*3.2. Numerical Model*

The abovementioned slab was modeled in a commercial program LS-DYNA® [33] and is presented in Figure 2a. A three-dimensional model was built using 8 nodes hexahedron 7 mm × 7 mm constant stress solid elements of type ELFORM 1. This type of element, with a single integration point, was chosen for better computational efficiency considering the relatively simple stress-state and shape of the modeled structure. Viscous control of hourglass (type 1) was chosen as it is recommended for higher velocity waves and is computationally the cheapest. Considering the relatively low size of mesh, good results were obtained with this simple modeling method and explicit integration.

**Figure 2.** Isometric view of Finite Element Models (**a**) model of 50 cm × 50 cm × 7 cm plate for validation; (**b**) model of infinitely large slab for layout testing.

Vertical displacements were constrained in corners on the lower face of the plate. The material was modeled as perfectly elastic, with modulus of elasticity 38 GPa, density 2400 kg/m3 and Poisson ratio 0.2, corresponding to C20/25 concrete [10]. The excitement was applied by force with sine function variability of 2 kN. Such variability is commonly used and its magnitude does not influence the results thanks to the elastic material model [6,9]. The excitation impulse lasted for 8.4 × 10−6 s, corresponding to a 2 mm ball [6]. Vertical displacement of the node in location of the transducer was registered for 2 ms, with a time step of 1.4 × 10−3 ms.

#### *3.3. Signal Processing*

To validate the model, two signals collected in different ways needed to be compared. During the experiment, variation of current voltage due to pressure waves acting on piezoelectric in transducer was registered, while the direct displacement of node could be obtained from the model. This is why a proper filtering is important [17].

For validation, the surface (Rayleigh) wave was removed by cutting the first 0.5 ms of signal. Then, the Butterworth filter was applied for frequencies outside 1 2 *f–*2*f* window, where *f* is the frequency expected due to plate thickness. The filtering was needed mostly due to numerical noise and eigenvibrations present in numerical results, as well as high frequency noise due to the concrete inhomogeneity in slabs. Then, the Fast Fourier Transform (FFT) was used to present and compare the frequency spectrum.

#### *3.4. Results*

Thickness of the tested plate, and depth of possible fault, can be found on the basis of the passage time of the pressure wave through the material. Since the wave is reflected multiple times from the bottom and top surfaces, frequency of the wave passage is used. The velocity of wave can be obtained from the empirical Equation (1) [6]:

$$C\_p = \sqrt{\frac{E(1-\nu)}{\rho(1+\nu)(1-2\nu)}}\tag{1}$$

where *E* stands for Young's modulus of elasticity of concrete, *ρ* for density of concrete and *ν* is Poisson's ratio. This velocity is, however, dependent on the element's shape; thus, for plates, an apparent velocity should be used [8,9], leading to the Equation (2):

$$T = \frac{\mathbb{C}\_{pp}}{2f} \tag{2}$$

where *f* stands for frequency of signal, *T* for thickness (depth) of element and *Cpp =* 0.96*Cp* is the reduced, apparent wave velocity for the concrete plate with *υ* = 0.2 due to resonance and the creation of Lamb waves [34,35].

A good correlation between registered signals and their frequency spectra was obtained. The dominating frequency from experiment is 27.40 kHz, while from the model it is

27.19 kHz. With *Cpp* = 3830 m/s, the thickness of 70.0 mm and 70.4 mm can be calculated, respectively.

Thus, the model was validated and good agreement with the experiment was found.

#### **4. Experimental Studies on a Large Span Floor**

The bigger the spacing between impactor and transducer, the larger the distance that wave travels in the material. Because of this, the area tested at once can be increased, reducing the time needed for the whole slab or floor, and IE can be used to test a certain volume of concrete at once. This is why balance between the reliability of results and the distance between impactor and receiver needed to be found.

An experiment was prepared to investigate the maximum distance between the impact and read-out points at which results remain clear and reliable. Because the circular wave reflects not only from faces of the element but from other boundaries as well, interference may influence the results. To avoid this, the large span 40 cm thick concrete floor was chosen. The span-to-depth ratio was big enough to considered it as an element of infinite area.

Measurements were taken in the three directions (each 45◦) to avoid influence of reinforcement. The distance between points of impact and signal reception varied from 10 cm to 300 cm. A 12 mm impactor was used according to the geometry of slab and detection ability as presented by Carino [9]. Each measurement was repeated three times.

Measurements show that the maximum distance between impactor and receiver giving reliable results is around 90 cm and above this distance, the wave reaching transducer was too weak (Figure 3). It has to be stressed that energy produced by the smaller ball is lower, and thus, this distance would decrease. This result can be influenced by the type of the concrete used and serves merely as estimation of possibility of change Impact-Echo from punctual into volumetric method. Taking into account the expected range of thicknesses of slabs to be tested with the device under design, as well as convenience of its use, a square 60 cm × 60 cm was assumed as a maximal testing area. Furthermore, it was concluded that an automated impact procedure should be implemented to make uniform the subsequent readouts. The exact results and discussion can be found in [31].

**Figure 3.** Frequency spectra of measurements taken at a large span floor in distance of 10 cm, 60 cm and 90 cm from impactor; frequency due to thickness marked with dashed line.

#### **5. Finite Element Model of Plate with Voids**

Knowing the maximum dimensions of the IE module that could be incorporated into the automated scanner combining different NDT techniques [5], the best layout was pursued. The IE module should allow for testing in an automated way the biggest possible area at once. At this stage, the presence or lack of fault or void should be determined. The depth and exact location within the tested area can be found using more precise testing later. In this way, the large area of slab can be scanned in a quicker manner, showing the points of possible further interest.

#### *5.1. Numerical Model Modification*

It was decided to model the plate for further investigation as an infinitely large slab. The purpose of this was to avoid possible reflections from the boundaries of the element. To do this, a square plate 90 cm × 90 cm × 20 cm was modeled with further extension to obtain a circular external surface (Figure 2b). To this side surface, nonreflective boundary conditions were assigned. The vertical supports were assigned at the mid-span on the whole perimeter.

The void was modeled by removal of elements in the box 20 cm × 20 cm × 2 cm at mid-depth (Figure 4). The expected peaks, calculated with formula (2), are presented in Table 1, respectively, for the top and bottom of the void, and for the thickness of whole element. Since the element's size, material properties and finite elements type remained the same as in validated model, no additional verification or validation was needed.

**Figure 4.** The plate with void: (**a**) view and (**b**) section.

#### *5.2. Possible Linear Layouts*

The standard IE layout consist of one impactor and one receiver. If the void or fault is below one of them or between them, it can be detected.

The first considered layout was one receiver and one impactor spaced by 40 cm, moving along the line perpendicular to them. This way, subsequent cross-sections of slab can be examined. However, to obtain the necessary resolution, many measurements were needed (e.g., every 10 cm), leading to a time-consuming procedure.

To cover a bigger area at once, a set of four impactor–receiver pairs each spaced at 10 cm, covering an area of 30 cm by 40 cm, can be used. All the impactors would be released at same time. However, due to wave interference, the readouts were difficult to analyze, and this approach was given up. Furthermore, the release of impactors at exactly the same time could be problematic.

