*6.3. Time-Dependent Seismic Fragilities of Aged Bridge System*

The joint impacts of the multi-deterioration of multiple components on system vulnerabilities are quantified by developing time-dependent fragility curves of the overall bridge. Figure 15 shows the aging bridge system fragility curves at three different points in time (e.g., 0, 25 and 50 years) for moderate and complete states. It can be clearly seen that the seismic fragility curves at the system level increased steadily with age from 0 to 50 years. However, the seismic fragility of the individual components tended to show a reduction in vulnerability when the bridge component continued to be corroded due to the individual consideration of multi-deterioration for a single component. Furthermore, the seismic fragility of the bridge expansion bearing along the transverse direction can decrease at the initial time (e.g., 0, 15 and 25 years) due to the added stiffness of the bearing NR pads induced by thermal oxidation. The results indicated the importance of considering the joint

effects of multi-deterioration mechanisms for multiple bridge components. Furthermore, it was found that the multi-deterioration of the aging MSC concrete girder bridge had a potentially negative influence on the overall seismic fragility at the system level. ing the joint effects of multi-deterioration mechanisms for multiple bridge components. Furthermore, it was found that the multi-deterioration of the aging MSC concrete girder bridge had a potentially negative influence on the overall seismic fragility at the system level.

*Materials* **2022**, *15*, x FOR PEER REVIEW 19 of 24

**Bridge Slight Moderate Extensive Complete Component Med. Disp. Med. Disp. Med. Disp. Med. Disp.**  RC columns 1.29 0.59 2.10 0.51 3.52 0.64 5.24 0.65 Fixed bearing—longitudinal 28.9 0.60 104.2 0.55 136.1 0.59 186.6 0.65 Fixed bearing—transverse 28.8 0.79 90.9 0.68 142.2 0.73 195.0 0.66 Expansion bearing—longitudinal 28.9 0.60 104.2 0.55 136.1 0.59 186.6 0.65 Expansion bearing—transverse 28.8 0.79 90.9 0.68 142.2 0.73 195.0 0.66

[47,48]. The JPSDMs can be written as Equation (48), where

*6.3. Time-Dependent Seismic Fragilities of Aged Bridge System*

calculated by using Monte Carlo analysis.

**Table 6.** Capacity limit state for different bridge components for an MSC concrete girder bridge.

The assessment of bridge system vulnerability is performed by assuming the bridge as a series system, as presented by Nielson [47,48]. The demands of the bridge components under seismic loading are considered dependent and then the correlation coefficient between the peak responses can be estimated by constructing a joint probability density function (JPDF) for component demands. The generalized formula for the aged bridge system fragility can be derived using joint probabilistic seismic demand models (JPSDMs)

the median values (in units of g PGA) and logarithmic standard deviations of the system fragility at different points in time, respectively. Solutions to Equation (48) can be directly

The joint impacts of the multi-deterioration of multiple components on system vulnerabilities are quantified by developing time-dependent fragility curves of the overall bridge. Figure 15 shows the aging bridge system fragility curves at three different points in time (e.g., 0, 25 and 50 years) for moderate and complete states. It can be clearly seen that the seismic fragility curves at the system level increased steadily with age from 0 to 50 years. However, the seismic fragility of the individual components tended to show a reduction in vulnerability when the bridge component continued to be corroded due to the individual consideration of multi-deterioration for a single component. Furthermore, the seismic fragility of the bridge expansion bearing along the transverse direction can decrease at the initial time (e.g., 0, 15 and 25 years) due to the added stiffness of the bearing NR pads induced by thermal oxidation. The results indicated the importance of consider-

γ

*sys* ( )*t* and

ζ

*sys* ( )*t* are

**Figure 15.** Time-dependent system seismic fragility curves for an MSC concrete girder bridge for (**a**) a moderate damage state and (**b**) a complete damage state under multi-deterioration of multiple components. **Figure 15.** Time-dependent system seismic fragility curves for an MSC concrete girder bridge for (**a**) a moderate damage state and (**b**) a complete damage state under multi-deterioration of multiple components.

#### *6.4. Time-Dependent Seismic Fragilities Considering Prestress Losses and Cracking*

A reference model for the corrosion-induced presetress loss was developed [20,21] by considering the effects of concrete cracking. Corrosion-induced prestress loss can be modeled as the difference between the effective prestress in an uncorroded strand and that in the corroded strand [49]. Here, it was suggested that the strain compatibility and force equilibrium equations in concrete bridge-girders could also be used to evaluate the effective prestress in the corroded strand. If the pre-stressing force in the pre-tensioned concrete bridge-girders is released, then the strand pre-stress would transfer to the concrete via the bonding stress at the stand-concrete interface. Then, the effective prestress in the corroded strand can be calculated using Equation (49) [49], where *Tp* represents the tension force of the corroded strand and *Ap*(*η*) denotes the residual cross-sectional area of the corroded strand.

