been in use for many years. The obtained information may also contribute to an improvement in the operating safety of power line towers. The presented fiber-based system intended for the measurement of strains enabled dynamic measurements (horizontal load) as well as long-term measurements. The results of the strain-state measurements of the tower legs were confirmed by geodetic measurements of the tower apex deviation from the plumb line. Using various research methods, e.g., combining the FBG system to measure strains with the assessment of the tower's strain-and-stress state using the RMF method, made it possible to evaluate the performance of a tower structure in very difficult geotechnical conditions.

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

**Acknowledgments:** The technical support from Tauron Company. **Conflicts of Interest:** The author declares no conflict of interest.


**Author details**

**7. Conclusions**

110 Advancements and Breakthroughs in Ultrasound Imaging

sion.

In summary, sonography is essential in the workup of a hypertensive patient. Abdominal sonography should be performed in the evaluation of hypertension. The last European guidelines have emphasized that treatment-induced changes of organ damage affect the incidence of cardiovascular events, thereby recommending performance of organ damage examinations including sonography during treatment. When a search for secondary hyper‐ tension is indicated, abdominal sonography and Doppler ultrasound of the renal arteries are also recommended. Table 2 summarizes the use of ultrasound in the evaluation of hyperten‐

Abdominal ultrasound Identification of subclinical and end-organ damage (recommended) • Aortosclerosis • Aortic aneurysm • Nephrosclerosis

• Renal parenchymal disease • Renal vascular disease • Adrenal adenomas • Phaeochromocytoma Echocardiography Identification of subclinical and end organ damage (recommended)

> • Left ventricular hypertrophy (LVH) • Systolic and diastolic dysfunction • Left atrium dimension and geomertry

• Renovascular hypertension Ultrasound of the carotid arteries Identification of subclinical and end-organ damage (recommended) • Intima – media thickness (IMT)

> • Carotid plaques • Carotid artery stenosis

• Endothelial dysfunction

In summary, sonography is essential in the workup of a hypertensive patient. Abdominal sonography should be performed in every newly diagnosed case of hypertension. Performance of further ultrasound techniques depends on age, concomitant diseases, symptoms, and overall cardiovascular risk. Table 2 summarizes the use of ultrasound in the evaluation of

Screening for secondary causes of hypertension

Identification of subclinical organ damage (not in clinical use)

**Ultrasound examination Use in diagnostic workup of hypertension**

Doppler ultrasound of the renal arteries Screening for secondary causes of hypertension

Assessment of flow-mediated dilation of

**Table 2.** Ultrasound examinations in hypertension

brachial artery

hypertension.

Nikolaos Pagonas, Stergios Vlatsas and Timm H. Westhoff

\*Address all correspondence to<EMAIL_ADDRESS>
Charité – Campus Benjamin Franklin, Dept. of Nephrology, Berlin, Germany


**7.3 Practical example**

of added units and their cost are reduced if the two system are interconnected

A 4 12.63 5.652 2 9.44 1.054 B 2 16.42 4.852 1 8.75 2.045

Therefore, it can be concluded from the above analysis that both systems will benefit from the interconnection. The reliability of both systems can be improved, and consequently the cost of service will be reduced through interconnection and reserve sharing. However, this is not the overall saving because the systems must be linked together in order to create an integrated system. The next stage must, therefore, assess the economic worth that may result from either interconnection or

Since embarking on the national industrial development and the industrials program in the Kingdom of Saudi Arabia, the Ministry of Energy, Industry and Mineral Resources launched two solar PV projects with a combined generation capacity of 1.51 GW enough to power 226,500 households. These projects will be tendered by mid-2019 to attract a total investment of \$1.51 billion Saudi Riyals creating over 4500 jobs during construction, operations, and maintenance [13]. The program will be phased and rolled out in a systematic and transparent way to ensure that the Kingdom benefits from the cost-competitive nature of renewable energy. The National Renewable Energy Program aims to substantially increase the share of renewable energy in the total energy mix, targeting the generation of 27.3 gigawatts (GW) of renewable energy by 2024 and 58.7 GW by 2030. This initiative sets out an organized and specific road map to diversify local energy sources, stimulate economic development, and provide sustainable economic stability to the Kingdom in light of the goals set for Vision 2030, which include establishing the renewable energy industry and supporting the advancement of this promising sector.