The third layout would be a modification of the above. Instead of using four impactors, only one could be used. However, the distance between the impactor and each of the receivers would not be equal and analysis of such a signal would be difficult.

On the basis of the numerical models of the three abovementioned arrangements, it was decided that for the proper layout, the distance between each of receivers and impactor should be equal. Furthermore, to avoid interference of waves, only one impactor should be used for the IE module.

#### *5.3. Square Layout*

As mentioned above, it was decided that the distance between impactor and all transducers should be equal for sake of simplicity of comparison. Although the maximum distance between points of impact and read-out was found to be 90 cm, the IE module should fit within the UIR integrated scanner. Therefore, the distances were reduced. The transducer layout should allow diagnostics of the largest possible area at once. This is why the square scheme was investigated with piezoelectric receivers in points 1 to 4 (Figure 5). Then, the applicability of this layout with different positioning of void was modeled.

**Figure 5.** Square measurement system layout: (**a**) isometric and (**b**) top views.

#### *5.4. Signal Processing*

The signal was processed in similar way as in the experimental validation (see Section 3.3). Filtering out the frequencies outside of 1 2 *f* –4 *f* was performed to exclude the eigenvibrations of plate and numerical noise, but to keep the high-frequency waves due to reflections from the void. The Raleigh wave was removed by cutting out first 0.5 ms of signal.

#### **6. Results of Simulations**

The results are compared in both qualitative and quantitative ways. The qualitative way is by comparison of frequency spectra and peaks that they reveal. This process can be automatized in the scanner. The quantitative ways used in this paper are: (I) integration of the frequency spectra, and (II) calculation of the root mean square (RMS) of the frequency spectra. The outcome of the comparison should be whether some anomaly in the measurement results can be spotted, and thus, if the void can be detected and indicate that there exists a need for further testing of the area.

#### *6.1. Solid Plate (No Void) vs. Plate with Void*

First, the comparison between solid plate and plate with void below the impactor and transducer was done.

In the case of the solid plate, the peak due to thickness (9.95 kHz) was clearly visible for all sensors (Figure 6). The second highest peak (18.0 kHz) lied the around half-depth (10.4 cm) and might be the result of wave interference. The integral and RMS values (Table 2) were slightly different, possibly due to numerical noise. However, the obtained variation remained below 3%. Thus, if the absolute value of variation (Δ) of both integral and RMS is outside of 10% interval of the Reference Value (RV), the fault is detected. If only one value is outside of the interval, it indicates warning. The RV was taken as the mean value of integrals and RMS from a solid plate.

**Figure 6.** Frequency spectra, solid plate; expected frequency marked with dashed line.

**Table 2.** Integral and RMS of frequency spectrum, solid plate.

1 Reference Value (RV); Detected Y—Yes, N—No, W—Warning.

When the void was located below impact point (Figure 7, Table 3), a big difference could be noticed from the previous case in the value of the integral and RMS. The values were smaller as the energy was largely dumped by discontinuity. Additional peaks for frequencies about 22.4 kHz were visible in the frequency spectrum, which allowed for detection of the void in the investigated area (Figure 8).

If the void was located only under one transducer (Figure 9), it was highly affected by dumping, as visible in Table 4. However, the sensor No.3 was surprisingly slightly dumped as well, possibly by interference with wave reflected from edge of the fault. In frequency spectra (Figure 10) for test point 1, the decrease in magnitude of peak due to plate thickness (9.95 kHz) was clear, as well as the additional peak due to the void (22 kHz).

**Figure 7.** Scheme of void and IE device layout.

**Table 3.** Integral and RMS of frequency spectrum, void below impactor.

Detected Y—Yes, N—No, W—Warning.

**Figure 8.** Frequency spectra, void below impactor; expected frequency marked with dashed line.

**Figure 9.** Scheme of void and IE device layout, void below sensor 1.

**Table 4.** Integral and RMS of frequency spectrum, void below sensor 1.

Detected Y—Yes, N—No, W—Warning.

**Figure 10.** Frequency spectra, void below sensor 1; expected frequency marked with dashed line.

#### *6.2. Edge of Void below Impactor*

Another interesting case is the location of edge of the void directly below the impact point (Figure 11). While comparing the integrals and RMS values (Table 5) or frequency spectra obtained here and for the solid plate, a reduction of energy delivered to transducers was visible. It is most evident for sensors close to the void (i.e., 1 and 4, Figure 12). Thus, the void can be detected and its approximated location can be given, but not the depth.

**Figure 11.** Scheme of void and IE device layout, edge below impactor.

**Table 5.** Integral and RMS of frequency spectrum, edge below impactor.

Detected Y—Yes, N—No, W—Warning.

#### *6.3. Void Moving Away from Impactor*

One more situation is the void moving away from the impact point (or, rather, when the scanner is moving away from the void, (Figures 13 and 14). Although the frequency spectra (Figures 15 and 16) did not precisely reveal the depth of the void, its location could be determined. Not only did the transducer closest to the fault reveal the biggest dumping of energy (Tables 6 and 7) as described previously, but also a linear relation between received energy and void position could be found. In the Figure 17, the variation

of RMS values with respect to reference value of solid slab are presented for three cases, as well as the linear fit quality.

**Figure 13.** Scheme of void and IE device layout, edge 5 cm from impactor.

**Figure 14.** Frequency spectra, edge 5 cm from impactor; expected frequency marked with dashed line.

**Figure 15.** Scheme of void and IE device layout, edge 15 cm from impactor.

**Figure 16.** Frequency spectra, edge 15 cm from impactor; expected frequency marked with dashed line.

**Table 6.** Integral and RMS of frequency spectrum, edge below impactor.

Detected Y—Yes, N—No, W—Warning.

Detected Y—Yes, N—No, W—Warning.

#### *6.4. Summary*

Simulations presented above clearly show that with a square set of 4 transducers and 1 impact point, the impact-echo method turns into volumetric, and a void can be detected if it lays within the area covered by the device. Its approximated position can be given in any case. However, the depth can be found only if it lays below the impact point or under one of the sensors. However, this precision is sufficient and thus, the proposed scheme can be adopted in UIR-Scanner.

The sensitivity of setup regarding minimum detectable fault was not analyzed. It can be expected that ability of detection is restricted by limits of impact-echo method [21], e.g., ratio of minimal lateral dimension of void to stress wavelength (impactor size) and element's depth. Furthermore, the numerical model presents an idealized medium, which is not the case in real application. Therefore, during the implementation of proposed layout into UIR-Scanner, the limitations and problems that are inherent in the chosen NDT method need to be borne in mind [36], i.e., (1) reflection coefficient R between fault and medium

needs to be large enough; (2) possible multiple reflections, e.g., due to reinforcement, can impair obtained results; (3) source of external vibrations and difference in vibration modes between types of plates can influence results.

**Figure 17.** RMS of signal received by each transducer with change of void edge distance from impact point.

#### **7. Experimental Validation of Adopted Layout**

Before implementation of an IE module in the UIR-Scanner, the layout was experimentally validated on a concrete slab using DOCter Mark IV transducers. The 50 cm thick slab of C30/37 concrete was used. At a depth of around 5 cm, a void was modeled by foamed polystyrene plate, 5 cm × 5 cm × 2 cm.

