**3. Basic Activities and Slips**

Basic activities are of special interest to our enquiry. Basic activities are those activities we automatically know how to perform; we pull them o ff by doing nothing else. They are the very source of agency, the material of which all other actions are made. As such they are a necessary condition for all other matters connected to agency. When someone performs basic activities, they do so by making bodily movements that constitute the fundamental atoms of what they are attempting to accomplish, grounding every other action. They do so without any need to determine the means by which the action should be performed.  Consider the example from Hornsby of someone saying "grass is green" [31]. The utterance is performed through movements of the tongue, mouth, teeth, etc. The agent does not make these movements because they believe that they are a means of saying "grass is green"; they probably have no particular beliefs about them and are hardly aware of them. They do not do them intentionally in the way they intentionally utters the sentence as a whole. From the agent's perspective, basic activities have a teleological structure, and one can perform them without any need to understand their details correctly. On such a teleological view, basic activities are relative to the agent: acts that are basic for one agent may not be for another. Moreover, something that is basic for an agent in one setting may not be in another. Consider the agent for whom using their own hot-water kettle is a basic action while using a hot-water kettle of unfamiliar design is not.

The possibility of slips is of special interest to the naturalistic view we defend. Slips—performances one can successfully do while intending something else—genuinely reveal what one can do in a basic sense, "just like that", precisely because one has all the necessary bodily skills to perform them. Because of that capacity, one can reasonably be expected to be able to perform them intentionally as well. A basic activity is one the agent can perform even while making a slip. We think those things that one is able to do even while making a slip are the ones that truly are basic. In other words, "slipping behavior" reveals basicness. A slip is the kind of performance that would often, in another context, be meaningfully intended. After all, slips are not random. Verbal slips show lexical biases, tend to result in grammatically correct utterances, and rarely violate the syntactic constraints of the language; so Fromkin [32] (p. 183) writes: "according to all linguists who have analyzed spontaneous speech errors, the errors are nonrandom and predictable". This is important, because it illuminates how an agent's knowledge how is operative when they slip. When an agent slips by grasping the salt instead of the sugar, then this is not because they are incompetent in distinguishing salt from sugar. What the slip shows is misdirected competence. Slips are small episodes of misdirected behavior in otherwise correctly performed action sequences, often closely resembling the correct act. Salt is not so far from sugar in terms of appearance or use. Contrast the act of grasping the salt instead of the sugar with that of accidentally taking a handful of soil from a pot of tulips: such action surely would be ba ffling, because it differs so much from what is expected. The point becomes particularly clear with so-called slips of the tongue: the agent who slips speaks comprehensible words, not mere nonsense.

To specify even more, slips are executive failures; you go left instead of right, you pour milk instead of water, you push the button marked "1" instead of the one marked "2" etc. In the case of a slip, the agent bluntly does something different from what they mean to be doing. The failure is not at a cognitive level, thus the agent does not fail because they have a false belief and the like [33–36]. Crucially, the agent slips despite knowing that their performance is an error. The agent who is about to add milk to their coffee, but pours juice instead does not err because they cannot tell the difference between milk and juice: clearly, they can. Competence does not provide immunity from slips: the person who slips does not do so because they lack the relevant ability. They are fully able to grab, lift, and pour from a container; they just happen to grab the wrong one. They slip not because their movements are beyond their control, like those made by someone suffering from a compulsive disorder or Anarchic Hand syndrome,4 but because, then and there, they simply make the wrong movements. Among other things, an important thing to notice here is that the agent has the correct propositional content and is normally able to apply it, but, for some reason, their knowledge that and their knowledge how came apart and they acted in some sense successfully: they performed actions that belong to their basic action repertoire (they pull them off "just like that")—i.e., they poured milk instead of juice, they did not start singing into the jug or jump up and down—on a different propositional content than they meant to act on. How can knowledge that and -how come apart like this if knowledge how is merely a species of the former? The topic of basicness in general and the above discussed split between knowledge how and knowledge that in particular is not discussed by Stanley. He does not consider the basicness of activities the way we do. Instead of focusing on basicness, he focuses on knowledge of truths and is ignorant towards executive mistakes in the sense we are interested in here, it just is not among his concerns. He states that when you learn some truths about swimming, then you know how to swim and after the acquisition of that fact it seems, on his intellectualist account, that you can, of course, do something wrong when swimming, boxing and cycling, but, crucially, you cannot bluntly apply the wrong content and be wrong about how you should swim or cycle. When you have learned how to swim, you simply know. In other words, when you have gained the knowledge of swimming, you cannot "unknow" it, in the same way as after the moment you genuinely learned the truths about how to walk, you cannot be wrong about walking, to walk is something you know how to do. One of our points is that Stanley's account can make one lose sight of neuro-psychological facts like the simple point that human beings sometimes slip and in the slip, knowledge how and knowledge that come apart, as we have shown in the above examples. The failure to see this is one of the things that we find biologically misconceived in the intellectualist account. This is, in a nutshell, our critique: slips show how knowledge how has epistemic properties not present in knowledge that. When an agent slips, they do something different from what they intended; nonetheless, the performance is guided by their knowledge how. This reveals a divide between the knowledge that actively guides behavior: the knowledge how that the agent applies sub-consciously; and the knowledge how they intend to guide their behavior in the first place, which they are under the illusion of acting on even as they slips. We argue that this divide between two levels of knowledge how operative in the slip case has no parallel when it comes to knowledge that. Therefore, knowledge how cannot be reduced to knowledge that. As we will explain in further detail below, a reason for why slips occur can be a slip-up in the communication between different cognitive processes in the mind of the agent at the time of acting.

4 Addressing Anarchic Hand syndrome, Marcel [37] (p. 77) writes: "the affected hand performs unintended but complex, well-executed, goal-directed actions. Often when the patient is trying to do something with the unaffected hand, the other hand appears to do the opposite or compete with it."


**Abstract**

With recent technologies, ultrasound has become an extremely useful imaging modality for evaluating children with acute abdominal symptoms. Higher frequency transducers can be used in children than in adults, owing to their small body size, the presence of less fat tissue in the abdominal wall and peritoneal cavity leading to higher resolution than computed tomography in many circumstances without exposure to ionizing radiation. Real-time ultrasound imaging provides information about motion such as peristalsis, and newly developed harmonic imaging enables improved resolution with decreased artifacts. Beyond gray-scale ultrasound, color Doppler ultrasound provides information on vascularity which increases in inflammatory processes. Point-of-care examination includes ability to focus on the symptomatic area of the patient while performing real-time ultrasound imaging. Ultrasound is sufficient for the diagnosis of several gastrointestinal diseases that cause acute abdominal pain in pediatric patients helping to an accurate patient management in the emergency settings. Common gastrointestinal indications for abdominal ultrasound in children are hypertrophic pyloric stenosis, acute appendicitis, intussusception, inflammatory bowel disease, malrotation, midgut volvulus, hernia, and necrotizing enterocolitis. In this chapter, typical sonographic findings of aforementioned diseases, and possible differential diagnoses were discussed.

**Keywords:** Acute appendicitis, intussusception, inguinal hernia, necrotizing enterocolitis, hypertrophic pyloric stenosis, inflammatory bowel disease

## **1. Introduction**

Non-traumatic acute gastrointestinal (GI) disorders are common causes of presentation in the pediatric emergency department. Children have wide range of potential diagnosis, different from adults including congenital and acquired lesions. The causes of acute abdomen vary according to ages of the children. Since children are unable to give reliable history, have atypical presentations and accompanying extra-abdominal manifestations; evaluation and establishing the correct diagnosis is challenging.

