4.3.3. Mutations in Complex IV Assembly Factors

*SURF1*, the human homolog of yeast *SHY1*, has been implicated in the maturation of the heme *a* centers of Complex IV [138]. Mutations in this gene are the most frequent cause of Leigh syndrome stemming from COX deficiency [139]. The first cases of Leigh syndrome caused by *SURF1* mutations were described in 1998 [140,141]. Since then, many other cases have been reported. A systematic review by Wedatilake et al. [139] lists 43 records describing 129 cases of Leigh syndrome with SURF1 deficiency caused by 83 different mutations. The authors also performed a study that included about 50 patients, in which the most frequently occurring mutation was L105\* (16 homozygous and 11 compound heterozygous) and no specific correlation of genotype to phenotype

was established [139]. Besides Leigh syndrome, there are also reports of *SURF1* mutations associated with Charcot–Marie–Tooth disease [142].

As already mentioned, Cox10 and Cox15 are required for the conversion of heme *b* to the heme *a* of the two redox centers in Cox1 (MTCO1). In *S. cerevisiae*, *cox10* and *cox15* mutants have no Complex IV activity [143,144]. Yeast *cox10* mutants can be functionally complemented by the human homolog of *COX10* [145]. Pathogenic mutations in *COX10* and *COX15* are associated with Leigh syndrome, cardiomyopathy, and encephalopathy, among others (Table 6), and, typically, such patients have an early fatal outcome due to respiratory failure. However, a single adult patient, a 37-year old woman, was identified with isolated COX deficiency associated with a relatively mild clinical phenotype (myopathy, demyelinating neuropathy, premature ovarian failure, short stature, hearing loss, pigmentary maculopathy, and renal tubular dysfunction) due to compound heterozygous mutations resulting in D336V and R339W substitutions in *COX10* [146]. Surprisingly, no COX was detected in blue native gels on mitochondria extracted from the patient's muscle cells. The mutations were introduced into yeast both individually and in combination, all resulting in the loss of the respiratory capacity, which supported the pathogenicity of the mutations [146].

**Table 5.** Pathologies resulting from mutations in genes encoding Complex IV subunits and assembly factors, and their yeast homologs.

#### **Table 5.** *Cont.*

**Table 5.** *Cont.*

1 Review describing many mutations. 2 In different patients. 3 Splicing mutation.

There is also a single case of a long surviving Leigh syndrome patient resulting from compound heterozygous mutations leading to S152\* and S344P substitutions in Cox15. The 16 year old patient presented 42% and 22% of residual COX activity in skeletal muscle cells and fibroblasts, respectively. A normal amount of assembled COX holoenzyme was present in cultured fibroblasts, which could account for the slower clinical progression of the disease [147].

Human SCO1 and SCO2 are copper proteins involved in the metalation of MTCO2 [148]. Although both proteins have homologs in yeast, only Sco1 is needed for metalation of Cox2 [149]. A role of Sco1 in assembly of COX is supported by its presence in a Cox2 assembly intermediate [150]. Pathological mutations in *SCO1* and *SCO2* have been described to result in cardioencephalomyopathy. Gurgel-Giannetti et al. [151] reviewed about 40 patients with mutations in *SCO2*, the majority presenting with cardioencephalomyopathy while two patients suffered from Leigh syndrome. With the exception of one patient that had a homozygous G193S substitution, all other patients presented the E140K substitution which was found either in homozygosis or in association with a second mutation [151]. Furthermore, mutations in *SCO2* have also been associated with Charcot–Marie–Tooth disease [152] and with high degree myopia [153,154].

**Table 6.** Human ATP Synthase subunits and theirs yeast homologs.

**Table 6.** *Cont.*

Additionally, in the past 10 years, pathogenic mutations have been identified in COX assembly factors, products of *FAM36A*, *COX14*, *PET117*, *COA5*, *PET100*, *COA6*, and *COA3* with a variety of clinical phenotypes (Table 5). The pathologies were found in infants with either homozygous or compound heterozygous mutations.

#### *4.4. ATP Synthase*

The F1Fo-ATP synthase or Complex V is a large multimeric protein complex located in the inner membrane of mitochondria. Its principal function is to phosphorylate ADP to ATP using the energy of the proton gradient formed during oxidation of NADH and succinate [188]. This means of making ATP, historically referred to as oxidative phosphorylation, is reversible, allowing the energy released when the ATP synthase hydrolyzes ATP to be stored as a proton gradient capable of driving other energy-demanding chemical, transport, and physical processes. The mitochondrial ATP synthase consists of three distinct structural components: the F1 ATPase, the peripheral stalk, and a membrane-embedded unit referred to as Fo [189]. In both mammalian and yeast cells, the F1 ATPase is composed of five distinct subunits: three α and three β subunits, that form a hexameric barrel structure, and the monomeric γ, δ, and ε subunits that constitute the central stalk [190]. The peripheral stalk is composed of four nuclear encoded subunits: b, d, OSCP, and h (yeast) or F6 (human). The membrane-embedded domain is comprised of eight subunits, three of which (Atp6, Atp8, and Atp9) are encoded in the mitochondrial genome of *S. cerevisiae* [191], but only two (MT-ATP6 and MT-ATP8) in mammalian mitochondria [192]. Atp9 is present in multiple copies in a ring that rotates during catalysis. The number of Atp9 molecules per ring differs depending on the organism. The yeast and human rings consist of ten and eight subunits of Atp9, respectively [193–195].

#### 4.4.1. Mutations in ATP Synthase Mitochondrially Encoded Subunits

The first mitochondrial disease caused by an ATP synthase dysfunction was found in patients with mutations in *MT-ATP6*, a mitochondrial gene encoding a key component of the Fo proton channel [196]. The clinical phenotypes of these patients depend largely on the relative levels of heteroplasmy. For instance, patients harboring an m.T8993G substitution with a 70–90% mutation load often exhibit 'milder' syndromes, such as NARP (neurogenic muscle weakness, ataxia, and retinitis pigmentosa) or FBSN (familial bilateral striated necrosis) [196]. Patients with the same m.T8993G substitution, but with a mutation load exceeding 90–95%, present with a more severe neurological disorder: maternally inherited Leigh syndrome characterized by fatal infantile encephalopathy [196].

