*2.4. Lipidomics Analysis*

Oxidation of polyunsaturated fatty acid arachidonic, eicosapentaenoic, docosahexaenoic, linoleic, and dihomo-γ-linolenic generate bioactive lipids. The development of mass spectrometry platforms enabling quantification of diverse lipid species in human urine is of crucial importance to understand metabolic redox homeostasis in normal as well as pathophysiological conditions. Here we demonstrate clearly how administration of *Coriolus* to MD patients increases significantly the powerful anti-inflammatory eicosanoid LXA4 in plasma and lymphocytes as compared to untreated MD patients (Figure 8a,b). The same results were observed in urine, where a large increase in LXA4 was measured after *Coriolus* supplementation (Figure 8c). Consistently, analysis of urine levels of pro-inflammatory eicosanoids 11-dehydro TXB2, isoprostane PGF2α, and isoprostane iPF2α-VI showed the opposite results with significantly higher levels of these bioactive lipids in MD subjects than the levels found in *Coriolus* administered MD patients (Figure 9a–c).

**Figure 8.** Lipidomic analysis of bioactive lipids. Biolipids are synthesized by oxidation of polyunsaturated fatty acids, arachidonic acid, eicosapentaenoic acid, docosahexaenoic acid, linoleic acid, and dihomo-γ-linolenic acid. The development of enabling mass spectrometry platforms for the quantification of diverse lipid species in human urine is of paramount importance for understanding metabolic redox homeostasis in normal and pathophysiological conditions. Anti-inflammatory eicosanoid LXA4 were measured in plasma, lymphocytes (**a**,**b**) and in urine (**c**), as compared to untreated MD patients.

**Figure 9.** *Cont*.

120

**Figure 9.** Lipidomic analysis of bioactive lipids. Analysis of urinay pro-inflammatory eicosanoids, 11-dehydro TXB2, isoprostane PGF2α, isoprostane iPF2α-VI, showing opposite results with significant higher levels of these bioactive lipids in MD subjects than the levels found in *Coriolus* administered MD patients are reported in (**a**–**c**).

Consistent with other findings showing that oxidative stress and altered thiol status in degenerating brain diseases correlates with systemic redox imbalance and oxidative stress, as in AD [31–34], the content of total GSH, reduced and oxidized glutathione and the GSH/GSSG ratio, was determined in the plasma of MD patients as a measure of the antioxidant status and compared with the levels of *Coriolus*-treated MD group (Table 4). We report the plasma from MD patients contained significantly lower levels of GSH as compared to *Coriolus*-supplemented patients, which paralleled to corresponding significantly higher GSSG levels (*p* < 0.05) (Table 4). These changes resulted in a plasma GSH/GSSG ratio which was significantly higher in the group of MD plus *Coriolus* subjects then the ratio found in the MD group alone (Table 4).

**Table 4.** Plasma and lymphocyte content of total, reduced (GSH) and oxidized (GSSG) glutathione in control and MD patients treated with Coriolus.

**\*** Significantly different from control (*p* < 0.05). **\*\*** Significantly different from MD alone (*p* < 0.05).

#### **3. Discussion**

MD is a chronic illness derived from combined neurodegenerative events occurring at level of spiral ganglion as well as hair cells of the inner ear, associated with a negative impact on the quality of life of individuals, presenting various symptoms, such as temporary hearing loss, dizziness, and tinnitus [7].

After its initial description by Prosper Meniere more than 150 years ago, the disease named after him is still at the center of scientific debate [1]. MD is a hydropic ear pathology, where episodic vertigo, tinnitus, and fluctuating hearing loss coexist with endolymphatic hydrops. [3]. Recent evidence indicates the involvement of oxidative stress in the development of endolymphatic hydrops associated with neuronal ganglion damage with apoptotic neuronal cell death as a prominent factor contributing to SNHL found in the later stages of MD [2]. Thus, it is conceivable that MD, as a systemic oxidant disorder [5], can be also considered, owing to its demonstrated neurodegenerative nature of the neuronal cochlear ganglion component, involved in its pathogenesis, a pursuable investigative model of neurodegeneration. Consistent with this possibility, the present study was undertaken to explore the hypothesis that changes in the redox status of glutathione, stress-responsive vitagenes, and lipidomics, the major determinants in the disruption of redox homeostasis affecting spiral ganglion neurons, may be positively impacted by nutritional intervention with *Coriolus*-MRL biomass supplementation.

Mushrooms have been present in traditional medicine for thousands of years, and are reportedly endowed with immunomodulatory actions, associated with antioxidant, anticancer, antiviral, bacteriostatic, and hepatoprotective properties [43]. Mushroom-derived therapeutics, mainly polysaccharopeptides isolated from *Coriolus versicolor*, are well characterized and commercially available. Here we tested the hypothesis that neurotoxicity is an important causative factor involved in MD pathogenesis, which can be evaluated by measuring markers of oxidative stress and cellular stress response proteins in the peripheral blood of patients with MD. We evaluated in the present study systemic oxidative stress and cellular stress response in 40 patients suffering from MD in the absence and in the presence of treatment with mushroom biomass preparation from *Coriolus*. Systemic oxidative stress was estimated in plasma and urines of patients with MD or MD plus *Coriolus*, by measuring protein carbonyls, HNE, and ultraweak luminescence, as well as active biolipids such as lipoxin A4 and F2- isoprostanes, whereas in the lymphocyte heat shock proteins (HSP) heme oxygenase-1 (HO-1), Hsp70 and thioredoxin (Trx) levels were measured to evaluate the systemic cellular stress response. Increased levels of DNPH, HNE, ultraweak luminescence, and F2-isoprostanes were found in all the samples from MD patients with respect to the MD plus *Coriolus*-treated group. This was paralleled by a significant induction of lymphocyte HO-1, Hsp70, TrxR-1 as well as Sirtuin-1 and by a significant increase in the plasma ratio-reduced glutathione GSH) vs. oxidized glutathione (GSSG).