During the corrosion process, RC components of bridges also suffer from the prestress and the expansive pressure. When the tensile stress induced by the expansive pressure exceeds the concrete tensile strength, the concrete is considered to be cracking. The concrete cover can contain a cracked inner region and an uncracked outer region. Here, the outer wires can be considered to be first corroded when the strand suffers from corrosion. The corrosion loss of a strand can be expressed as Equation (50) [50], where *R*0 and *Rρ* are the radiuses of wire before and after corrosion, respectively, and *Ap* is the strand crosssectional area. Meanwhile, it is assumed that the smeared cracks in the cracked region are distributed uniformly, and then a reduction factor can be used to reflect the residual tangential stiffness in the cracked concrete. Consequently, by combining stress equilibrium equations with the strain compatibilities, the crack width on the concrete surface can be written as Equation (51) [50], where *Rt* is the radius of wire with corrosion products; *Rc* = *R*0 + *C*, where *C* is the concrete cover; *νc* = √ *ν*1*ν*2, where *ν*1 and *ν*2 are the Poisson ratios of concrete in the radial and tangential directions, respectively; *a* is a reduction factor; *ft* is the concrete tensile strength under the biaxial stress state; and *Ec* is the elastic modulus of concrete.

Subsequently, the combined effects of the prestress losses and cracking on the seismic fragilities of bridge systems can be quantified by using Equation (48), which also includes the effects of the multi-deterioration of multiple components. Figure 16 shows the aging bridge system fragility curves at three different points in time (e.g., 0, 25 and 50 years) for moderate and complete states. It can be derived from Figures 15 and 16 that the system fragility when considering the combined effects of prestress losses and cracking was more conservative than that without considering these effects. The results indicated

that the combined effects of the prestress losses and cracking should not be neglected when performing the seismic fragility of aging bridge systems. *Materials* **2022**, *15*, x FOR PEER REVIEW 21 of 24

Finally, it is stressed that other time-variant approaches, such as the empirical exper-

1. Deals with multi-deterioration mechanisms among multiple compo-

iment and trial-and-error [51–53], for the corrosion process of aging bridge systems are very expensive and very unrealistic when it comes to obtaining a series of multi-deterioration mechanisms among multiple components of aging bridge systems. Moreover, the empirical experiment and trial-and-error method are very resource-consuming when dealing with the time-dependent system fragility of such complex aging bridges when undergoing the earthquake excitation test. Therefore, when we would like to efficiently develop the overall time-variant deterioration process of aging bridge systems, the finite element modeling combined with the theoretical modeling of the corrosion process is the best choice for performing the time-dependent overall seismic fragility curves of aging bridge systems. The applicability of different approaches can be summarized in Table 7. **Table 7.** Applicability of different approaches. **Different Approaches Applicability**  Finally, it is stressed that other time-variant approaches, such as the empirical experiment and trial-and-error [51–53], for the corrosion process of aging bridge systems are very expensive and very unrealistic when it comes to obtaining a series of multi-deterioration mechanisms among multiple components of aging bridge systems. Moreover, the empirical experiment and trial-and-error method are very resource-consuming when dealing with the time-dependent system fragility of such complex aging bridges when undergoing the earthquake excitation test. Therefore, when we would like to efficiently develop the overall time-variant deterioration process of aging bridge systems, the finite element modeling combined with the theoretical modeling of the corrosion process is the best choice for performing the time-dependent overall seismic fragility curves of aging bridge systems. The applicability of different approaches can be summarized in Table 7.

nents (e.g., RC columns, bearing systems); **Table 7.** Applicability of different approaches.

## **7. Conclusions**

This paper provides a probabilistic method for identifying the time-dependent fragility of an aging bridge system under earthquake events by considering the impacts of multideterioration of multiple bridge components, as well as the combined effects of the prestress

losses and cracking. A typical MSC concrete girder bridge is used to evaluate the seismic performance by considering the uncertainty models in structural material and corrosion parameters. Chlorine corrosion from deicing salts, which are widely utilized across northern China, can be considered the cause of the degradation and aging of bridge systems. Here, the multi-deterioration mechanisms include the corrosion deterioration of an RC column due to loss of both the steel area (i.e., longitudinal bars, stirrups) and concrete covers, and the deterioration of elastomeric bearing assemblies due to the reduction in both the shear stiffness of bearing NR pads and steel dowel area. The multi-deterioration mechanisms of RC components of the bridge systems affect the lateral force resistance and seismic responses. In addition, the models for corrosion-induced prestress loss and cracking are introduced to develop time-dependent seismic fragilities of bridge systems. The overall seismic demands found using PSDMs showed a steady increase as the growing service life when joint effects of multi-deterioration of bridge multiple components (e.g., RC columns and fixed bearings) were considered. However, there was a decrease in the demand (e.g., bearing deformation) on other multiple components (e.g., RC columns and expansion transverse bearings).

Time-variant PSDMs and the components' capacities were constructed for calculating the seismic fragility of the MSC concrete bridges, which considered the variability in attributes of bridges, ground motion and degraded parameters. The seismic fragility curves at the system level demonstrated a steady increase over time due to corrosion aging. However, individual components, such as expansion bearings in the transverse direction, revealed a decreased vulnerability at the initial time due to the added bearing pad shear stiffness. Subsequently, the dominant effect of the loss of steel dowel areas led to an increase in vulnerability. Moreover, the system seismic fragility considering the combined effects of prestress losses and cracking was more conservative. That meant the effects of both prestress losses and cracking should not be ignored when investigating the seismic fragility of the aging bridge systems. All these system fragility curves presented a more authentic estimation of the seismic vulnerability of aging bridges, and they offered a more accurate basis for life-cycle cost analysis.