The m.T8993G pathogenic mutation in *MT-ATP6* was the first reported mitochondrial disease associated with an ATP synthase defect [197]. Since then, more than 40 pathogenic variants have been reported [69]. Four of these, m.T8993G, m.T8993C, m.T9185C, and m.T9185C, constitute most of all known cases, while the remaining variants mostly appear as isolated cases [198]. The clinical presentations of these patients are heterogeneous, with Leigh syndrome and NARP being the most frequently reported (Table 7). Recurrent phenotypes also include Charcot–Marie–Tooth peripheral neuropathy, spinocerebellar ataxia, and familiar upper motor neuron disease. Isolated cases of MLASA (mitochondrial lactic acidosis and sideroblastic anemia), HCM, primary lactic acidosis, 3-methylglutaconic aciduria and optic neuropathy have also been reported [198].

Due to the heteroplasmy accompanying mitochondrial deficiencies caused by *MT-ATP6* mutations, the pathogenic mechanisms underlying these disorders have been challenging to elucidate. In this respect, homoplasmic *S. cerevisiae* clones carrying the pathogenic *ATP6* mutations have served as a good model for characterizing the etiology of *MT-ATP6* diseases. The first modeling in yeast of a pathogenic mutation in *ATP6* was done by Rak et al. [199]. These authors have introduced in yeast the equivalent of the T8993G mutation responsible for NARP. Although the ATP synthase was correctly assembled and present at 80% of wild-type levels, the yeast mutant showed poor respiratory growth and mitochondrial ATP synthesis was only 10% of that of the wild-type. The mutant also had lower steady state levels of COX, suggesting a co-regulation of ATP synthase activity and COX expression [199]. Additionally, there is more evidence that the biogenesis of these two enzymes may be coupled. It was recently showed that Atco, an assembly intermediate composed of COX and ATP synthase subunits, namely Cox6 and Atp9, is a precursor and the sole Atp9 source for ATP synthase assembly [200].

Another study showed that a Leigh syndrome causing m.T9191C mutation with an L242P substitution in *ATP6* reduced both assembly of the yeast ATP synthase and the efficiency of ATP synthesis by 90% [201]. Based on the biochemical phenotypes of the mutant and of revertants with amino acid substitutions at this position, the proline was proposed to disrupt the terminal α-helix causing a displacement of other neighboring helices involved in proton transfer at the Atp6 and Atp9 interface [202]. Additionally, the conformational change induced by the mutations promoted proteolysis of Atp6, thereby accounting for the reduction of assembled ATP synthase. Revertants with replacements of the helix-disrupting proline by threonine or serine completely restored the assembly defect, but only partially the efficiency of proton translocation. These observations, combined with modeling of the interface between the two subunits, suggested that the suppressor mutations did not completely compensate for the displacement of residues involved in release of protons from the Atp9 ring and their transfer to a neighboring aspartic acid residue in Atp6 [202]. These findings are consistent with previous models of the disease, suggesting that certain pathogenic *ATP6* mutations do not completely block the proton translocation mechanisms of the Fo domain, but rather disrupt proton transport during rotation of the ring. As the conformational changes in the F1 moiety are induced by rotation of the Atp9 ring, the uncoupling leads to the inability of ATP synthase to harness the energy normally released from the translocation of protons for ATP synthesis [203].

The different biochemical anomalies discerned in the numerous *MT-ATP6* pathogenic variants suggest several pathophysiological mechanisms responsible for diseases associated with defects in the ATP synthase [198]. These include decreased holoenzyme assembly, destabilization of the proton pore resulting in mitochondrial membrane potential buildup, impairment of the proton pump leading to decreased membrane potential, reduced ATP synthesis and abnormal sensitivity to the ATP synthase inhibitor oligomycin [198].

A smaller subset of mitochondrial mutations causing ATP synthase deficiencies has been ascribed to the second mitochondrial gene, *MT-ATP8,* encoding a subunit of Fo. The first pathogenic mutation in *MT-ATP8* was identified in a 16-year-old patient with apical HCM and neuropathy, with a marked reduction in ATP synthase activity in fibroblasts and muscle tissue [204]. Since then, several other patients have been identified with pathogenic *MT-ATP8* mutations. One of the patients was a seven-month-old infant diagnosed with tetralogy of Fallot, the most common type of congenital heart defect characterized by ventricular septal defect, pulmonary stenosis, right ventricular hypertrophy and aortic dextroposition [205].

*MT-ATP6* and *MT-ATP8* genes overlap 46 nucleotides that span 16 codons [206]. On the MITOMAP [69] are presently listed four known pathogenic mutations in this region that contribute to an amino acid change in both genes, and three other variants that have a hypothesized deleterious effect. An ATP synthase deficiency has been associated with an m.C8561G mutation in two siblings with cerebral ataxia and loss of neuromuscular function. The mutation, resulting in P12R and P66A changes in *MT-ATP6* and *MT-ATP8*, respectively, when expressed in homoplasmic myoblasts, reduced cellular ATP by 15% but had only a marginal effect on steady state concentrations of the ATP synthase [207]. Even though there was no obvious decrease in the steady-state concentration of ATP synthase, a substantial increase of an uncharacterized assembly intermediate was noted. Another study reported an m.C8561T mutation with other amino acid substitutions in a patient with a similar biochemical but more severe clinical presentation [208]. Neither studies examined the effect of the singular or combined *ATP8* and *ATP6* mutations on the yeast ATP synthase.