It is suggested that genetic factors may contribute partly to the etiologies of MD, as some associations have been reported for polymorphisms related to gene coding for protein involved in inflammation, circulation, and blood vessels, such as interleukin 1A (–889C/T), interleukin 6–572C/G), protein kinase C beta type (1425G/A), matrix metalloproteinase-1 (–1607G/2G), methylenetetrahydrofolate reductase (MTHFR) (C677T), prothrombin (G20210A), and complement factor H [44–51], and genes involved in free-radical processes. Although the initial causative factors triggering the disease have not been clarified, various genes and variants have been confirmed to be related to MD, which also suggests a specific family of genetic predisposition and implies genetic factors as key players in the initiation and progression of MD [52]. Consistent with this scenario, inflammation and oxidative stress-induced endolymphatic hydrops have been identified as a secondary pathogenesis of the disease [53]. Thus, MD etiology and pathogenesis appears to be an aberrant response of the adaptive or innate immune system, ultimately mediated by pro-inflammatory and oxidative processes underlying its physiopathological determinism [54]. Several mechanisms are involved in the development of immune-mediated inner-ear pathology, including (a) similarity with potentially harmful component of virus or bacteria, such as cross-reactive epitope inducing inner-ear damage; and (b) generation of pro-inflammatory Interleukin 1 β (IL-1B) or Tumor necrosis factor α (TNF) cytokines and transcriptional nuclear factor kB (NF-kB) [55]. Toll-like receptor coding genes, including TLR3, TLR7, TLR8, and TLR10, are widely reported to contribute to the disease, being directly related to the initiation and progression of MD, thus implying a specific role for the immune system during the pathological processes [56]. This is confirmed by recent findings highlighting the relationships between increased serum levels of IL6 and IL1 with vertigo, a specific complication of MD.

To survive different types of injuries and adapt to environmental changes, neuronal cells have evolved networks of responses capable of detecting and controlling different forms of stress [26–62]. As such, integrated survival mechanisms exist in the brain based on the activity of redox-dependent genes, called vitagenes, capable of sensing stress and including HSP (Hsps), thioredoxin, γ-GC ligase, and sirtuin family proteins, which together with bioactive lipids represent the last step in the "omic" cascade starting from genome, through transcriptome, proteome, and finally to metabolome. Lipid mediators as signaling factors play a fundamental role in the initiation, amplification, and resolution of inflammation [33,34]. Thus, use of urine sample for lipidomic analysis enables reproducible quantification of several lipid metabolites generated by lipoxygenase, cyclooxygenase, and cytochrome P450 activities, such as octadecanoids, eicosanoids, and docosanoids. Lipidomic analysis of urine reveals quantitative data that reflects the alterations in in eicosanoids levels seen in MD patients as compared to normal controls. Lipoxin A4, in particular, is a metabolic product of arachidonic acid, acting as an endogenous "breaking signal" towards inflammatory processes, actively operating in the detection and control of diverse forms of stress in the brain. Owing to its potent anti-inflammatory properties LXA4 positively influences the outcome in many inflammatory disorders, such as nephritis, periodontitis, arthritis, and inflammatory bowel disease [63,64]. Chronic inflammation sustains the progression of neurodegenerative pathologies, including AD and Parkinson's disease, but also in specific neuronal districts, as in the cochleovestibular apparatus and the spiral ganglion neural cells. Thus, identification of mechanisms capable of favorably impacting the pro-inflammatory environment generated in the MD pathology represents an area of active investigation. Consistent with this notion, the activation of the LXA4 pathway could therefore serve as a potential therapeutic target to treat MD-associated inflammation and cochleovestibular dysfunction. As LXA4 action is mediated by LXA4 receptor (ALX), a formyl-peptide receptor-like 1 (FPRL1) present on cellular membrane [33], the discovery of agents with the potential of increasing Lipoxin A4 (LXA4), and consequently of reducing inflammatory-mediated endolymphatic hydrops, can be relevant to therapeutics of this disease. Eicosanoid lipoxin A4 (LXA4) decreases toxic compounds such as ROS, inhibits recruitment of activated neutrophils and blocks accumulation of pro-inflammatory cytokines, thereby promoting resolution of inflammation [65].

Our results obtained with a nutritional approach based on a *Coriolus versicolor* biomass supplementation are relevant to innovative therapeutic anti-inflammatory strategies aimed to minimize consequences associated with neurodegeneration and oxidative stress of cochleovestibular system pathologies including not only MD but also sudden sensorineural hear loss (SSNHL) where it has recently demonstrated a critical role played by NLRP3 inflammasome [41]. NLRP3 is a sensor of the intracellular innate immune response expressed in immune cells, including monocytes and macrophages. Activation of the NLRP3 inflammasome results in augmentation of IL-1β secretion and cochlear autoinflammation. [66,67].

Due to different biological routes of actions, ranging from anticancer, antiviral, bacteriostatic, and regulation of of immune function, as well as antioxidant and protectant of hepatocytes [29,68], relevant to the inflammatory disease pathogenesis, mushrooms in the past have been diffusely applied for therapeutic use in traditional medicine [27,28]. It has been shown, in fact, that cytokine response triggered by activated immune cells occurs after stimulation with immunostimulatory molecules derived from mushroom preparations, which are mainly β-glucans [30,57,69–71]. Despite this, however, the active ingredients are not fully characterized, which makes mushroom extracts very difficult to reconcile with current pharmaceutical practices involving highly purified compounds and, therefore, difficult to patent, as they are complex mixtures of molecules of unknown concentrations to be administered for therapeutic purposes. In addition, mushroom-derived polysaccharides are complex molecules that cannot be synthesized, as the mass production of these compounds would require timely and costly extraction processes. Consequently, most research efforts have focused on low molecular weight compounds, such as cordycepin [72], which is a cytotoxic nucleoside analog inhibitor of cell proliferation. However, polysaccharopeptides isolated from *Coriolus versicolor* are well characterized and their commercial diffusion well established. In addition to its medical applications, *Coriolus versicolor* is widely used to degrade organic pollutants such as pentachlorophenol (PCP) [73]. Notably, as previously mentioned, several studies have demonstrated significant ultrastructural reductions in dendritic innervation densities, at level of cochlear ganglion neurons, pointing the possibility that neurotoxicity plays an important role in the pathology of MD [6]. Interestingly, a recent study in mice has found that *Coriolus versicolor* biomass promotes significant increases in dendritic length and branching and total dendritic volume of immature neurons, suggesting a positive effect of oral *Coriolus versicolor* administration on hippocampal neurogenic reserve [74]. Taking all this into account and given the inflammatory pathogenesis of MD degenerative damage, our findings of reduction in oxidative stress and inflammatory mediators associated with increased anti-inflammatory metabolites in mushroom-treated patients has innovative therapeutic potential.

