**3.3 Growth characteristics and colonial morphology**

In contrast to classical tubercle bacilli, we found that L-form variants, obtained after nutrient starvation stress of *M. tuberculosis in vitro,* grew and developed colonies phenomenally faster, mimicking rapidly replicating bacteria.

The morphology of growths underwent progressive changes, which resulted in formation of typical L-form colonies with "fried egg" appearance (Fig.7 b, c).

As pointed out by other authors, dark centers of "fried egg" colonies usually consist of dense granular elements, which are deeply embedded in the medium but at the periphery of the colony large pleomorphic bodies are frequently found (Domingue, 1982; Mattman, 2001; Prozorovski et al., 1981). The shape of L-form colonies resulted from the variety of individual structural units and the way that they divided (Mattman, 2001). It should be pointed out that fully developed L-type colonies appeared between 36 and 48 hours after plating on Middlebrook semisolid agar, in contrast to control *M. tuberculosis* microcolonies.

Fig. 6. Morphological phases during L-form conversion and reversion of mycobacteria.

Spacer sequences and IS *6110* PCR, verified them as *M. tuberculosis* (n. d.). DNA sequencing analysis is currently in progress (n. d.).We consider that the invisible Lconversion phase is followed by a state of active reproduction of non- acid fast and nonrecognizable as mycobacteria L-forms usually with coccoid morphology. Taken together, these data may argue that the curious morphology and growth characteristics of mycobacterial L-forms, their extremely different habit of existence define them as specific type of unrecognizable and hidden persisters. As seen in Fig.6, L-form conversion cycle of mycobacteria is schematically outlined with emphasis on ability of different L-structures to form colonies. In this sense, L-form persistence phenomenon substantially differs from the current understanding for latency as persistence of few ''non-replicating''or

In contrast to classical tubercle bacilli, we found that L-form variants, obtained after nutrient starvation stress of *M. tuberculosis in vitro,* grew and developed colonies phenomenally

The morphology of growths underwent progressive changes, which resulted in formation of

As pointed out by other authors, dark centers of "fried egg" colonies usually consist of dense granular elements, which are deeply embedded in the medium but at the periphery of the colony large pleomorphic bodies are frequently found (Domingue, 1982; Mattman, 2001; Prozorovski et al., 1981). The shape of L-form colonies resulted from the variety of individual structural units and the way that they divided (Mattman, 2001). It should be pointed out that fully developed L-type colonies appeared between 36 and 48 hours after plating on Middlebrook semisolid agar, in contrast to control *M. tuberculosis*

**Stress induction of L-forms Reversion**

**Transitional incomplete reversion**  non - acid fast rod-shaped forms that form smooth

colonies

**Complete reversion**  to acid-fast, slow growing mycobacteria formation of typical rough colonies

Fig. 6. Morphological phases during L-form conversion and reversion of mycobacteria.

**L-phase variants of mycobacteria**

''dormant'' bacteria.

microcolonies.

 **"Invisible"** cryptic state of Lforms that do not form colonies: giant L-structures (filaments or large "mother" L-bodies) and filterable Lgranules

**3.3 Growth characteristics and colonial morphology**

typical L-form colonies with "fried egg" appearance (Fig.7 b, c).

**"Visible"**  L-phase growth of non- acid fast polymorphic or coccoid cells resulting in formation of "fried eggs" or smooth colonies

faster, mimicking rapidly replicating bacteria.

We suggest that the lack of cell walls and easier permeation of nutrients is the reason for the unique ability of mycobacterial L- forms to grow faster in comparison to classical tubercle bacilli. Pla Y Armengol (1931) found that a large inoculum of tubercle bacilli grows rapidly on all routine media, appearing as large L-body spheres and also vegetated mycelia. In our study, L-form variants were adapted without difficulties to grow on conventional nutrient agar. Light and electron microscopy also provided interesting results about the appearance of non-acid fast coccoid cell morphology of stressed *M. tuberculosis*, that support observations of other authors. The appearance of non-acid fast coccoids in cultures of mycobacteria has been reported by others in the beginning of the last century but the phenomenon was not clearly explained and proven at that time (Csillag, 1964; Juhasz, 1962; Xalabander, 1958;). More surprising was the fact that mycobacterial coccoid L-forms not only mimicked the morphology of staphylococci or other coccus- shaped bacteria, but also exhibited extremely rapid growth and colonial development in contrast to classical TB bacilli (n. d.). Coccoid cells were initially mistaken by us as contaminants, but the specific DNA testing (amplification of 16SrRNA gene fragment, 16S-23S rRNA gene Internal Transcribed Spacer sequences, IS*6110* PCR and DNA sequencing analysis) identified them as *M. tuberculosis* (n. d.). We suppose that non-acid fast coccoid L-form variants of mycobacteria resulted probably from the more regular mode of multiplication, synchronization and stabilization of L-form cells under specific condition of cultivation. Thus, it can be presumed why such coccoid forms of *M. tuberculosis* remain often unrecognized or are mistaken for contaminants.

Fig. 7. Light microscopy of (a) control *M. tuberculosis* rough microcolony and (b, c) typical "fried eggs" shaped colonies of *M.tuberculosis* L-forms obtained after nutrient starvation stress (n. d.).

a. b. c.

Standard plating techniques are often inadequate for accurate enumeration of microbial dormant forms, because some of them may be in a "nonculturable" state (Shleeva et al., 2010). When it comes to L-forms**,** they are considered to be both "difficult-to-cultivate" and "difficultto-identify". Because of their altered morphology and fully changed bacterial life cycle, Lforms are difficult to be identified in clinical materials. The isolation of arising *in vivo* L-forms is generally possible only with special procedures ensuring their enrichment and resuscitation to actively growing state i.e. having an ability to form colonies (Michailova et al., 2000a; Zhang et al., 2001; Zhang, 2004). The use of specially supplemented liquid and semisolid media, as well special techniques, like so called "blind" passages, are absolutely necessary for isolation of L-forms from specimens (Michailova et al., 2005; Markova et al., 2008a).

Cell Wall Deficiency in Mycobacteria: Latency and Persistence 203

L-forms within natural populations of other bacteria as well as about relations of concurrence and interference between them under different conditions (Boris *et al.*, 1969; Fodor and Roger, 1966). Extreme morphological plasticity of bacteria has been found to provide survival advantages (Justice *et al*., 2008; Young, 2007). It is assumed that L-forms occur along with resistance to factors that trigger their appearance (Prozorovski, 1981).

We found that under stress *in vitro* and *in vivo* (Markova et al, 2008a) the balance within mycobacteria was shifted in favor of cell wall deficient forms and the population continued to exist, replicating predominantly as L-forms. Our *in vitro* experiments aimed to induce Lconversion of *M. tuberculosis,* by means of nutrient starvation stress (n. d.). Once the process in favor of L-form development was induced and shifted, further selective separation of Lform variants was made, based on the unique ability of mycobacterial L- forms to grow faster in comparison to classical tubercle bacilli due to the lack of cell walls and easier permeation of nutrients. Selection of mycobacterial L-forms was achieved technically through transfers of stressed mycobacterial cultures at weekly intervals on semisolid Middlebrook agar. Due to their growth advantage, mycobacterial L-form variants became the prevailing subpopulation, overgrowing classical TB bacilli during the performed five passages, which resulted in isolation of L-form cultures. As has been demonstrated in our previous study, similar L-form transformation of *E. coli* was found to appear under conditions of starvation and, more surprisingly, after lethal heat stress (Markova et al., 2010). However, it has been found that cell wall deficient forms of *E. coli* developed slower than classical walled forms. In contrast with interactions between both subpopulations during L-form transformation of *E. coli*, we recognized the opposite relations between classical and L-forms in mycobacteria, which were strongly influenced by the special

biochemical structure and physiology of TB bacilli.