Traditionally, pediatric abdominal ultrasound (US) examination focuses exclusively on parenchymal organs, putting less interest on the gastrointestinal tract [1]. However, recent US technologies and new transducers are able to perform a detailed examination with great contrast resolution of each section of the digestive system in pediatric age because of their smaller body size and less impaired by gas content and adipose tissues. The other well-known advantages of US, particularly its lack of ionizing radiation, easy access, low-cost and without need of patient

preparation, makes this imaging modality an ideal one for the evaluation of pediatric population in the emergency settings. Currently in many places, US is the first line of imaging over computed tomography (CT) and radiography for patients with acute abdominal pain. The main role of diagnostic imaging with US and color Doppler in the emergency is to determine whether the acute abdomen is due to a surgically or medically treatable disease, even though the exact pathology has not been diagnosed.

This chapter presents the basic aspects of US for evaluating the pediatric GI tract, including techniques, equipment, patient preparation and the anatomy. Then indications and sonographic findings of frequently encountered acute non-traumatic GI diseases in neonates, infants and children are highlighted with some exemplary cases. Acute traumatic GI tract injuries, oncologic emergencies, acute abdomen due to hepatobiliary or urogenital diseases are beyond the scope of this chapter.

### **2. Ultrasound technique and appropriate equipment**

New generation ultrasound equipment including the wide spectrum frequency probes provides high quality images of the gastrointestinal system, adjacent mesentery and related structures.  Therefore US is increasingly used as the initial and follow-up study for investigating gastrointestinal tract pathologies in children and it is sufficient for the radiological diagnosis in majority of cases.

The contrast resolution of an US probe is dependent on the frequency, the velocity of sound in tissue and the number of cycles in the US pulse [2]. Depending on the age and size of the patient, a large convex-array (1–5 MHz) or smaller convex-array transducer (5–8 MHz) is a good option for beginning the examination for overview of the entire abdomen [3]. Following initial overview, a detailed analysis of the bowel wall and adjacent structures should be evaluated with a high frequency (10–18 MHz) linear-array transducer [1]. Tissue harmonic imaging is newly developed imaging software to increase resolution of the superficial parts of the field-of-view. It should be used to improve the delineation of bowel wall layers [2]. While evaluating anxious children in the acute setting, dynamic range should be lowered and the number of foci should be reduced to increase frame rate [4]. To demonstrate peristalsis, normal or abnormal motility, and motion of air bubbles in perforation or necrotizing enterocolitis; extended field-of-view can be helpful and cine clips should be recorded [5].

Doppler US evaluation is essential in GI system imaging, especially when looking at inflammatory diseases or neoplastic conditions. Doppler should be performed with a low wall filter and pulse repetition frequency should be adjusted as low as possible to prevent aliasing [6]. Power Doppler is a good method to overcome motion artifact in uncooperative children. As there are modern equipment and software, newer vascular imaging techniques, such as B-flow and superb microvascular imaging are brought into use by different vendors which are able to assess smaller vessels in the bowel wall [4].

US elastography is an emerging US technique to assess the stiffness of a tissue [5]. There are some studies in the literature regarding the usage of elastography for GI tract diseases, particularly in inflammatory conditions [7, 8]. The bowel is a hollow viscus with a lumen containing gas and fecal contents. The anatomy of the bowel is not ideal for US elastography as solid organs (e.g. liver or kidney). However, bowel wall thickening due to inflammation or tumor often reduces

### *Ultrasound of the Pediatric Gastrointestinal Emergencies DOI: http://dx.doi.org/10.5772/intechopen.99759*

motility and luminal contents that enable to perform US elastography more reliable [2]. Some studies suggest using US elastography in inflammatory bowel disease to differentiate inflammatory and fibrotic stenosis [9, 10].

Contrast enhanced US (CEUS) can be used to evaluate bowel wall vascularity and perfusion in real time [5]. It is performed after the intravenous injection of microbubbles that resonate and give rise to more intensely reflected signals [2]. Enhancement pattern, contrast quantification at peak intensity and dynamic contrast enhancement can be analyzed with CEUS [11, 12]. Enhancement pattern following bolus injection is used as a qualitative parameter. For example, patients with absent bowel wall enhancement can be separated from those with detected enhancement [2]. It can also be used in patients with complicated GI disorders when trying to differentiate a phlegmon from an abscess [13].

US examination of GI system must involve a systematic approach. While evaluating large bowel, the transducer is applied to the right iliac fossa to identify the cecum. Afterwards, colon can be followed through the ascending colon, transverse colon, descending colon, sigmoid colon and finally the rectum. Since the rectum is visualized behind the bladder, filled bladder is better to evaluate rectum and sigmoid colon. Longitudinal placement of the transducer is often better to identify the haustrations of colon segments [2]. The examination of the small intestine begins with the identification of ileocecal valve and the terminal ileum at the right iliac fossa. The examiner should identify the appendix, often inferior to the terminal ileum and follow the ileum as far as possible. Tracking the whole small bowel is generally not possible, therefore the abdomen should be scanned cranially and caudally parallel scans covering the whole abdominal area. The scanning approach may differ according to clinical scenario. For surgical disorders or trauma, a faster and a targeted approach are preferred, whereas for general and nonspecific complaints, more detailed examination can be performed.

 It decreases the distance between the transducer and target organ and enables to reach deeper with high frequency transducers. Although it was introduced for the diagnosis of acute appendicitis by Puylaert [14], now it has been performed for detection of bowel thickening and compressibility, and for specific diseases such as diverticulitis and colonic polyps [15, 16].

### **3. Patient preparation and clinical indications**

As a general principle, no preparation of the patient is required to perform gastrointestinal US, particularly in the emergency setting. However, to decrease the amount of food and gas in the gut, and to examine the gallbladder and biliary tree, a fasting period of 3 hours in newborn and 5 hours in children is recommended [1]. Physical activity also reduces the splanchnic flow, therefore patients should avoid from extensive activity before the examination [2]. Since the cold gel is one of the major complaints of children, gel warmer to warm the coupling gel can be used. If the infants or neonates are anxious and reluctant to be scanned; examiner can sit them on their mother's lap, get her lie down on the couch along with the child.

For stomach and pyloric examination, oral fluid intake or fluid ingestion via nasogastric tube is useful [4]. The distention of colon with anechoic fluid (water) ingestion, or with oral administration of hyperosmotic solutions allows the detailed examination of the haustration of colonic wall and adjacent structure [2]. The scanning of small intestine following the ingestion of iso-osmolar polyethylene glycol (PEG) solution is called US enterography or small intestine contrast US (SICUS).

Since the PEG solution is non-absorbable in the small bowel, retained fluid distends the intestine and induces the wall contractility. The PEG solution moves distally and distends whole loops of the entire small bowel. Following PEG ingestion, small bowel lumen diameter > 30 mm and wall thickness > 3 mm is abnormal [17].

Before beginning a US examination, examiner should be familiar with the abdominal symptoms, clinical presentations and laboratory findings of acute GI diseases. The most common presentations are pain, vomiting, diarrhea, fever, hematochezia and melena. Although some diseases have peculiar clinical findings, majority of cases have non-specific symptoms and clinical appearances [3]. US is generally suggested as the first line imaging modality in children with acute abdomen. Most common indications for gastrointestinal US in children are acute appendicitis, intussusception, hernia, hypertrophic pyloric stenosis, inflammatory bowel disease, and volvulus. Further indications involve necrotizing enterocolitis, duplication cysts, malrotation of the bowel [4]. Also US is widely performed for the disease of other intraabdominal structures such as mesenteric lymphadenitis, lymphoid hyperplasia of the appendix, infectious enterocolitis, omental infarct, epiploic appendagitis, specific inflammations such as tuberculosis, colitis with hemolytic uraemic syndrome and Henoch-Schönlein purpura [4]. The recent COVID-19 pandemic associated multisystem inflammatory syndrome in children (MIS-C) can also manifest with gastrointestinal system dysfunction which has been also a novel US indication since 2020 [18].