As a result of the continuous subsidy and generous support of the government for the electricity sector, the ministry has been able to accomplish many electrical projects in both urban and rural areas, resulting in electric services that can reach remote areas and sparsely populated areas, over rough roads and rugged terrain. In fact, electric services require large sums of money to finance, build, operate, safeguard, and sustain. Another important component that must be considered along with the continuous operation and maintenance expenditures is fuel costs. Therefore, constant maintenance measures ought to be implemented to ensure the level and continuity of the flow of electrical energy without fluctuation, decline, or

**No. of unit Cost (MSR)** *ϵENS* **(MWh) No. of unit Cost (MSR)** *ϵENS* **(MWh)**

**System Isolated Interconnected**

increasing generating capacity individually and independently.

**7. Transmission and distribution reliability evaluation**

**7.2 Role of the government in the electricity sector**

rather than being isolated.

**7.1 Introduction**

interruption.

**156**

System costs as isolated and interconnected:

*Reliability and Maintenance - An Overview of Cases*

One practical example demonstrating the evolving of industry of electric sector in the Kingdom of Saudi Arabia will be shown in this section. The availability of network can be analyzed in a similar manner to that used in generating capacity evaluation (Section 3.1). Therefore, the probability of failing to satisfy the criterion of service adequacy and continuity can be evaluated. Provided the appropriate component reliability indices are known, it is relatively simple to evaluate the expected failure rate (*λ*) of the system, the average duration of the outage I, and the unavailability or annual outage time (*U*). To do this, the values of *λ*, *r*, and *U* are required for each component of the system.

### *7.3.1 State probabilities*

The state-space transition diagram for a two-component system is shown in **Figure 10**.

The probability of a component being in the up state is . Also, the probability of a component being in the down state is *λ λ*þ*μ*.

$$\text{Probability of being in state } 1 = \frac{\mu\_1}{\mu\_1 + \lambda\_1} \cdot \frac{\mu\_2}{\mu\_2 + \lambda\_2}$$

$$\text{Probability of being in state } 2 = \frac{\lambda\_1}{\mu\_1 + \lambda\_1} \cdot \frac{\mu\_2}{\mu\_2 + \lambda\_2}$$

$$\text{Probability of being in state } 3 = \frac{\mu\_1}{\mu\_1 + \lambda\_1} \cdot \frac{\lambda\_2}{\mu\_2 + \lambda\_2}$$

$$\text{Probability of being in state } 4 = \frac{\lambda\_1}{\mu\_1 + \lambda\_1} \cdot \frac{\lambda\_2}{\mu\_2 + \lambda\_2} \tag{10}$$

The most accurate method for analyzing networks including weather states is to use the Markov modeling. However, this becomes impractical for all except the simplest system. Instead, therefore, an approximate method is used based upon simple rules of probability.

**Figure 10.**

*State-space diagram for two-component system, where λ is the failure rate and μ is the repair rate* ¼ 1 *r* ð Þ *r* ¼ *repair time :*

#### *7.3.2 Series components*

The requirement is to find the reliability indices of a single component that is equivalent to a set of series-connected components as shown in **Figure 11**.

If the components are in series from a reliability point of view, both must operate, i.e., be in upstate, for the system to be successful, i.e., the upstate of a series system is state 1 of the state-space diagram shown in **Figure 11**.