**4. Formation and persistence of mycobacterial L-forms in vivo**

Animal models for the study of tuberculosis include guinea pigs, mice, rabbits and nonhuman primates. Despite the difficulty in modeling human latency in experimental animals, the understanding of both host and microbial factors that contribute to the establishment and maintenance of a persistent *M. tuberculosis* infection has progressed and the information gathered is pertinent to human latent tuberculosis (Flynn & Chan, 2001). Formation of *M. tuberculosis* L-forms *in vivo* were demonstrated by means of biological experiments on guinea pigs (Li, 1990; Markova et al., 2008b ; Ratnam &Chandrasekhar, 1976;

In our study, we established a rat model of experimental tuberculosis that produces mycobacterial cell-wall deficient forms *in vivo* (Markova et al, 2008a). Although rats are not a common animal model for TB research, we attempted, on basis of our previous experience with other bacterial L- form experimental infections (Markova et al, 1997; Michailova et al., 2000), to use the capability of these animals to exhibit high innate resistance to infections, thus ensuring inhibition of classical bacterial forms and inducing the occurrence of cell-wall deficient forms. After intraperitoneal and intranasal infection with *M. tuberculosis*, samples from lung, spleen, liver, kidney, mesenterial and inguinal lymph nodes and bronchoalveolar and peritoneal lavage liquid were taken and plated simultaneously on Löwenstein-Jensen medium or inoculated into specially supplemented for L-forms Dubos broth at weekly intervals over five weeks. Mycobacterial L-form cultures were isolated throughout

Snitinskaia et al., 1990;), mice (Belianin et al., 1997) and rats (Markova et al., 2008a).

#### **3.4 Yin-Yang hypothesis for co-existence of classical and L- forms within natural mycobacterial population**

The Yin-Yang hypothesis is based on the idea that classical and cell wall deficient forms coexist within natural mycobacterial populations. The Chinese concept of the complementary alternating forces of Yin and Yang provides opportunities to better understand the natural phenomenon of heterogeneity and correspondence between both subpopulations in mycobacteria. The Yin-Yang point of view, suggesting the hypothesis for coexistence of classical and cell wall deficient forms, is illustrated in Fig.6.

Fig. 8. Alternating "Yin-Yang"–life phases of classical walled bacteria and cell wall deficient L-forms: "Yang" - monomorphic population of classical rod shaped bacteria under optimal conditions ensuring yield and nutrients for growth and cell division; "Yin"- polymorphic population of L-forms. Polymorphism ensures survival advantages and arsenal of various notoriously resistant to environmental assaults L-form structures under unfavorable conditions.

The morphological diversity within bacterial populations is often related to heterogeneous environments observed under natural conditions. Population-based morphological variability and cell wall deficiency of *M. tuberculosis* might be considered as a natural phenomenon ensuring the adaptive strategy of this pathogen for environmental change (Markova, 2009; Mattman, 2001). By making use of our Yin-Yang concept, by utilizing available scientific data on this subject and our own findings, we try to figure out how classical walled and cell wall deficient subpopulations interact under different conditions. We found that both classical walled and cell wall deficient L-forms coexist within clinical strains of *M. tuberculosis* freshly isolated from sputum of patients has been demonstrated in our study (Michailova et al., 2005). This finding supports the concept that natural mycobacterial population usually consists of prevalent classical forms and small numbers of L- forms. There is data reporting about coexistence of classical walled and cell wall deficient

The Yin-Yang hypothesis is based on the idea that classical and cell wall deficient forms coexist within natural mycobacterial populations. The Chinese concept of the complementary alternating forces of Yin and Yang provides opportunities to better understand the natural phenomenon of heterogeneity and correspondence between both subpopulations in mycobacteria. The Yin-Yang point of view, suggesting the hypothesis for coexistence of

Fig. 8. Alternating "Yin-Yang"–life phases of classical walled bacteria and cell wall deficient L-forms: "Yang" - monomorphic population of classical rod shaped bacteria under optimal conditions ensuring yield and nutrients for growth and cell division; "Yin"- polymorphic population of L-forms. Polymorphism ensures survival advantages and arsenal of various notoriously resistant to environmental assaults L-form structures under unfavorable

The morphological diversity within bacterial populations is often related to heterogeneous environments observed under natural conditions. Population-based morphological variability and cell wall deficiency of *M. tuberculosis* might be considered as a natural phenomenon ensuring the adaptive strategy of this pathogen for environmental change (Markova, 2009; Mattman, 2001). By making use of our Yin-Yang concept, by utilizing available scientific data on this subject and our own findings, we try to figure out how classical walled and cell wall deficient subpopulations interact under different conditions. We found that both classical walled and cell wall deficient L-forms coexist within clinical strains of *M. tuberculosis* freshly isolated from sputum of patients has been demonstrated in our study (Michailova et al., 2005). This finding supports the concept that natural mycobacterial population usually consists of prevalent classical forms and small numbers of L- forms. There is data reporting about coexistence of classical walled and cell wall deficient

**3.4 Yin-Yang hypothesis for co-existence of classical and L- forms within natural**

classical and cell wall deficient forms, is illustrated in Fig.6.

**mycobacterial population**

conditions.

L-forms within natural populations of other bacteria as well as about relations of concurrence and interference between them under different conditions (Boris *et al.*, 1969; Fodor and Roger, 1966). Extreme morphological plasticity of bacteria has been found to provide survival advantages (Justice *et al*., 2008; Young, 2007). It is assumed that L-forms occur along with resistance to factors that trigger their appearance (Prozorovski, 1981).

We found that under stress *in vitro* and *in vivo* (Markova et al, 2008a) the balance within mycobacteria was shifted in favor of cell wall deficient forms and the population continued to exist, replicating predominantly as L-forms. Our *in vitro* experiments aimed to induce Lconversion of *M. tuberculosis,* by means of nutrient starvation stress (n. d.). Once the process in favor of L-form development was induced and shifted, further selective separation of Lform variants was made, based on the unique ability of mycobacterial L- forms to grow faster in comparison to classical tubercle bacilli due to the lack of cell walls and easier permeation of nutrients. Selection of mycobacterial L-forms was achieved technically through transfers of stressed mycobacterial cultures at weekly intervals on semisolid Middlebrook agar. Due to their growth advantage, mycobacterial L-form variants became the prevailing subpopulation, overgrowing classical TB bacilli during the performed five passages, which resulted in isolation of L-form cultures. As has been demonstrated in our previous study, similar L-form transformation of *E. coli* was found to appear under conditions of starvation and, more surprisingly, after lethal heat stress (Markova et al., 2010). However, it has been found that cell wall deficient forms of *E. coli* developed slower than classical walled forms. In contrast with interactions between both subpopulations during L-form transformation of *E. coli*, we recognized the opposite relations between classical and L-forms in mycobacteria, which were strongly influenced by the special biochemical structure and physiology of TB bacilli.


**5. Transition metal based singlet oxygen probe**

Though lanthanide based fluorescent probes possess many advantages including low background interference, widely applicable pH range, and excellent water solubility; these probes can be expected to utilise for visualising spatial and temporal distribution of 1 O2 in aqueous system but a major drawback of these probes is that they need ultraviolet light for excitation which might cause cell damage, thus limiting their application in biological system. Liu et al. demonstrated a ReI complex, Re(CO)3Cl(aeip){aeip = 2-(anthracen-9-yl)-1-ethyl-imidazo[4,5-f] [1, 10], phenanthroline, which can be excited via visible light of 410 nm wavelength in aqueous medium thus minimising the effect of cell damage (shown in **Figure 11**) [31]. The ReI complex is non-luminescent in the native state probably due to quenching of luminescence of Re → aeip (M → L) charge transfer transition in the excited state through exchange triplet-triplet intramolecular energy transfer by anthryl moiety

**Figure 11.** *The ReI complex and the formation of endoperoxide via reaction with 1 O2 (adapted from [37]).*

#### **Figure 12.**

*Changes in the luminescence intensity of ReI complex (*λ*ex = 410 nm) with increasing concentration of 1 O2 in (a) in neutral and (b) in alkaline medium. The inset of these figures show that the sharp change in luminescence intensity at 565 nm with gradually increasing concentration of 1 O2 (adapted from [40]).*

as mentioned in similar type ReI complexes [37]. The strong enhancement of luminescence of ReI complex due to the formation of endoperoxide in both neutral and alkaline medium is perceived, that due to the termination of electronic coupling between the anthryl and the parent ReI complex (**Figure 11**). In comparison to other fluorescent probes of Eu3+ and Tb3+ complexes, ReI complex exhibits higher molar absorption at the visible wavelength of 410 nm and fluorescence can also be initiated with this wavelength of light [31].