**6. Study of a heat exchanger channel**

416 Heat Exchangers – Basics Design Applications

It must be noted that Focke et al.[15] , who also measured heat transfer coefficients in a corrugated plate heat exchanger having a partition of celluloid sheet between the two plates, reported that the overall heat transfer rate is the 65% of the corresponding value without the partition. **Figure 15** shows that the mean *j-*Colburn factor values calculated using the *overall*  Nusselt number are practically equal to the 65% of the values measured by Vlasogiannis et al. This holds true for all Reynolds numbers except the smallest one (Re=400). In the latter case the Nusselt number is greatly overpredicted by the CFD code. This is not unexpected, since the *two-equation turbulence* model is not capable to predict correctly the heat transfer characteristics for such low Reynolds number.The CFD results reveal that the corrugations enhance the heat transfer coefficient, whereas the pressure losses due to the augmentation of friction factor *f* are increased **(Table 3)**, compared to a smooth-wall plate heat exchanger. Additionally, comparison of the normalized values of Nusselt number and the friction factor, with respect to the corresponding values for the smooth plate (*fsm*, *Nusm*), indicates that as the Reynolds number increases, heat transfer enhancement is slightly reduced, while the friction factor ratio, *f/f* , is increased. This is typical for plate heat exchangers with

Re Nuvlasog 65% Nuvlasog Nu all Nu sm Nu ave/ Nu sm F / fsm 400 13.2 8.6 20.5 - - - 900 38.0 24.7 27.3 9.4 2.9 12.4 1000 41.2 26.8 28.6 10.2 2.8 12.8 1150 44.2 28.7 28.8 11.0 2.7 13.5 1250 46.8 30.4 30.9 11.7 2.7 13.9 1400 49.5 32.2 32.0 12.5 2.6 14.5 Table 3. Experimental values, calculated Nusselt numbers and normalised values of *N*u and *f*

Fig. 14. Comparison of friction factor predictions (CFD) with experimental data.

corrugations [16].

The results for the simplified geometry confirm the validity of the CFD code and strongly encourage the simulation of a module (pass) consisting of two corrugated plates of a compact heat exchanger (**Figure16a**). In order to quantitatively evaluate the results of this simulation, the experimental setup of Vlasogiannis et al.[16] was used as the design model (**Figure 16b**). Due to the increased computational demands, an AMD AthlonXP 1.7GHz workstation with 1GB RAM was used. The geometric characteristics of the new model are presented in **Table 4.**

Table 4. Geometric characteristics of the model with two corrugated plates.

Preliminary results of the present study, which is still in progress, are shown in **Figure 17**. It is obvious that the herringbone design promotes a symmetric flow pattern (**Figure 16b**). Focusing on the left half of the channel (**Figure 17a**), a close-up of the flow streamlines (**Figure17b**) reveals a "*peacock-tail*" pattern as the liquid flows inside the furrows and over the corrugations. The same flow pattern, which is characteristic for this type of geometry, has also been observed by Paras et al.[14] in similar cross-corrugated geometries (**Figure17c**), where "dry areas" of ellipsoidal shape are formed around the points where the

The Characteristics of Brazed Plate Heat Exchangers with Different Chevron Angles 419

corrugations come into contact. The effect of fluid properties (e.g. surface tension, viscosity) on the shape and the extent of these areas, which are considered undesirable, will be examined in the course of this study.

Fig. 16. (a) Module of a corrugated plate exchanger; (b) The CFD model and (c) Detail of the grid distribution over the corrugated wall.

corrugations come into contact. The effect of fluid properties (e.g. surface tension, viscosity) on the shape and the extent of these areas, which are considered undesirable, will be

Fig. 16. (a) Module of a corrugated plate exchanger; (b) The CFD model and (c) Detail of the

grid distribution over the corrugated wall.

examined in the course of this study.

The Characteristics of Brazed Plate Heat Exchangers with Different Chevron Angles 421

it very difficult to generate an adequate 'database' covering all possible configurations. Thus, CFD simulation is promising in this respect, as it allows computation for various geometries, and study of the effect of various design configurations on heat transfer and

In an effort to investigate the complex flow and heat transfer inside this equipment, this work starts by simulating and studying a simplified channel and, after gaining adequate experience, it continues by the CFD simulation of a module of a compact heat exchanger consisting of two corrugated plates. The data acquired from former simulation is consistent with the single corrugated plate results and verifies the importance of corrugations on both flow distribution and heat transfer rate. To compensate for the limited experimental data concerning the flow and heat transfer characteristics, the results are validated by comparing the overall Nusselt numbers calculated for this simple channel to those of a commercial heat exchanger and are found to be in reasonably good agreement. In addition, the results of the simulation of a complete heat exchanger agree with the visual observations in similar

Since the simulation is computationally intensive, it is necessary to employ a cluster of parallel workstations, in order to use finer grid and more appropriate CFD flow models. The results of this study, apart from enhancing our physical understanding of the flow inside compact heat exchangers, can also contribute to the formulation of design equations that could be appended to commercial process simulators. Additional experimental work is needed to validate and support CFD results, and towards this direction there is work in progress on visualization and measurements of pressure drop, local velocity profiles and

flow characteristics.

geometries.

**8. Appendix Nomenclature**

D diameter [m] f friction factor G mass flux [kg/m2s]

i enthalpy [J/kg]

j superficial velocity [m/s]

m mass flow rate [kg/s]

heat transfer coefficients in this type of equipment.

Cp constant pressure specific heat [J/kg K]

Ge non-dimensional geometric parameter g gravitational acceleration [m/s2] h heat transfer coefficient [W/m2K]

L c distance between the end plates [m] L h distance between the ports [m] L v vertical length of the fluid path [m] L w horizontal length of the plates [m] LMTD log mean temperature difference [°C]

N cp number of channels for the refrigerant

A heat transfer area of plate [m2] b mean channel spacing [m]

Fig. 17. (a) Streamlines in the left half of the channel; (b) Close up of the flow pattern; (c) Photo of the flow in the cross-corrugated geometry [14].