Measurements were executed with one transducer and one 2 mm impactor. The transducer was subsequently moved between positions 1 and 4, and the impact was applied in the center of setup (Figure 5). Two cases were considered—with no void, and with void below the impact point. The measurement was repeated 7 times at each measurement location (measurement A to G).

For obtained frequency spectra, Integral and RMS were calculated in range 0 Hz–70 Hz, where 70 Hz corresponds to twice the frequency due to the mid-depth of the void according to formula (2). The results for each measurement are presented in Tables 8–11.

**Table 8.** Integral of frequency spectrum (10−1), slab with no void.

**Table 9.** RMS of frequency spectrum (10−3), slab with no void.

**Table 10.** Integral of frequency spectrum (10−1), slab with void below impactor.

**Table 11.** RMS of frequency spectrum (10−3), slab with void below impactor.

For each measurement, the elastic wave was induced by separate impact and transducer was lifted and pressed again every time. Therefore, the measurements are uncorrelated. To analyze the results, and eliminate isolated events of different impact energy or imperfect contact of transducer with surface, average values from seven measurements (A to G) were calculated and presented in Tables 12 and 13 for slab without and with the void, respectively. The same criteria of detection as for numerical model were used; therefore, Δ above 10% for one of indicators (Integral of RMS) results in warning and for both indicators results in detection.

**Table 12.** Integral and RMS of frequency spectrum, solid slab.

1 Reference Value (RV); Detected Y—Yes, N—No, W—Warning.

**Table 13.** Integral and RMS of frequency spectrum, slab with void below impactor.

Detected Y—Yes, N—No, W—Warning.

Despite relatively large discrepancies between individual measurements due to manual excitation of elastic stress-wave, average values clearly indicate presence of the void. The results confirm the need for automated excitation and simultaneous measurement with all four transducers. This experiment confirmed applicability of IE as a volumetric method. Therefore, the numerical modeling results were validated, and the IE module was implemented into the UIR-scanner (Figures 18 and 19) and issued for further sensitivity studies.

**Figure 18.** UIR-Scanner (a prototype) for nondestructive testing using complementary NDT methods: GPR (Ground Penetrating Radar), IE (Impact-Echo) and UPV (Ultrasonic Pulse Velocity) equipped with computer systems for signal analysis.

**Figure 19.** Impact-Echo module integrated into scanner.

### **8. Conclusions**

The aim of research presented in this paper was to find the optimal design of an Impact-Echo module for automated detection of horizontal faults in concrete slabs. The IE module was to be incorporated into integrated UIR-Scanner combining three nondestructive methods. The IE module should determine possible locations of faults in the slab in the rapid, volumetric manner. Then, in indicated locations, further tests can be conducted to confirm the outcome.

The following recommendations were issued: (1) the impact should be automated to allow comparison of magnitude of frequency spectra between the measurements; (2) layout with four transducers at corners of square 60 cm by 60 cm and one impact point in the middle should be adopted as it allows the most efficient testing; (3) clear rules for signal analysis and interpretation, with use of frequency spectra's integral and RMS, are established. They can be further introduced in the software of the scanner to automatize the procedure of detection. This layout was adopted into the UIR-Scanner, validated and issued for further experimental testing.

The current research has clearly presented that relatively simple Impact-Echo method, usually used for punctual measurement of element's thickness or detection of faults, can be modified into volumetric method by use of multiple transducers. Despite loss of precision and ability to localize the fault, this approach allows for much faster scanning of structures and opens new possibilities of application of the IE method for nondestructive testing of concrete.

**Author Contributions:** Conceptualization, B.S., T.P. and A.G.; methodology, T.P.; software, B.S.; validation, T.P. and B.S.; formal analysis, B.S.; investigation, B.S.; resources, T.P. and A.G.; data

curation, B.S. and T.P.; writing—original draft preparation, B.S.; writing—review and editing, T.P. and A.G.; visualization, B.S. and T.P.; supervision, A.G.; project administration, T.P.; funding acquisition, A.G. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by the National Centre for Research and Development of Poland, grant number N R04 0024 10.

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

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The data presented in this study are available in [31] (numerical modeling and validation of models) or is available on request from the corresponding author (validation of layout).

**Acknowledgments:** Authors are grateful to Marcin Balcerzak for fruitful discussions and help with numerical modeling.

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


Hip Replacement *Edited by Carlos Suarez-Ahedo*

Published in London, United Kingdom

Hip Replacement http://dx.doi.org/10.5772/intechopen.98034 Edited by Carlos Suarez-Ahedo

#### Contributors

Nicolas Padilla-Raygoza, Gilberto Flores-Vargas, Maria De Jesus Gallardo-Luna, Efrain Navarro-Olivos, Francisco J. Magos-Vazquez, Marissa Padilla-Morales, Srino Bharam, Munif Hatem, Hal David Martin, Richard Feng, Livija Šakić, Kata Šakić, Šime Šakić, Jonathan Montomoli, Raffaele Mitri, Emiliano Gamberini, Bijan Dehghani, Neil P. Sheth, Avi Dravid, Praneeth Thota

#### © The Editor(s) and the Author(s) 2022

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**2. The different types of installations**

The first difficulty for French people who want to invest in photovoltaic panels is to choose the type of their future installation. There are currently two main families.

The first is the total resale also called total injection (**Figure 1**) [4]. All the energy produced is resold to a supplier and is redistributed on the national grid. The supply of the house is classically done by the network. Here the individual will still be subject to

**Figure 1.** *Total resale.*

*What is the Profitability of a Photovoltaic Installation in France for an Individual? DOI: http://dx.doi.org/10.5772/intechopen.109859*

the inflation of electricity. This type of installation is finally a simple financial investment in renewable energy.

The second possibility is self-consumption, which has been widely developed in 2015 (**Figure 2**) [5]. The energy produced is primarily consumed directly by the individual. Some variants exist for the management of the surplus energy. It can either be injected into the grid and bought back by the supplier or not sold and then lost or stored in batteries or virtually. The self-consumption allows direct reduction of the electricity bill of a private individual.

In the continuation of this article, the profitability of installation in total resale and in self-consumption with surplus will be compared.


**2. Progression of CSR**

Howard Bowen in 1953 made a proposition titled "Social Responsibilities of the Businessman," which became an explicit initiation into the articulation of social responsibility [10]. Articles on CSR in the 1950's mostly focused on conceptualizing the manager's function as a trustee for the society, balancing resource allocation amongst rivalries, and organizational philanthropy [11]. Irrespective of these concepts, scholars also argued that organizations' engagement should be narrowed to the exclusive optimization of shareholders' interest, hence being strategically prudent in allocating, utilizing, and optimizing resources [12].

The 1960s experienced an increased recognition of CSR relevance; this was evident via industrial, civil, and academic interest that questioned organizational practices in line with equality, legality, sustainability, and social norms. The focus on CSR interest in this era was streamlined to the social responsibilities of an organization. The interrelation between organization and society especially as it concerns resources (land, capital, manpower, etc.) is inseparable; hence, organizations relatively owe society certain responsibility that goes beyond organizations' economic interest [13, 14]. Organizations should be socially responsive to the interest of their host society, and the influencing consequence of their operations in society.