Moreover, increasing evidence suggests that alteration of redox status, overloading of peroxidative product hydroxynonenals (HNE) or protein carbonyls can severely alter redox homeostasis [1]. Thus, the ensuing oxidative stress is a primary causative factor underlying endolymphatic hydrops pathogenesis, associated with cellular degenerative damage and apoptotic cell death affecting vulnerable cells of cochleovestibular apparatus, and thus contributing to the SNHL and vestibular dysfunction found in later stages of MD.

Moreover, it is known that normal auditory function depends on maintenance of the unique ion composition in the endolymph. Hence, reduction of microvascular alterations due to decreased oxidative stress in the inner ear after mushroom treatment has relevant implications [34]. Our data on the modulation of the stress-responsive protein involved in stress tolerance and cell survival are relevant as a potential target of mushrooms therapeutics and nutritional redox approaches, as the ability of neurons to cope with stressful conditions relies upon the capability to activate stress-responsive pro-survival pathways that normally function at a very low level and that result generally in increased synthesis of antioxidant and anti-apoptotic molecules. Among the cellular pathways conferring protection against oxidative stress, a key role is played by vitagenes, which include HSP (Hsps) Hsp70, heme oxygenase-1, and small Hsps, together with thioredoxin, enzymes of Meister cycle for the synthesis of glutathione and sirtuins [10,24]. Given the broad cytoprotective properties of the heat shock response there is now emerging interest in developing pharmacological agents able to potentiate

neuroprotective stress responses [26]. When appropriately activated, cellular stress response can restore redox equilibrium and neuronal homeostasis.


**2. The Simulation-Decomposition Approach**

SimDec is an analytical approach that was recently introduced to expand the explanatory capabilities of Monte Carlo by exploring inherent cause–effect links between combinations of input variable groupings and their resulting impacts on output variables [24]. While this section reviews the key steps for the decomposition of a simulation, more extensive descriptions can be found in [24–27].

The SimDec procedure constructs sub-distributions of the entire simulation output distribution by partitioning certain input variables into pre-determined states, constructing various multi-variable combinations of these states, and then clustering the simulated outputs using these partition combinations [25,27]. This process enables the construction of both an "overall" output distribution and the simultaneous projection of the decomposed multi-variable input combinations onto this figure [26]. In decomposing an overall output distribution, SimDec simultaneously highlights multi-variable combination impacts using only a single simulation run, which, thereby, circumvents the need to perform individual simulation runs to test each input combination separately. Therefore, SimDec explicitly can be considered an explicit variance reduction approach for evaluating simulated outputs [25]. The visualization from SimDec is subsequently obtained by color-coding each portion of the overall distribution represented by each of the multi-variable partitions [24,26]. Because the projected effect of each subdivided partition can be clearly visualized on the output distribution, SimDec can visually expose previously unrecognized relationships between the multi-variable input partitions and their resulting fundamental consequences on the outputs [26].

The specific algorithmic steps in SimDec are as follows [25,27]:

Step (1) From the complete set of input variables that are to be simulated in the Monte Carlo model, choose a subset of variables that are of interest for more explicit scrutiny.

Step (2) Create relevant states that correspond to different outcomes for each of the variables identified in Step 1 (e.g., good-bad, optimistic-expected-pessimistic, etc.).

Step (3) For each state of each of the variables, construct suitable numerical boundaries that correspond to that variable's possible value ranges. These boundary ranges must be mutually exclusive and collectively exhaustive for the set of states of each variable.

Step (4) Construct a listing of every possible combination of the different variable state partitions. Each combination represents a multi-variable partition of the inputs in the future decomposition.

Step (5) Perform a Monte Carlo simulation. On each simulated iteration, map the randomly generated values of each selected input variable into its corresponding partition state, then map the specific combination of all individual states for the iteration onto the corresponding multi-variable partition combination. Allocate the result of each simulated iteration to the output distribution corresponding to the "complete" simulation, while simultaneously keeping track of the decomposed state combination that produced it.

Step (6) Construct output graphs and/or tables of the simulation outputs. These graphs/tables will portray both the overall summaries of the outputs together with the state decompositions superimposed on top of the global figures.

In summary, the SimDec procedure can be used to break down the regions of the simulation's overall output distribution into a set of distinct partitions [24]. The corresponding stratification enables an effective visualization and assessment of any inherent cause–effect relationships within the simulation results [26]. The determination of which input combinations to use in any given decomposition is at the discretion of the decision-maker. SimDec can be added to any Monte Carlo study with essentially negligible additional computational overhead and can be incorporated independently of the simulation context [25]. In the subsequent sections, SimDec will be employed to analyze the impacts from a simulation model of aviation electrification.


*Experimental Analysis of Waverider Lift-to-Drag Ratio Measurements in Rarefied… DOI: http://dx.doi.org/10.5772/intechopen.100328*

simulating the waverider with an incidence of 10° with conditions similar to those obtained experimentally with a Mach 4–8 Pa flow.

To achieve similarity between numerical and experimental curves, the accomodation coefficients which correspond to the specular reflection fraction and the absorbed fraction at surface are adapted. The sum of both fraction need to be equal to 1 for a consistent simulation. These coefficients are summarized in **Table 8** for each nozzle.

#### **Table 8.**

*Reflection and absorption accomodation parameters.*

**Figure 17.** *Comparison of experimental and DS3V results for Mach 2–8 Pa and Mach 4–8 Pa.*

**Figure 18.** *Comparison of experimental and DS3V results for Mach 4–2.6 Pa and Mach 4–71 Pa.*

For each of the experimental conditions i. e. nozles, the simulation of the flow around the wavereider was performed for the same incidences as those tested experimentally. Comparison between experimental and numerical results are presented on **Figures 17** and **18**. One can observe à good correlation between the numerical and the experimental results. Nevertheless, there are some differences in particular for the case Mach 2–8 Pa and Mach 4–2 Pa wich are the more rarefied conditions and presents small force values. The coefficient of the specular reflexion parameter seems to decrease with the rarefied parameter (Kn, *ψ* ¼ *M*ffiffiffiffiffi *Re* p or Re2). For low altitudes, typically the condition Mach 4–71 Pa, the reflection parameter tends to 1.

## **6. Discussion**

#### **6.1 Influence of rarefaction effects on fligth performance**

The optimal flight conditions are given by the maximum values of the drag-lift ratio. These values will depend on the effects of rarefaction as summarized in

*Experimental Analysis of Waverider Lift-to-Drag Ratio Measurements in Rarefied… DOI: http://dx.doi.org/10.5772/intechopen.100328*

**Table 9** in which are reported the maximum values of the ratio drag-lift, the angle of incidence corresponding for the various conditions of experiment studied in this work. Similarly, for each case, the values of the accommodation coefficient optimized in the framework of the DSMC numerical simulations are reported.