**5. Real Data Analysis**

In this subsection, a real data set is considered to illustrate the use of the inference procedures discussed in this paper. This data set consisted of 30 successive values of March precipitation in Minneapolis–Saint Paul, which were reported by Hinkley [31]. The data set points are expressed in inches as follows: 0.32, 0.47, 0.52, 0.59, 0.77, 0.81, 0.81, 0.9, 0.96, 1.18, 1.20, 1.20, 1.31, 1.35, 1.43, 1.51, 1.62, 1.74, 1.87, 1.89, 1.95, 2.05, 2.10, 2.20, 2.48, 2.81, 3.0, 3.09, 3.37 and 4.75 in.

This data was used by Barreto-Souza and Cribari-Neto [32] for fitting the generalized exponential-Poisson (GEP) distribution and by Abd-Elrahman [20] for fitting the Bilal and GB distributions. In the complete sample case, the MLEs of *β* and *λ* were 0.4168 and 1.2486, respectively. In this case, we calculated the maximum likelihood estimate of the entropy as H(*f*) = 1.2786. For the above data set, Abd-Elrahman [20] pointed out that the negative of the log likelihood, Kolmogorov–Smirnov (K–S) test statistics and its corresponding p value related to these MLEs were 38.1763, 0.0532 and 1.0, respectively. Based on the value of p, it is clear that the GB distribution was found to fit the data very well. Using the above data set, we generated an adaptive Type-II progressive hybrid censoring scheme with an effective failure number m (m = 20).

When we took T = 4.0 and *R*1 = *R*2 = ... = *R*5 = 1, *R*6 = *R*7 = ... = *R*15 = 0, *R*16 = *R*17 = ... = *R*20 = 1, the obtained data in Case I were as follows:

Case I: 0.32, 0.52, 0.77, 0.81, 0.96, 1.18, 1.20, 1.31, 1.35, 1.43, 1.51, 1.62, 1.74, 1.87, 1.89, 1.95, 2.10, 2.48, 2.81 and 3.37.

When we took T = 2.0, *R*1 = 1, *R*2 = *R*3 = ... = *R*8 = 0, *R*9 = *R*10 = ... *R*15 = 1, *R*16 = *R*17 = ... = *R*19= 0 and *R*20 = 2, the obtained data in Case II were as follows:

Case II: 0.32, 0.47, 0.52, 0.59, 0.77, 0.81, 0.9, 0.96, 1.18, 1.20, 1.35, 1.43, 1.74, 1.87, 1.95, 2.10, 2.20, 2.48, 2.81 and 3.09.

Based on the above data, the maximum likelihood estimation and Bayesian estimation of the entropy and the two parameters could be calculated. For the Bayesian estimation, since we had no prior information about the unknown parameters, we considered the noninformative gamma priors of the unknown parameters as a = b = c = d = 0. For the Linex loss and general entropy functions, we set *h* = −1.0, 1.0 and *q* = −1.0, 1.0, respectively. The MLEs and Bayesian estimations of the entropy and the two parameters were calculated by using the Newton–Raphson iteration and Lindley's approximation method. These results are tabulated in Tables 7 and 8. In addition, the 95% asymptotic confidence intervals (ACIs) and Bayesian credible intervals (BCs) of the two parameters and the entropy were calculated using the Newton–Raphson iteration, delta method and MCMC method. These results are displayed in Table 9.

**Table 7.** MLEs and Bayesian estimations of the parameters and the entropy.

**Table 8.** Bayesian estimations of the parameters and the entropy under two loss functions.

From Tables 7–9, we can observe that the MLEs and Bayesian estimations of the parameters and the entropy were close to the estimations in the complete sample case. In most cases, the length of the Bayesian credible intervals was smaller than that of the asymptotic confidence intervals.

**Table 9.** The 95% asymptotic confidence intervals (ACIs) and Bayesian credible intervals (BCIs) with the corresponding interval lengths (ILs) of the two parameters and the entropy.

#### **6. Conclusions**

In this paper, we considered the estimation of parameters and entropy for generalized Bilal distribution using adaptive Type-II progressive hybrid censored data. Using an iterative procedure and asymptotic normality theory, we developed the MLEs and approximate confidence intervals of the unknown parameters and the entropy. The Bayesian estimates were derived by Lindley's approximation under the square, Linex and general entropy loss functions. Since Lindley's method failed to construct the intervals, we utilized Gibbs sampling together with the Metropolis–Hastings sampling procedure to construct the Bayesian credence intervals of the unknown parameters and the entropy. A Monte Carlo simulation was provided to show all the estimation results. The results illustrate that the proposed methods performed well. The applicability of the considered model in a real situation was illustrated, based on the data of March precipitation in Minneapolis–Saint Paul. It was observed that the considered model could be utilized to analyze this real data appropriately.

**Author Contributions:** Methodology and writing, X.S.; supervision, Y.S.; simulation study, K.Z. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work is supported by the National Natural Science Foundation of China (71571144, 71401134, 71171164, 11701406) and the Program of International Cooperation and Exchanges in Science and Technology funded by Shaanxi Province (2016KW-033).

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

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not available.

**Acknowledgments:** The authors would like to thank the editors and the anonymous reviewers.

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

#### **Appendix A. Proof of Theorem 1**

We set *y* = exp (−*βxλ*), then 0 < *y* < 1. The cumulative distribution function of GB distribution can be written as

$$F(x; \beta, \lambda) = 1 - 3y^2 + 2y^3, 0 < y < 1$$

By setting *u* = 1 − 3*y*2 + 2*y*3, 0 <*u*< 1, then we get 3*y*2 − 2*y*3 + *u* − 1 = 0,0 <*y*< 1. Set *ρ*(*y*) = 3*y*2 − 2*y*3 + *u* − 1, take the first derivative of *ρ*(*y*) with respect to *y*, and we have *dρ*(*y*) *dy* = 6*y* − 6*y*2 > 0, as 0 < *y* < 1.

Notice that *ρ*(*y*) is a monotonically increasing function when 0 < *y* < 1. Thus, there is a unique solution to the equation 3*y*2 − 2*y*3 + *u* − 1 = 0 when 0 < *y* < 1. As such, we have proven that the equation *Xi*:*m*:*n* = *F*−1(*Ui*) has a unique solution (*i* = 1, 2, . . . , *m*).