From the above equation (state 1), the probability of being in this upstate is In addition, since , the above equation becomes

$$r\_s = \frac{\lambda\_1 r\_1 + \lambda\_2 r\_2 + \lambda\_1 \lambda\_2 r\_1 r\_2}{\lambda\_s} \tag{11}$$

$$=\frac{\lambda\_1 r\_1 + \lambda\_2 r\_2}{\lambda\_2} \tag{12}$$

*λs* ¼ *λ*1 þ *λ*2 ¼ ∑

*rs* ¼ ∑*n*

In particular, the order of evaluation is usually *λs*ð Þ ¼ ∑*λ , Us*ð Þ ¼ ∑*λ r* and

Although these equations were derived from the assumption of exponential distribution, they are expected or average values and can be shown to be valid

Many systems consist of both series and parallel connections. These systems can

In this case, the requirement is to find the indices of a single component that is

If the components are in parallel from a reliability point of view, both must fail for resulting in a system failure, i.e., the down state of a parallel system is state 4 of the state-space diagram shown in **Figure 10**. From (10), the probability of being in

Also, the rate of transition from state 4 of the two-component state-space dia-

¼ *λp λp* þ *μp*

*λ*1*λ*2 ð Þ *μ*1 þ *λ*1 ð Þ *μ*2 þ *λ*2

be seen in transmission lines, in combinations of transformers, cables, feeders, relays, protection and control devices, etc. As an example, **Figure 12** displays two parallel lines that are both connected in series with another line. In these situations, and from a reliability point of view, it is essential to consequently reduce the network in order to estimate its overall reliability. This is accomplished by repeatedly combining sets of parallel and series components into equivalent network components until a single component remains. The reliability of the last component

is equal to the reliability of the original system (**Figure 12**).

equivalent to two parallel components as shown in **Figure 12**.

*rs*ð Þ ¼ *Us=λs* .

*7.3.3 Parallel components*

this downstate is

gram is . Therefore

**Figure 12.**

**159**

*State-space diagram for a two-component system.*

irrespective of the distribution assumption.

*Reliability Evaluation of Power Systems DOI: http://dx.doi.org/10.5772/intechopen.85571*

Thus, the unavailability for series systems (*US*Þ can be expressed as

*n i*¼1

*i*¼1*λi ri* ∑*n i*¼1*λi*

*λi* (14)

*US* ¼ *λs rs* (16) ¼ ∑*λ r* (17)

(15)

(18)

$$\dot{r} = \frac{\sum\_{i=1}^{n} \lambda\_i \ r\_i}{\lambda\_i} \tag{13}$$

Also, the rate of transition from state 1 of the two-component state-space diagram is , therefore

**Figure 11.** *State-space diagram for two-component system.*

*Reliability Evaluation of Power Systems DOI: http://dx.doi.org/10.5772/intechopen.85571*

$$
\lambda\_t = \lambda\_1 + \lambda\_2 = \sum\_{i=1}^n \lambda\_i \tag{14}
$$

$$r\_s = \frac{\sum\_{i=1}^{n} \lambda\_i \ r\_i}{\sum\_{i=1}^{n} \lambda\_i} \tag{15}$$

Thus, the unavailability for series systems (*US*Þ can be expressed as

$$U\_S = \lambda\_s \ r\_s \tag{16}$$

$$= \sum \lambda r \tag{17}$$

In particular, the order of evaluation is usually *λs*ð Þ ¼ ∑*λ , Us*ð Þ ¼ ∑*λ r* and *rs*ð Þ ¼ *Us=λs* .

Although these equations were derived from the assumption of exponential distribution, they are expected or average values and can be shown to be valid irrespective of the distribution assumption.

### *7.3.3 Parallel components*

*7.3.2 Series components*

*r* ð Þ *r* ¼ *repair time :*

*Reliability and Maintenance - An Overview of Cases*

**Figure 10.**

*repair rate* ¼ 1

diagram is , therefore

*State-space diagram for two-component system.*

**Figure 11.**

**158**

The requirement is to find the reliability indices of a single component that is

From the above equation (state 1), the probability of being in this upstate is

*rs* ¼ *λ*1*r*1 þ *λ*2*r*2 þ *λ*1*λ*2*r*1*r*2 *λs*

> ¼ *λ*1*r*1 þ *λ*2*r*2 *λs*

> > *i*¼1*λi ri λs*

¼ ∑*n*

Also, the rate of transition from state 1 of the two-component state-space

(11)

(12)

(13)

equivalent to a set of series-connected components as shown in **Figure 11**. If the components are in series from a reliability point of view, both must operate, i.e., be in upstate, for the system to be successful, i.e., the upstate of a series

system is state 1 of the state-space diagram shown in **Figure 11**.