With increasing concentration of 1 O2 the luminescence intensity increases as shown in **Figure 12** and the luminescence quantum yield changes from 8.9 × 10−5 to 7.1 × 10−4 and 4.7 × 10−5 to 8.7 × 10−4 in neutral and alkaline media [37]. The limit of detection obtained using ReI complex is found to be 4.9 nM/L and 10.5 nM/L in neutral and alkaline medium respectively, which are very much comparable with that obtained for Eu3+ and Tb3+ complex [31, 37, 39].

The additional benefit of visible light excitation and long lifetime enable ReI complex to be used in biological systems.


**Author details**

Anand Iyer and Sumit Yadav

Department of Cardiothoracic surgery, Townsville Hospital, Queensland, Australia

### **References**

day progresses, which may cause aspiration or impaired physiotherapy due to inability to cough effectively. A laryngoscopy is done to confirm the diagnosis and adduction of the affected vocal cord or sluggish motion will be absent. Treatment depends on whether the injury is temporary or permanent. A fibre optic evaluation is necessary to test swal‐ lowing and sensation. To assist with pulmonary physiotherapy and decrease the risk of aspiration, medialization laryngoplasty may be suggested [136]. This can be done as an office procedure with the aid of autologous fat, Gel foam, collagen, or polytetrafluoro‐

Infectious complications after pulmonary surgery include operative wound infection, em‐ pyema, and nosocomial pneumonia. Antibiotic prophylaxis should therefore be guided against these three entities. The incidence varies from 5% to 24.4%. They are responsible for increased hospital mortality to up to 19% as well as increased costs and length of hos‐ pital stay. In one study 53.6% of the germs identified were gram-negative bacteria, 39.3% gram-positive bacteria, and 7.1% were fungi [137]. These infections should be aggressive‐ ly treated with appropriate antibiotics after culture. Chest physiotherapy, pain control, bronchodilators, and early ambulation should be done for all patients but regardless of these pneumonia develops. Postoperative atelectasis after pulmonary surgery should be aggressively managed before it deteriorates into pneumonia. Our policy is to give Ticar‐ cillin Sodium and Potassium Clavulanate 3.1 g four times a day in divided doses till a

The incidence of empyema is dropping but could happen if there is prolonged air leak. Generally they are managed with antibiotics but may necessitate thoracotomy and wash out.

Other complications include pulmonary embolism, deep venous thrombosis, renal failure, strokes, major gastrointestinal bleed and late empyema. These complications should be recognised very early and aggressive management should be instituted if they are to be tackled

Thus postoperative care and management of postoperative complications is a team approach and good preoperative and intraoperative measures minimize the incidence of postoperative complications and early recognition and treatment is essential for successful outcomes.

Department of Cardiothoracic surgery, Townsville Hospital, Queensland, Australia

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**Author details**

Anand Iyer and Sumit Yadav

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**Chapter 4**

**Management of Malignant Pleural Effusion**

Pleural effusions can form basing on the disease of the pleural membranes themselves or thoracic or abdominal organs [1]. The pleura is also important to maintain local fluid homeo‐ stasis. The exact mechanisms of pleural fluid production and absorption are complex and not

The normal pleural space is approximately 18 to 20 μm in width, although it widens at its most dependent areas. It has been shown that the pleural membranes do not touch each other and

Classically described; pleural effusion is the accumulation of fluid in the pleural gap that may be caused by any reason [4]. If there is an evidence of invasion by the tumor or any malignant cells detected in this fluid, it is described as malignant pleural effusion. Although there has been no epidemiologic study with respect to pleural effusion yet, it is a common clinic problem which is estimated to be a million cases in the United States of America every year. Malignant diseases account for over 22% of all cases that means; approximately 220 000 new patients in

Primary tumours of the pleural space are less common [6]. Pleural metastasis may be caused by any organ. Malignant pleural effusions (MPE) are most frequently produced by carcinomas of the lung (37%), breast (25%), and ovary (10%). Other reasons include malignancies of the genitourinary (7%) or gastrointestinal tract (9%) and lymphoma (10%) [7]. Even today, in up

The incidence and prevalence of mesothelioma may vary from region to region. Interestingly, despite its grim reputation, mesothelioma whose curative treatments are not yet available, offers better survival than does metastatic pleural disease, with a median survival of less than

and reproduction in any medium, provided the original work is properly cited.

© 2013 Esme and Calik; licensee InTech. This is an open access article 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.

© 2013 The Author(s). Licensee InTech. 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,

to 10% of the malignant pleural effusions, the origin of tumour is not identified [8].

Hidir Esme and Mustafa Calik

http://dx.doi.org/10.5772/54441

**1. Introduction**

fully understood [2, 3].

12 months [6].

Additional information is available at the end of the chapter

that the pleural space is a real gap, not a potential space [1].

the United States and 40 000 in the United Kingdom [5].


**1. Introduction**

126 Sociological Landscape – Theories, Realities and Trends

Zelizer, Viviana A. (2005), *The Purchase of Intimacy*, Princeton and Oxford, Princeton

Since 1970s, along with the emerging of concept of complex problems, especially in the fields of environment, socioeconomic, population and sustainable development, there has been more and more studies turned from mathematical modeling or other qualitative methods to qualitative analysis and synthesis. Partly it is because that the studies becomes more and more cross-disciplined, on the other hand, difficulties to quantify them are the reasons. But as yet, little accumulation of the understandings have been gained from these studies. Compared to the considerable amount of attention on quantitative modeling and analysis, the attentions on the qualitative synthesis still keep a relative lack generally.

Along with increasing recognisation on the important implications for both knowledge development and the utilization of qualitative research methods in practice,and along with the explosively growing amount of scientific research, there progressed the integration synthesis method – meta-analysis. Meta-analysis helps to ensure that relevant qualitative studies are not lost in the growing body of research(Evans 2002); also meta-analysis permits those studies to be appraised and their findings to be combined (Jones 2004). More importantly, under the current situation that qualitative research is still falsely characterized as ungeneralizable, when generalization is narrowly conceived in terms of sampling and statistical significance (Sandelowski, Docherty et al. 1997), meta-analysis could achieve greater generalizability with higher level of abstraction(Estabrooks, Field et al. 1994).

Vulnerability to natural hazard is a typical research area of qualitative and multidisciplined. A wealth of empirical case studies on risk and vulnerability has been undertaken at scales ranging from household to global level. The experience in undertaking such assessments is diverse and the findings are highly context and place specific (B. L. Turner, Kasperson et al. 2003). Also, the understanding of the causal structures and dynamics of vulnerability remains patchy and anecdotal despite the advances of vulnerability research in the past two decades (Adger et al., 2005; Kasperson 2006). To-date, very few rigorous comparative studies that aim to synthesise this collective experience have been undertaken. Examples are the work of Misselhorn (2006) in the area of food insecurity in Southern Africa and that of Geist (2004) and Geist and Lambin (2004) in the area of land cover change.

A Meta-Analysis Framework and

(Matarazzo and Nijkamp 1997).

other methods.

1. Vote-counting

2. Classic or Glassian Meta-analysis

qualitative research. (Sandelowski and Barroso 2003).

in the final product(Sandelowski and Barroso 2003).