**Figure 19** shows the maximum value of the L/D ratio and the corresponding angle as a function of the Knudsen number. It can be seen that the variation of the optimum angle of incidence increases linearly with the number of Knudsen, while the value of the L/D ratio decreases linearly with the logarithm of the number of Knudsen and this without distinction of the Mach number.

The study of the evolution of the ratio L/D with the rarefaction parameter, shows the influence of the Mach number as illustrated in **Figure 20**. Indeed, both the maximum value of the ratio L/D and the corresponding angle of incidence follow a linear variation for the experimental conditions at Mach 4, while the values for Mach 2 do not follow this trend. Isobar results shows that lower Mach number needs higher angle of incidence to optimize de ratio L/D.

As shown in **Figure 21**, the reflection accommodation coefficient used for the DSMC numerical simulations also follows a linear trend with the Knudsen number and increases towards 1 with decreasing Knudsen number. The same conclusions are made with the DSMC parameter (reflection parameter). However, when the comparison is made with the rarefaction parameter, only the results obtained with the same number of mach follow a linear trend.

In conclusion, for each parameter, the Knudsen number regroup all nozzles on a same trend (linear or logarithmic. It is not the case for the rarefaction parameter but a study isomach seems possible. To valid these conclusions, studies in hypersonic Mach 20 will be realized.

### **6.2 Estimation of the skin friction contribution**

'The different effects of Mach number and geometry optimization on the aerodynamic performance of waveriders have been demonstrated. However, the effects of viscous drag, which have been little studied, can also have an impact on an elementary waverider geometry. For comparison purposes, and to complete our results, we consider the results presented by Rasmussen, carried out with a Mach number of 4 and with a geometry similar to the one used for the present study [48].

The ratio L/D can be expressed as:

$$L/D = \frac{L}{D\_0 + D\_f + D\_b} \tag{5}$$

where L is the lift force, *D*0 is the invicid wave drag, *Df* is the friction drag and *Db* is the base drag. In the following we assume that the base pressure is equal to the freestream pressure so that the base drag can be negleted [29]. The friction drag can be written as follows:

$$D\_f = q \, \mathbb{S}\_w \, \mathbf{C}\_f \tag{6}$$

**Table 9.** *Reflection and absorption parameters.*

#### **Figure 19.**

*Value of maximum L/D ratio and value of the corresponding angle of incidence as a function of the Knudsen number.*

where q is the dynamic pressure, *Sw* is the wetted area of the waverider and *Cf* is the friction coefficient.

Friction effets are related to the development of the boundary layer, that can be influenced by many factors. The friction coefficient may depend of such factors as the Mach and Reynolds numbers, the wall temperature, and in continuum regime others physical properties such turbulence and flow

*Experimental Analysis of Waverider Lift-to-Drag Ratio Measurements in Rarefied… DOI: http://dx.doi.org/10.5772/intechopen.100328*

#### **Figure 20.**

*Value of maximum L/D ratio and value of the corresponding angle of incidence as a function of rarefaction parameter value.*

separation. This means that the definition of the friction coefficient can be a complex function that strongly depends on the flow properties and the objet model geometrie. For the current study, the waverider geometrie can be

**Figure 21.**

*Evolution of the DS3V reflection parameter as a function of the Knudsen number and the rarefaction parameter.*

assimilated to a sharp plate, without the formation of a bow shock at the leading edge. Under this assumption, the skin friction can be defined by the following equation:

*Experimental Analysis of Waverider Lift-to-Drag Ratio Measurements in Rarefied… DOI: http://dx.doi.org/10.5772/intechopen.100328*

$$C\_f = \frac{1.328f(M, T\_w/T\_\infty, Re)}{\sqrt{\frac{\rho\_\infty V\_\infty l}{\mu\_\infty}}} \tag{7}$$

Where *f M*ð Þ , *Tw=T*∞, *Re* is a function depending on Mach number, wall temperature and Reynolds number. For simplicity this function value can be assumed to be equal to 1 for *Tw=T*∞ ¼ 1, wich is our case. For the present study, the subscribe inf corresponds to the values of the free stream noted with the subscribe 1 in **Tables 1**–**4** presenting our experimental conditions.

**Table 10** summarizes values of the friction coefficient for the experimental conditions presented by Rasmussen and those of the present experimental work as well as the maximum value of L/D ratio and the corresponding incidence angle of

#### **Table 10.**

*Sumarize of the parameters for the optimum L/D ratio corresponding to the experimental conditions of this work and those predicted by Rasmussen.*

**Figure 22.** *Evolution of the maximum value of L/D as a function of the volume ratio.*

the waverider. The value *V*2*=*3 *=*ð Þ *S cos* Θ , corresponds to the volume ratio wich is a function of the incidence angle Θ.

**Figure 22** plots the Rasmussen data for the Mach 4 case and our experimental resuls which presents the linear evolution of the maximum L/D value with the

**Figure 23.** *Evolution of the volume angle as a function of the friction coefficient.*

**Figure 24.** *Evolution of the maximum value of L/D as a function of the friction coefficient.*

*Experimental Analysis of Waverider Lift-to-Drag Ratio Measurements in Rarefied… DOI: http://dx.doi.org/10.5772/intechopen.100328*

volume ratio. These results confirm the increase of the L/D maximum value as approaching continuous regime, the Rasmussen conditions presents lower friction coefficient values compared to those of our experimental conditions.

Moreover the evolution of the volume ratio with the friction coefficient presented on **Figure 23** seems to show that there is a limite value for volume ratio as rarefaction effects increases, showing that there is also a limite for the angle of attack to optimize the L/D ratio at high altitudes for a given geometrie. As presented in **Figure 24** the maximum L/D value decreases drastically with the increase of the friction coefficient which reflects the increase of the viscous effects.