**Author Contributions:** Data curation, W.Z.; Funding acquisition, X.L.; Investigation, P.S. and M.L.; Resources, P.S.; Visualization, W.Z.; Writing—original draft, X.L.; Writing—review & editing, M.L. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by National Natural Science Foundation of China, grant numbers 51801149 and 11802224.

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

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** No data were used to support this study.

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

#### **References**

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www.mdpi.com ISBN 978-3-0365-7366-3


**5. Retargeting Strategies**

Here, a range of retargeting strategies is discussed, and both CRAds and oncolytic virus results are considered in this section together. This is due to the abilities of the targeting strategies to be applied in either context.


**Qing Liu**

Qing Liu is a Professor at the University of Science and Technology Beijing. His research interests include the fine control of the solidification process in continuous casting, metallurgical process engineering, simulation and optimization of metallurgical process, and highly efficient utilization of metallic resources. He has published around 200 peer-reviewed papers.


**2. The first step of the analysis: simplification and complexification cycles**

Considering the network to be a universally diffused model structure, we examine the main typologies of macro structures that make more evidently the form of governance (**Figure 2**).

In a basic evolutionary model, network macro structures span from the largest organizations (measured by the number of employed people), structured as *Network Analysis in the Information Systems Management: Implications for a Transdisciplinary… DOI: http://dx.doi.org/10.5772/intechopen.109298*

#### **Figure 1.**

*Components of transdisciplinary model for network analysis.*

autocratic networks, to smaller organizations that can employ as few as a single person managing activities.

Once established, the decentralized network produces an increase in networking among its units and, in the next phase, the emergence of a leader organization, which centralizes some strategic functions dominating the network. This step just precedes the creation of an integrated network, restarting the cycle.

The existence of different network typologies is accepted by organizational theory [16]. The novelty comes from the studies on the motivation for these differences and of their creation.

Starting from these organizational typologies, (**Figure 2**) a hypothesis on evolutionary model of macrostructures takes as an engine of change the continuous simplification or complexification cycle, which leads to the intrinsic quality of the process/ product from one side and an extrinsic quality referred to as the network organization as a whole from the other side [17] (**Figure 3**).

According to the vision of this model, studies on the behavior of systems from the perspective of greater efficiency of performances consider that, when environmental conditions highlight the limits of a greatly integrated and autocratic organization, the drive toward decentralization begins, finding application in the fragmentation of the production process. Its extreme application uses point analysis and a focus on quality because of single actions [18, 19].

#### **Figure 2.**

*Basic structures of network governance/dimensions.*

This process is achieved by reducing the field of attention of analytical theories and methodologies that constitute a single package of phenomena that leads to a decentralized network as part of the simplification cycle [20].

*Network Analysis in the Information Systems Management: Implications for a Transdisciplinary… DOI: http://dx.doi.org/10.5772/intechopen.109298*

With the rationalization of production and its greater repeatability, this process eventually facilitates the transition to the outsourcing of product components in external business units that become increasingly complex. External units result in greater autonomy from the parent company, favoring decentralization. Consequently, the evolutionary process moves toward a participatory network organization with specializations related to outsourcing relations centered on the production supply [21].

This evolution led some of these companies to switch to the production of increasingly complex components, allowing some of them to assume pre-eminent dimensions using positions of competitive advantage. In this phase the attention is focused on the extrinsic quality of the production, referring to the company's overall organization and the local environment from which it draws its culture. This process highlights the cycle of complexification with an expansion of the field of attention, applying synthetic methodologies, such as field analysis, and triggering a process that will again lead to centralized organizations [22].

The idea is to apply this interpretative model to the network, in general, considering that the context of a network is not strictly referred to a business organization but can be extended to a family, a condominium, a neighborhood, a city, a state, or the whole world. Once the network elements have been referred to as coherent, understanding models, the analysis can focus on the links between elements [3].


*<IP_ADDRESS> Length of treatment with benzodiazepines*

Due to the possible occurrence of dependence and abstinence syndrome, the duration of therapy with benzodiazepines should be short, for several weeks. However, because of the chronic character of the disease, sometimes they should be administered for several months, even for a year with continuous monitoring of the patient [47].


**5. Conclusions**

Hesperidin (HSD) was obtained from citrus peels through a pH-triggered precipitation method conducted just in water. The extracted hesperidin purity and yield were excellent when compared to standard methods of its extraction and a commercially available compound. HSD showed chelating activity toward bivalent ions and interacted with collagenase. HSD was used for the formulation of a promising anti-ageing face cream. Upon nanonizing, HSD nanoparticles (150 to 400 nm) were employed into up to 12 months stable nanoemulsions, whose applicability was tested in vitro on artificial skin. No nocive e ffects were observed, and the best face cream formulation (cream A2) showed good results in reducing the black circles in the under eye region. Moreover, daily topical applications of hesperidin nanoemulsion have shown a significant skin whitening e ffect, reduction in trans-epidermal water loss, and inhibition of an irritation e ffect after exposure to UV rays. This way, a clean cream active ingredient is proposed, and a promising cosmeceutical was formulated starting from agro-industrial waste.