*State-space diagram for two-component system, where λ is the failure rate and μ is the*

In addition, since , the above equation becomes

Many systems consist of both series and parallel connections. These systems can be seen in transmission lines, in combinations of transformers, cables, feeders, relays, protection and control devices, etc. As an example, **Figure 12** displays two parallel lines that are both connected in series with another line. In these situations, and from a reliability point of view, it is essential to consequently reduce the network in order to estimate its overall reliability. This is accomplished by repeatedly combining sets of parallel and series components into equivalent network components until a single component remains. The reliability of the last component is equal to the reliability of the original system (**Figure 12**).

In this case, the requirement is to find the indices of a single component that is equivalent to two parallel components as shown in **Figure 12**.

If the components are in parallel from a reliability point of view, both must fail for resulting in a system failure, i.e., the down state of a parallel system is state 4 of the state-space diagram shown in **Figure 10**. From (10), the probability of being in this downstate is

$$\frac{\lambda\_1 \lambda\_2}{(\mu\_1 + \lambda\_1)(\mu\_2 + \lambda\_2)} = \frac{\lambda\_p}{\lambda\_p + \mu\_p} \tag{18}$$

Also, the rate of transition from state 4 of the two-component state-space diagram is .

Therefore

**Figure 12.** *State-space diagram for a two-component system.*

$$\frac{1}{r\_p} = \frac{1}{r\_1} + \frac{1}{r\_2} \tag{19}$$

where 8760 is the total number of hours in a year, using Eq. (20)

¼ 5 � 5

¼ 2*:*854 � 10�4 � 2*:*5*=*8760

¼ 7*:*135 � 10�4 h*=*yrs*:*

*λC* ¼ *λB* þ *λ*3

*rC* ¼ *UB* þ *λ*3*r*3 *λC*

¼ 9*:*977 h*:*

*UC* ¼ *λCrC*

events are very unreliable, the opposite effect may occur.

applying the previous series equations to these overlapping outages.

*7.3.4 Network reduction for failure mode analysis*

above) and then combined with line 3 in series, using Eq. (14):

5 þ 5 ¼ 2*:*5 h*:*

¼ 8*:*145 � 10�8 yrs*=*yrs ¼ *probability*

To find indices at busbar C, lines 1 and 2 must be combined in parallel (as done

¼ 2*:*854 � 10�4 þ 0*:*1 ¼ 1*:*003 � 10�1 *f =yr*

*rC* ¼ 7*:*135 � 10�4 þ 0*:*1 � 10 1*:*003 � 10�1

∴*UC* ¼ 1*:*003 � 10�1 � 9*:*977 ¼ 1*:*001 h*=*yrs*:*

In this case, it is seen that the indices of busbar C are dominated by the indices of line 3. This is clearly expected since busbar C will be lost if either line 3 or lines 1 and 2 simultaneously fail. Consequently, loss of line 3 is a first-order event, and loss of lines 1 and 2 are a second-order event. It must be stressed that this is only true if the reliability indices of the components are comparable; if the component forming the low-order event is very reliable and the components forming the higher order

In some cases, some critical or unreliable areas become absorbed into equivalent elements and become impossible to identify. The alternative is to impact the system and compose a list of failure nodes, i.e., component outages that must overlap to cause a system outage. These overlapping outages are effectively parallel elements and can be combined using the equations for parallel components. Any one of these overlapping outages will cause system failure and therefore, from a reliability point of view, are effectively in series. The system indices can therefore be evaluated by