### **4. Challenges of GI ultrasound**

Major challenges of US is based on its operator-dependency and reproducibility [5]. The European Federation of Societies for Ultrasound in Medicine and Biology (EFSUMB) suggests to set standards of training and education curriculum for GI system US to provide high quality performance in clinical practice [2]. According to EFSUMB recommendations; the operator should be able to recognize the normal anatomy of small intestine and large bowel initially. Following recognizing normal appearance of normal GI tract, the investigator should be able to perform a complete scanning of the gut; evaluation for focal or diffuse diseases, the presence of diverticular disease and its complications (perforation and obstruction), the peritoneal cavity, the mesentery, and the omentum for the inflammatory, infectious or malignant diseases [2].

There are other challenging factors related to the patient such as noncollaboration, obesity and interposition of large amount of gas [5]. Particularly retroperitoneal, paraaortic and retroduodenal areas are often danger zones that are not well delineated on US. If the graded compression technique is ineffective to eliminate gas interposition and US findings are unremarkable; intravenous contrast enhanced CT should be performed in patients with acute abdominal pain, especially if there is suspicion of gut perforation.

### **5. Normal anatomy**

While examining normal anatomy of GI structures; position, size, wall thickness and stratification should be evaluated. Many GI disorders appear as bowel wall thickening but normal bowel wall thickness may vary depending on peristalsis and the degree of distention [3]. Recent studies with high frequency transducers suggest that both normal small and large bowel wall thickness should be <2 mm when distended [19]. The exceptions are the pylor/duodenal bulbus and rectum wall which

*Ultrasound of the Pediatric Gastrointestinal Emergencies DOI: http://dx.doi.org/10.5772/intechopen.99759*

should be < 3 mm and < 4 mm respectively [20]. If the measurements were made from collapsed bowel wall, it should be reported since the wall of collapsed bowel is shown as thicker [2].

When examined with high frequency transducers, five sonographic layers of the bowel wall can be seen. When imaging the anterior wall (closer to transducer); the innermost echogenic layer is called as the mucosa-lumen interface which is not a part of actual GI wall. The second hypoechoic layer correspond to the deep mucosa, the third hyperechoic layer is submucosa which is most prominent in the colon [3]. The muscularis propria is the hypoechoic fourth layer which is most pronounced in the stomach. The outermost hyperechoic layer is the interface between muscularis and serosa. As the interface are hyperechoic and located distal to the real tissue, correspondence of histology and US layers are slightly different in the dorsal wall [2]. Therefore, evaluation of the layers should be made from the anterior bowel wall in diffuse inflammatory diseases. Bowel wall thickness measurement should be made perpendicular to the wall from innermost to the outermost echogenic layers [2].

The small intestine has three segments. The duodenum passes into the jejunum at the ligament of Treitz located in the left upper quadrant. The jejunum is often located in the left upper quadrant and usually collapsed with prominent folds, also known as valvula conniventes. They decrease and shorten from jejunum to ileum and best demonstrated at the fluid filled loops [2]. The ileum is located at the right lower quadrant and frequently involves fluid in normal patients. Sometimes cecum may be located intraperitoneal in variable positions even at the left lower quadrant of abdomen. The cecum and ileocecal valve is important landmarks to identify appendix which is usually below to the ileocecal valve. Although appendix is typically seen over the iliopsoas muscle medial to the cecum, lateral elevation or retrocecal course are not infrequent [2]. The normal appendix can be visualized in about 70% of healthy children with graded compression and it may increase depending on the experience of examiner and the resolution of transducer [21].

### **6. Acute appendicitis**

Acute appendicitis accounts for 80% of all abdominal surgical emergencies in pediatric population [22]. It is most frequently seen in second decade and is rare in children under two years of age, probably due to the funnel shape of appendix in infancy, which reduces the possibility of obstruction [23, 24]. Possible predisposing factors include lymphoid hyperplasia (due to past viral infection), dehydration, and low dietary intake of fiber [24]. Although the typical clinical presentation is acute onset of abdominal pain that may occur in the periumbilical area, radiating to the right lower quadrant, one-third of children have atypical clinical findings and symptoms, especially younger ones [23]. Other clinical signs are; fever, elevated acute phase reactants, nausea, vomiting and leg pain. Diarrhea is not present unless there is perforation and peritonitis, more frequently occurs in young children and confused with gastroenteritis [24]. Following clinical assessment and laboratory findings, imaging is the third component while evaluating the patients with suspected appendicitis. The routine US examination in suspected appendicitis reduces the negative appendectomies 50% and decreases the surgical complications and costs [25].

In patients with localized pain, transducer is applied to the point of maximum tenderness or pain. Self-localization facilitates the scanning, especially in patients with an aberrantly located appendix, and reduces the time of examination. If the patient cannot localize the pain or uncooperative; systematic evaluation starts in

transvers plane to identify ascending colon. Lowermost part of the ascending colon is the cecal pole and medial to the cecum ileocecal valve can be demonstrated. The most common origin of the appendix is 2–3 cm below to the ileocecal valve [26]. Pressure is gradually increased to displace gas and fecal materials in the cecal lumen to adduct appendix to the transducer. In obese children, a left oblique body position or an upward graded compression technique may be useful to displace the fat tissue of the abdominal wall [27]. Anatomical variations require a systematic approach to evaluate appendix and experience plays an important role in examination. There are several US features to distinguish between normal and inflamed appendix which are valid for both children and adults (**Table 1**) [25, 26, 28, 29].

The inflamed appendix is shown as a fluid-filled non-compressible distended aperistaltic tubular structure with a blind end (**Figure 1**). In the axial plane, it has a target appearance with thickened echogenic mucosal interface and hypoechoic muscular wall. Appearance of an appendicolith, which is an echogenic focus with a posterior acoustic shadowing, is supportive finding for the diagnosis (**Figure 1C**) [23]. However, intraluminal air is also echogenic and can mimic appendicolith (**Figure 1D**). A heterogeneous mass around appendix representing phlegmon, and a walled-off fluid collection representing abscess are often the signs of complicated appendicitis and perforation [23]. Complicated appendicitis can occur either as a gangrenous appendicitis (focal or diffuse necrosis of the wall) or as a perforation. There is continuous transition from phlegmonous uncomplicated to gangrenous appendicitis during the disease course. The most important indicator of gangrenous appendicitis is the loss of normal hyperechoic mucosa-lumen interface [30]. Other ancillary finding is the lack of vascularity on color Doppler. The rate of perforation following acute appendicitis is around 60% for a 3-year-old child, 50% for a 5-year-old child, and this incidence reduces with increasing age, because of limited ability to communicate and define complaints in little ones [31]. Moreover, small children are more prone to peritonitis and abscess formation, rather than phlegmon, following perforation due to underdeveloped omentum which confines purulent material [24].

Non-visualization of the appendix is an important problem while evaluating appendicitis. The major reason for false-negative scanning is inexperience examiner in GI US. Other challenging situations are retrocecal or pelvic position of appendix, thick abdominal fat tissue in very obese patients, or focal appendicitis confined to distal tip that account for 5% of cases [25]. Thus, the entire appendix should be delineated clearly [32]. In perforated appendicitis, an abscess may be misinterpreted as a gas-containing bowel loop. In these cases, indirect signs of appendicitis should be scrutinized around cecum [33].