Its Application for Exploring the Driving Causes to Social Vulnerability 129

of manifest frequency effect sizes while meta-synthesis is an interpretive integration of qualitative findings that are themselves interpretive syntheses of data, including the phenomenologies, ethnographies, grounded theories, and other integrated and coherent descriptions or explanations of phenomena, events, or cases that are the hallmarks of

Here the definition of "meta-analysis" is simply taken as the general term of all the different nominal meta-methods, as "…an analytical framework for comparative research that aims to draw inferences on common issues with different but allied empirical backgrounds"

Meta-analysis has now become a widely accepted research tool, encompassing a range of procedures used in a variety of disciplines, such as medicine, nursing, psychology, labor economics, environmental science, and transportation science (Gaarder 2002; Yu 2002; Greenaway, Milne et al. 2004; Travisi, Florax et al. 2004). The wide employment of metaanalysis is partially because that it is an integration which is more than the sum of parts in that it offers novel interpretations of findings(Sandelowski and Barroso 2003). In the study of Sandolowski and Barroso(2003), they found that this kind of interpretations will not be found in any single report, but rather are inferences derived from taking all of the reports in a sample as a whole. Their validity does not reside in replication logic, but rather in inclusive logic whereby all findings are accommodated and in the craftsmanship exhibited

Under the Meta-analysis framework, appropriate methods can be selected according to different research questions. Commonly used methods include the counting method, classical Meta-analysis method, Meta-analysis on effectiveness, homogeneity testing and

This approach is similar to the narrative review, which divides the results of previous researches into three groups of significant positive results, significant negative results, and non-significant results. The result of the group with most literature number then represents the entire field of study. This method is relatively simple to determine the general trend of a large number of case studies. However, this is an inaccurate statistics which relies on the statistical significance. Also each individual study is limited by the collection of samples, so

This approach evolves from the early Glass Meta-analysis. It defines research questions first, then collects case studies, followed by encoding the outputs of each features, and finally analyzes the relationship between the output values and the study characteristics. This method of Meta-analysis and its subsequent improved methods have three common characteristics: First, the selection criteria of literature is liberal, generally based on the research needs. Second, the units of analysis are the results of each single studies, and through selecting the appropriate sample size (ie, the number of literature)**,** the comparative analysis is taken. Third, Meta-analysis methods usually weaken the characteristics of each

the final results of vote-counting do not necessarily reflect the true situation.

individual study, and present the overall average characteristics instead.

Therefore, the rationale of this study is promoted by factors on both sides of methodology and research question:

To achieve the above aims, this paper applies meta-analysis in the qualitative studies with the context of the vulnerability research questions. In the second section, the methodology of meta-analysis is introduced; in the third section, the findings of the application of metaanalysis in vulnerability research are presented; finally, in the forth section, there are the discussions on both the vulnerability and the implementation of meta-analysis itself.


**7. Results**

Typical results obtained in the extraction experiments are shown in Figs 12 and 13, in the first case the aqueous solution contained vanillin and ferulic acid, in the second one vanillin and vanillylamine.

Apparently vanillin was rapidly removed and reached the concentrations corresponding to the partition coefficient measured in batch experiments, whereas the ferulic acid or vanillylamine concentrations in the aqueous phase remained almost constant. The membrane

Recovery of Biosynthetic Products Using Membrane Contactors 639

0 60 120 180

Fig. 14. Vanillin concentration in the organic and aqueous phases vs. time in the counter extraction from buthyl-acetate to water at pH = 12. Solvent tube side, solvent volume 0.5 L,

water volume 0.3 L, solvent flow rate 25 L/h, feed flow rate 45 L/h

**Time** *(min.)*

**Time (***min* **.)**

**Cw Cs**

y = -0,0448x

= 0,9989

R2

0 60 120 180

Fig 14 refers to a counter-extraction experiment at pH 12, and reports the time course of the vanillin concentration in the organic and in the aqueous phases. Due to the favourable partition coefficient vanillin effectively moved towards the aqueous phase. The mass transfer was somewhat slower than in the extraction runs performed in similar conditions,

Fig. 15. Evaluation of the module efficiency through Eq. (20); same data as Fig. 13

0

**ln [...]**

0

1000

2000

3000

**C (***mg/L* **)** 4000

based solvent extraction is thus a good technique for the selective removal of vanillin without removing the substrates of the bioconversion.

Fig. 12. Vanillin and ferulic acid concentrations vs. time in the extraction with buthylacetate. Feed shell side, feed volume 0.5 L, solvent volume 0.3 L, feed flow rate 45 L/h, solvent flow rate 25 L/h, pH 7

Fig. 13. Vanillin and vanillylamine concentrations vs. time in the extraction with buthylacetate. Feed shell side, feed volume 0.5 L, solvent volume 0.3 L, feed flow rate 45 L/h, solvent flow rate 25 L/h, pH 7

based solvent extraction is thus a good technique for the selective removal of vanillin

0 60 120 180

Fig. 12. Vanillin and ferulic acid concentrations vs. time in the extraction with buthylacetate. Feed shell side, feed volume 0.5 L, solvent volume 0.3 L, feed flow rate 45 L/h,

0 60 120 180

Fig. 13. Vanillin and vanillylamine concentrations vs. time in the extraction with buthylacetate. Feed shell side, feed volume 0.5 L, solvent volume 0.3 L, feed flow rate 45 L/h,

**Time (***min* **.)**

Cw, van Cs, van Cw VanNH2

**Time (***min.* **)**

Cw, van Cs, van Cw, fer

without removing the substrates of the bioconversion.

0

solvent flow rate 25 L/h, pH 7

1500

**C (***mg/L* **)**

0

solvent flow rate 25 L/h, pH 7

500

1000

500

1000

**C (***mg/L* **)**

1500

Fig. 14. Vanillin concentration in the organic and aqueous phases vs. time in the counter extraction from buthyl-acetate to water at pH = 12. Solvent tube side, solvent volume 0.5 L, water volume 0.3 L, solvent flow rate 25 L/h, feed flow rate 45 L/h

Fig. 15. Evaluation of the module efficiency through Eq. (20); same data as Fig. 13

Fig 14 refers to a counter-extraction experiment at pH 12, and reports the time course of the vanillin concentration in the organic and in the aqueous phases. Due to the favourable partition coefficient vanillin effectively moved towards the aqueous phase. The mass transfer was somewhat slower than in the extraction runs performed in similar conditions,

Recovery of Biosynthetic Products Using Membrane Contactors 641

(up to 180 min) enzymatic conversion was performed in a conventional stirred tank reactor, the reactor was then connected to the hollow fibre module (as in Fig. 6). Apparently the vanillin was quickly transferred to the solvent and the reaction (vanNH2 → vanillin)

The results were not equally successful in the case of microbial conversion of ferulic acid to vanillin. After the start up of the extraction, the microbial activity seemed to stop almost at all. May be the solvent had a strong inhibitory effect, or the solvent itself was used as a

> Cw van Cw vanNH2 Cs van

0 60 120 180 240 300 360

Asimakopoulou, A.G. & Karabelas, A.J., (2006a). Mass transfer in liquid–liquid membrane-

Asimakopoulou, A.G. & Karabelas, A.J., (2006b). A study of mass transfer in hollow-fiber

Bao, L. & Lipscomb G.G., (2002). Mass transfer in axial flows through randomly packed fiber bundles with constant wall concentration, *Journal of Membrane Science* 204, 207–220 Bao, L. & Lipscomb G. G. (2003). Mass transfer in axial flows through randomly packed fiber

Bird, R.B., Stewart, W.E. & Lightfoot, E.N. (2007). *Transport Phenomena*. John Wiley & Sons.

Elsevier Science B.V., ISBN: 0-444-51175-X, Amsterdam.

based extraction at small fiber packing fractions, *Journal of Membrane Science*

membrane contactors - The effect of fiber packing fraction. *Journal of Membrane*

bundles, In: *New Insights into Membrane Science and Technology: Polymeric and Biofunctional Membranes,* Bhattacharyya D. & Butterfield D.A. (Editors), pp. 5 – 26,

*Time(min)*

substrate instead of ferulic acid; this point require further investigations.

proceeded with the same kinetics.

0

271,151–162.

*Science* 282, 430-441

**8. References**

Fig. 16. Coupling extraction and enzymatic conversion

ISBN: 978-0-470-11539-8, New York.

40

80

120

*C (mg/L)*

160

this behaviour can be clearly explained considering that, in this case, due to the partition coefficient value, the mass transfer resistance through the membrane was quite large.