*rB* ¼ *r*1 *r*2 *r*1 þ *r*2

*Reliability Evaluation of Power Systems DOI: http://dx.doi.org/10.5772/intechopen.85571*

*UB* ¼ *λBrB*

Using Eq. (23)

**161**

or

$$r\_p = \frac{r\_1 r\_2}{r\_1 + r\_2} \tag{20}$$

From the above equations, it yields that

$$
\lambda\_p = \frac{\lambda\_1 \lambda\_2 (r\_1 + r\_2)}{1 + \lambda\_1 r\_1 + \lambda\_2 r\_2} \tag{21}
$$

$$=\lambda\_1 \lambda\_2 (r\_1 + r\_2) \tag{22}$$

Thus, the unavailability for parallel systems *Up* can be expressed as

$$U\_p = \lambda\_p r\_p \tag{23}$$

In practice, the order of evaluation is usually

$$
\lambda\_s = \sum \lambda \qquad \qquad \nu\_s = \sum \lambda \cdot r \qquad \qquad \text{and} \qquad \qquad r\_s = \frac{\upsilon\_s}{\lambda\_s}
$$

Although these equations were derived from the assumption of exponential distribution, they are expected or average values and can be shown to be valid irrespective of the distributional assumption.

**Example (series/parallel):** To illustrate the applications of these techniques, let us consider the transmission lines supplying the newly large industrial park constructed near Riyadh city (the capital of the KSA) within what is called "industrial cities" in the main cities of the KSA. The transmission lines with their data load points are given below (see **Figure 13**). It is required to evaluate the load point (busbar) reliability indices at busbars B and C.

To find the indices at busbar B, lines 1 and 2 must be combined in parallel using Eq. (22):

$$\begin{aligned} \dot{\lambda}\_{\mathcal{B}} &= \dot{\lambda}\_1 \dot{\lambda}\_2 \, (r\_1 + r\_2) \\ &= \mathbf{0}. \mathbf{5} \times \mathbf{0}. \mathbf{5} (\mathbf{5} + \mathbf{5}) / \mathbf{8760} \\ &= \mathbf{2.854} \times \mathbf{10}^{-4} f / \mathbf{y} \end{aligned}$$

**Figure 13.** *Transmission lines configuration with data load points.*

1 *rp* ¼ 1 *r*1 þ 1 *r*2

From the above equations, it yields that

*Reliability and Maintenance - An Overview of Cases*

Thus, the unavailability for parallel systems *Up*

In practice, the order of evaluation is usually

irrespective of the distributional assumption.

(busbar) reliability indices at busbars B and C.

*Transmission lines configuration with data load points.*

*rp* ¼ *r*1 *r*2 *r*1 þ *r*2

*λp* ¼ *λ*1 *λ*2ð Þ *r*1 þ *r*2 1 þ *λ*1*r*1 þ *λ*2*r*2

Although these equations were derived from the assumption of exponential distribution, they are expected or average values and can be shown to be valid

us consider the transmission lines supplying the newly large industrial park constructed near Riyadh city (the capital of the KSA) within what is called "industrial cities" in the main cities of the KSA. The transmission lines with their data load points are given below (see **Figure 13**). It is required to evaluate the load point

**Example (series/parallel):** To illustrate the applications of these techniques, let

To find the indices at busbar B, lines 1 and 2 must be combined in parallel using

*λB* ¼ *λ*1 *λ*2 ð Þ *r*1 þ *r*2

¼ 0*:*5 � 0*:*5 5ð Þ þ 5 *=*8760

¼ 2*:*854 � 10�4*f =y*

¼ *λ*1*λ*2ð Þ *r*1 þ *r*2 (22)

can be expressed as

*Up* ¼ *λprp* (23)

or

Eq. (22):

**Figure 13.**

**160**

(19)

(20)