### **Table 1.**

*Primary and secondary sonographic features of acute appendicitis.*

*Ultrasound of the Pediatric Gastrointestinal Emergencies DOI: http://dx.doi.org/10.5772/intechopen.99759*

### **Figure 1.**

*Three different cases with acute appendicitis.  Ultrasound image of a 9-year-old boy (C) shows appendicolith (dashed arrow) within the appendix lumen, fluid level (asterisk) and dilatation distal to the obstruction. Ultrasound image of a 5-year-old girl (D) demonstrates inflamed appendix with a diameter of 8.6 mm and periappendiceal reactive fluid. Despite the inflammation, lumen is filled with air seen as echogenicity with dirty posterior shadow (thin arrows).*

Recent publications confirm the mild forms of appendicitis which is spontaneously resolved under antibiotic therapy without need for surgery [34]. Unfortunately, there are not any reliable criteria to differentiate mild courses on US that probably not require surgery [25]. Other pitfalls that lead to a false-positive diagnosis of acute appendicitis are; incorrect identification of the terminal ileum as inflamed appendix, Meckel's diverticulitis, cecal diverticulitis, dilated Fallopian tube or gonadal vein thrombosis [25]. Contrarily, appendiceal thickening can occur by other conditions such as Crohn's disease, infectious enterocolitis, peritonitis, ascites and appendiceal tumors such as mucocele, cystadenoma or carcinoid [25].

Over the last decades, the sensitivity of US for the diagnosis of appendicitis has reached to 95%, with specificity above 90% [23, 35, 36]. The accuracy of US is currently equivalent to CT and magnetic resonance imaging (MRI), even more accurate particularly in small children with less intraabdominal fat tissue. Pointof-care ultrasonography (POCUS) is increasingly done by emergency physicians for the diagnosis of appendicitis, but US is a highly operator dependent tool that requires experience and sufficient equipment. Consequently, adequate equipment, structured training program and quality control should be provided before clinical application. Consistent preoperative use of US for right lower quadrant pain can decrease the additional CT/MRI examinations to a low fraction [35, 37]. When initial US is inconclusive, second US following an observation period, or an additional MRI or CT examination can be considered. In children, MRI should be performed if possible to support the ALARA (radiation as low as reasonably achievable) principle. Some guidelines recommend several scoring systems for US to diagnose acute appendicitis [38]. Since these scoring systems roughly estimate the likelihood and do not prove appendicitis, they are not obligatory to use in routine practice [25].


2. Theoretical foundation of probabilistic modelling for engineering systems

#### 2.1. Statement for probabilistic modelling problems of engineering systems

The peculiarity of the above multi-level concept (Figure 1) ensuring operability of engineering systems in the form (1) is that each of the stages I–VIII considers its own, specific, calculating situations (Figure 2). At each stage, special fundamental problems of the mechanics of solids are solved:

• boundary problems for stress determining in the most loaded elements, in cross sections A and local volumes V(x, y, z)

$$\{\sigma\_{i\dot{\jmath}}, e\_{\dot{\imath}\jmath}\} = F\_{\sigma}\{Q, A, V(x, y, z)\}$$

• experimental problems of obtaining metal deformation diagrams (equations of state)

$$\{\sigma\_{\max}, e\_{\max}\} = F\_{\sigma, e} \{\sigma\_{i\circ}, e\_{i\circ}\}.$$

• experimental problems of estimating the criterial values of stresses and deformations corresponding to the achievement of the conditions for breaking strength (fracture)

$$\{\sigma\_c, e\_c\} = F\_c \{\sigma\_b, e\_f\}.$$

The nominal stresses σn and deformations en, local stresses σl and strains el, fracture stresses σf and deformations ef, as well as actual and critical dimensions of technological and operational defects l and lf are used as the determining parameters. The values of fracture stresses and deformations characterize the limiting states and are determined taking into account the loading regime in terms of the number of cycles N and time τ, the fatigue diagrams (σf � Nf) and (ef � Nf); long-term strength (σf � τf) and (ef � τf); fracture toughness (σf � lf) and (ef � lf).

The basic characteristics of strength Rσ, stiffness Rδ, steadiness Rλ, and durability RN,τ are considered for design situations when the values of all parameters are in the deterministic limits established by the project:

$$\{R\_{\sigma}, R\_{\delta}, R\_{\lambda}\} = F\_{\mathbb{R}}\{ (\sigma\_n, \mathfrak{e}\_n); (\sigma\_l, \mathfrak{e}\_l); (\mathfrak{e}\_f, \mathfrak{e}\_f) \}\tag{3}$$

$$R\_{\mathcal{N},\boldsymbol{\tau}} = F\_{\mathcal{N},\boldsymbol{\tau}}\{ (\mathcal{N},\boldsymbol{\tau}); (R\_{\mathcal{o}}, R\_{\mathcal{\delta}}, R\_{\lambda}) \}\tag{4}$$

U, given by margin factors for nominal and local stresses nσ and nσl, nominal and local strains ne

As probabilistic modelling methods evolved, problems (3) and (4) were considered in a probabilistic formulation, when the basic parameters are given by probability distribution functions. In this case, by the methods theory of probability and reliability theory, one can obtain diagrams of limiting states in the coordinates (σf, ef) � (N, τ, δ, λ, l) for different probabilities P

The reliability of engineering systems is determined in the presence of probability distribution functions of the basic parameters of operability. In a general case, reliability is estimated by the given probabilistic properties P of the characteristics of strength, stiffness, steadiness, durability:

The survivability of engineering systems is considered for design situations and beyond design situations with considering damage accumulation processes D. In engineering, practice damage is characterized by the sizes of the technological and operational defects L or scalar

Survivability can be estimated in deterministic and probabilistic formulation by using expression:

f g Rσ;Rδ; Rλ U ¼ FR ð Þ σn=nσ;en=ne ; σl=nσl ð Þ ;el=nel ; σf =nσf ;ef =nef (5)

f g RN,τ U ¼ FN,τf g ð Þ N=nN; τ=nτ ;ð Þ Rσ;Rδ;Rλ (6)

Probabilistic Modelling in Solving Analytical Problems of System Engineering

http://dx.doi.org/10.5772/intechopen.75686

7

PP,N, τ ¼ FPf g Pj ð Þ Q; N; τ ;ð Þ Rσ;Rδ;Rλ; RN,τ (7)

; l ¼ Fl l f g ið Þ N; τ ; i ¼ 1; m (8)

and nel, destroying stresses nσf, and deformations of nef:

of their realization (1%, 50%, 99%) (Figure 3).

measure of accumulated damage d:

D ¼ f g d; l ; d ¼ Fd

Figure 3. Probabilistic diagrams of limiting states.

N Nf ; τ τf ; l lf ; δ δf ; λ λf ; σ σf ; e ef

If statistical properties are taken into account for combinations ð Þ σn;en ; σl ð Þ ;el ; σf ;ef , the characteristics of strength, stiffness and resource can be determined with use quantile of probability

Figure 2. State diagram of engineering systems.

U, given by margin factors for nominal and local stresses nσ and nσl, nominal and local strains ne and nel, destroying stresses nσf, and deformations of nef:

$$\{R\_{\boldsymbol{\sigma}}, R\_{\boldsymbol{\delta}}, R\_{\boldsymbol{\lambda}}\}\_{\mathcal{U}} = F\_{\mathcal{R}}\left\{ (\sigma\_n/\mathbf{n}\_{\boldsymbol{\sigma}}, \mathbf{e}\_n/\mathbf{n}\_{\boldsymbol{\varepsilon}}); (\sigma\_l/\mathbf{n}\_{\boldsymbol{\sigma}l}, \mathbf{e}\_l/\mathbf{n}\_{\boldsymbol{\varepsilon}l}); \{\sigma\_f/\mathbf{n}\_{\boldsymbol{\sigma}f}, \mathbf{e}\_f/\mathbf{n}\_{\boldsymbol{\varepsilon}f}\} \right\} \tag{5}$$

$$\{R\_{\mathcal{N},\tau}\}\_{\mathcal{U}} = F\_{\mathcal{N},\tau}\{ (\mathcal{N}/\mathfrak{n}\_{\mathcal{N}}, \tau/\mathfrak{n}\_{\tau}); (R\_{\sigma}, R\_{\delta}, R\_{\lambda}) \}\tag{6}$$

As probabilistic modelling methods evolved, problems (3) and (4) were considered in a probabilistic formulation, when the basic parameters are given by probability distribution functions. In this case, by the methods theory of probability and reliability theory, one can obtain diagrams of limiting states in the coordinates (σf, ef) � (N, τ, δ, λ, l) for different probabilities P of their realization (1%, 50%, 99%) (Figure 3).