The module efficiency was calculated from the vanillin concentration vs. time data as explained in the theoretical section (paragraph 3.1), i.e. plotting the left side of Eq. (20) vs. time. As shown in Fig. 15, which reports to the same data of Fig. 13, the data were well fitted by a straight line, of course only the points sufficiently apart from the equilibrium were considered, up to 90 minutes of experiment in this case.

From the slope of the straight (*0.0448*) the efficiency was calculated to be *Eff = 2.8 %,* finally the overall mass transfer coefficient, calculated from Eq. (15) was *Kw = 1.3 10-5 m/s*.

Tab. 3 summarizes the results obtained in the same way for all the extraction experiments. There is a pretty good agreement between the experimental and theoretical values of the mass transfer coefficients, which of course refers to the actual interface, the inner surface for aqueous feed flowing through the lumen, and the outer surface for aqueous feed in the shell.

Table 3. Module efficiency, experimental and theoretical values of the mass transfer coefficients in the extraction runs at different aqueous phase and solvent flow rates

The mass transfer coefficients were lower for feed flowing shell side with respect to the feed flowing through the lumen; however, it has to be considered that the interfacial area is substantially larger in the latter case, being the external surface of the fibres. As a result the mass transfer rates were comparable in the two cases.

The relative role played by the various mass transfer resistances involved were estimated from Eqs (25) or (26) based on the theoretical values of the individual mass transfer coefficients. In all cases the main resistance was associated to the aqueous phase boundary layer (70-80%). The membrane resistance too was appreciable (20-25%) while the solvent boundary layer played a minor role.

As expected, behaviour is different in counter-extraction. From the data of Fig. 14, the module efficiency was calculated to be nearly 0.9 and the membrane is responsible for 95% of the overall resistance; the solvent boundary layer played a minor role (nearly 5 %), whereas the aqueous phase mass transfer resistance was completely negligible. Of course in the counter-extraction hydrophilic membranes would be more convenient than the hydrophobic membranes used in this work.

Extraction experiments with the whole bioconversion broth gave nearly the same results, showing that fouling did not represent a serious problem. The coupling of the membrane contactor with the bioreactor exhibited good results for the enzymatic conversion of vanillylamine to vanillin. Fig. 16 reports one test performed as follows: in the first period (up to 180 min) enzymatic conversion was performed in a conventional stirred tank reactor, the reactor was then connected to the hollow fibre module (as in Fig. 6). Apparently the vanillin was quickly transferred to the solvent and the reaction (vanNH2 → vanillin) proceeded with the same kinetics.

The results were not equally successful in the case of microbial conversion of ferulic acid to vanillin. After the start up of the extraction, the microbial activity seemed to stop almost at all. May be the solvent had a strong inhibitory effect, or the solvent itself was used as a substrate instead of ferulic acid; this point require further investigations.

Fig. 16. Coupling extraction and enzymatic conversion

#### **8. References**

640 Mass Transfer - Advanced Aspects

this behaviour can be clearly explained considering that, in this case, due to the partition

From the slope of the straight (*0.0448*) the efficiency was calculated to be *Eff = 2.8 %,* finally

Tab. 3 summarizes the results obtained in the same way for all the extraction experiments. There is a pretty good agreement between the experimental and theoretical values of the mass transfer coefficients, which of course refers to the actual interface, the inner surface for aqueous feed flowing through the lumen, and the outer surface for aqueous feed in the shell.

> Feed tube side 12 10 4.76 1.4 10-5 1.45 10-5 20 20 5.36 1.6 10-5 1.62 10-5 45 25 2.0 1.5 10-5 1.98 10-5 Feed shell side 20 35 4.52 9.7 10-6 7.6 10-6 45 25 2.77 1.3 10-5 9.2 10-6

Kw *(m/s)* Kw theor *(m/s)*

coefficient value, the mass transfer resistance through the membrane was quite large. The module efficiency was calculated from the vanillin concentration vs. time data as explained in the theoretical section (paragraph 3.1), i.e. plotting the left side of Eq. (20) vs. time. As shown in Fig. 15, which reports to the same data of Fig. 13, the data were well fitted by a straight line, of course only the points sufficiently apart from the equilibrium were

the overall mass transfer coefficient, calculated from Eq. (15) was *Kw = 1.3 10-5 m/s*.

η *%*

Table 3. Module efficiency, experimental and theoretical values of the mass transfer coefficients in the extraction runs at different aqueous phase and solvent flow rates

The mass transfer coefficients were lower for feed flowing shell side with respect to the feed flowing through the lumen; however, it has to be considered that the interfacial area is substantially larger in the latter case, being the external surface of the fibres. As a result the

The relative role played by the various mass transfer resistances involved were estimated from Eqs (25) or (26) based on the theoretical values of the individual mass transfer coefficients. In all cases the main resistance was associated to the aqueous phase boundary layer (70-80%). The membrane resistance too was appreciable (20-25%) while the solvent

As expected, behaviour is different in counter-extraction. From the data of Fig. 14, the module efficiency was calculated to be nearly 0.9 and the membrane is responsible for 95% of the overall resistance; the solvent boundary layer played a minor role (nearly 5 %), whereas the aqueous phase mass transfer resistance was completely negligible. Of course in the counter-extraction hydrophilic membranes would be more convenient than the

Extraction experiments with the whole bioconversion broth gave nearly the same results, showing that fouling did not represent a serious problem. The coupling of the membrane contactor with the bioreactor exhibited good results for the enzymatic conversion of vanillylamine to vanillin. Fig. 16 reports one test performed as follows: in the first period

considered, up to 90 minutes of experiment in this case.

S *(L/h)*

mass transfer rates were comparable in the two cases.

boundary layer played a minor role.

hydrophobic membranes used in this work.

W *(L/h)*

Recovery of Biosynthetic Products Using Membrane Contactors 643

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*Science* 288, 41–50.

197-216.

York.

**28**

*Brazil*

Marco Aurelio Cremasco

*Chemical Engineering School/ University of Campinas*

**Taxol® Separation in a Simulated Moving Bed**

Cancer is a public health concern worldwide that must be considered in various area of the knowledge. In USA, appear a million cases each year. In the South East of the Brazil, cancer is the second largest cause of death. The introduction of chemotherapy to combat the cancer results in significant tumors cure that didn't control with success by exclusive use of surgery and/or radiotherapy (Bonadonna, 1990). Researchers around the world have particular attention in the study of natural products as possible source of antineoplasic agents. Due to the diversity of the chemical structures founded in theses products, there are big chances to identify news molecules with anti-tumor activities (Cremasco & Starquit, 2010). The Taxol® (commercial name for Paclitaxel) discovery offers good points for this reasoning (Holanda et

According to Rhoads (1995), while many drugs act to disrupt the cancer cells, Taxol® paralyzes the internal structure. In the metaphase stage of cell replication, chromosome pairs split and move to the opposite ends of the cell and wait to become part of a daughter cell. Rhoads (1995) reported that these chromosomes were guided by the microtubules made of tubulin. These bundles of microtubules must be dismantled before the cell be divided. However, Taxol® prevents the cells from dividing further and essentially halts the cancer growth. It has been approved by the FDA, in the USA, for the treatment of advanced breast cancer, lung cancer, and refractory ovarian cancer. Taxol® is a diterpene compound (Figure

**1. Introduction**

al., 2008).

1).

Fig. 1. Chemical structure of Taxol®


**3.1 Generalised Pareto distribution (GPD)**

Definition 1The random variable Z has a Generalised Pareto Distribution if the cumulative distribution function of Z is given by:

$$F\_{\left(\zeta,\nu,\sigma\right)}\left(\mathbf{z}\right) = \begin{cases} 1 - \left(\mathbf{1} + \frac{\zeta\left(\mathbf{z} - \nu\right)}{\sigma}\right)^{-1/\zeta} & \text{for } \zeta \neq \mathbf{0} \\ 1 - \exp\left(-\frac{\mathbf{z} - \nu}{\sigma}\right) & \text{for } \zeta = \mathbf{0} \end{cases} \tag{13}$$

for *z*>*ν* and 1 þ *ζ*ð Þ *z* � *ν σ* � � > 0 and parameters: location *ν*>0, scale *σ* >0,

shape *ζ* ∈ .