In responding to societal interest and influence, organizations need to conceptualize the theme of CSR and the rationale, techniques, and benefits inherent in its engagement; hence, this became the focus of CSR in the 1970s. A relative shift was also conceptualized from CSR to CSP (Corporate Social Performance); hence the 1970s explores themes on organizational social responsibility, responsiveness, and performance in considering the social environment [15–18], and recalibrating organizational effort to align to beneficial social expectations and obligations.

The 1980s experienced the articulation of CSR structures, techniques, and models streamlined for assessing operational CSR perspectives for decision making [19–21].

The global appeal to comprehending CSR and ensuring sustainable development of its engagement was established in the 1990s' [22, 23]. As organizations cross national boundaries for their economic interest, globalization of CSR engagement and standardization or relative flexibility in its engagement becomes relevant in addressing the unique social dynamic of their social environment irrespective of the potency of the policy directive and regulatory framework of the host society.

The 2000s' witnessed the exploration of strategic insight into comprehending the influence of CSR on the various dimensions of the organization's environment. Hence diverse studies explored the influencing roles of CSR on organizations' internal and external variables and mediating factors [23, 24].


**2. Chemical aspects**

Endosulfan is an organochlorine insecticide (6,7,8,9,10,10-hexachloro-1,5,5a, 6,9,9a-hexahydro-6, -9-methane-2,3,4-benzo-dioxathiepin-3-oxide) with a CAS Number 115-29-7 that has a cyclodiene structure. It contains a sulfite diester group that is relatively reactive and infers persistence in the environment. The condensed chemical formula is C9 H6 Cl6 O3 S.

This pesticide has been widely used since its introduction in the 1954 by Farbwerke Hoechst because it has a broad spectrum of activity. The commercial grade of endosulfan is a mixture of α- and β-endosulfan isomers (**Figure 1**), in a 7:3 ratio, respectively. Its main degradation product is endosulfan sulfate, which has similar properties to the compounds of origin [9–11].


**Table 4.**

*Persistence and half-life volatility of the GARCH models of daily log zenith Bank stock returns.*

**Model**

**114**

**eGARCH (1,1)**

Robust Standard Errors: Estimate

0.35726

0.021440

–16.6632

0.00000

omega

omega alpha1

beta1 gamma1

shape Weighted Ljung-Box Test on

Standardized

——————————————————————————————————

Lag [1] Lag[2\*(p+q)+(p+q)-1]

Lag[4\*(p+q)+(p+q)-1]

d.o.f=0 H0: No serial correlation

Weighted ARCH LM Tests

——————————————————————————————————

Statistic

ARCH Lag [3] ARCH Lag [5] ARCH Lag [7]

> **Table 3.**

*Parameter*

 *estimates and ARCH LM tests of the GARCH models.*

0.06498

 2.315

0.04570

1.440

1.667 1.543

0.9998

ARCH Lag [7]

0.06276

 2.315

0.9957

ARCH Lag [5]

0.04417

 1.440

0.02173

0.500

2.000

0.8828

ARCH Lag [3]

0.02100

 0.500

 Shape

Scale

P-Value

 [5]

 [2]

statistic

19.23 19.28 19.95

1.999e-05

d.o.f=0

H0: No serial correlation

Weighted ARCH LM Tests

——————————————————————————————————

Statistic

 Shape

Scale 2.000 1.667 1.543

0.9998

0.9959

0.8848

P-Value

Lag[4\*(p+q)+(p+q)-1]

 [5]

6.872e-06

Lag[2\*(p+q)+(p+q)-1]

 [2]

1.160e-05

 Lag [1]

 p-value

 Residuals

2.64439

0.347058

 7.6194

0.53417

0.080367

 6.6467

0.94958

0.001992

 476.7729

0.065840

0.11687

0.00000 0.00000 0.00000

skew shape Weighted Ljung-Box Test on

Standardized

——————————————————————————————————

statistic

18.99 19.04

19.71

2.335e-05

7.944e-06

1.314e-05

 p-value

 Residuals

2.64681

0.345965

 7.6505

1.02439

0.012253

 83.6013

gamma1

0.53018

0.079261

 6.6891

beta1

0.95011

0.001801

 527.6448

 alpha1

 Std. Error

 t value

 Pr(>|t|)

**Student t distribution**

**Skewed Student t distribution**

Robust Standard Errors: Estimate

0.35394

0.065963

 -1.6065

0.020239

–17.4879

0.00000

0.10817

0.00000

0.00000

0.00000

0.00000

*Linked Open Data - Applications,Trends and Future Developments*

 Std. Error

 t value

 Pr(>|t|)

not significant at 5% level except for eGARCH (1,1) model that provided significant coefficients in most cases. In the overall, most of the estimated GARCH models revealed absence of serial correlation in the error terms and absence of ARCH effects in the residuals. Because of limited space, we presented only the result of

Persistence of GARCH model measure whether the estimated GARCH model is stable or not as shown in **Table 4** above. In financial time series literature it should be less than 1 [3, 36]. Most of the models are stable except for iGARCH model. The half-life measure how long it will take for mean-reversion of the stock returns. The

The **Table 5** above presented the backtesting test of some selected GARCH model. The backtesting result of the apARCH (2,2) was not available while

eGARCH(1,1) with Skewed student t-distribution, NGARCH(1,1), NGARCH(2,1), and TGARCH (2,1) failed the backtesting but eGARCH (1,1) with student tdistribution passed the backtesting approach which is supported by the results in **Table 5** above. Therefore with the backtesting approach, eGARCH(1,1) with student t-distribution emerged the superior model for modeling Zenith Bank stock returns in Nigeria [30, 31]. This chapter recommended the backtesting approach to

This book chapter investigated the place of backtesting approach in financial time series analysis in choosing a reliable GARCH Model for analyzing stock returns. To achieve this, The chapter used a secondary data that was collected from www.cashcraft.com under stock trend and analysis. Daily stock price was collected on Zenith bank stock price from October 21st 2004 to May 8th 2017. The chapter used nine different GARCH models (sGARCH, gjrGARCH, eGARCH, iGARCH, aPARCH, TGARCH, NGARCH, NAGARCH and AVGARCH) with maximum lag of 2. Most the information criteria for the sGARCH model were not available because the model could to converged. The lowest information criteria were associated with apARCH (2,2) with Student t distribution followed by NGARCH(2,1) with skewed student t distribution. The caution here is that GARCH model should not be selected only based on information criteria only but the significance value of the coefficients, goodness-of-test fit and backtesting should be considered also [3].

The backtesting result of the apARCH (2,2) was not available while eGARCH (1,1) with Skewed student t distribution, NGARCH(1,1), NGARCH(2,1), and TGARCH (2,1) failed the backtesting but eGARCH (1,1) with student t distribution

I wish to acknowledge my PhD student and M.Sc. students that have worked

passed the backtesting approach. Therefore with the backtesting approach, eGARCH(1,1) with student distribution emerged the superior model for modeling Zenith Bank stock returns in Nigeria [30, 31]. This chapter recommended the

backtesting approach to selecting reliable GARCH model.

The Author declares no conflict of interest.

under my supervision in the area of financial time series analysis.

result revealed an average of 10 days for mean-reversion to take place.

selecting reliable GARCH model for estimating stock returns in Nigeria.

eGARCH (1,1) model in **Table 3** above.