The reliability of engineering systems is determined in the presence of probability distribution functions of the basic parameters of operability. In a general case, reliability is estimated by the given probabilistic properties P of the characteristics of strength, stiffness, steadiness, durability:

$$P p\_{\cdot, \mathcal{N}, \mathsf{T}} = F p\{P | \, (Q, \mathcal{N}, \mathsf{T}); \left(R\_{\mathcal{O}}, R\_{\mathcal{S}}, R\_{\lambda}, R\_{\mathcal{N}, \mathsf{T}}\right)\}\tag{7}$$

The survivability of engineering systems is considered for design situations and beyond design situations with considering damage accumulation processes D. In engineering, practice damage is characterized by the sizes of the technological and operational defects L or scalar measure of accumulated damage d:

$$D = \{d, l\}; d = F\_d\{\frac{N}{N\_f}, \frac{\pi}{\tau\_f}, \frac{l}{l\_f}, \frac{\delta}{\delta\_f}, \frac{\lambda}{\lambda\_f}, \frac{\sigma}{\sigma\_f}, \frac{e}{e\_f}\}; l = F\_l\{l\_l(N, \tau), i = 1, m\} \tag{8}$$

Survivability can be estimated in deterministic and probabilistic formulation by using expression:

Figure 3. Probabilistic diagrams of limiting states.

f g σmax;emax ¼ Fσ,e σij;eij

• experimental problems of estimating the criterial values of stresses and deformations corresponding to the achievement of the conditions for breaking strength (fracture)

σc f g ;ec ¼ Fc σb;ef

The nominal stresses σn and deformations en, local stresses σl and strains el, fracture stresses σf and deformations ef, as well as actual and critical dimensions of technological and operational defects l and lf are used as the determining parameters. The values of fracture stresses and deformations characterize the limiting states and are determined taking into account the loading regime in terms of the number of cycles N and time τ, the fatigue diagrams (σf � Nf) and (ef � Nf); long-term strength (σf � τf) and (ef � τf); fracture toughness (σf � lf) and (ef � lf). The basic characteristics of strength Rσ, stiffness Rδ, steadiness Rλ, and durability RN,τ are considered for design situations when the values of all parameters are in the deterministic

f g Rσ;Rδ;Rλ ¼ FR ð Þ σn;en ; σl ð Þ ;el ; σf ;ef

acteristics of strength, stiffness and resource can be determined with use quantile of probability

If statistical properties are taken into account for combinations ð Þ σn;en ; σl ð Þ ;el ; σf ;ef

(3)

, the char-

RN, τ ¼ FN,τf g ð Þ N; τ ;ð Þ Rσ;Rδ;Rλ (4)

limits established by the project:

6 Probabilistic Modeling in System Engineering

Figure 2. State diagram of engineering systems.

:

$$L(\pi) = \{l\_i(N, \pi), i = 1, m\} \tag{9}$$

Theoretical basis for calculating the reliability of structures in form (7) was formulated for case

In the 1960s and 1970s, Polovko et al. developed methods for probabilistic calculation of fatigue life RNτ of and reliability of machine parts PP,N,τ according to expressions (5) and (6). These methods have been used to calculate the probability diagrams of fatigue characteristics

According to F. Freudenthal (1956) and M. Shinozuki (1983), the reliability problem was formulated for a finite number of random variables X = {xi, i = 1, n} (geometrical parameters, material properties, loads, environmental factors, etc.). In this case, it was assumed that probabilistic properties of random variables are determined by joint probability distribution function f(X). Reliability is determined by computing a multi-fold integral on given security

ΩS

Difficulty in computing this probability has led to the development of various approximation methods: the first-order reliability method (FORM) (Hasofer, Lind, 1974) and the second reliability method (SORM) (Tvedt L., 1988). These methods are widely used in engineering practice [4, 5]. The main drawback of these methods is that they relate to cases when changing random parameters in time does not exceed the limits of their statistical variability character-

The further development of probabilistic methods was obtained in the 1970–1980s of the twentieth century on the basis of three conceptual ideas [6]. The first idea was that the external conditions of operation structure and its reaction to these conditions are random processes. Therefore, probabilistic methods for calculating structures should be based on methods of the theory of random functions. The second idea was that the failure of the structures in most cases is a consequence of the accumulation of damage (d, l). These damages, reaching a certain value, begin to interfere with the normal operation of structures. The third idea was that the main indicator of reliability should be probability staying of system parameters in a certain permissible region. Violation of normal operation (accident)

f Xð ÞdX, ΩS ¼ f g XjG Xð Þ > 0 (13)

Probabilistic Modelling in Solving Analytical Problems of System Engineering

http://dx.doi.org/10.5772/intechopen.75686

9

of two random variables: the load q and the strength r (Figure 4a).

P Xð Þ¼ P Xf g¼ jG Xð Þ > 0 ∭

of aircraft, transport, and other equipment.

region ΩS:

ized by function f(X).

Figure 4. Failure models for calculating reliability.

In the probabilistic formulation, solution of problem (8) consists of obtaining probability distribution function of the survivability F(Ld,l) for given probabilistic properties of accumulated damage. Here it should be noted that at stresses above the yield point, the calculation of damages in the stress values d = σ/σf is significantly more complicated. Therefore, the damage is calculated in terms of relative deformations, d = e/ef.

From these positions, in the analysis of survivability, new calculation cases are considered such as deviations from design situations, beyond design situations, and hypothetical situations that characterize the transition from failures to accidents and disasters (Figure 2).

Currently, national and international programs to ensure the safety of engineering systems, engineering infrastructures, and natural environment (Rio-1992, Johannesburg-2002, Kobe-2005, Hyogo-2015) focus attention on security characteristics S. Quantitative assessments of safety characteristics are based on complex analysis of reliability and survivability of engineering systems [2, 3]:

$$S(\pi) = F\_S\{P\_{P,N,\pi}, L\_{d,l}\} \tag{10}$$

The safety is the ability of the engineering systems to remain operative in damaged states and fracture states. In engineering practice, quantitative safety characteristics have become associated with the risks of accidents and disasters. Risk in quantitative form is defined as a function of the probabilities Pf of accidents and catastrophes and the associated losses Uf:

$$R(\pi) = F\_{\mathbb{R}}\left\{P\_{\mathcal{P},\mathcal{N},\pi}, L\_{d,l}; \mathcal{U}\_f\right\} = F\_{\mathbb{C}}\left\{P\_f, \mathcal{U}\_f\right\}, \\ P\_f = F\_f\{P\_{\mathcal{P},\mathcal{N},\pi}, L\_{d,l}\} \tag{11}$$

It is important to note that the probabilities Pf are estimated for beyond design and hypothetical situations, with the extreme values of Qextr operation parameters and extreme strength and resource characteristics, not envisaged by the project:

$$P\_f = F\_P\{P|\left(Q^{\text{extr}}, N, \tau\right); \left(R\_o, R\_\delta, R\_\lambda, R\_{N,\tau}\right)^{\text{extr}}\}\tag{12}$$

The presented analysis shows that probabilistic models and probabilistic methods acquire an increasingly important role in ensuring the operability of engineering systems.