#### **Appendix B. The Specific Steps of the Newton–Raphson Iteration Method**

**Step 1:** Give the initial values of *θ*= (*β*, *λ*); that is, *θ*(0)= (*β*(0), *λ*(0)).

**Step 2:** In the *k*th iteration, calculate *∂l ∂β* , *∂l ∂λ β* = *β*(*k*) *λ* = *λ*(*k*) and *I*(*β*(*k*), *λ*(*k*)), where

*I*(*β*(*k*), *λ*(*k*)) = - *I*11 *I*12 *I*21 *I*22 *β* = *β*(*k*) *λ* = *λ*(*k*) is the observed information matrix of the parame-

.

ters *β* and *λ*, and *Iij*, *i* = 1, 2, 3 are given by Equations (10)–(13).

**Step 3:** Update (*β*, *λ*) *T* with

$$\left(\boldsymbol{\beta}^{(k+1)},\boldsymbol{\lambda}^{(k+1)}\right)^{T} = \left(\boldsymbol{\beta}^{(k)},\boldsymbol{\lambda}^{(k)}\right)^{T} + I^{-1}(\boldsymbol{\beta}^{(k)},\boldsymbol{\lambda}^{(k)}) \times \begin{pmatrix} \frac{\partial l}{\partial \boldsymbol{\beta}^{\prime}} \frac{\partial l}{\partial \boldsymbol{\lambda}} \end{pmatrix}^{T} \\ \boldsymbol{\p} = \boldsymbol{\p}^{(k)} \\ \boldsymbol{\lambda} = \boldsymbol{\lambda}^{(k)}$$

Here, (*β*, *λ*) *T* is the transpose of vector (*β*, *λ*), and *I*−1(*β*(*k*), *λ*(*k*)) represents the inverse of the matrix *I*(*β*(*k*), *λ*(*k*)).

**Step 4:** Setting *k* = *k* + 1, the MLEs of the parameters (denoted by *β*ˆ and *λ*ˆ ) can be obtained by repeating Steps 2 and 3 until |(*β*(*k*+1), *λ*(*k*+1)) *T* − (*β*(*k*), *λ*(*k*)) *T* | < *ε*, where *ε* is a threshold value that is fixed in advance.


**6. Management**

**5.3. Radiology**

**5.4. Biomarkers**

after an AECOPD.

in clinical practice.

A chest X-ray is mainly useful for excluding other pathology like pneumothorax, pleural fluid, congestive heart failure or otherwise. It may reveal consolidations or other pathology. In the acute phase a chest CT-scan has no additive value in the tract of diagnosing an exacerbation of COPD. It can be performed if doubts exist about the presence of pulmonary embolisms as an explanation for dyspnea and/or desaturation. In a patient with recurrent airways infections

Biomarkers can be used as indicators of a physiological state in which a patient is or may become, it can help in diagnosis, aetiology and prognosis. In theory, biomarkers could be used to predict exacerbations, to determine if a patient has increased inflammation, to distinguish type of inflammation (bacterial or viral infection or otherwise) or to predict clinical outcome

Many biomarkers have been researched of which many of them are of little clinical use. At this moment the most important biomarkers in AECOPD are CRP, serum IL-6, 8-isoprostane, H2O2 and procalcitonin (ProCT). These biomarkers are closely related to oxidative stress and inflammation. C-reactive protein is momentarily the most widely used marker of inflammation

In patients with frequent exacerbations, both CRP and serum IL-6 levels are increased during a stable phase but also during the recovery period of an AECOPD [58, 59] compared to patients with infrequent exacerbations. Interleukin-6 is a cytokine which is widely expressed and produced in the body, and is not specific to the lung. Serum IL-6 has no additional value above CRP in clinical decision making. Interleukin-6 levels in sputum may be of use to predict therapy response [58], although more research is needed before clinical decisions can be made based on this biomarker. Similarly, there is a lack of studies which investigate the use of exhaled biomarkers 8-isoporstane and H2O2 for clinical purposes. Procalcitonin may be a biomarker which can discriminate in aetiology of an exacerbation but may also be used as therapeutic response parameter. Procalcitonin is the precursor of calcitonin and is released in response to a bacterial infection by many tissues under stimulation of several cytokines. Procalcitonin levels are minimally raised in viral infections [60], making it a relative specific diagnostic tool for bacterial infections. Most research has been performed in patients with community acquired pneumonia (CAP) [61]. It is suggested that ProCT could become a useful tool in clinical decision making regarding antibiotic therapy. There have been several trials to assess the utility of ProCT in AECOPD. In general ProCT-guided antibiotic therapy compared to standard management in AECOPD showed no differences in death from any cause, rates of intensive care unit (ICU) admission for any reason, duration of ICU stay, improvement of symptoms, difference in the quality-of-life score, re-exacerbation and readmission [62]. Procalcitonin-guided antibiotic therapy showed reduction in antibiotic prescription [62] and in one study [63] also reduction in antibiotic therapy duration, which in turn decreases the patient's exposure to antibiotics and related side effects, lowers the burden of antibiotic use and the risk of antimicrobial resistance. Procalcitonin is not yet being implemented in standard

a CT-thorax can be performed to investigate whether bronchiectasis is present.

82 Oncogenesis, Inflammatory and Parasitic Tropical Diseases of the Lung

The treatment of an AECOPD consists of supportive therapy, maximal bronchodilation, steroids to reduce the inflammation and treatment of the cause.

#### **6.1. Supportive therapy**

Oxygen delivery is one of the first supportive therapies which can be provided for a patient. Oxygen saturation should be at least 90% though in some cases lower saturations may also be accepted. Too much oxygen may cause hypercapnia as the drive to breathe in some COPD patients may rely on arterial O2 pressure. Symptoms of acute hypercapnia are somnolence, headache, drowsiness, confusion, flushed skin or agitation. Physiotherapy during an admis‐ sion for an AECOPD can prevent deterioration in skeletal muscle function and improve exercise capacity [64, 65]. Because an AECOPD is accompanied by an impaired energy balance due to a decreased dietary intake and an increased resting energy expenditure, nutritional support may also benefit the patient in terms of general well-being and prevention of muscle wasting [66-68].