*DOI: http://dx.doi.org/10.5772/intechopen.94112*

*Financial Time Series Analysis via Backtesting Approach*

**6. Conclusions**

**Acknowledgements**

**Conflict of interest**

**117**

*Note: uc.LRstat: the unconditional coverage test likelihood-ratio statistic; uc.critical: the unconditional coverage test critical value; uc.LRp: the unconditional coverage test p-value; cc.LRstat: the conditional coverage test likelihood-ratio statistic; cc. critical: the conditional coverage test critical value; cc.LRp: the conditional coverage test p-value; NA: not available.*

#### **Table 5.**

*Backtesting of the GARCH models: GARCH roll forecast (backtest length: 1070) for the log daily zenith Bank stock returns.*

*Financial Time Series Analysis via Backtesting Approach DOI: http://dx.doi.org/10.5772/intechopen.94112*

not significant at 5% level except for eGARCH (1,1) model that provided significant coefficients in most cases. In the overall, most of the estimated GARCH models revealed absence of serial correlation in the error terms and absence of ARCH effects in the residuals. Because of limited space, we presented only the result of eGARCH (1,1) model in **Table 3** above.

Persistence of GARCH model measure whether the estimated GARCH model is stable or not as shown in **Table 4** above. In financial time series literature it should be less than 1 [3, 36]. Most of the models are stable except for iGARCH model. The half-life measure how long it will take for mean-reversion of the stock returns. The result revealed an average of 10 days for mean-reversion to take place.

The **Table 5** above presented the backtesting test of some selected GARCH model. The backtesting result of the apARCH (2,2) was not available while eGARCH(1,1) with Skewed student t-distribution, NGARCH(1,1), NGARCH(2,1), and TGARCH (2,1) failed the backtesting but eGARCH (1,1) with student tdistribution passed the backtesting approach which is supported by the results in **Table 5** above. Therefore with the backtesting approach, eGARCH(1,1) with student t-distribution emerged the superior model for modeling Zenith Bank stock returns in Nigeria [30, 31]. This chapter recommended the backtesting approach to selecting reliable GARCH model for estimating stock returns in Nigeria.


*5.3. ROS as Signals*

It is now established that ROS can act as second messengers [265–274] by modulating the expression of several genes involved in signal transduction. The effects related to ROS signals are different and even opposite, depending on the concentration. ROS may be oncogenic and promote proliferation, invasiveness, angiogenesis and metastasis [275,276], and accordingly ROS generation increases in various cancers. Nevertheless, ROS can also promote anti-tumorigenic signaling and trigger oxidative stress-induced tumor cell death.

Many of the ROS-mediated cellular signals paradoxically protect the cell against oxidative stress, but above a given threshold ROS become harmful and induce oxidative stress [268]. Not all ROS are equally suitable for signal transduction: the OH· radical is too aggressive to participate in catalyzed reactions, whereas O2 − and H2O2 are known as important signaling molecules. Moreover, other reactive species are involved in redox signaling, such as nitric oxide, hydrogen sulfide and oxidized lipids [274].

Because some ROS such as H2O2 are oxidants, they modify the redox state of signaling proteins by oxidizing specific sulfhydryl groups [274,277,278] in enzyme-catalyzed reactions.

Several transcription factors contain redox-sensitive cysteine residues at their DNAbinding sites [279,280]. The ensuing formation of disulfide bonds acts as a redox switch to transduce the response of the protein to redox signaling [271,281].

Following the oxidation of signaling proteins by ROS, other post-translational changes (e.g., phosphorylation, acetylation, ubiquitination, and SUMOylation [270]) may occur in the same protein and in other proteins of the signaling cascade.

Nrf2 is an important example of mitochondrial ROS signaling which leads to nuclear gene expression changes [282]; in the presence of ROS, NRf2 is transferred from the cytoplasm to the nucleus, where it binds the DNA antioxidant response element of genes involved in the antioxidant response (e.g., heme oxygenase, NRF-1 and other inducers of mitochondrial biogenesis) [283].

Signaling proteins modified by ROS include phosphoprotein phosphatases (PTPs), Ras, large G-proteins, serine/threonine kinases of the MAPK families, transcription factors as AP-1, NFκB, p53 and others. A different effect is exerted on these proteins: PTPs are inhibited, while nuclear transcription factors are activated [284]. Different combinations of activation or deactivation of these proteins may drive the cell to either survival or death.

Mitochondrial ROS production is involved in preconditioning, by which low doses of a noxious stimulus promote a protective response against future injury [285–287]. Some protective pathways converge on the inhibition of mPTP opening during reperfusion [287].

Mitochondrial ROS are also important signals which rule the inflammation by activating the inflammasome [288,289]; treatment with antioxidants could scavenge excessive ROS and attenuate inflammatory responses by suppressing inflammasome activation [290]. ROS also regulate autophagic processes including mitophagy [291].

#### 5.3.1. Regulation of Mitochondrial ROS in Cell Signaling

Mitochondrial ROS levels depend on the dynamic equilibrium between their rates of production and removal.

Studies on ROS generation under different substrate, inhibitor conditions and different oxygen tensions in rat liver mitochondria lead to the conclusion that only CI may be a significant source of ROS at physiological O2 concentration [292]. The factors directly associated with respiratory activity (e.g., the redox potential of the NAD+/NADH couple and the proton-motive force) regulate the reduction in oxygen [268]) but these factors are in turn dependent on other parameters (cf. also Section 5.2).

Moreover, mitochondria enhance ROS generation in response to external stimuli, such as TNFα [293], hypoxia ([294], cf. Section 5.3.2), serum deprivation [295] and oxidative stress itself (ROS-induced ROS release, Zorov et al. [296]). Several proteins, such as p53, p66Shc, the Bcl-2 family and Romo-1 [267] control mitochondrial ROS generation.

An interplay of mitochondria with non-mitochondrial ROS generating systems also occurs, as with the NADPH oxidases (NOX) family [297–299].

On the other hand, control of ROS signaling may be operated by their removal by a series of enzymatic systems [300], including various isoforms of superoxide dismutase, catalyzing the dismutation of superoxide, whereas catalase, glutathione peroxidase and peroxiredoxins remove H2O2. In addition, an integrated set of thiol systems in mitochondria prevents oxidative damage [271] and may transduce redox signals.

Peroxiredoxins (Prxs) are small dithiol proteins constituting a major family of peroxidases (six isoforms in mammals). Due to their high sensitivity to oxidation by H2O2, Prxs are sensors and transducers of H2O2 signaling [301] by transferring their oxidation state to effector proteins. The mitochondrial matrix contains large amounts of Thioredoxin-2 [302,303] and Prx3 [304].

The appropriate mitochondrial redox environment is greatly ascribed to glutathione [305–307] which is abundant and versatile to counteract hydrogen peroxide and lipid hydroperoxides, being a cofactor of glutathione peroxidase or glutathione-*S*-transferase. The mitochondrial GSH:GSSG ratio generally exceeds 100 and is widely used as an indicator of the redox status [308].