#### 2.2. The development of traditional probabilistic methods

The development of theoretical foundations' probabilistic approaches to the analysis of the operability of engineering systems covers a significant historical period (stages I–VI, Figure 1). The first studies in this direction were carried out by M. Mayer (1926), N.F. Hotsialov (1929), and W. Weibull (1939). In these studies, the significant variation of strength characteristics for structural materials was shown, and the idea of introducing safety factors was proposed. Essential development of these studies was the work of N.С. Streletsky (1935). In his studies, the strength characteristics of materials (σf, ef) and load parameters (σn, en) were considered as random variables. The further development of this approach was made by A.R. Rzhanicyn (1947). In his works, the relationship between safety factor nσ and reliability P was established. Theoretical basis for calculating the reliability of structures in form (7) was formulated for case of two random variables: the load q and the strength r (Figure 4a).

In the 1960s and 1970s, Polovko et al. developed methods for probabilistic calculation of fatigue life RNτ of and reliability of machine parts PP,N,τ according to expressions (5) and (6). These methods have been used to calculate the probability diagrams of fatigue characteristics of aircraft, transport, and other equipment.

According to F. Freudenthal (1956) and M. Shinozuki (1983), the reliability problem was formulated for a finite number of random variables X = {xi, i = 1, n} (geometrical parameters, material properties, loads, environmental factors, etc.). In this case, it was assumed that probabilistic properties of random variables are determined by joint probability distribution function f(X). Reliability is determined by computing a multi-fold integral on given security region ΩS:

$$P(X) = P\{X|G(X) > 0\} = \iint\_{\Omega} f(X)dX, \Omega\_S = \{X|G(X) > 0\} \tag{13}$$

Difficulty in computing this probability has led to the development of various approximation methods: the first-order reliability method (FORM) (Hasofer, Lind, 1974) and the second reliability method (SORM) (Tvedt L., 1988). These methods are widely used in engineering practice [4, 5]. The main drawback of these methods is that they relate to cases when changing random parameters in time does not exceed the limits of their statistical variability characterized by function f(X).

The further development of probabilistic methods was obtained in the 1970–1980s of the twentieth century on the basis of three conceptual ideas [6]. The first idea was that the external conditions of operation structure and its reaction to these conditions are random processes. Therefore, probabilistic methods for calculating structures should be based on methods of the theory of random functions. The second idea was that the failure of the structures in most cases is a consequence of the accumulation of damage (d, l). These damages, reaching a certain value, begin to interfere with the normal operation of structures. The third idea was that the main indicator of reliability should be probability staying of system parameters in a certain permissible region. Violation of normal operation (accident)

Figure 4. Failure models for calculating reliability.

Lð Þ¼ τ l f g ið Þ N; τ ; i ¼ 1; m (9)

Sð Þ¼ τ FSf g PP,N, τ; Ld,l (10)

Pf ¼ FP Pj Qextr; N; τ ;ð Þ Rσ;Rδ;Rλ; RN,τ extr (12)

, Pf ¼ Ff f g PP,N,τ; Ld,l (11)

In the probabilistic formulation, solution of problem (8) consists of obtaining probability distribution function of the survivability F(Ld,l) for given probabilistic properties of accumulated damage. Here it should be noted that at stresses above the yield point, the calculation of damages in the stress values d = σ/σf is significantly more complicated. Therefore, the damage

From these positions, in the analysis of survivability, new calculation cases are considered such as deviations from design situations, beyond design situations, and hypothetical situations

Currently, national and international programs to ensure the safety of engineering systems, engineering infrastructures, and natural environment (Rio-1992, Johannesburg-2002, Kobe-2005, Hyogo-2015) focus attention on security characteristics S. Quantitative assessments of safety characteristics are based on complex analysis of reliability and survivability of engineer-

The safety is the ability of the engineering systems to remain operative in damaged states and fracture states. In engineering practice, quantitative safety characteristics have become associated with the risks of accidents and disasters. Risk in quantitative form is defined as a function

It is important to note that the probabilities Pf are estimated for beyond design and hypothetical situations, with the extreme values of Qextr operation parameters and extreme strength and

The presented analysis shows that probabilistic models and probabilistic methods acquire an

The development of theoretical foundations' probabilistic approaches to the analysis of the operability of engineering systems covers a significant historical period (stages I–VI, Figure 1). The first studies in this direction were carried out by M. Mayer (1926), N.F. Hotsialov (1929), and W. Weibull (1939). In these studies, the significant variation of strength characteristics for structural materials was shown, and the idea of introducing safety factors was proposed. Essential development of these studies was the work of N.С. Streletsky (1935). In his studies, the strength characteristics of materials (σf, ef) and load parameters (σn, en) were considered as random variables. The further development of this approach was made by A.R. Rzhanicyn (1947). In his works, the relationship between safety factor nσ and reliability P was established.

that characterize the transition from failures to accidents and disasters (Figure 2).

of the probabilities Pf of accidents and catastrophes and the associated losses Uf:

¼ Fc Pf ; Uf

increasingly important role in ensuring the operability of engineering systems.

Rð Þ¼ τ FR PP,N,τ; Ld,l; Uf

2.2. The development of traditional probabilistic methods

resource characteristics, not envisaged by the project:

is calculated in terms of relative deformations, d = e/ef.

8 Probabilistic Modeling in System Engineering

ing systems [2, 3]:

of the system was interpreted as an output of parameters from this area (Figure 4b). Taking these ideas into account, reliability was determined in the form:

$$P\{X(\tau)\} = P\{V(X,\tau) \in \Omega\_S, \tau \in [0,T]\}\tag{14}$$

The final level in this expansion is criterial risk, which allows the connection of systemic risk

Probabilistic Modelling in Solving Analytical Problems of System Engineering

http://dx.doi.org/10.5772/intechopen.75686

11

When constructing a system of models, implementing decomposition (16), it is necessary to take into account the following problem features of the engineering systems as the objects of risk analysis. First, in most cases, we have to analyse situations that have not been seen before, since the coincidence of all circumstances of disasters is an almost impossible event. Second, the analysis is carried out under conditions of high uncertainty associated with both the random nature of external influences and processes in the elements of systems, and with the ambiguity of objectives and safety criteria, as well as alternatives to decisions and their consequences. Third, the analysis is performed with time limit. At the stage of analysis of design decisions, these restrictions are determined by the design time, at the stage of opera-

These features make specific requirements for model representations, the computer, and the information base for risk analysis. The development of model representations and a computational technology is connected with the solution of a number of specific problems. The first task is to describe the engineering systems from the standpoint of integrity and hierarchy. The creation of a substantial and compact model with a large number of significant parameters belongs to the number of difficult tasks, even with the use of modern mathematical and

The second task is to formulate information support for risk analysis. This task has two aspects. The first aspect is related to the task of processing information. Information in the hierarchical system comes in the language of the level that is being analysed. For conclusions at a higher hierarchical level, generalization is required, and at a lower level, detailing this information is needed. In both cases, this translation is ambiguous. The second aspect is related to the need to construct hypotheses about the states of elements on base the available information. The reliability of such hypotheses depends on the level of completeness of infor-

The third task is connected with the choice of the risk criterion. It can be solved on the basis of an analysis or development of special indicators that have the necessary properties of indicators of limit states of engineering systems. This choice can also be ambiguous or multicriteria. Finally, the fourth task is to create theory and methods for risk analysis at given parameters. This apparatus can be considered as a set of mathematical models that reflect the mechanisms of catastrophes in a given sequence of the process of risk analysis. Here it is necessary to take into account the accidental nature of the catastrophe event of the system and the possibility of

a formalized description and measurement of the random parameters of the systems.