(21)

where 8760 is the total number of hours in a year, using Eq. (20)

$$r\_B = \frac{r\_1 r\_2}{r\_1 + r\_2} = \frac{5 \times 5}{5 + 5} = 2.5 \text{ h}.$$

$$U\_B = \lambda\_B r\_B$$

$$= 2.854 \times 10^{-4} \times 2.5 / 8760$$

$$= 8.145 \times 10^{-8} \text{ yrs/yrs} =
probability$$

$$= 7.135 \times 10^{-4} \text{ h/yrs}.$$

To find indices at busbar C, lines 1 and 2 must be combined in parallel (as done above) and then combined with line 3 in series, using Eq. (14):

$$\begin{aligned} \dot{\lambda}\_C &= \dot{\lambda}\_B + \dot{\lambda}\_3\\ &= 2.854 \times 10^{-4} + 0.1\\ &= 1.003 \times 10^{-1} f/yr\\ r\_C &= \frac{U\_B + \dot{\lambda}\_3 r\_3}{\dot{\lambda}\_C} \\ r\_C &= \frac{7.135 \times 10^{-4} + 0.1 \times 10}{1.003 \times 10^{-1}} \\ &= 9.977 \text{ h} \end{aligned}$$

Using Eq. (23)

$$\begin{aligned} U\_C &= \lambda\_C r\_C \\ \vdots U\_C &= \mathbf{1.003} \times \mathbf{10^{-1}} \times \mathbf{9.977} \\ &= \mathbf{1.001} \,\mathrm{h/yrs} .\end{aligned}$$

In this case, it is seen that the indices of busbar C are dominated by the indices of line 3. This is clearly expected since busbar C will be lost if either line 3 or lines 1 and 2 simultaneously fail. Consequently, loss of line 3 is a first-order event, and loss of lines 1 and 2 are a second-order event. It must be stressed that this is only true if the reliability indices of the components are comparable; if the component forming the low-order event is very reliable and the components forming the higher order events are very unreliable, the opposite effect may occur.

#### *7.3.4 Network reduction for failure mode analysis*

In some cases, some critical or unreliable areas become absorbed into equivalent elements and become impossible to identify. The alternative is to impact the system and compose a list of failure nodes, i.e., component outages that must overlap to cause a system outage. These overlapping outages are effectively parallel elements and can be combined using the equations for parallel components. Any one of these overlapping outages will cause system failure and therefore, from a reliability point of view, are effectively in series. The system indices can therefore be evaluated by applying the previous series equations to these overlapping outages.

The following case study showcases the existing tie-line interconnecting the eastern region (ER) with the central region (CR) (400 km apart) in the Kingdom of Saudi Arabia (KSA). The ER is actually the incubator of the oil industry and all its refineries and infrastructures. Riyadh is located in the CR, which is the domicile of the Saudi Electric Company (SEC). The latter is envisioning tremendous expansion with vast increasing industrial future loads. Therefore, a huge bulk of electric power is transferred from the ER to the CR via the interconnecting tie-line. Therefore, to evaluate its reliability using the concepts and methodology stated above, the tie-line (see **Figure 14**) is considered bearing the following data:


**PRINCIPLES AND APPLICATIONS IN NUCLEAR ENGINEERING - RADIATION EFFECTS, THERMAL HYDRAULICS, RADIONUCLIDE MIGRATION IN THE ENVIRONMENT**

Edited by **Rehab O. Abdel Rahman** and **Hosam El-Din M. Saleh**

http://dx.doi.org/10.5772/65990 Edited by Rehab O. Abdel Rahman and Hosam El-Din M. Saleh

### **Contributors**

Bingqi Zhu, David Ryan, Roger Saint-Fort, Roland Wisniewski, Jianjun Xu, Tianzhou Xie, Xuezhi Zhang, Lei Yang, Sannappa J., Rehab O. Abdel Rahman

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Principles and Applications in Nuclear Engineering - Radiation Effects, Thermal Hydraulics, Radionuclide Migration in the Environment Edited by Rehab O. Abdel Rahman and Hosam El-Din M. Saleh p. cm.

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