Theorem 1.2 If there exists sequences of constants *cn* and *dn*, such that

≤ *y*

*G y*ð Þ¼ exp � 1 þ *ζ y* � *ν*

*σ* � �

where G is a non-degenerate distribution function, then G is a member of the

The shape parameter determines the tail behaviour under the same values of location and scale, and thus indicates the type of extreme value distribution:

• If *ζ* ¼ 0, the GEV becomes a Gumbel distribution and the tail decays

• If *ζ* <0, the GEV becomes a negative Weibull distribution with the upper

• If *ζ* >0, the GEV simplifies to a Frechet distribution with a heavy tail and

Modelling using block maxima is inefficient as it is wasteful of the data, considering that the complete dataset is available. An alternative approach is to model all the data above some high threshold, in what is commonly referred to as threshold

*Fu*ð Þ¼ *y P Z*ð Þ � *v*≤*y*j*Z* > *v* , 0≤*y*≤*z*þ � *v* (10)

1 � *F v*ð Þ ¼ *F z*ð Þ� *F v*ð Þ

*Fv*ð Þ*z* ≈*F*ð Þ *ζ*,*ν*,*σ* ð Þ*z* , *v* ! ∞ (12)

1 � *F v*ð Þ (11)

Given a set of independent and identically distributed random variables *Z*1, … , *Zn*, having a common distribution function,F, we are interested in estimating the conditional excess distribution function, *Fv*, of random variable *X* above a high

where *y* ¼ *z* � *v* are the exceedances and *z*þ is the right endpoint of F. We can

Piklands [23] posed that if the underlying distribution F(z) is in the maximum domain of attraction of extreme value distribution, then the conditional excess

1 � *F v*ð Þ ¼ *F v*ð Þ� þ *z* � *v F v*ð Þ

distribution function *Fv*ð Þ*z* for a large *v*, can be approximated by:

where *F*ð Þ *ζ*,*ν*,*σ* ð Þ*z* is the Generalised Pareto Distribution (GPD).

**3. Threshold models and the generalised Pareto distribution**

modelling or Excess over Threshold (EOT) modelling.

*F v*ð Þ� þ *y F v*ð Þ

*σ* h i � � �1*=ζ* � �

��!*n*!∞ *G y*ð Þ (8)

>0 and with parameters: scale *σ* >0,

(9)

*P Mn* � *dn cn*

*Natural Hazards - Impacts, Adjustments and Resilience*

defined on y such that 1 þ *ζ y* � *ν*

location *ν*∈ and scale *ζ* ∈ .

endpoint being finite.

which decays polynomially.

exponentially.

threshold *v*:

**278**

express *Fv*ð Þ*y* in terms of *z* as:

*Fv*ð Þ¼ *y*

GEV family:

� �

Remark 1 (Special Cases) Under specific conditions, the GPD simplifies to other continuous distributions:

The mean of the GPD is:

$$E(Z) = \nu + \frac{\sigma}{1 - \zeta}, \text{for } \zeta < 1\tag{14}$$

The Variance of the GPD is:

$$\text{Var}(Z) = \nu + \frac{\sigma^2}{\left(1 - \zeta\right)^2 \left(1 - 2\zeta\right)}, \text{for } \zeta < \frac{1}{2} \tag{15}$$

In general, the *r* � *th* moment of the GPD only exists if *ζ* < 1 *r* .

The shape parameter, *ζ*, determines the tail distribution of the GPD as indicated in remark 1. When *ζ* ¼ 0, there exists a decreasing exponential tail, when *ζ* >0, there is a heavy tail and when *ζ* < 0, the tail is short, with finite upper end point *ν* � *σv ζ* .

#### **3.2 Relationship between GEV and GPD**

Theorem 1.3 Let *Z*1, … , *Zn* be a sequence of independent and identically distributed random variables with a common cumulative distribution function F, and let *Mn* ¼ max f g *Z*1, … , *Zn* satisfying the conditions to be approximated by GEV, i.e., for large n:

$$P\{M\_N \le x\} = G(x)\text{, where}\\
\mathbf{G(z)} = \exp\left\{-\left[\mathbf{1} + \zeta\left(\frac{\mathbf{z}-\nu}{\sigma}\right)\right]^{-1/\zeta}\right\}\tag{16}$$

Then, for a sufficiently high threshold *v*, the conditional distribution function of ð Þ *Z* � *v* , conditioned to *Z* > *v* is approximately given by

*Natural Hazards - Impacts, Adjustments and Resilience*

$$H(\mathbf{y}) = \mathbf{1} - \left(\mathbf{1} + \frac{\zeta \mathbf{y}}{\delta}\right)^{-1/\zeta} \tag{17}$$

Therefore,

constant.

where, *y* >0, 1 þ *ζy*

*δ*

*DOI: http://dx.doi.org/10.5772/intechopen.94578*

modelling extreme events using GPD.

For any higher threshold *r*>*v*:

life plot changes linearly with *v*.

**3.3 Threshold selection**

*3.3.1 Mean residual life plot*

for *ζ* < 1 is:

**281**

*P Z*f ≤*v* þ *y*j*Z* >*v*g ¼ 1 � 1 þ *ζy*

Theorem 1.3 implies that we can use GPD as an approximation to the distribution of maxima using EOT as alternative to GEV in block maxima. We can observe how the parameters of the GPD are uniquely determined by those of the GEV. In particular, the shape parameter is equal in both cases. When the block sizes change in the GEV, the parameters *ν* and *σ* change, while the shape parameter remains

Eq. (23) clearly indicates the dependence of the scale parameters *σ* on the threshold. The threshold choice is an important part of threshold modelling. As with the case with the block sizes in GEV, the choice of threshold is a trade-off between the bias and variance [13]. If the threshold is too low, we violate the asymptotic arguments underlying the GPD, whereas, if the threshold is too high, we will generate few exceedances to estimate the parameters, resulting to a large variance. We now describe the process of selecting the appropriate threshold, to be used in

In modelling using EOT, the threshold is usually chosen before the model is fitted. We will present three tools that will help in identifying the threshold:

excesses *z* � *v* are approximated by a GPD for a high threshold *v*, the mean excess,

*e v*ð Þ¼ *E Z*ð Þ¼ � *v*∣*Z* >*v σv*

Therefore, the mean excess function *e r*ð Þ is a linear function of *v*, once a suitable high threshold has been reached. The sample mean residual life plot is drawn using:

where *z*ð Þ*i* is the observation, *i*, above the threshold, *v*, and *nv* is the total number of observations above *v*. For a high *v*, all the exceedances, *r*> *v*, in the mean residual

Using this result, the procedure for estimating the threshold is as follows:

This method is based on the mean of the GPD: *E Z*ð Þ¼ *σ*

*e r*ð Þ¼ *E Z*ð Þ¼ � *r*∣*Z* > *r σr*

*v*, 1 *nv* X*nv i*¼1

� � >0 and *δ* ¼ *σ* þ *ζ*ð Þ *v* � *ν* .

Eq. (23) is the generalised Pareto family of distributions.

*On Modelling Extreme Damages from Natural Disasters in Kenya*

*δ* � ��1*=ζ*

1�*ζ*

1 � *ζ* ¼ *σv* þ *ζ*ð Þ *r* � *v*

*z*ð Þ*i* � *v* � � ! (26)

, when *ζ* < 1. If the

1 � *ζ* (24)

1 � *ζ* (25)

(23)

where *y* ¼ *z* � *v*>0, 1 þ *ζy δ* � � > 0 and *δ* ¼ *σ* þ *ζ*ð Þ *v* � *ν* .