A separate and difficult task is modelling the processes of accumulation of damage. In the general case, it is necessary to consider multicriterial damage (MCD) for each element and

To take into account multifocal character of damages and their structural hierarchy, we use the principle of selective scale and select the hierarchy of scales M = {∪Mi, i = 1, n} on which damages develop. Each scale Mi is considered as internal for a given level and is analysed by appropriate methods. For example, for the scale level of structural elements can be used by the

tion—by the time of response to an emergency or emergency situation.

with mechanisms of catastrophes.

computational technologies.

mation and its reliability.

multi-structural damage for system (MSD).

Thus, the interpretation of reliability as the probability of the fulfilment of some inequality connecting random variables gave way to a more adequate and in-depth interpretation in form emissions of random functions from an admissible region [6–8].

In subsequent years, based on the achievements of reliability theory, extensive studies were carried out to substantiate and improve the normative design calculations using probabilistic methods and reliability theory. Research is carried out in nuclear engineering construction [9], aerospace technology [10], and other industries. An important role in this was played by the achievements of fracture mechanics, taking into account the presence of technological and operational defects and structural damage [11, 12]. The development of probabilistic models of fracture mechanics made it possible to create a concept and methods for probabilistic risk analysis of engineering systems [13, 14].

At the present time, probabilistic modelling and probabilistic methods of calculation have become an integral part of a wide class of problems of statics and dynamics of engineering systems, in which randomness plays an essential role and is introduced by the variations of their geometric and physical properties. To this class belong the problems of strength of microinhomogeneous materials, composite materials, and structures, including nanomaterials and microstructures. Significant progress in this direction is associated with the development of numerical methods of analysis and computational technologies [15, 16].

### 2.3. New directions for solving engineering problems of security and safety by risk criteria

Engineering systems, with rare exceptions, are complex structures of elements of different nature. The problems of probability modelling of such structures turn out to be multivariate and lead to ambiguous solutions. In conditions of complexity and statistical diversity of states of the engineering systems, the diversity of elements, the multiplicity of the mechanisms of catastrophes, it seems unlikely that an integrated comprehensive risk model will be constructed in the near future. A more promising direction can be development individual models of risk, based on the representation of the engineering systems in the form of a structure Σ, consisting of subsystems σ and elements e [13].

$$
\Sigma = \underbrace{\cup}\_{i} \sigma\_{i} \left( \bigvee\_{j} e\_{ij} \right), \ i = 1, n, \ j = 1, m. \tag{15}
$$

These models must realize the decomposition of R-characteristics (risk-decomposition) of structure (13) in the next form [14].

$$R\_{\Sigma} \longrightarrow \{R\_i\} \longrightarrow \{R\_{\vec{\eta}}\} \longrightarrow \{R\_{\vec{\eta}k}\} \tag{16}$$

where RΣ is integral (system) risk, Ri is complex (subsystem) risk, Rij is elemental risk, and Rijk is criterial risk.

The final level in this expansion is criterial risk, which allows the connection of systemic risk with mechanisms of catastrophes.

of the system was interpreted as an output of parameters from this area (Figure 4b). Taking

Thus, the interpretation of reliability as the probability of the fulfilment of some inequality connecting random variables gave way to a more adequate and in-depth interpretation in form

In subsequent years, based on the achievements of reliability theory, extensive studies were carried out to substantiate and improve the normative design calculations using probabilistic methods and reliability theory. Research is carried out in nuclear engineering construction [9], aerospace technology [10], and other industries. An important role in this was played by the achievements of fracture mechanics, taking into account the presence of technological and operational defects and structural damage [11, 12]. The development of probabilistic models of fracture mechanics made it possible to create a concept and methods for probabilistic risk

At the present time, probabilistic modelling and probabilistic methods of calculation have become an integral part of a wide class of problems of statics and dynamics of engineering systems, in which randomness plays an essential role and is introduced by the variations of their geometric and physical properties. To this class belong the problems of strength of microinhomogeneous materials, composite materials, and structures, including nanomaterials and microstructures. Significant progress in this direction is associated with the development of

P Xf g ð Þτ ¼ PVX f g ð Þ ; τ ∈ ΩS; τ∈½ � 0; T (14)

these ideas into account, reliability was determined in the form:

emissions of random functions from an admissible region [6–8].

numerical methods of analysis and computational technologies [15, 16].

Σ ¼ ∪ i σi ∪ j eij

2.3. New directions for solving engineering problems of security and safety by risk

Engineering systems, with rare exceptions, are complex structures of elements of different nature. The problems of probability modelling of such structures turn out to be multivariate and lead to ambiguous solutions. In conditions of complexity and statistical diversity of states of the engineering systems, the diversity of elements, the multiplicity of the mechanisms of catastrophes, it seems unlikely that an integrated comprehensive risk model will be constructed in the near future. A more promising direction can be development individual models of risk, based on the representation of the engineering systems in the form of a structure Σ, consisting of sub-

These models must realize the decomposition of R-characteristics (risk-decomposition) of

where RΣ is integral (system) risk, Ri is complex (subsystem) risk, Rij is elemental risk, and Rijk

! Rijk

RΣ ! f g Ri ! Rij

, i ¼ 1, n, j ¼ 1, m: (15)

(16)

analysis of engineering systems [13, 14].

10 Probabilistic Modeling in System Engineering

criteria

systems σ and elements e [13].

structure (13) in the next form [14].

is criterial risk.

When constructing a system of models, implementing decomposition (16), it is necessary to take into account the following problem features of the engineering systems as the objects of risk analysis. First, in most cases, we have to analyse situations that have not been seen before, since the coincidence of all circumstances of disasters is an almost impossible event. Second, the analysis is carried out under conditions of high uncertainty associated with both the random nature of external influences and processes in the elements of systems, and with the ambiguity of objectives and safety criteria, as well as alternatives to decisions and their consequences. Third, the analysis is performed with time limit. At the stage of analysis of design decisions, these restrictions are determined by the design time, at the stage of operation—by the time of response to an emergency or emergency situation.

These features make specific requirements for model representations, the computer, and the information base for risk analysis. The development of model representations and a computational technology is connected with the solution of a number of specific problems. The first task is to describe the engineering systems from the standpoint of integrity and hierarchy. The creation of a substantial and compact model with a large number of significant parameters belongs to the number of difficult tasks, even with the use of modern mathematical and computational technologies.

The second task is to formulate information support for risk analysis. This task has two aspects. The first aspect is related to the task of processing information. Information in the hierarchical system comes in the language of the level that is being analysed. For conclusions at a higher hierarchical level, generalization is required, and at a lower level, detailing this information is needed. In both cases, this translation is ambiguous. The second aspect is related to the need to construct hypotheses about the states of elements on base the available information. The reliability of such hypotheses depends on the level of completeness of information and its reliability.

The third task is connected with the choice of the risk criterion. It can be solved on the basis of an analysis or development of special indicators that have the necessary properties of indicators of limit states of engineering systems. This choice can also be ambiguous or multicriteria.

Finally, the fourth task is to create theory and methods for risk analysis at given parameters. This apparatus can be considered as a set of mathematical models that reflect the mechanisms of catastrophes in a given sequence of the process of risk analysis. Here it is necessary to take into account the accidental nature of the catastrophe event of the system and the possibility of a formalized description and measurement of the random parameters of the systems.

A separate and difficult task is modelling the processes of accumulation of damage. In the general case, it is necessary to consider multicriterial damage (MCD) for each element and multi-structural damage for system (MSD).