**Supplementary Materials:** The following are available online, Figure S1. Steps of hesperidin water extraction: (a) squeezing orange peel, alkaline medium solution; (b) acidic solution and first precipitate of hesperidin; (c) precipitated hesperidin after 7 days at 4 ◦C; (d) filtration of precipitated hesperidin; (e) dried yellow powder of hesperidin. Figure S2. HSQC contour plot of hesperidin (20 mg mL−1) in DMSO-d*6* (2.50 ppm; 39.50 ppm) as a solvent, on Bruker *AVANCE* III 600 MHz equipment at 25 ◦C. Figure S3. HMBC contour plot of hesperidin (20 mg mL−1) in DMSO-d*6* (2.50 ppm; 39.50 ppm) as a solvent, on Bruker *AVANCE* III 600 MHz equipment at 25 ◦C. Figure S4. Chromatogram obtained from injection of the extracted hesperidin sample by separation through ultra-high-performance liquid chromatography (UHPLC) with reverse phase C18; the peak with the retention time at 6.877 min corresponds to hesperidin. Figure S5. Fluorescence suppression - quenching e ffect of hesperidin solution in DMSO (concentration from 0.00 to 5.09 mmol L−1) on collagenase (*Clostridium histolyticum*, Sigma-Aldrich) at 37 ◦C. Figure S6. Fluorescence suppression—quenching e ffect of hesperidin solution in DMSO (concentration from 0.00 to 5.22 mmol L−1) on collagenase (Clostridium histolyticum, Sigma-Aldrich) at 30 ◦C.

**Author Contributions:** Conceptualization, D.S. and L.T.; methodology, D.S., R.V.d.S., A.F.C., L.H.B.L.; formal analysis, D.S., R.V.d.S., A.F.C. and L.H.B.L.; investigation, D.S.; resources, L.T.; data curation, D.S., N.D. and L.T.; writing—original draft preparation, D.S.; writing—review and editing, D.S., N.D. and L.T.; supervision, L.T. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received funding from CAPES (code 01), CNPq (Grant number: 140837/2015-3), FUNCAMP-CITROSUCO (Grant Number 5417).

**Acknowledgments:** Authors acknowledge the Laboratory of Biology of the Skin, coordinated by Silvya Stuchi Maria-Engler, Faculty of Pharmaceutical Sciences, University of Sao Paulo for the artificial skin tests performed.

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


**3. Results**

Of 107 trauma patients undergoing general emergency noncardiac surgery, 12 patients were excluded from the study after application of the exclusion criteria. The remaining 95 patients were assigned using the permuted block randomization design in a 1:1 ratio to the standard monitoring group (SMG) or to the entropy-SPI standard monitoring group (ESMG). Of these patients, 11 and 10 subjects, respectively, were excluded from data analysis either because they remained intubated at the end of the procedure or because the length of the procedure was less than 2 h (Figure 1).

**Figure 1.** Data collection flowchart.

Patient characteristics were similar in both groups (SMG, ESMG; Table 1), and no significant difference was found in the preoperative data except for the duration of anesthesia. Due to the heterogeneity of trauma patients and the variety of surgical procedures employed, no significant statistical analysis could be performed given the small sample for each group studied. Regarding comorbidities, the most frequently associated pathologies were represented by cardiovascular disease (arterial hypertension, ischemic cardiomyopathy) and obesity.

The total dose of fentanyl administered to patients was lower in the ESM Group than in the SM Group, with a statistically significant difference between the two groups(*p* < 0.0001). Sevoflurane uptake per hour was significantly lower in the study group than in the control group (*p* < 0.0001) (Table 2). Anesthesia length was approximately 17 min shorter in the

entropy and SPI monitored group than in the standard monitored group (132.52 vs. 150.05 min, *p* = 0.0013). The shorter anesthesia length in the ESM group might be a cofounding factor with regard to the anesthetic volatile consumption.

**Table 1.** Patient characteristics.

\* ASA, American Society of Anesthesiologists. \*\* Categorical data were expressed as number and percentage.

**Table 2.** Comparison of entropy and SPI-guided anesthesia in contrast with standard monitoring-guided anesthesia.

Data were analyzed using the Mann–Whitney test.

In regard to intraoperative fluid management, fewer fluids were used for the ESM Group, and statistically significant results between the two groups were found only for crystalloid (*p* = 0.010). As for the noradrenaline dosage, the ESM Group received a smaller dose of vasopressor in comparison to the SM Group (*p* < 0.0001) (Table 2).

Hemodynamic events are listed in Table 3. Intraoperative hypotension was encountered more frequently in the control group (*p* < 0.0001). No statistically significant differences were noted between the two groups regarding the incidence of other hemodynamic disturbances.

**Table 3.** Comparison of entropy and SPI-guided anesthesia in contrast with standard monitoringguided anesthesia regarding adverse intraoperative hemodynamic events.

Nominal data were compared using Fisher's exact test.