#### **6.2. Pharmacotherapy**

An exacerbation is the result of increased inflammation causing increased flow limitation. Treatment should be directed towards controlling this exacerbated inflammation and maxi‐ mizing bronchodilation. Short acting agents like salbutamol and ipratropium are mostly used for maximal bronchodilation, usually delivered by nebulizer. Many patients may not be able to generate the flows required to use other devices during an exacerbation. Corticosteroids have been proven to reduce time to recovery and treatment failure, increase FEV1 and arterial hypoxemia [8]. Treatment schemes have been reported varying from 30 mg prednisolone orally to 60 mg intravenous, ranging from 5 days to two weeks. Studies showed that there is no difference in clinical outcome if a patient is treated with oral steroids compared to parenteral steroids [69]. Antibiotic treatment can be initiated when a bacterial infection is suspected. With the Anthonisen criteria [70] one can decide whether antibiotic treatment is necessary or not. These criteria are derived from a randomized placebo-controlled crossover trial which has been performed in the '80s where patients with COPD exacerbations were treated with antibiotics or placebo. The cardinal symptoms of infection in this study were increased sputum volume and purulence in combination with increased dyspnea. An exacerbation with all the previous 3 symptoms is called a type 1 exacerbation; two out of three symptoms have to be present for a type 2 exacerbation; one out of three and at least one other "minor symptom" (see table 2) have to be present for it to be a type 3 exacerbation. Patients with type 1 and type 2 exacerbations are most likely to benefit from antibiotic therapy. In Spain a pilot study was performed with hospitalized patients with AECOPD, where antibiotic therapy was given to patients with self-reported purulent sputum and withheld in patients with non-purulent sputum [71]. There was no difference between the two groups in treatment failure on day 3, suggesting patient reported non-purulent sputum may be a valid criterion to withhold antibiotics [71]. A Dutch study showed that addition of doxycycline to the treatment regimen with glucocorticoids of a patient with an exacerbation was superior on day 10 but equivalent on day 30 in terms of clinical success and clinical cure compared to glucocorticoids alone, even in patients not showing signs of infection [72]. Most recently Spanish investigators performed a multicenter trial where they suggested that treatment of a mild to moderate exacerbation with amoxicillin/clavulanate, independent of glucocorticoids treatment, might give better clinical cure after 10 days compared to placebo [73]. In this study the median time to next exacerbation was also increased in patients receiving antibiotics compared to placebo. Unfortunately, because of recruitment problems this study did not reach the calculated amount of patients needed, so that definite conclusions cannot be made from the results of this study.

patients with COPD. Investigation on this subject is ongoing. Of the non-pharmacologic interventions, pulmonary rehabilitation is the most effective in reducing hospital admissions and mortality and improving health-related quality of life in COPD patients who have recently

Acute Exacerbations of Chronic Obstructive Pulmonary Disease

http://dx.doi.org/10.5772/54867

85

Long-acting bronchodilators can be divided in two groups: long acting muscarinic receptor antagonists (LAMAs) and long acting β-agonists (LABAs). Both have proven to show a positive effect on exacerbation reduction and improvement in quality of life [75-79]. An overview of

Of the long-acting bronchodilators, indacaterol and glycopyrronium are the most recent additions for the treatment of COPD. Indacaterol is proven to be superior to formoterol, salmeterol and tiotropium in terms of use of rescue medication, dyspnoea score and health related quality of life. Compared to salmeterol and formoterol it is also superior in improving spirometry values. Indacaterol is non-inferior to tiotropium but when added to tiotropium therapy it is superior compared to tiotropium alone [80]. Indacaterol also lowers the risk of AECOPD compared to placebo [78, 81, 82]. Glycopyrronium has been approved in 2012 as therapy for COPD. It provides significant improvements in lung function, dyspnoea, health status, exacerbation frequency and rescue medication use versus placebo, and is comparable to tiotropium [83, 84]. The combination of glycopyrronium and indacaterol has shown superiority in bronchodilation compared to indacaterol alone [85]. Glycopyrronium has not

Inhalation corticosteroids (ICS) can be given to patients with high risk of exacerbations. In several studies ICS provided a reduction of symptoms (dyspnea, cough) and reduced the frequency of exacerbations [86-88]. The GOLD guidelines advise treatment for high exacerba‐ tion risk patients with few symptoms (group C) with a combination of ICS/LABA or a LAMA alone, or a combination of LABA and LAMA [8]. For high exacerbation risk patients who have many symptoms (group D) the same treatment is advised as for group C, also a combination

suffered an exacerbation of COPD [74].

the long-acting bronchodilators is given in table 3.

**LABA LAMA** Formoterol Tiotropium Arfomoterol Glycopyrronium

**Table 3.** An overview of available long-acting bronchodilators.

been compared to other LABAs yet.

of all three classes of inhalation drugs is possible [8].

**7.3. Inhalation corticosteroids**

**7.2. Long-acting bronchodilators**

Salmeterol Indacaterol

**Table 2.** Classification of acute exacerbations of COPD according to Anthonisen criteria [70]


**2.8 Trans-papillary drainage of PFCs**

*Pancreatitis*

pancreatic fistulas (5 vs 32%, p < 0.01) and the length of hospital stay were lower in the endoscopy group [7]. In another randomized trial including 66 patients with infected WON, ETD was associated with significantly reduced major complications (0.15 vs. 0.69), lowered costs (75,830 \$ vs. 117,492 \$), lower incidence of pancreatic fistula (0 vs. 28.1%), and increased quality of life as compared to minimally invasive surgery [45]. In a recent systematic review including two randomized trials and four observational studies, ETD was associated with lower mortality, risk of major organ failure, adverse events, and length of hospital stay [44]. These trials suggest that endoscopic step-up approach should be preferred over minimally invasive surgical