To take into account multifocal character of damages and their structural hierarchy, we use the principle of selective scale and select the hierarchy of scales M = {∪Mi, i = 1, n} on which damages develop. Each scale Mi is considered as internal for a given level and is analysed by appropriate methods. For example, for the scale level of structural elements can be used by the methods of fracture mechanics, and for the level of construction, by the methods of structural mechanics. It should be noted that if fracture of individual elements, caused by MCD, can be considered as independent events, then at structure level there is an agreed redistribution of loads, and formation of the focus of MSD should be considered as a cooperated process.


**COPD CLINICAL PERSPECTIVES**

#### **COPD Clinical Perspectives**

http://dx.doi.org/10.5772/57036 Edited by Ralph J. Panos

#### **Contributors**

Peter Lenz, Ralph J. Panos, Tomas Patrick Carroll, Emmet O'Brien, Noel G. McElvaney, Hatice Tel Aydın, Cormac McCarthy, Emer P. Reeves, David Bergin, Radostina Cherneva, Ognian Borissov Georgiev, Daniela Stoichkova Petrova, Emil Manov, Julia Petrova, Martín-Valero Rocio, Rodriguez-Martínez Mc, Cantero-Téllez R., Villanueva-Calvero E., Fernández-Martín F., William Eschenbacher

#### **© The Editor(s) and the Author(s) 2014**

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#### **Notice**

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First published in Croatia, 2014 by INTECH d.o.o. eBook (PDF) Published by IN TECH d.o.o. Place and year of publication of eBook (PDF): Rijeka, 2019. IntechOpen is the global imprint of IN TECH d.o.o. Printed in Croatia

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Anxiety as Modulator of Life

**95**

**Chapter 7**

**Abstract**

disturbances, meta-analysis

**1.1 Insomnia in patients with PD**

**1. Introduction**

A Meta-Analysis of Sleep

*Geneviève Belleville and Alenka Potočnik*

Disturbances in Panic Disorder

The nature and prevalence of sleep disturbances in panic disorder (PD) have been often discussed but remain unclear. The objective of this systematic review and meta-analysis is to document sleep disturbances in PD. Systematic database search and standardized extraction were conducted. Meta-analysis was computed on self-report (subjective) and polysomnographic (PSG) (objective) data and on prevalence rates of nocturnal panic attacks (NPA). Of the 1262 publications retrieved, 31 were included. PD patients were compared to healthy controls on subjective and objective measures. Patients had higher Pittsburgh sleep quality index (PSQI) global scores (hedges' g = 1.306, 95% CI [0.532, 2.081]), longer PSG sleep latency (hedges' g = 0.81, 95% CI [0.576, 1.035]), poorer PSG sleep efficiency (hedges' g = −0.79, 95% CI [−1.124, −0.432]), and shorter stage 2 (hedges' g = 0.70, 95% CI [−1.231, −0.120]) and total sleep time (hedges' g = −0.739, 95% CI [−1.127, −0.351]). Among patients, 52.1% (95% CI [0.464, 0.577]) reported NPA (≥1/lifetime). Patients with PD demonstrate subjective and objective sleep alterations. More than half have experienced NPA. These sleep

disturbances could have a significant role in maintaining PD symptoms.

**Keywords:** panic disorder, nocturnal panic attacks, insomnia, sleep, sleep

Panic disorder (PD) is a common anxiety disorder, with a prevalence rate of 3.7% in the general population [1]. It is characterized by sudden and recurrent surges of anxiety known as panic attacks, apprehensiveness about panic, and avoidance of potential future panic attacks [2]. In PD, as in many anxiety disorders [3], sleep may be affected. The existing literature describes two primary types of sleep problems in patients with PD: insomnia and nocturnal panic attacks (NPA).

DSM-IV-TR defines insomnia as difficulty initiating or maintaining sleep, early awakening, or non-restorative sleep [4]. Symptoms must be present at least three times per week for at least 1 month and must be the source of significant distress or dysfunction [4]. Compared to DSM-IV-TR, DSM-5 added new criteria for insomnia, including early awakening and dissatisfaction with sleep quality [2]. Furthermore, the minimum duration of symptoms was increased to 3 months [2]. Insomnia is assessed using a wide variety of measures that can be generally classified as subjective or objective. The former uses self-report questionnaires and diaries or

**Chapter 7**


Contents

Chapter

Abstract

Rafael Vázquez-Duhalt

virus-like particles are reviewed and discussed.

virus-like particles, virus, capsids

1. Introduction

reduced space [1].

1

Keywords: bionanotechnology, nanotechnology, nanomedicine,

Nanotechnology involves the study, design, and production of materials at a nanometric scale, from 1 to 100 nm at least in one of their dimensions. At this scale the materials show singular physicochemical properties at electric, optical, and mechanical levels, among others, which originated from the dramatic increase of the ratio of surface area to volume, as also from the electron confinement in a

Bionanotechnology or nanobiotechnology is a section of nanotechnology that is focused on the research and development of new materials at nanometric scale based on biomolecules, such as proteins, nucleic acids, and carbohydrates for specific uses. Among these natural materials there are the pseudoviral particles or virus-like nanoparticles (VLPs) that have gained attention due to their potential applications in the biomedical field or nanomedicine [2]. In spite of the fact that the viral nanoparticles have been largely used as vaccines [3], new biomedical applica-

The VLPs, opposite to viruses, do not contain their natural genetic material, and

tions have been proposed, and they are reviewed and discussed here.

thus they are noninfectious and unable to replicate themselves. These viral

Viral Structures in Nanomedicine

Nanotechnology has made progress in the creation of new materials with potential applications in the biomedical field. The potential uses of viral particles in nanomedicine include applications, in areas such as drug delivery, medical imaging, biosensors, and enzyme replacement therapies. Virus capsids are used as protein cages, scaffolds, and templates for the production of bionanostructured materials, where organic and inorganic molecules could be incorporated in a precise and a controlled fashion. Potential applications of virus particles include the following: (i) gene therapy, in which the virus particle is used as a carrier to deliver the therapeutic gene to target cells; (ii) drug delivery to ensure that pharmaceuticals get into the body and reach the tissue where they are really needed; (iii) imaging, where virus-like particles are coupled with an imaging agent, and then using ultrasound, magnetic resonance, or even traditional X-ray, to visualize the inside of the targeted organ; (iv) biosensors for the detection of diverse analytes or to measure some physicochemical conditions of the target tissue; and (v) VLPs, which have been recently proposed as carriers to deliver enzymatic activity for enzyme replacement therapies. In this work, these potential biomedical applications of


*Article* **The Effect of Different Cleaning Methods on Protein Deposition and Optical Characteristics of Orthokeratology Lenses**

**Chen-Ying Su 1,†, Lung-Kun Yeh 2,3,†, Yi-Fei Tsao 1 , Wen-Pin Lin 4,5, Chiun-Ho Hou 2,3, Hsueh-Fang Huang 4 , Chi-Chun Lai 2,3 and Hsu-Wei Fang 1,6,\***

**Abstract:** Orthokeratology lenses are commonly used for myopia control, especially in children. Tear lipids and proteins are immediately adsorbed when the lens is put on the cornea, and protein deposition may cause discomfort or infection. Therefore, we established an in vitro protein deposition analysis by mimicking the current cleaning methods for orthokeratology lens wearers for both shortterm and long-term period. The results showed that the amounts of tear proteins accumulated daily and achieved a balance after 14 days when the lens was rubbed to clean or not. Protein deposition also affected the optical characteristics of the lens regardless of cleaning methods. Our results provided an in vitro analysis for protein deposition on the lens, and they may provide a potential effective method for developing care solutions or methods that can more effectively remove tear components from orthokeratology lenses.

**Keywords:** orthokeratology lens; protein deposition; optical characteristics; rubbing