#### *Postoperative Delirium and Cognitive Dysfunction*

Although fewer patients in the intervention group experienced postoperative cognitive dysfunctions episodes in comparison to the control group, the results were not statistically significant (*p* = 0.08). The study showed a statistically significant inverse correlation between fentanyl and the NEECHAM Confusion Scale at 24 h (r = −0.32, *p* = 0.0005) and 48 h (r = −0.46, *p* = 0.0002), sevoflurane and the NEECHAM Confusion Scale at 24 h (r = −0.38, *p* = 0.0014) and 48 h (r = −0.52, *p* = 0.0002), and noradrenaline and POCD events in the first 48 h (r = −0.46, *p* = 0.0013 for the first 24 h respectively, and r = −0.46, *p* = 0.0002

for the next 24 h) (Figure 2). There was no statistically significant correlation between fentanyl, sevoflurane, or noradrenaline and POCD at 72 h (Figure 2).

**Figure 2.** Correlation matrix. The table above shows correlations coefficients between the following variables: Fentanyl (μg), sevoflurane (mL/h), noradrenaline (μg/kg/min) and NEECHAM score at 24 h, 48 h, and 72 h. The colorencodes the sign of correlation between each 2 variables: Blue for positive r values and red for negative r values.

> In order to identify how we couldavoid postoperative cognitive dysfunction, we developed a logistic regression model that used a NEECHAM score higher than 24 points (indicating absence of cognitive dysfunction) at 24 h as a dependent variable. A fourpredictor logistic model was fitted to the data to test the research hypothesis regarding the relationship between the use of entropy and the doses of anesthetic drugs and vasopressor with the advent of postoperative cognitive dysfunctions.

> The logistic regression hadan overall model fit described by a nullmodel-2 Log Likelihood of 74.150 and a full model-2 Log Likelihood of 65.311, with a chi-squared value of 8.840 (*p* = 0.06). The goodness of fit of this regression model was calculated with Cox&Snell (R2 = 0.19). According to the model, the log of the odds of a patient to develop POCD was negatively related to the dose of fentanyl, sevoflurane, or noradrenaline and positively related toentropy and SPI monitoring (Table 4).

**Table 4.** Logistic regression analysis of 74 patients for POCD appearance.

## **4. Discussion**

The main finding of this study was that entropy and Surgical Pleth Index-guided anesthesia versus standard monitoring may reduce the incidence of postoperative cognitive dysfunction in the first 72 h for patients undergoing general emergency noncardiac surgery. Also, entropy and SPI may offer a protective role in developing postoperative cognitive dysfunctions. The reported incidence varies greatly in the literature [16,17], especially because neuromonitoring anesthesia has been studied less during emergency noncardiac surgery in comparison to elective surgery.

In our research, we found a substantial reduction in anesthesia duration in the entropy and Surgical PlethIndexmonitored group than in the standard monitored group (132.52 vs. 150.05 min, *p* = 0.0013). The shorter anesthesia length in the ESM Group might be a confounding factor with regard to the anesthetic volatile consumption. In our study, we observed significantly lower sevoflurane doses in the ESM Group. Previous studies demonstrated that neuromonitoring may lead to a less 'roller-coaster'-like anesthesia [18] and less fluctuation from a defined target than the clinical estimation of anesthetic depth only [19]. Hor et al. conducted a randomized controlled trial in order to assess sevoflurane uptake in patients undergoing major surgery andfounda significant reduction in sevoflurane uptake with the use of entropy, in addition to a faster extubation [20]. Fedorow et al. highlighted that using neuromonitoring in order totitrateanesthetic agents may avoid an unnecessary increase in anesthesialevels and possible neurotoxic effects, especially in high-risk patients [21]. Our data suggest that anesthetic agents may represent a risk factor for developing POCD in the first 48 h. This finding is consistent with previouslypublished studies. According to Micha et al., sevoflurane has a negative influence on short-termcognition [22].

Another pharmacological factor, fentanyl, can be considered a causal factor for the presence of POCD, and we have identified significant dose reduction in the entropy-SPI monitored group in comparison to the standard monitored group. In our study, we identified that fentanyl may represent a risk factor for developing POCD in the first 48 h, but the results cannot be extended topatients who develop POCD in the next 24 h. Although the incidence of cognitive disorders is highly dependent on the type of surgery and general anesthesia management [23,24], opioid treatment remains very influential in POCD occurrence [25].

Emergency surgery is usually closely related to hemodynamic instability. Thus, another favorable trend for the entropy-SPI studied group is represented by fewer hypotensive eventsin the intervention group and by the significantly decreased demand for vasopressor. Intraoperative hypotension was encountered more frequently in the control group (*p* < 0.0001). It is well known that, in addition to uncontrolled anesthetic exposure, another important factor that may increase the risk of developing POCD is represented by blood pressure fluctuation [26,27]. As Wu et al. investigated in a randomized controlled trial, this

may be related to sevoflurane consumption [28]. However, we must keep in mind that, in trauma settings, other important factors may contribute to hemodynamic alteration (type of injury, intravascular volemic status, volemic resuscitation, response to tissue injury, tissue perfusion, etc.) [29]. Our findings highlight that noradrenaline may contribute to cognitive impairment in the first 48 h after surgery. Although vasopressors are a cornerstone for treating refractory hypovolemic shock, they may also exhibit negative side effects with harmful repercussion on cerebral perfusion [30,31].