**Advanced Materials for Electrochemical Energy Conversion and Storage Devices**

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**2.3 Dynamic mode decomposition**

In fluid flow analysis studies, generally, computationally expensive Global stability analysis method where classical approaches are used, is performed. Proper Orthogonal Decomposition (POD) method based on snapshots of flow and achieving the most active modes is used in these methods. DMD approach based on matrix decomposition has been proffered as a solution to computationally cost of these previous approaches. Systems are analyzed in space using the DMD method in which temporal orthogonality is used. However, using the POD method utilizing spatial orthogonality, systems could be analyzed in time [30]. The behavior of nonlinear and dynamic systems such as biological signals cannot be completely revealed by classical time-frequency analysis methods. By evaluating the measurements collected over a certain period of time with the DMD method, both the system can be expressed with a function, and information about the future behavior of the system can be predicted. The basic idea of the DMD method is to obtain the dynamic modes that best represent the system by achieving the eigenvalues and eigenvectors of the system that linearized with the Least-Squares Approximation (LSA) method [31, 34].

In literature, previously, *K* � *T*� sized multi-channel EEG signals are evaluated using the DMD approach. Here, T is the sample size of a single EEG channel, and N is the number of channels. Using this data matrix, *K* � *L*� sized *X* data matrices in which L denotes the time samples named "snapshot" is obtained, and the DMD algorithm is applied to this obtained data matrices [31]. In our study, both the multi-channel DMD approach used in the literature is performed and the singlechannel DMD approach is proposed, unlike the literature, and *K* � *L*� sized *X* data matrices are constructed using this two different approaches.

In the **single-channel DMD approach (SC-DMD)**, the single-channel EEG signals with *T*� samples long are divided into non-overlapping, *L* samples long EEG segments. The ð Þ *K* � *L* EEG data matrices are constructed using *K* of these obtained segments. For our epileptic seizure classification experiment, *L* ¼ 140 and *K* ¼ 5 are chosen.

Additionally, in the **multi-channel DMD approach (MC-DMD)**, ð Þ *K* � *L* EEG data matrices with no overlap are generated using *L* ¼ 140 samples of *K* ¼ 5 different EEG channels. In our experiment, these data matrices are obtained using the *K* ¼ 5�EEG channel in the left hemisphere (Fp1-F7, F7-T1, T1-T3, T3-T5, Fp1- F3) and the *K* ¼ 5�EEG channel in the right hemisphere (Fp2-F8, F8-T2, T2-T4, T4-T6, Fp2-F4). Also 10 ð Þ � 120 EEG data matrices are constructed using the *K* ¼ 10�EEG channel with *L* ¼ 120 sample long in both hemispheres.

In order to achieve a sufficient number of modes to demonstrate the dynamics of neurological activity efficiently, the number of ð Þ *K* measurements must be at least twice the number of *L* time points named snapshots [16]. Therefore, the data augmentation process is applied to the data matrix *X* based on the Hankel matrix creation principle as detailed in [34] and the *N* � *M*,ð Þ *N* ≥2*M* dimensional augmented data matrix *Xa* is obtained.

*Epilepsy - Update on Classification, Etiologies, Instrumental Diagnosis and Treatment*

$$X\_a = \begin{bmatrix} \vdots & \vdots & \dots & \vdots \\ \infty\_1 & \infty\_2 & \dots & \infty\_{M-1} \\ \vdots & \vdots & \dots & \vdots \end{bmatrix} \qquad X'\_a = \begin{bmatrix} \vdots & \vdots & \dots & \vdots \\ \infty\_2 & \infty\_3 & \dots & \infty\_M \\ \vdots & \vdots & \dots & \vdots \end{bmatrix} \tag{4}$$

$$X'\_a = A X\_a \tag{5}$$

Transition matrix A that denoted in Eq. (5) should be obtained to achieve relation based on the high-dimensional linear regression between *Xa* matrix and its time-shifted version *X*0 *a* matrix (given in Eq. (4)). This transition matrix can be calculated using the pseudo-inverse of the *Xa* matrix *A* ¼ *X*0 *aX*þ *a* � �, but for higherdimensional data such as biosignal, this can cause computational complexity. Using the DMD algorithm;

Singular value decomposition (SVD) of augmented data matrix *Xa* ¼ *U*Σ*V* ∗ is calculated, and formulation of transition matrix rewrite again using the Left singular vectors *U*, the inverse of the singular values Σ�1 , and the Right singular vectors *V A* ¼ *X*0 *aX*þ *a* ¼ *X*0 *aV*Σ�1 *U* ∗ . The low-rank approximation value *A*~ of the transition matrix *A* can be obtained using Eq. (6)

$$
\tilde{A} = U^\* X\_a' V \Sigma^{-1} \tag{6}
$$

The Eigen decomposition of *A*~ matrix is calculated (*AW*~ ¼ *W*Ω) and the matrix of eigenvectors *W*, the diagonal matrix Ω of eigenvalues are achieved. Finally, DMD modes of augmented data matrix *Xa* are calculated using Eq. (7) where each column of *ϕ* includes the DMD mode *ϕm* related to eigenvalues *λm* [31, 34].

$$
\phi = X\_a' V \Sigma^{-1} W \tag{7}
$$

In our DMD based epileptic seizure classification experiment, using the DMD spectrum, various features based on DMD subband powers and Higher-order DMD spectral moments (DMD-HOS) are calculated and classification performances of approaches are compared.

The real part, of DMD modes associated with the complex eigenvalues *λm*, indicates the decay frequency of the dynamic modes, while the imaginary part of these modes shows the oscillation frequencies of the dynamic modes. To obtain the DMD spectrum of pre-seizure and seizure EEG segments, oscillation frequencies, and powers, of the dynamic modes, should be calculated. The oscillation frequencies *f m* (*Hz*) are calculated using Δ*t* ¼ 0*:*01*s* time difference between sequential snapshots, and the complex eigenvalues *λm* of DMD modes; *f m* ¼ ∣*imag ωm* 2*π* � �∣, *ωm* ¼ *log* ð Þ *λm* Δ*t* (the imaginary part of a complex number is calculated using *imag*ð Þ*:* operation). The frequency set *FDMD* ¼ *f m* � � is obtained by aligning the oscillation frequencies containing different mode frequencies. Additionally, power *Pm* ¼ k k *ϕm* 2 of these modes are calculated using the Euclidian norm [34]. The total DMD mode power *f m* � �∈*FDMD* (given in Eq. (8)) for the *f m* frequency is calculated by summing the power value of *Lk* DMD modes at the *f m* frequency. This process is repeated for all frequencies in the *FDMD* set and a single DMD power corresponding to each frequency is calculated. In order to obtain the **DMD spectrum**, the obtained DMD power set *PDMD*, ∀ *PDMD f m* � � � � ∈*PDMD* is plotted according to the oscillation frequency set *FDMD*.