**Proof.** Denote the distribution function of the random variable Z by F. By theorem 1.2, for large *n*,

$$\begin{split} G(z) &= F^{\mathfrak{n}}(z) \approx \exp\left\{-\left[\mathbbm{1} + \zeta\left(\frac{z-\nu}{\sigma}\right)\right]^{-1/\zeta}\right\} \\ &n \log F(z) \approx \left\{-\left[\mathbbm{1} + \zeta\left(\frac{z-\nu}{\sigma}\right)\right]^{-1/\zeta}\right\} \end{split} \tag{18}$$

For large values of *z*, Taylor series expansion implies:

$$\log F(z) \approx -\left\{1 - F(z)\right\} \tag{19}$$

Hence,

$$\begin{aligned} n\{1 - F(z)\} &\approx \left[1 + \zeta\left(\frac{z - \nu}{\sigma}\right)\right]^{-1/\zeta} \\ \{1 - F(z)\} &\approx \frac{1}{n} \left[1 + \zeta\left(\frac{z - \nu}{\sigma}\right)\right]^{-1/\zeta} \end{aligned} \tag{20}$$

So, for *z* ¼ *v* þ *y*

$$\{\mathbf{1} - F(\nu + \jmath)\} \approx \frac{\mathbf{1}}{n} \left[\mathbf{1} + \zeta \left(\frac{\nu + \jmath - \nu}{\sigma}\right)\right]^{-1/\zeta} \tag{21}$$

Thus,

$$\begin{aligned} P\{Z > v + y | Z > v\} &= \frac{1 - P(Z < v + y)}{1 - P(Z < v)} \\ &\approx \frac{1 + \zeta(v + y - \nu)/\sigma}{[1 + \zeta(v - \nu)/\sigma]^{-1/\zeta}} \\ &= \left[\frac{1 + \zeta(v + y - \nu)/\sigma}{1 + \zeta(v - \nu)/\sigma}\right]^{-1/\zeta} \\ &= \left[\frac{1 + \zeta(v - \nu)/\sigma + \zeta y/\sigma}{1 + \zeta(v - \nu)/\sigma}\right]^{-1/\zeta} \\ &= \left[\frac{1 + \zeta(v - \nu)}{1 + \zeta(v - \nu)} + \frac{\zeta y/\sigma}{1 + \zeta(v - \nu)/\sigma}\right]^{-1/\zeta} \\ &= \left[1 + \frac{\zeta y/\sigma}{\sigma + \zeta(v - \nu)}\right]^{-1/\zeta} \\ &= \left[1 + \frac{\zeta y}{\sigma + \zeta(v - \nu)}\right]^{-1/\zeta} \\ &= \left[1 + \frac{\zeta y}{\sigma + \zeta(v - \nu)}\right]^{-1/\zeta} \end{aligned} \tag{22}$$

*On Modelling Extreme Damages from Natural Disasters in Kenya DOI: http://dx.doi.org/10.5772/intechopen.94578*

Therefore,

*H y*ð Þ¼ 1 � 1 þ *ζy*

**Proof.** Denote the distribution function of the random variable Z by F.

Eq. (23) is the generalised Pareto family of distributions.

Theorem 1.3 implies that we can use GPD as an approximation to the distribution of maxima using EOT as alternative to GEV in block maxima. We can observe how the parameters of the GPD are uniquely determined by those of the GEV. In particular, the shape parameter is equal in both cases. When the block sizes change in the GEV, the parameters *ν* and *σ* change, while the shape parameter remains constant.

Eq. (23) clearly indicates the dependence of the scale parameters *σ* on the threshold. The threshold choice is an important part of threshold modelling. As with the case with the block sizes in GEV, the choice of threshold is a trade-off between the bias and variance [13]. If the threshold is too low, we violate the asymptotic arguments underlying the GPD, whereas, if the threshold is too high, we will generate few exceedances to estimate the parameters, resulting to a large variance. We now describe the process of selecting the appropriate threshold, to be used in modelling extreme events using GPD.

### **3.3 Threshold selection**

In modelling using EOT, the threshold is usually chosen before the model is fitted. We will present three tools that will help in identifying the threshold:

#### *3.3.1 Mean residual life plot*

This method is based on the mean of the GPD: *E Z*ð Þ¼ *σ* 1�*ζ* , when *ζ* < 1. If the excesses *z* � *v* are approximated by a GPD for a high threshold *v*, the mean excess, for *ζ* < 1 is:

$$e(v) = E(Z - v | Z > v) = \frac{\sigma\_v}{1 - \zeta} \tag{24}$$

For any higher threshold *r*>*v*:

$$\epsilon(r) = E(Z - r | Z > r) = \frac{\sigma\_r}{1 - \zeta} = \frac{\sigma\_v + \zeta(r - v)}{1 - \zeta} \tag{25}$$

Therefore, the mean excess function *e r*ð Þ is a linear function of *v*, once a suitable high threshold has been reached. The sample mean residual life plot is drawn using:

$$\left(v, \frac{1}{n\_v} \sum\_{i=1}^{n\_v} (z\_{(i)} - v)\right) \tag{26}$$

where *z*ð Þ*i* is the observation, *i*, above the threshold, *v*, and *nv* is the total number of observations above *v*. For a high *v*, all the exceedances, *r*> *v*, in the mean residual life plot changes linearly with *v*.

Using this result, the procedure for estimating the threshold is as follows:

## *3.3.2 Parameter stability plot*

Assuming that the exceedances, (*z* � *v*), over a threshold *v* follow a GPD (*ζ*, *σv*), the exceedances will still follow a GPD for any higher threshold *r*>*v*, with the same *ζ*, but with scale parameter of:

$$
\sigma\_r = \sigma\_v + \zeta(r - v) \tag{27}
$$

rather than from the start to the end. The starting point of change in the series of differences, and hence the threshold, is the the intersection point of the series

We use data for all the natural disasters that has been recorded in Kenya in the period 1964 2018. The data is obtained from CRED database, which is the currently the most comprehensive database for natural events. The data was also crossreferenced with that from other sources including UN-agencies and NDMU. The impact of natural disasters is quantified in terms of the total number of people affected on an annual basis, which we deemed to be more reliable than the the total damage in monetary terms. The total number of people affected includes those who were injured, died, left homeless or affected in any other way by natural disasters. A total of 112 events have been recorded over that period of time with a resulting

Descriptive statistics for both the annual occurrence and the impacts are provided in **Table 1**. The minimum number of disasters and the resulting impact is zero, which corresponds to those years where no natural disasters occurred. A total of 22 years recorded no natural disaster events. The average annual number of natural disaster occurrences in Kenya is two, and about 1*:*3 million people are affected every year. The maximum number of natural disaster occurrences observed in any year is 9 and the worst disaster recorded in any year affected approximately 23, 331, 469 people. The mean is greater than the median for both variables, indicating that the data is right-skewed. We can also observe that the spread of the impacts is large as suggested by both the standard deviation and the inter-quantile range (about 3*:*5 million and 252718 respectively), as opposed to that

We are interested in the distribution of the number of occurences and the corresponding impact of natural disasters in Kenya in the period of study. **Figure 1** shows the distribution of the number of natural disaster occurrences in the last 55 years. The number of natural disasters between 1964 and the late 1990s was fairly low, with no year experiencing more than two events. We can then observe a sharp

**Statistic Annual Occurrence Annual Impact** N 55 55 Total 112 62,160,910 Mean 2 1,130,198 Std. Dev 2.26 3,494,302 Minimum 0 0 st Quantile 0 0 Median 1 15000 rd Quantile 4 252718 Maximum 9 23,331,469 Inter Quantile Range 4 252,718

damage of approximately 62 million people affected.

*On Modelling Extreme Damages from Natural Disasters in Kenya*

*DOI: http://dx.doi.org/10.5772/intechopen.94578*

*Ur* and *Up*.

**4. Data analysis**

of the occurrence.

**Table 1.**

**283**

*Descriptive Statistics.*

(This follows from theory 1.3).