Endoscopic and surgical cyst-gastrostomy have been compared in several studies

[46–50]. Initial non-randomized trials found surgical drainage to be superior to endoscopic drainage of pseudocysts [50]. However, subsequent randomized studies concluded that endoscopic drainage achieves similar outcomes as compared to surgical drainage [46, 49, 47]. In addition, EUS guided cyst-gastrostomy is less invasive, cost saving, and associated with a shorter length of a post procedure hospital stay when compared with surgical cyst-gastrostomy [46, 47]. In a recent systematic review and meta-analysis including six studies (342 patients), there was no significant difference between surgical and endoscopic treatment success rates, adverse events, and recurrence for pancreatic pseudocysts [51]. To conclude, the current evidence suggests that endoscopic drainage is as efficacious as surgical cyst-

gastrostomy for pseudocysts with shorter hospital stay and reduced costs.

Percutaneous catheter drainage remains an important modality even in the era of minimally invasive endoscopic or surgical treatments. In different studies, percutaneous drainage alone was successful in 35–50% of cases with WON [52]. Percutaneous drainage can be used as an adjunctive to endoscopic drainage in selected cases with large PFCs extending into paracolic gutters or pelvis. In addition, percutaneous drainage is useful in acute or ill-defined PFCs (<4 weeks) where endoscopic drainage may not be feasible. Percutaneous tract can also be utilized for endoscopic and VARD [43]. Having described all the major advantages of percutaneous catheter drainage, the major limitation remains the development of external

As compared to percutaneous approach, endoscopic drainage is associated with

Dual modality drainage (DMD) involves the simultaneous or sequential use of endoscopic and percutaneous approaches for symptomatic PFCs. Several studies have concluded the utility of DMD in symptomatic PFCs especially WON [54, 55]. The proposed advantages of this technique include a quicker recovery and reduced chances of forming an external pancreato-cutaneous fistula. In the study by Gluck et al., the use of DMD was associated with reduced length of hospital stay, and less

significantly better clinical success, a lower re-intervention rate, and a shorter hospital length of stay [53]. Therefore, percutaneous drainage is only performed in cases where either endoscopic drainage is not available or not feasible (ill-defined or

step-up approach for the management of PFCs.

**2.6 Endoscopic vs. percutaneous drainage**

distantly located collections).

**2.7 Dual modality drainage**

pancreatocutaneous fistula which may be difficult to treat.

requirement of radiological or endoscopic interventions [55].

**2.5 Endoscopic vs. surgical drainage: pseudocysts**

**14**

Trans-papillary drainage (TPD) of PFCs may be useful in certain scenarios as follows: (a) small size of cyst (<5 cm) communicating with main pancreatic duct (PD), (b) as an adjunct to ETD in cases with PD leak or disconnected PD, (c) chronic pancreatitis with an obstructed PD communicating with a pseudocyst, and (d) management of external pancreatic fistula after percutaneous or surgical drainage [22]. When used as a primary modality, TPD provides the path of least resistance for the pancreatic juice, thereby diverting it away from the cyst. There is a potential of cyst infection with TPD and therefore, antibiotics should be routinely given to these patients. TPD may be useful in preventing recurrences of PFCs following ETD in cases with PD leak and disconnected PD [57]. We do not routinely perform TPD as an adjunct to ETD in all the cases. In our practice, we evaluate the PD anatomy using an magnetic resonance cholangiopancreatogram (MRCP) prior to removal of stents placed during ETD. In cases with a PD stricture, leak or disconnection we attempt placing a trans-papillary PD stent. Subsequently, trans-papillary stents are removed or exchanged (as per the PD morphology) after 4–6 weeks. However, trans-papillary stenting may not be always feasible especially in cases with a disconnected PD. In these cases, transmural plastic stents can be left in situ and metal stents can be exchanged with plastic stents [58]. However, the latter approach needs to be substantiated by high quality randomized studies. Nevertheless, metal stents should be removed between 2 and 4 weeks irrespective of the PD anatomy due to the risk of buried stent syndrome and delayed bleeding.


**Simonetta Palmas**

Simonetta Palmas is a Chemical Engineer, PhD, Full Professor, at the Dept of Mechanical Chemical and Materials Engineering of the University of Cagliari in the scientific sector of Industrial Chemistry and Technology (SSD ING/IND27). She also attained the National academic qualification for full professor in Chemical Technology Fundamentals (SSD CHIM/07). Her scientific and didactics activity is specifically addressed to Electrochemical Engineering and applications related to environmental remediation and energy conversion and storage.

Her contribution to these topics is also relevant at the international level: she is the Italian Delegate in the sitting members of the Working European Party on Electrochemical Engineering, in the European Federation of Chemical Engineering (EFCE). Moreover, she was the vice chair of the ISE (International Society of Electrochemistry) Division 5 (Electrochemical Process Engineering and Technology) from 2018 to 2021.


**Abstract**

Advancements in the treatment of systemic cancer have improved life expectancy in cancer patients and consequently the incidence of spinal metastasis. Traditionally, open spinal approaches combined with cEBRT (conventional external beam radiation therapy) allowed for local tumor control as well as stabilization and decompression of the spine and neural elements, but these larger operations can be fraught with one complications and delayed healing as well as additional morbidity. Recently, minimally invasive spine techniques are becoming increasingly popular in the treatment of spinal metastasis for many reasons, including smaller incisions with less perioperative complications and potential for expedited time to radiation therapy. These techniques include kyphoplasty with radiofrequency ablation, percutaneous stabilization, laminectomy, and epidural tumor resection through tubular retractors, as well as minimally invasive corpectomy. These techniques combined with highly conformal stereotactic radiosurgery have led to the advent of separation surgery, which allows for decompression of neural elements while creating space between neural elements and the tumor so adequate radiation may be delivered, improving local tumor control. The versatility of these minimally invasive techniques has significantly improved the modern management of metastatic disease of the spine by protecting and restoring the patient's quality of life while allowing them to quickly resume radiation and systemic treatment.