$$P\_{\text{DMD}}\left(\boldsymbol{f}\_{m}\right) = \sum\_{i=1}^{L\_{k}} P\_{m}^{i}\left(\boldsymbol{f}\_{m}\right) \qquad \forall \left\{\boldsymbol{f}\_{m}\right\} \in F\_{\text{DMD}}.\tag{8}$$

*Epileptic EEG Classification by Using Advanced Signal Decomposition Methods DOI: http://dx.doi.org/10.5772/intechopen.93810*

To reveal the advantages of the DMD approach, the traditional Power Spectral Density is estimated using the Welch method [5, 35] where the Hamming window and 50% overlapping are chosen, for each seizure, and pre-seizure EEG segments (140 samples long = 1.4 sec). Examples of the proposed Single-Channel EEG based DMD spectra and traditional Welch PSD estimates for pre-seizure and seizure epileptic EEG data are demonstrated in **Figure 2**. The similarity between the average PSD values of the 5 EEG segments (shown with bold black lines in **Figure 2(c)** and **(f)**) whose PSDs are calculated separately by the Welch method and the DMD spectrum, given in **Figure 2(b)** and **(e)**, is remarkable.

In DMD based epileptic seizure detection approach, sub-band powers based and DMD-HOS moments based features are introduced using the DMD spectrum. In computer-aided epileptic seizure detection and prediction studies, EEG subband powers of different frequency bands like delta (0–4 Hz), theta (4–8 Hz), alpha (8–12 Hz), beta (12–30 Hz), and gamma (30–60 Hz), and DMD-HOS moments are calculated using conventional Power Spectral Density [17, 40]. Using the estimated DMD spectrum, similar to the classical PSD approach, Delta (*Pδ*), Theta (*Pθ*), Alpha (*Pα*), Beta (*Pβ*), and Gamma (*Pγ*)) **subband powers** are calculated as

$$P\_{sb} = \sum\_{f\_m \in f\_{sb}} P\_{\text{DMD}} \left( f\_m \right), \quad sb = \{ \delta, \theta, a, \beta, \gamma \} \qquad P\_T = \sum\_{f\_m} P\_{\text{DMD}} \left( f\_m \right) \tag{9}$$

We propose another set of features called **DMD-HOS moments** *Mj DMD*, *j* ¼ 1, 2, 3, ⋯ defined by

$$M\_{\rm DMD}^j = \sum\_{f\_m \in F\_{\rm DMD}} (f\_m)^j P\_{\rm DMD}(f\_m), \qquad j = 1, 2, 3, \dots \tag{10}$$

In Eqs. (9) and (10), *fsb* is a subset of oscillation frequencies in *FDMD* ¼ *f m* � � of extracted DMD modes corresponding to sub-band frequencies *f δ*, *f θ*, *f α*, *f β*, *f γ* n o

#### **Figure 2.**

*First 5 DMD modes of 5 pre-seizure EEG segments (a) and its DMD spectrum (b) obtained using Single Channel EEG based dynamic mode decomposition, PSD of these 5 pre-seizure EEG segments together (c); first 5 DMD modes of 5 seizure EEG segments (d) and its DMD spectrum (e) obtained using Single Channel EEG based dynamic mode decomposition, PSD of these 5 seizure EEG segments together (f). Bold black lines denote the average of 5 PSD in (c) and (f).*

of EEG, *PT* denotes the total power of DMD spectrum, and *Mj DMD* indicates the *j th* order DMD spectral moment. In our computations, we extract 6 DMD subband power-based features, and 3 DMD-HOS moments features for each seizure and pre-seizure EEG segment.

#### **2.4 Synchrosqueezing transform**

Synchrosqueezing Transform is a member of TF reassignment methods (RM) family which developed to improve the localization properties of TFRs. In RM methods, using the reassignment process, TF coefficients *X t*ð Þ ,*ω* that computed utilizing classical TF analysis method, are reassigned into the instantaneous frequency (IF) trajectory close to the ideal TFR which have high frequency and time resolution ð Þ *t*,*ω* ↦ ð Þ *τ*0ð Þ *t*, *ω* , *ω*0ð Þ *t*, *ω* . On the other hand, using the squeezing process, this TF coefficients *X t*ð Þ ,*ω* are squeezed into the IF trajectory close to the ideal TFR which have high-resolution in only frequency ð Þ *t*, *ω* ↦ ð Þ *t*, *ω*0ð Þ *t*, *ω* . Although lower TF resolution is achieved using the SST method, signal reconstruction may be performed [29, 36].

SST method based on STFT or CWT can be performed to obtain high-resolution TFRs of signals. Hence, the TF coefficients of the studied signals are obtained by STFT or CWT, and by using these coefficients with the SST approach, high-resolution TFR is obtained.

In the STFT method, the signal is divided into short-time, and usually overlapping segments and the Fourier transforms of these short-term segments are calculated. In our computations, STFT of 1-second EEG segment *x t*ð Þ, are calculated as, *X t*ð Þ¼ ,*ω* Ð ∞ �∞*x*ð Þ*τ w*ð Þ *τ* � *t e*�*jωτdτ* where *w t*ð Þ denotes the used window function. Using the Fourier transforms of analyzed segment *X*ð Þ *ω* and used window function *W*ð Þ *ω* , STFT may be rewritten again as given in Eq. (11).

$$X(t,\omega) = \frac{1}{2\pi} \int\_{-\infty}^{\infty} X(\xi)W(\omega - \xi)e^{j\xi t}d\xi. \tag{11}$$

In the SST approach, computing the derivative of STFT *X t*ð Þ , *ω* according to time, the instantaneous frequency *ω*0ð Þ¼� *t*, *ω j ∂tX t*ð Þ ,*ω X t*ð Þ , *ω* is obtained. By using synchrosqueezing operator Ð ∞ �∞*δ η*ð Þ � *ω*0ð Þ *t* � *ω dω* of SST and IF *ω*0(t, *ω*), SST *T t*ð Þ , *η* with high-resolution is obtained by collecting the STFT coefficients which have the same frequency where they should appear.

$$T(t,\eta) = \int\_{-\infty}^{\infty} X(t,\alpha)\delta(\eta - \alpha\_0(t - \alpha))d\alpha \tag{12}$$

An example TF representations of 1-sec pre-seizure and seizure EEG segments achieved utilizing SST and STFT approaches are shown in **Figure 3**. We observe in **Figures 3(b)**, **(c)**, **(e)** and **(f)** that the SST approach is able to represent pre-seizure and seizure EEG segments better in the TF plane than the STFT method. Although the window size, which is the most important parameter of STFT [19], is chosen to give the best time and frequency resolution, the SST approach provided better TF resolution.