Let us re-parametrise the scale parameter *σr*:

$$
\sigma^\* = \sigma\_r - \zeta\_r \tag{28}
$$

such that:

$$
\sigma\_r = \sigma\_v + \zeta r - \zeta v \tag{29}
$$

$$
\sigma\_r - \zeta\_r = \sigma\_v - \zeta v
$$

$$
\sigma^\* = \sigma\_v - \zeta v
$$

The parameter *σ* ∗ now only depends on a sufficiently high threshold *v*. The parameter stability plot involves plotting the GPD parameter estimates for a range of values *v*. The threshold is chosen to be the point where the shape and the modified scale parameters become stable (that is, the parameter estimates is constant above the threshold at which the GPD becomes valid). We use confidence interval to select this point.

#### *3.3.3 Gertensgarbe and Werner plot*

The test was proposed by Gertensgarbe and Werner (1989) and is used to select a threshold by detecting the starting point of the extreme region. The idea behind the test is that the behaviour of a series of differences that correspond to the extreme observations is different from the one corresponding to the non-extreme observations. So, given a series of differences Δ*r* ¼ *z*ð Þ*r* � *z*ð Þ *r*þ1 , *i* ¼ 2, 3, ⋯, *n*, of the order statistics, *z*ð Þ1 ≤*z*ð Þ2 ≤⋯≤*z*ð Þ *n* , the starting point of the extreme region, and hence the threshold, will be the point at which the series of differences exhibit a significant statistical change.

To detect this point, we apply a sequential version of the Mann-Kendall test to check the null hypothesis that there is no change in the series of differences. Define a series:

$$U\_r = \frac{U\_r^\* - \frac{r(r-1)}{4}}{\sqrt{\frac{i(r-1)(i+5)}{72}}} \tag{30}$$

where *U* ∗ *r* ¼ P*r j*¼1*n j* and *n j* is the number of values in the the series of differences Δ1, ⋯, Δ *j* less than Δ *j*. We also define another series, *Up*, by applying the same procedure to the series of differences from the end to start,Δ*n*, ⋯, Δ1,

rather than from the start to the end. The starting point of change in the series of differences, and hence the threshold, is the the intersection point of the series *Ur* and *Up*.


**3. Background**

#### **3.1 The lifting scheme**

MRA like the lifting scheme is used to design different wavelets. This wavelet transform is named as the second-generation wavelet transform and developed in Sweldens [32]. It uses convolution operations instead of filters, simplifying mathematical operations [33, 34]. The lifting scheme splits the signal in even and odd samples to apply them simple operations, as shown in **Figure 1**. The general version of the lifting scheme was presented in Sole and Salembier [36]. The Lifting Scheme steps are detailed in Trevino-Sánchez and Alarcón-Aquino [22]. The Wavelet Lifting Scheme decomposes the 1D Signal into two coefficients: approximations (L: Low Frequency) and details (H: High Frequency).

**Figures 1**–**3** show three wavelet functions for a 1D lifting scheme: Haar, Daubechies 4 (Db4) and Daubechies 6 (Db6) accordingly, where (↓2) indicates that the signal is downsampled by half. Using *Z* means that a previous sample is used, while *Z*1 is for the next one. Additionally, *Z*1 also states that the signal is splitted in even and odd components [35].

*Random Wavelet Coefficients Pooling for Convolutional Neural Networks DOI: http://dx.doi.org/10.5772/intechopen.105162*

#### **Figure 1.**

*The Haar Wavelet Lifting Scheme for a 1D Signal [35].*

**Figure 2.**

*The Daubechies 4 Wavelet Lifting Scheme for a 1D Signal [35].*

**Figure 3.**

When the lifting scheme needs to be applied to an image a 2D version is required, as shown in **Figure 4**. In this example a Haar wavelet function is used but it can be applied to any other wavelet function. It simply repeats the same block two more times, one for the low and one for high frequency coefficients. The first block splits the signal in one direction (horizontal), while the other two blocks divide the signal in the other direction (vertical) [37]. At the end of the decomposition process, four coefficients are obtained, they are also known as approximations (LL: low-low pass filters), verticals (HL: high-low pass filters), horizontals (LH: low-high pass filters) and diagonals (HH: high-high pass filters).

#### **3.2 Pooling**

The pooling layer is a subsampling technique used to reduce the size of the information. This method shirks a predefined region into one single value. The most used pooling methods are max-pooling [38] and average pooling [39]. Max-pooling takes the highest value of each region *R* of size of *rxr* using a stride of *SxS* and no padding,

*The Daubechies 6 Wavelet Lifting Scheme for a 1D Signal [35].*

#### **Figure 4.**

*Haar Wavelet Lifting scheme for 2D decomposes an image into four subbands. The subbands names are approximations (LL), horizontals (LH), verticals (HL), and diagonals (HH).*

until the entire image is reduced. In this study, both parameters *r* and *S* take the value of 2, these parameters need to be equal to avoid skipping any value, and thus ignore that piece of information.

The equation for max-pooling is described in Eq. (1).

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>>>>>>:

$$F\_{\max}(\mathbf{x}', \mathbf{y}') = \max\_{k=a \dots a+(r-1)} \{ I(k, l) \} \tag{1}$$

$$l = \{ 0, \ 1, \ 2, \ \dots, \ n \}, \ \mathbf{x}' = i + 1,$$

$$j = \{ 0, \ 1, \ 2, \ \dots, \ m \}, \ \mathbf{y}' = j + 1,$$

$$I(k, l) \mid \quad a = ((\mathbf{S} \* i) + 1), n \mid a \le (\mathbf{x} - (r - 1)),$$

$$b = ((\mathbf{S} \* j) + 1), m \mid b \le (y - (r - 1)),$$

$$\forall \ (k, l) \exists! (a, b), \quad \forall \ I(k, l) \in I(\mathbf{x}, \ y)$$

where *I* is the input image and ð Þ *x*, *y* its dimensions. *F max* is the obtained output and *x*0 , *y*0 ð Þ are indexes that point out to each element of the reduced information map. *I k*ð Þ , *l* is the pooling region *R* and the indexes ð Þ *k*, *l* indicate each value of the region. Additionally, ð Þ *a*, *b* are variables used to slide the region indexes through the entire images at a *S* pace, while ð Þ *n*, *m* prevents from overpassing the image size considering both *S* and *r*. Finally, ð Þ *i*, *j* are the iterations required to cover all possible regions in the image.

Similarly, to max-pooling, average pooling reduces the feature map by calculating the average value of each region. The equation for average pooling is shown in Eq. (2).

$$F\_{\text{avg}}(\mathbf{x}', \mathbf{y}') = \frac{1}{|I(k, l)|} \sum\_{l=1}^{l} \sum\_{k=1}^{k} I(k, l) \tag{2}$$

where *Favg x*0 , *y*0 ð Þ is the output, and j j *I k*ð Þ , *l* is the magnitude or number of elements in the pooling region. The elements of the pooling region are added by row and by column until all have been added, then the result is divided by the number of elements to obtain the average value of the entire region.

*Random Wavelet Coefficients Pooling for Convolutional Neural Networks DOI: http://dx.doi.org/10.5772/intechopen.105162*

There are also two probabilistic pooling methods: mix pooling [40] and stochastic pooling [41]. Mix pooling takes either the maximum or the average value randomly during the training process. Mix pooling can select values the region or between channels. Mix pooling is described in Eq. (3).

$$F\_{\rm mix}(\mathbf{x}', \mathbf{y}') = \lambda F\_{\rm max}(\mathbf{x}', \mathbf{y}') + (\mathbf{1} - \lambda) F\_{\rm avg}(\mathbf{x}', \mathbf{y}') \tag{3}$$

where *λ* is a random value from the interval 0, 1 ½ �.

For the stochastic pooling, each value within the region is assigned with a probability, the higher the value, the higher the probability it gets. All probability values from the same region add up 100%. Then a value is selected based on the probabilities of the region. The Eq. (4) normalizes the value of each element within a pooling region to calculate their probabilities *p k*ð Þ , *l* .

$$p(k,l) = \frac{I(k,l)}{\sum^{l} \sum^{k} I(k,l)} \tag{4}$$

$$F\_{stch}(\mathbf{x}', \mathbf{y}') = P(p(k, l)) \tag{5}$$

where *P*ðÞ is a function that selects a sample from the multinomial distribution created with the probabilities obtained by the Eq. (4).