Protein glutathionylation is a regulatory mechanism that occurs through thiol disulfide exchange by protein disulfide isomerase [309,310]; the primary sistem catalyzing de-glutathionylation of protein-mixed disulfides with glutathione is glutaredoxin [311]. Mitochondrial proteins are highly susceptible to reversible *S*-glutathionylation, a posttranslational modification which is favored by the unique physico-chemical properties of the mitochondrion [312], which contains a variety of *S*-glutathionylation targets playing important physiological roles: if these reactions are defective, pathological consequences are expected to occur.

#### 5.3.2. Hypoxia and ROS Production

Among the many signaling functions, ROS appear as hypoxic signaling molecules. It seems paradoxical that a decrease in the level of the required substrate, O2, would result in an increase in ROS production. However, there is large evidence of its occurring [313–315].

Indeed, ROS appear to activate the hypoxia-inducible factor HIF-1α. Rho0 cells, which lack mtDNA and thus electron transport, do not show the HIF-1 DNA-binding activity following hypoxia [316]. Therefore, mitochondrial respiration is required for propagation of the hypoxic signal. Exogenous or endogenous H2O2 stabilize HIF-1α, thus inducing its activation during normoxia [316], suggesting that HIF stabilization and activation may be induced by ROS.

Many studies demonstrate activation of HIF-1α by ROS [317,318], that are supposed to act by inhibiting the prolyl-4-hydroxylase that addresses the factor to proteolytic digestion. Once stabilized, HIF-1α binds to hypoxia-responsive elements in the DNA and stimulates the expression of a large array of genes [319].

The oxidized cyt *c* level in the IMS seems to be essential to control mitochondriallyderived ROS [320,321]; accordingly, cyt. *c* in the IMS oxidizes superoxide produced by CIII to O2, thus preventing H2O2 production [321,322].

Inhibition of cytochrome *c* oxidase by hypoxia [323] enhances ROS formation by the respiratory chain; most likely because of the increased membrane potential [324] or by inducing a more reduced state of cyt. *c*.

The ROS produced by mitochondrial CIII seem to be critical for hypoxia signaling [294,325–328]. Hernansanz-Augustin et al. [329], however, showed that CI is involved in the superoxide burst under acute hypoxia in endothelial cells.

In addition, it should be pointed out that the plasma membrane NADPH oxidase [313,330] also seems to be involved in the enhanced ROS production during hypoxia.

#### *5.4. ROS and Mitochondrial Quality Control*

A major device for physiological control of the cells is the removal of damaged molecules; in particular, oxidized proteins are ubiquitinated and directed to the proteasome, a member of the ATP-dependent AAA+ proteases, where they are completely digested [331,332].

Mitochondrial proteins may particularly suffer from oxidative damage since they are close to the main sites of their generation, so that they must be removed in order to maintain mitochondrial integrity [333,334]. Internal mitochondrial proteins are translocated to the outer mitochondrial membrane, where they are ubiquitinated and then presented to the proteasome for degradation.

Mitochondrial dysfunction due to loss of cellular protein homeostasis (proteostasis) is a hallmark of aging and aging-related degeneration disorders [335], such as Alzheimer's disease and Parkinson's disease. Thus, mitochondrial proteins should be finely tuned. Although mitochondria form a proteasome-exclusive compartment [336], it is the cytosolic ubiquitin–proteasome system that plays a major role in the quality control of mitochondrial proteins.

The ATP-stimulated Lon protease in the mitochondrial matrix is devoted to the selective degradation of oxidized proteins, as for example the selective degradation of the Cox 4-1 subunit during hypoxia [337,338]. Defects in protein degradation have been involved in the age-related accumulation of oxidized proteins [339,340].

Also, entire cellular organelles undergo turnover and are finally directed to autophagy by digestion in the lysosome compartment [341–343].

Non-selective autophagy as well as selective mitophagy are triggered by ROS in response to several stressing signals [291,344,345]. Damaged mitochondria promote ROS generation, and excessive ROS can trigger mitophagy so as to remove impaired mitochondria and reduce ROS levels. Therefore, mitophagy helps to maintain cellular homeostasis under oxidative stress. Low ROS levels can trigger mitophagy in a mitochondrial fission-dependent way, if these levels are insufficient to trigger non-selective autophagy [346]. Therefore, a very specific and selective signaling cascade initiated by ROS has been suggested.

#### *5.5. Supercomplexes Protect Complex I from ROS Damage and Limit ROS Generation*

Our group first suggested that SC arrangement represents the missing link between oxidative stress and energy deficiency [96]. We speculated that oxidative stress dissociates the SCs, with loss of electron channeling and causing electron transfer to depend only upon the diffusion-coupled collisional encounters of the free ubiquinone molecules with the partner complexes.

#### 5.5.1. Supercomplex Association Protects from ROS Damage

As predicted by Lenaz and Genova [96], SC dissociation also induces disassembly of CI and CIII and consequent loss of their catalytic activity. Therefore, the alteration of electron transfer may stimulate ROS generation. Here we briefly summarize the experimental evidence supporting this hypothesis.

Analysis of the SCs in patients with an isolated deficiency of single complexes [347] and in cultured cell models harboring cytochrome *b* mutations [348–350] showed that SCs enhance the stability of CI. Genetic mutations causing loss of CIII prevent SC formation and determine a secondary loss of CI, and consequently primary CIII assembly deficiencies appear as joint CIII/I defects. On the other hand, however, the absence of CI does not affect CIII stability.

It was recently suggested that the absence of CIII blocks CI biogenesis by preventing the incorporation of the NADH module rather than decreasing its stability [351].

Most evidence, however, is in line with the idea that misassembly of CIII affects CI stability because of their physical interaction within the SC. Misassembled CIII would prevent SC formation, and a lack of SC would induce an enhanced ROS generation from CI (see Section 5.5.2), with consequent damage to CI itself [350,352] which is vulnerable to oxidative stress both directly and through the lipid peroxidation, particularly of CL [353]. According to Guaras et al. [120], saturation of CoQ oxidation capacity keeps a highly reduced state of CoQ itself and induces reverse electron transport from reduced CoQ to CI; the resulting local superoxide generation oxidizes specific CI proteins, triggering their degradation and the disintegration of the complex.

An ischemia/reperfusion injury enhances ROS generation in mitochondria which promotes the opening of the nonselective mPTP [354]. The mPTP opening further compromises cellular bioenergetics and increases mtROS, resulting in SC disintegration and ultimately leading to cell death.

A reconstitution study [71] showed that lipid peroxidation before formation of CI-CIII proteoliposomes abolishes the SC formation, as determined by flux control analysis. It is likely that the distortion of the lipid bilayer induced by peroxidation provokes the dissociation of the SC.

Mitochondrial ROS also affect CI and CIV activity through CL peroxidation in beef heart SMP [353,355]. CL liposomes exogenously added to mitochondria from aged rats almost completely restored the activity of these enzyme complexes to the values of young control animals [356,357]. Other phospholipid classes, as well as peroxidized CL, could not mimic the CL effect.

#### 5.5.2. Supercomplex Association Limits ROS Generation

Indirect considerations are compatible with the possibility that loss of SC organization may enhance ROS generation by the respiratory chain [12,96,358]. There are two possible reasons to support this hypothesis: a tight assembly of the respiratory complexes within SCs may screen auto-oxidizable groups hindering their reaction with oxygen (cf. [55]), and/or enhanced electron flow from NADH in the chain because of channeling would keep the prosthetic groups in a more oxidized form, thus preventing their interaction with oxygen [250]. On the other hand, on succinate oxidation, the reverse electron flow through CI keeps its centers more reduced favoring production of superoxide.