In our SST based epileptic seizure detection study, high-resolution joint TF distributions of pre-seizure and seizure EEG segments are calculated. Two different feature extraction approaches are presented to achieve efficient features from the magnitude square of the SST matrix *S n*ð Þ ,*ωk* :

*Epileptic EEG Classification by Using Advanced Signal Decomposition Methods DOI: http://dx.doi.org/10.5772/intechopen.93810*

a. Log-normalized **higher-order joint TF (HOJ-TF) moments**, <*ni ωj k* > ; *i*, *j* ¼ 1, 2, … [37], <*ni ωj k* > ¼ log P*N*�1 *n*¼0 P*N*�1 *k*¼0 *ni ωj kS n*ð Þ , *ωk* !, *i*, *j* ¼ 1, … (13)

*i*!*j*!

where *N* is the length of the EEG segments, and *ωk* ¼ 2*π N k*, *k* ¼ 0, … , *N* � 1.

b. TFR obtained by SST is used as image and **Gray Level Co-occurrence Matrix (GLCM)** texture descriptors are obtained from this TFR image.

GLCM is a prediction of the joint probability distribution of two neighboring gray-level image pixel pairs with a certain position that consists of distance (*d*) and direction (*θ*) information. The GLCM of this image can be expressed as given in Eq. (14) using image pixel pair position information (Δ ¼ ð Þ *θ*, *d* ).

$$G\_{\Delta}(i, j) \qquad \left(i, j = 0, 1, \ldots, N\_{\mathcal{g}} - 1\right) \tag{14}$$

where, *i* and *j* indicate the intensity values of two pixels, and *Ng* is the number of gray levels in the image [28, 38]. Second-order statistical features such as contrast, correlation, energy, and homogeneity [39] are calculated as features from the GLCM matrix of TF images corresponding to pre-seizure and seizure EEG segments. In order to evaluate the performance of the SST approach, same features are calculated using the magnitude square of STFT, i.e., the spectrogram j j *X t*ð Þ , *ω* 2 , which is a classical TF approach and is also used in the SST algorithm [19]. In our experiments, 3 HOJ-TF moments based features, and 4 GLCM based features are calculated for each pre-seizure and seizure EEG segment using both SST and STFT approaches.

**Figure 3.**

*(a) 1-sec pre-seizure EEG segment, its (b) magnitude SST, and (c) magnitude STFT; (d) 1-sec seizure EEG segment, its (e) magnitude SST, and (f) magnitude STFT.*

#### *2.4.1. Classification and performance evaluation*

In the proposed study, features extracted utilizing the three different approaches are classified using six different classifiers such as SVM, kNN, NB to distinguish seizure and pre-seizure EEG segments.

In SVM, one of the well-known supervised learning algorithms, decision boundaries, called hyper-planes', is determined to categorize data. While there are many possible hyper-planes that may be constructed, it is essential to determine the hyper-plane where the best classification performance is obtained. The optimal hyper-plane is achieved by maximizing the margin, which is the distance between different classes'support vectors. Once the optimum hyper-plane is determined, the data falling on different sides of the hyper-plane are assigned as elements of different classes. While this process used for the only linearly separable datasets, using the kernel functions SVM is performed to distinguish linearly non-separable datasets. In our proposed study, linear kernel function is performed [10, 13].

The basic and efficient machine learning method kNN is one of the most widely used supervised learning approaches. The distance between each sample *x*0 to be classified in the test data and the training data is calculated for all data set which is randomly divided into tests and trains. By determining the k neighbors that have the minimum distance, the most common class among these k neighbors is assigned as the class of this sample. Although there are various distance calculation metrics such as Euclidean, Manhattan, Minkowski, and Hamming, the Euclidean distance metric, which is the most commonly used in the literature, is used in our study. In addition, the value of k is chosen as 10 for the proposed study [39, 40].

The NB classifier is one of the probabilistic classifiers in which the classification is performed according to Bayes' theorem. Membership probabilities *P M*ð Þ *i=x*0 (*Mi* indicates the class, *c* denotes the number of class) to "c" classes of sample *x*0 to be classified are calculated, separately. This sample is assigned as a member of the class in which the highest probability of membership among the "c" class is calculated [39, 40].

To achieve a stable classification accuracy, 10–fold cross-validation is employed in our experiment. Using Accuracy (ACC), and *F*1-score metrics, performance evaluation of proposed methods and utilized classifiers are investigated.

$$\text{ACC} = \frac{\text{TP} + \text{TN}}{\text{TP} + \text{FN} + \text{FP} + \text{TN}}, \quad F\_{\text{Score}} = 2 \ast \frac{\text{PRE} \ast \text{REC}}{\text{PRE} + \text{REC}} \tag{15}$$

where true-positive (TP) is the number of samples of *class*\_1 classified in the same class, and true-negative (TN) denotes the number of samples of *class*\_0 classified in *class*\_0. While false-positive (FP) is the number of samples not in *class*\_1 but classified in *class*\_1, false-negative (FN) indicates the number of samples in *class*\_1 but classified in *class*\_0. Recall and Precision metrics are formulated respectively as, *REC* ¼ *TP TP*þ*FN*, and *PRE* ¼ *TN FP*þ*TN* [18].

#### **3. Experiments and results**

In the following, we give the performance evaluation of seizure and pre-seizure EEG classification by using three different advanced signal representation methods presented in Section 2. The classification process is performed using SVM, kNN, and NB classifiers and compared the performance of each approach and classifier. In the **Tables 1**–**5**, highest classification performances are indicated with boldface numbers for each approach and component.

*Epileptic EEG Classification by Using Advanced Signal Decomposition Methods DOI: http://dx.doi.org/10.5772/intechopen.93810*

#### **Table 1.**

*Performance results (%) of EMD and EEMD based seizure detection approach.*

**Table 2.**

*Performance results (%) for seizure detection using the subband power based feature set of DMD based approach.*

#### **3.1 Results of EMD methods**

In EMD and EEMD based seizure detection approaches, various features in the time-domain, spectral-domain, and non-linear are calculated to separate the seizure and pre-seizure EEG segments. To compare the performances of EMD based approaches, DWT approach is implemented to the pre-seizure and seizure EEG

#### **Table 3.**

*Performance results (%) for seizure detection using the DMD-HOS moment based feature set of DMD based approach.*

#### **Table 4.**

*Performance results (%) for seizure detection using the HOJ-TF moment based feature set of SST and STFT based approaches.*

#### **Table 5.**

*Performance results (%) for seizure detection using the GLCM based feature set of SST and STFT based approaches.*

segments, and same features are calculated from the Approximation Coefficient (AC) and 3 Detail Coefficients (DC) of DWT. Additionally, without using any signal processing approach the same features are extracted from the EEG signals itself.