In our study, the majority of patients experiencedthe following comorbidities: Cardiovascular disease (arterial hypertension, ischemic cardiomyopathy) and obesity. Current data do not support the hypothesis that these comorbidities are potential cofounders for developing postoperative cognitive dysfunctions [32,33].

## **5. Limits**

Although in the intervention group, fewer patients experienced postoperative cognitive dysfunctions episodes in comparison to the control group, the results were not statistically significant (*p* < 0.08). We consider that one of the main drawbacks of the study was the inability to control all ofthe risk factors that contribute to the development cognitive disorders.

Another study limitation is the consequence of not being to further evaluate postoperative cognitive disorders after 72 h because the majority of patients were discharged from ICU. We also considered that, after 72 h, other factors may interfere with cognitive function and mislead POCD screening.

Due to the fact that neuromonitoring anesthesia and nociception have been studied less frequentlyduring emergency noncardiac surgery in comparison to elective surgery, the available papers do not allow us to entirely compare the magnitude of our findings with the previous published data.

The present research included a small number of patients in each group. In order to establish future relevant knowledge for improving patients' cognitive outcome, we con-sider it imperative to recruit a higher number of patients.

## **6. Conclusions**

The present study was designed to reflect routine clinical practice in emergency settings. It is difficult to isolate one perioperative risk factor for POCD in studies even when excluding individual factors. Despite the extensive research conducted in recent years onthe subject, the causes and pathophysiological mechanismsresponsible for postoperative cognitive decline remain unclear. Entropy and SPI monitoring during anesthesia may play an important role in diminishing the risk ofdeveloping immediate postoperative cognitive dysfunctions after emergency surgery. Also, sevoflurane, fentanyl, and noradrenaline may be closely associated with POCD occurrence in the first 48 h. In order to confirm our hypothesis, we considered that our study required a higher number of patientsto be enrolled. Building upon the data found inour research, we suggest monitoring intraoperative anesthetic depth using entropy and nociception through the SurgicalPlethIndex (SPI) in patients with pre-existing cognitive impairment in order to investigate postoperative cognitive dysfunction in future research.

**Author Contributions:** Conceptualization, A.-M.C., C.C., M. ¸T. and I.M.G.; Data curation, A.-M.C., C.C., M. ¸T., A.E.B. and D.M.I.; Formal analysis, A.E.B.; Investigation, A.-M.C., C.C., M. ¸T., A.E.B. and D.M.I.; Methodology, A.-M.C., C.C., M. ¸T. and I.M.G.; Project administration, A.-M.C. and I.M.G.; Resources, C.C. and I.M.G.; Software, A.E.B. and D.M.I.; Supervision, D.M.I. and I.M.G.; Validation, A.-M.C., C.C., M. ¸T. and A.E.B.; Visualization, I.M.G.; Writing—original draft, A.-M.C., C.C., M. ¸T., A.E.B., D.M.I. and I.M.G. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** This prospective randomized study was carried out in the Anaesthesia and Intensive Care Clinic, Clinical Emergency Hospital of Bucharest, between August 2018 and January 2019. All the procedures performed during this study were in accordance with the Dec-laration of Helsinki. The study was approved by the Research Ethical Committee of our hospital (registration number 2100/2021).

**Informed Consent Statement:** All the patients provided written informed consent.

**Data Availability Statement:** No data were reported.

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


**3.3. Constructing simulation models of a family of optoelectronic matrices in WinALT**

#### *3.3.1. Mapping digital schemes onto a customizable cellular automaton*

The cellular automaton with Margolus (further CA) neighborhood [13], in which setting cells for execution of a certain set of elementary transformations of information, serves as a logical basis for the construction of a family of optoelectronic matrices. The CA is a double layer automaton. Its first layer functions in the same way as the Margolus automaton, being a rectangular matrix of cells. Let us split the matrix to blocks of 2x2 cells. Let us call it Epartition. Let us split the matrix again to blocks that are shifted as related to the blocks of Epartition by one cell along the vertical and horizontal axes. Let us call it O-partition. Each cell of the first layer can be in one of the three states: "white", "gray" or "black". Let us call this layer *informational*. The layer under the informational one is called *control* layer. Its Epartition coincides with that of the informational layer. This layer keeps the table of settings the control layer of CA. The size of a cell in the table coincides with that of a block. The CA is shown in figures as a sweep of two layers in a plane. The informational layer is on the left side and the control layer is on the right side. The blocks of E-partition are limited by solid lines. The blocks of O-partition are limited by dashed lines. An elementary transformation of information performed in the informational layer is a parallel substitution. Its left and right

parts are matrices with 2x2 cells. These matrices are composed of white, gray and black cells. The elementary transformations performed in a CA are enumerated. Setting a CA consists in writing numbers of those elementary transformations that can be performed in the block of informational layer above a cell into that cell. Digital (combinatory) schemes of different kinds (adder, multiplier, etc.) can be implemented by setting a CA. A source combinatory scheme is initially transformed in a way that any of its gates has no more than two inputs and two outputs. All the cells of the informational layer are white in its initial state. The picture of a scheme to be imitated in CA, which is made by gray cells in informational layer of CA is called *image* of digital scheme. The signals transformed in a digital scheme are depicted by black cells in its image. The states of cells in each block of the information layer of a CA form a certain picture called *image* of a block.