The molecular structure of the individual complexes and of the SCs does not provide structural evidence of such screening, since the prosthetic groups of CI in the matrix arm do not seem to be in close contact with CIII [359,360]. However, the SC I1III2IV1 from bovine heart has a different CI conformation with respect to the free complex, that appears to be bent in such way as to be closer to CIII [359]. This observation agrees with the notion that CI may undergo important conformational changes [361].

A different kind of indirect evidence on the protection exerted by SC organization against ROS generation comes from the observation that high mitochondrial membrane potential supports ROS generation, while uncoupling decreases ROS production [243,249]. Although these effects may have different explanations, they are compatible with the suggestion [87] that high membrane potential induces SC dissociation.

A direct demonstration that loss of SC organization enhances ROS production by CI was obtained in our laboratory [362] using a model system of reconstituted CI/CIII proteoliposomes at high lipid-to-protein ratio (30:1), where formation of the SC I1III2 is prevented. In this system, the generation of superoxide was much higher than in a similar system reconstituted at a 1:1 ratio, which is rich in SCs. In addition, we also dissociated the reconstituted proteoliposomes by mild detergent treatment using dodecyl maltoside and observed that the dissociation of CI was accompanied by a three/four-fold increase in ROS generation. An increase in ROS also occurs in mitochondrial membranes after detergent treatment.

A significant finding supporting our in vitro conclusions comes from a study of mitochondrial CI supramolecular structure in neurons and astrocytes. Lopez-Fabuel et al. [363] observed that CI is largely assembled into SCs in neuronal mitochondria, whereas astrocytes have higher content of free CI. The presence of free CI in astrocytes correlates with the severalfold higher ROS production by astrocytes compared with neurons. Thus, regulation of ROS generation by CI assembly into SCs may contribute to the bioenergetic differences between neurons and astrocytes. Nevertheless, ROS levels were found to be controlled by an efficient antioxidant system in astrocytes, to regulate redox signaling [364]. By exerting this control in ROS levels, metabolic functions are finely tuned in both neural cells.

A study of CI activity in the basidiomycete *Ustilago maydis* [365] suggested that the contacts between CI, CIII2 and CIV in the respirasome increase the catalytic efficiency of CI and regulate its activity to prevent ROS production.

The results of our proteoliposome study [362] are supported by many observations in cellular and animal models showing that SC dissociation is concomitant with enhanced ROS production.

Diaz et al. [352] showed enhanced ROS generation in mouse lung fibroblasts lacking the Rieske FeS protein of CIII and hence devoid of the SCs containing CI.

Mouse fibroblasts expressing the activated form of the *k*-ras oncogene and having low levels of high molecular weight SCs also produce higher ROS in comparison with wild type fibroblasts [366]. Hyperglycemia prevents SC formation, while increasing ROS levels in liver mitochondria of streptozotocin-diabetic rats. On the other hand, physical exercise was found to induce the chronic assembly of CIs into SCs in skeletal muscle [367], thus protecting mitochondria against oxidative damage.

Other studies in yeast mutants lacking the SC assembly factor Rcf1 and thus devoid of SCs CIII-CIV [117,368,369], showed enhanced ROS generation. Since the yeast *S. cerevisiae* lacks CI, in this case we may consider the origin of the extra ROS being presumably CIII. Thus, a major function of SC assembly appears to be this limitation of ROS production [370]: in the above case the decreased ROS generation by the Rcf1-stabilized SC III2-IV2 may be due to the more efficient electron transfer between CIII and CIV by cyt. *c*.

Several compounds including phospholipids, proteins, and certain chemicals are known to promote or stabilize mitochondrial SCs directly or indirectly [371], thus hindering ROS generation. Overexpression of the CL conversion enzyme ALCAT1 reduced SC formation and promoted ROS production, while preventing upregulation of coupled respiration [75]. These data suggest that the amount of ALCAT1 is critical for coupling mitochondrial respiration and metabolic plasticity.

The CL defect in Barth syndrome, a cardio-skeletal myopathy with neutropenia characterized by respiratory chain dysfunction, results in destabilization of the SCs, with higher levels of superoxide production in lymphoblasts from patients, compared to control cells [67,68]. Analogous results were obtained un studies on CL-lacking yeast mutants [372,373]. Moreover, Chen et al. [368] observed that yeast mutants, which cannot synthesize CL, exhibit increased protein carbonylation, an indicator of ROS.

Stein et al. [374] described a highly conserved 56-amino-acid microprotein named mitoregulin (Mtln). Mtln localizes to the mtIM where it binds CL and influences protein complex assembly. In cultured cells, Mtln overexpression increases mitochondrial SCs and mitochondrial activity while decreasing mitochondrial ROS.

The subunit composition of CI is crucial for SC formation and control of ROS production. Hou et al. [375] demonstrated that CI subunit AB1 (NDUFAB1), also known as mitochondrial acyl carrier protein, coordinates the assembly of respiratory CI, CII, and CIII, and SCs and is a crucial regulator of mitochondrial energy and ROS metabolism.

Jang and Javadov [376] observed that the pharmacological inhibition of CI and CII stimulated disruption of the respirasome accompanied by reduced ATP formation and increased ROS production. Overall, these studies provide biochemical evidence that the CI activity, and the NDUFA11 subunit are important for assembly and stability of the respirasome. The SDHC subunit of CII is not involved in the respirasome however the complex may play a regulatory role in respirasome formation.

Ramirez-Camacho et al. [377] found that mitochondria from reperfused hearts treated with *N*-acetyl-cysteine reduced oxidative stress and maintained SCs assemblies containing CI, CIII, CIV and the adapter protein SCAF1. The associations of the mitochondrial respiratory chain components into SCs could have pathophysiological relevance in metabolic diseases, as supramolecular arrangements, by sustaining a high electron transport rate, might prevent ROS generation [378].

#### **6. Physiological and Pathological Implications**

As we have pointed out in the Introduction, mitochondria are deeply involved in pathological processes. Mitochondrial dysfunction is often present in pathological states: at the end of this review, we intend to demonstrate that mitochondrial dysfunction is causative in the pathogenesis of most systemic diseases.

What are the signs showing mitochondrial dysfunction? There are many of them that are more or less specific. Among these we have changes of electron transfer, such as uncoupling, i.e., the occurrence of electron transfer not accompanied by ATP synthesis, changes of mitochondrial shape and number, alterations in quality control, changes in supramolecular structure (SCs) accompanied by decreased respiration and enhanced ROS generation, and finally opening of the mPTP and cell death.

We first briefly examine OXPHOS uncoupling. As for ROS generation cf. Section 5, for quality control see Section 5.4, and for the nature and role of the mPTP cf. Section 4.4. A possible role of SC disassembly as the initial pathogenetic event in many complex diseases will be described in Section 6.3.