**Keywords:** minimally invasive spine, spinal tumors, spinal metastasis, separation surgery, spinal stabilization

### **1. Introduction**

The spine is the most common site of bony metastases [1]. Significant improvements in treatment modalities in the form of chemotherapy, immunotherapy, and radiation therapy have led to increased life expectancy for cancer patients [2]. Consequently, the incidence of metastatic cancer has been increasing. Twenty to seventy percent of patients with metastatic cancer are expected to develop spinal metastases during the course of their disease [3, 4]. The increased incidence of spinal metastases has increased the need for surgical treatment of its complications including symptomatic cord compression and mechanical instability. The goal of neurosurgical treatment includes addressing mechanical instability, correcting deformity, halting or reversing neurologic deficit, and improving pain and quality of life [5]. Traditionally, open surgical approaches have been used for surgical management of spinal metastatic disease. Through the advances made in minimally invasive spine surgery (MISS) for trauma and deformity, MISS for tumors

is becoming more common due to decreased perioperative morbidity in cancer patients with similar efficacy to traditional open approaches.

## **2. Evaluation of patients with spinal metastases**

Patients with metastatic spinal cancer often have significant comorbidities and complex clinical scenarios that require multidisciplinary evaluation and treatment. The NOMS (neurologic, oncologic, mechanical, systemic) framework, developed at the Memorial Sloan-Kettering Cancer Center, assesses neurologic, oncologic, mechanical, and systemic factors during the decision-making process for the treatment of spinal tumors across multiple specialties. The oncologic factors include the predicted responses and durability of available treatment modalities including chemotherapy, immunotherapy, and radiotherapy [5, 6]. The systemic consideration predicts both the patient's ability to tolerate multimodal treatments and overall survival based on the grade and stage of disease as well as the overall health of the patient [5]. The neurologic and mechanical criteria are of particular interest to the neurosurgeon involved in the patient's care.

The neurologic component of the NOMS framework assesses the presence of myelopathy or radiculopathy and is related to epidural compression of the spinal cord and nerve roots. It is estimated that symptomatic cord compression occurs in up to 20% of patients with metastatic cancer and may be the initial symptom in 5–10% [7, 8]. Cord compression above the conus may present with myelopathy, weakness, numbness, urinary urgency. Below the level of the conus, compression of the cauda equina may present with lower motor neuron symptoms of unilateral or bilateral motor weakness, radiculopathy, numbness, or urinary retention. Such symptoms require urgent neurosurgical intervention to either stabilize or improve neurologic function.

The mechanical criteria concerns the stability of the vertebral column affected by metastatic tumor and can be further analyzed by the SINS (spinal instability neoplastic score) criteria [9]. The SINS criteria assess the location of the spine affected including junctional areas, the presence of mechanical pain, type of bony lesions, spinal alignment, amount of vertebral body collapse, and posterolateral involvement [9]. Scores of 0–6 are deemed stable, whereas 7–12 are indeterminate but suggest the possibility of instability, 13–18 are unstable. SINS scores of 7–18 warrant neurosurgical consultation. Overall, the sensitivity and specificity of the SINS criteria for potentially unstable and unstable spinal lesions are 95.7% and 79.5%, respectively [9].

### **3. Traditional/open operative intervention**

Historically, symptomatic metastatic spine disease has been treated with open surgical approaches. Traditional open approaches provide adequate visualization of tumor as well as spinal anatomy. The wide exposures allow for sufficient decompression of the spinal cord and nerve roots, stabilization for mechanical instability, and the opportunity for gross total resection, if indicated. However, the larger incisions with open approaches often lead to prolonged wound healing, which may delay postoperative chemotherapy and radiation. Larger surgical incisions also involve greater blood loss, which is concerning given the high rate of bone marrow toxicity and anemia in metastatic cancer patients, essentially all of whom exhibit preoperative anemia. Larger incisions also have higher incidence of wound breakdown and infections. Greater tissue damage contributes

to greater postoperative pain, opioid requirements, and poor quality of life in patients with limited life expectancy.


**Abstract**

The river valleys located in volcanic regions are prone to various catastrophic processes, including those catalyzed by eruptions. First, to be mentioned among them are volcanic mudflows known as lahars. They commonly result from melting of ice, snow on the mountaintop, and rainfalls immediately following the eruption. This sequence of catastrophic events—"eruption-volcanic mudflow"—is quite common and has been well studied. When viewed closely the mud and debris flow in the volcanic regions appears to be brought on by various causes, with many factors and agents involved. Quite commonly, an eruption triggers not a single endo- or exogenic event, but a sequence of interrelated catastrophes following one after another. The studied cases allow identifying and describing up to two tens of probable scenarios—successions of catastrophic events in river valleys of the volcanic regions. The specific chain in any particular case depends on volcanic activities and accompanying events, such as seismic shocks, changes in local topography, hydrothermal activity, and erosion. The river valleys and adjoining areas are the most hazardous and vulnerable areas within as much as a few kilometers from the eruption center as the erupted material tends to accumulate in valleys and rapidly transported downstream.

**Keywords:** lava flow, pyroclastic material, gas-hydrothermal manifestations, valley infilling, dammed lake, mudflow, river network restructuring


*4.3. Steam Remediation of Heterogeneous Aquifers Contaminated by Nitrobenzene*

## 4.3.1. Temperature Distribution of Layered Heterogeneous Aquifer

The temperature distribution of the layered heterogeneous aquifer is shown in Figure 6. Due to the high hydraulic conductivity of the lower medium and the low hydraulic conductivity of the upper medium, the upward transmission of steam was inhibited, resulting in heat accumulation below the interface. Therefore, when R > 1, a blocking interface is formed, resulting in the formation of steam override below the interface and high temperature in the area below the interface. The higher the R value, the higher the temperature below the interface, and the greater the lateral migration distance of the steam. The steam in the lower layer primarily relies on heat convection to transfer heat, whereas it primarily relies on heat conduction in the upper low-permeability zone.