*Epileptic EEG Classification by Using Advanced Signal Decomposition Methods DOI: http://dx.doi.org/10.5772/intechopen.93810*

The performance evaluation results for different IMF combinations are demonstrated in **Table 1**. In all tables, we indicate the highest classification performance with boldface numbers for each case. In **Table 1**, the components column shows that the features for classifications are calculated by using the corresponding component. For example, the classification results of the features calculated using IMF1 are given in the first row, and the classification results of the features calculated from the EEG signal itself are given in the last row. NB classifier provides the highest classification successes for both EMD (96.88% ACC, 96.77% *F*1-score) and EEMD (97% ACC, 96.91% *F*1-score) approaches by using features calculated from IMF1-IMF3 (the first two IMFs decided by the IMF selection process) of the corresponding approach. While, the maximum (94.56% ACC, 94.43% *F*1-score) classification successes are achieved using the NB classifier for the DWT approach; using the kNN classifier and EEG signals itself, maximum (93.25% ACC, 93.35% *F*1 score) values are obtained.

#### **3.2 Results of DMD methods**

Performance evaluation results of SC-DMD and MC-DMD based and PSD based epileptic seizure detection approaches are summarized in **Tables 2**–**3**. For the SC-DMD and PSD approaches, the classification results of the feature set created by combining the features obtained from the Left Hemisphere (Fp1-F7, F7-T1, T1-T3, T3-T5, Fp1-F3), Right hemisphere (Fp2-F8, F8-T2, T2-T4, T4-T6, Fp2-F4), and both hemisphere (Fp1-F7, F7-T1, T1-T3, T3-T5, Fp1-F3, Fp2-F8, F8-T2, T2-T4, T4- T6, Fp2-F4) channels separately are denoted with "Left Hems", "Right Hems "and "Two Hems", while the same components show the classification results of DMD features obtained from the EEG data matrix created using the respective hemisphere channels in the MC-DMD approach.

For all three approaches, the highest classification performance for both the subband based feature set and the moment based feature set is obtained from the Left Hems. While the kNN classifier is yield to highest classification accuracy 94.1% and *F*1-score 95.5% for subband power-based feature set obtained from the Left Hems of SC-DMD approach, the maximum 92.2% ACC and 93.9% *F*1-score values are achieved with the SVM classifier using the moment-based feature set of the SC-DMD approach. On the other hand, in the MC-DMD approach, the classification performances of subband power-based (kNN: 93.9% ACC, 95.5% *F*1-score) and moment-based (SVM: 92.9% ACC, 93.4% *F*1-score) feature sets are close to each other for Left Hems and Two Hems. Additionally, using the PSD approach, a maximum of 92.2%, and 92.5% classification accuracies are achieved using the kNN and SVM classifiers for the subband power-based and moment-based feature sets of Left Hems, respectively. The results show that both SC-DMD and MC-DMD approaches are more successful than the classical PSD approach.

#### **3.3 Results of SST and STFT methods**

Performance evaluation results of the SST based approach are given in **Tables 4** and **5**. Analyzes for SST and STFT approaches are carried out separately for each channel. The classification result of the feature set created by combining the features obtained from the left hemisphere channels is given with the "Left Hems" component. Similarly, while the classification result of the feature set obtained for the right hemisphere is given with "Right Hems", the classification result of the feature set created by combining the features obtained from all channels is given with the "Two Hems" component.

Classification performance of HOJ-TF based feature set is higher than that of GLCM based feature set for each component of SST and STFT approaches. In both approaches, the classification success of both the HOJ-TF moment based feature set and the GLCM based feature set is higher in Left Hems than in Right Hems. While the highest 93.1% ACC and 94.6% *F*1-score are provided with SVM classifier by using the HOJ-TF moment-based feature set for Left Hems of SST, the maximum 92.6% ACC and 94.2% *F*1-score are obtained with the kNN classifier using the GLCM based feature set. On the other hand, in the STFT approach, 92.1% ACC and 93.8% *F*1-score values are achieved with the SVM using the HOJ-TF moment-based feature set, while the classification performance of GLCM based feature set is 90.4% ACC, and 92.4% *F*1-score for kNN classifier.

*F*1-scores obtained by the proposed methods, and by the classical approaches are calculated for comparison and given in **Figure 4**. The *F*1-scores of the proposed EMD and EEMD-based approaches, in **Figure 4a**, are higher than those of DWT and EEG-based approaches, except for the kNN classifier. In the DMD-based seizure detection approach, higher *F*1-score values are obtained in all classifiers than that of the traditional PSD approach for the subband power-based feature set, while the DMD approach provided higher *F*1-score values in the moment-based feature set, except for the NB classifier, shown in **Figure 4b**. Finally, in the SST-based epileptic seizure detection approach, higher *F*1-score values are obtained for each feature set and classifier compared to the STFT approach as shown in **Figure 4c**.

Channel-based classification performances of the proposed SC-DMD, SST, EMD, and EEMD approaches are given with a topographic maps in **Figure 5**. The topographic map is created by averaging the ACC values obtained with all classifiers for each method. It was stated by the expert neurologists that epileptic attacks in the used data set are left hemisphere-focused. It is noteworthy that the channel-based classification success of the EEG-based seizure detection approach (shown in **Figure 5a**) is very low, while is very high for the EEMD-based seizure detection approach (given in **Figure 5c**). It is also remarkable that in all proposed methods, the channels in the left hemisphere yielded successful results of seizure detection (given in **Figure 5b**–**5e**).

#### **Figure 4.**

*Changing of F*1*-score values of (a) EMD and EEMD based, (b) DMD based, and (c) SST and STFT based epileptic seizure detection approaches.*

*Epileptic EEG Classification by Using Advanced Signal Decomposition Methods DOI: http://dx.doi.org/10.5772/intechopen.93810*

**Figure 5.**

*Topographic map of channel based classification accuracies of (a) EEG based (b) EMD based (c) EEMD based (d) SC-DMD based, and (e) SST based approaches.*