#### *6.1. Uncoupling: When Proton Movement and ATP Synthesis Are Disjointed*

The term uncoupling in bioenergetics indicates that the H+ pumping activity of respiratory complexes which forms the ∆*p* is not exploited to synthesize ATP from ADP and Pi by F1FO-ATPase. Uncoupling is often associated with another term, mitochondrial dysfunction, which suggests that mitochondria do not work properly and are unable to fully perform their bioenergetic task. Uncoupling can have variable extent. We can distinguish between mitochondrial uncoupling, due to the downhill H+ flux through pathways outside the F1FO-ATPase, and intrinsic F-ATPase uncoupling, which means that the enzyme complex itself cannot match ATP synthesis to H+ channeling, due to molecular defects. While the mitochondrial uncoupling has a recognized physiological role, even if many mechanisms remain to be clarified [257], as far as we are aware the F1FO-ATPase uncoupling only represents a basic biochemical symptom of pathologies [379].

#### 6.1.1. Mitochondrial Uncoupling Due to Dissipative Pathways

The mitochondrial uncoupling can be defined as the detachment of H+ movement across the mtIM from the F1FO-ATPase activity [134]. Accordingly, the mitochondrial membrane potential generation is not used to build ATP. Even if it seems surprising, normally OXPHOS is not completely coupled, and the coupling extent depends on multiple factors. The mitochondrial uncoupling can be detected directly as a decrease in ∆*p* or indirectly as a decrease in the phosphorylation efficiency, namely in the ADP/O ratio and or in the respiratory control ratio (RCR), which corresponds to the ratios of State 3 (ADP-stimulated) and State 4 (basal) respiratory activities. State 4 respiration, after subtraction of the non-mitochondrial oxygen consumption detected upon respiratory chain inhibition, mirrors the oxygen consumption of the so-called proton leak. The latter consists in the futile cycle of H+ that from the IMS flow downhill in the mitochondrial matrix through pathways independent of the F1FO-ATPase [380]. The proton leak extent can be modified by protein complexes, exogenous compounds or permeability changes due to

changes in the mtIM composition. Even if, at first, the mitochondrial uncoupling was only associated with mitochondrial dysfunction, at present, it emerges as key ruler of biological processes, as suggested by the occurrence of endogenous natural uncouplers, even if they can also have pathological meaning [257]. Accordingly, dissipative pathways normally occur in variable amounts in different cell types. In mammals, the most known physiological uncoupling occurs in the brown adipose tissue, where an integral membranebound protein (UCP-1) channels H+ and dissipates the electrochemical gradient resulting in thermogenesis. Other uncoupling proteins (UCP-2 and UCP-3) rule insulin secretion in pancreatic β cells and fatty acid metabolism in muscle, brown adipose tissue and heart, respectively [381]. Additionally, the four-membered family of adenine nucleotide translocators (ANTs), which catalyzes the ATP/ADP exchange across the mitochondrial membrane, possesses uncoupling properties [382].

Lastly, mitochondrial uncoupling can be also produced by exogenous chemicals, protonophores, namely lipophilic weak acids which can cross the mtIM, or non-protonophores, able to activate latent proton leaks.

A severe mitochondrial uncoupling leads to ATP depletion and eventually cell death, while mild mitochondrial uncoupling can have positive effects. Mitochondrial uncoupling can play opposite roles: it can promote cell death but also helps to protect cells against cell death, according to the cell type, the uncoupler and the uncoupling extent [257]. Uncoupling should prevent an excessive ∆Ψ rise which would block electron transfer along the respiratory chain. The decrease in ∆Ψ and consequently in ∆*p* also decreases ROS generation and vice versa, an increased ROS generation is known to decrease proton leak. On the other hand, the ATP synthase inhibition leads to electron accumulation in the respiratory complexes and ROS overproduction, which leads to oxidative stress and mitochondrial dysfunction. Endogenous mitochondrial uncoupling could prevent excessive ROS production. Accordingly, mitochondrial uncouplers have been tried to treat diseases featured by oxidative stress such as diabetes, obesity, cardiovascular diseases, neurodegenerative and aging-related diseases [134].


**1. Introduction**

In the ever-advancing world of electronics, the demand for materials that combine exceptional mechanical properties with electrical conductivity is ever-increasing. Traditional epoxy materials are renowned for their excellent mechanical strength, chemical resistance, and adhesive properties, making them widely utilized in various applications [1–4]. However, their inherent insulating nature limits their usefulness in applications where electrical conductivity is required. The introduction of conductive

materials, such as metallic particles, metallic nanowires, carbon nanotubes (CNTs), and graphene-based materials, has enabled the incorporation of electrical conductivity into epoxy composites (ECs). The conductive materials need to exhibit excellent conductivity while also demonstrating strong compatibility with the host polymer. Yet, these materials remain vulnerable to damage caused by repeated deformations, which can give rise to the formation of microcracks and fractures. Such structural impairments disrupt electrical pathways, yielding functional deficiencies that ultimately compromise performance and lifespan in electronic applications [5–8]. A captivating development aimed at addressing this demand is the fusion of selfhealing properties with electrical conductivity in epoxy materials. Self-healing ECs endowed with electrical conductivity not only ensure the longevity and dependability of electronic components but also enable the development of advanced electronic systems that boast enhanced resilience and durability. This self-repairing capability is achieved through the incorporation of dynamic chemical bonds within the polymer matrix, including noncovalent bonds (hydrogen bonds [9, 10], metal-ligand coordination [11, 12], etc.) and reversible covalent bonds (hindered urea bonds [13, 14], disulfide bonds [15, 16], Schiff base [17, 18], etc.). **Figure 1** visually depicts the utilization of electrically functional epoxy composites in self-healing electronic components. The impetus for exploring the fusion of self-healing attributes and electrical conductivity in epoxy materials arises from the surging demand for robust materials possessing both mechanical vigor and electrical prowess. The amalgamation of these attributes opens avenues to augment the dependability and lifespan of electronic devices, while concurrently bolstering their resilience against mechanical and electrical adversities.

Within this chapter, we embark on a comprehensive exploration to present a panoramic overview of the substantial progress achieved in the application of epoxy composites (ECs) endowed with both self-healing capabilities and electrical functionality, specifically tailored for versatile and flexible applications. Our primary objective is to delve into their diverse implementation across various domains. These domains encompass adhesives, flexible coatings designed for anticorrosion purposes, sensors,

#### **Figure 1.**

*Explore the electronic applications where epoxy composites with self-healing and electrical conductivity functionalities are utilized.*

*Electrically Conductive Self-Healing Epoxy Composites for Flexible Applications: A Review DOI: http://dx.doi.org/10.5772/intechopen.1003037*

electronic components such as EMI shielding, soft actuators, and energy devices. We place distinct emphasis on meticulously unraveling the foundational differences between the mechanisms and strategies governing the healing of mechanical fractures and electrical breakdowns within ECs.

Furthermore, we endeavor to articulate the core principles, self-healing assessment, and design strategies of conductive networks that underpin self-healing EC-based devices. This highlighting showcases their inherent capacity not only to restore mechanical integrity but also to reinstate functionality and performance, even in the presence of simultaneous mechanical and electrical damage. While acknowledging the frontier that lies ahead, we also shed light on the challenges that await and the promising opportunities for future research. Through these efforts, this chapter aims to provide a comprehensive, up-to-date, and thorough understanding of the ever-evolving realm of conductive self-healing ECs within the landscape of flexible devices.