The graphic images of commands of parallel substitutions are depicted in Figure 5, a. A number of a command is shown above an arrow. The transformations of information in Margolus cellular automata are performed by alternating E- and O-partitions [13]. The alternation of partitions is substituted by alternation of two groups of shifts of the image of simulated scheme as related to the fixed control layer in a CA. A group of shifts set into correspondence with E-partition is called *E-group*. A group of shifts set into correspondence with O-partition is called *O-group*. The introduction of a setting for CA allows reducing the number of parallel substitution commands that are executed by a single block to two. The command, whose number is specified first in a cell of the settings table of the control layer, can be executed when E-group is active, while the command, whose number is listed second, can be executed when O-group is active. A command is executed if its left part coincides with the image of a block in the informational layer. The execution of a command sets its right part as the image of a block.

Possible variants of signal transmission in the image of a digital scheme (horizontal and diagonal transmissions, branching and crossing of signals) and the indications to the functional elements (AND gate is denoted by the sign '&', OR gate is denoted by '1', addition by modulo 2 is denoted by '=1', half-adder" is depicted at end) are shown in Figure 5, b.

When E-group of shifts is active, the commands are executed for the source disposition of the image of a digital scheme, then for the image shifted by one row of blocks from Epartition up as related to the source image, and then one row of blocks down as related to the source image. The shifts are introduced in order to provide the execution of commands imitating the operation of gates and crossing of signals transmission channels in the image of a digital scheme. When O-group of shifts is turned on, commands are executed for the image obtained by shifting the source one by one row down and one column to the left.

The horizontal transmission of a signal is simulated by commands 1, 2. The diagonal transmission is performed by commands 3, 4. The signal branching is done by 5, 6 and signal crossing - by 8, 10, 15. The operation of AND gate is simulated by the two sets of commands: 9, 16, 17 and 12, 16, 17, because the result on the output of the gate can be recorded either in the right top cell or in the right bottom cell. of the block. Similarly, the

simulation of OR gate is done by commands 7, 8, 9 and 10, 11, 12 and the simulation of addition - by modulo two is done by commands 7, 8, 18 and 10, 11, 18. A block of E-partition that does not contain white cells can simulate a gate operation not only with one output, but also with two outputs. Thus, the operation of half-adder is simulated by commands 7, 8, 12. The capability to simulate digital schemes with two inputs and two outputs allows performing both the signal transfer, e.g. by one of the diagonals, and a logical transformation of this signal and another signal. For example, a signal transition from the right bottom cell into the right top cell of a block along with performing AND operation with signals from the left column of cells in the block with writing the result to the right bottom cell of the block is simulated by commands 8, 15, 16.

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of a CA form a certain picture called *image* of a block.

sets its right part as the image of a block.

column to the left.

parts are matrices with 2x2 cells. These matrices are composed of white, gray and black cells. The elementary transformations performed in a CA are enumerated. Setting a CA consists in writing numbers of those elementary transformations that can be performed in the block of informational layer above a cell into that cell. Digital (combinatory) schemes of different kinds (adder, multiplier, etc.) can be implemented by setting a CA. A source combinatory scheme is initially transformed in a way that any of its gates has no more than two inputs and two outputs. All the cells of the informational layer are white in its initial state. The picture of a scheme to be imitated in CA, which is made by gray cells in informational layer of CA is called *image* of digital scheme. The signals transformed in a digital scheme are depicted by black cells in its image. The states of cells in each block of the information layer

The graphic images of commands of parallel substitutions are depicted in Figure 5, a. A number of a command is shown above an arrow. The transformations of information in Margolus cellular automata are performed by alternating E- and O-partitions [13]. The alternation of partitions is substituted by alternation of two groups of shifts of the image of simulated scheme as related to the fixed control layer in a CA. A group of shifts set into correspondence with E-partition is called *E-group*. A group of shifts set into correspondence with O-partition is called *O-group*. The introduction of a setting for CA allows reducing the number of parallel substitution commands that are executed by a single block to two. The command, whose number is specified first in a cell of the settings table of the control layer, can be executed when E-group is active, while the command, whose number is listed second, can be executed when O-group is active. A command is executed if its left part coincides with the image of a block in the informational layer. The execution of a command

Possible variants of signal transmission in the image of a digital scheme (horizontal and diagonal transmissions, branching and crossing of signals) and the indications to the functional elements (AND gate is denoted by the sign '&', OR gate is denoted by '1', addition by modulo 2 is denoted by '=1', half-adder" is depicted at end) are shown in Figure 5, b.

When E-group of shifts is active, the commands are executed for the source disposition of the image of a digital scheme, then for the image shifted by one row of blocks from Epartition up as related to the source image, and then one row of blocks down as related to the source image. The shifts are introduced in order to provide the execution of commands imitating the operation of gates and crossing of signals transmission channels in the image of a digital scheme. When O-group of shifts is turned on, commands are executed for the image obtained by shifting the source one by one row down and one

The horizontal transmission of a signal is simulated by commands 1, 2. The diagonal transmission is performed by commands 3, 4. The signal branching is done by 5, 6 and signal crossing - by 8, 10, 15. The operation of AND gate is simulated by the two sets of commands: 9, 16, 17 and 12, 16, 17, because the result on the output of the gate can be recorded either in the right top cell or in the right bottom cell. of the block. Similarly, the

**Figure 5.** Graphic representation of parallel substitution commands, a - images of commands, b symbols of signals and functional elements

Let us demonstrate an image of a full adder in CA as a simple sample of what was stated above. It is presented in Figure 6.

Let us comment on this figure. The numbers of commands listed in Figure 5, a are used in the settings table. An image of a digital scheme with mnemonic specification of the functions of its composing blocks except those imitating the transfer of signals under Opartition is given in Figure 6, c in addition to the image in Figure 6, a, b. A sign of operation or an arrow in the image of scheme denotes a cell where result of transformation or data transfer is placed. Such a representation is rather easy to grasp and is introduced solely for the purpose of the reader's convenience. This helps in comparing a combinatory scheme and its image without the table of settings.

Usually, the signal transfers will be omitted when using such a kind of representation of a digital scheme unless that hampers the perception of the image of a scheme. Let us describe the resulting image of a digital scheme. Each of blocks (2, 2) and (3, 3) corresponds to a halfadder, which is a composition of AND gates and of addition by modulo two. Blocks (4, 2) correspond to OR gate.

**Figure 6.** Full adder: a - a combinatory scheme, b - an image of scheme, c - a correspondence of blocks, d - the settings table

Some or all of the gray cells in the first column of CA have to be altered to black ones in order to introduce input signals to a full adder.

A more complicated and realistic sample is presented in Figure 7. The following heuristic criteria are selected for the estimation of quality of a particular mapping. A mapping is optimal if there is at least one such chain from the inputs of a scheme to its outputs, that is composed only of blocks that imitate gates connected with other by corner cells. The image of an eight-bit pyramidal adder [17] transformed into a scheme, in which each gate has two inputs and one or two outputs is presented in Figure 7.

**Figure 7.** A pyramidal adder: a - the combinatory scheme of a four-bit adder, b - a concise image of eight-bit adder scheme

The image of a four-bit adder, which scheme is depicted in Figure 7, a, is a source fragment for its construction. The images of four-bit adders are contoured by a bold line in Figure 7, b. The rest of the scheme image provides daisy chaining of the selected images of adders. The image of an adder presented in Figure 8, b meets the heuristic criteria. The proposed way of constructing an image of a digital scheme with a specified bit width by connecting its homogeneous fragments of smaller bit width, for each of which the best image is already found, can be used for other kinds of schemes as well.

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d - the settings table

eight-bit adder scheme

order to introduce input signals to a full adder.

inputs and one or two outputs is presented in Figure 7.

**Figure 6.** Full adder: a - a combinatory scheme, b - an image of scheme, c - a correspondence of blocks,

Some or all of the gray cells in the first column of CA have to be altered to black ones in

A more complicated and realistic sample is presented in Figure 7. The following heuristic criteria are selected for the estimation of quality of a particular mapping. A mapping is optimal if there is at least one such chain from the inputs of a scheme to its outputs, that is composed only of blocks that imitate gates connected with other by corner cells. The image of an eight-bit pyramidal adder [17] transformed into a scheme, in which each gate has two

**Figure 7.** A pyramidal adder: a - the combinatory scheme of a four-bit adder, b - a concise image of

**Figure 8.** A project window of simulation model of CA that implements an eight-bit adder

From a logic standpoint, a fine-grain structure (a micro-pipeline) is implemented by setting a CA up. This structure simulates a simultaneous operation of many copies of the same digital scheme. Each copy (let us call it a virtual digital scheme) performs a transformation of its own data set. A *stage* of a micro-pipeline forms a vertical column of blocks in Epartition of matrix. Each stage is a "cut" of image of a virtual scheme in a certain phase of transformation of the relevant information. This feature of matrix makes possible to obtain new results in each cycle. A cycle of micro-pipeline operation includes transformation and transfer of data from one stage to another. It means that a cycle includes an execution of the both groups of shifts. A model is constructed in WinALT in order to evaluate the correctness of an eight-bit adder implemented as CA.

## *3.3.2. CA simulation model implementing eight-bit adder*

The screenshot of a window of this project is presented in Figure 8. This window contains sheets with all the graphic objects of the model.

The sweep of a double layer cellular array **byte::CellStruct** is presented at sheet **Model.3do**. The upper layer containing the image of an eight-bit adder is presented at the left. The bottom layer is shown at the right. It contains a computer-aided representation of the settings table of an adder. The division of array layers into blocks is done by setting the cells of the bottom layer with both even coordinates into a state dedicated for this purpose. The numbers of substitution commands are represented by color in the settings table. The numbers of commands are distributed by the block cells as follows: the right and left top cells of block keep the numbers of the first and second commands respectively. The rest of cellular arrays shown in this window are auxiliary. Array **inp** keeps a set of input data. The columns of array **inp** are written in each cycle to the leftmost column of the informational layer of array **byte::CellStruct** using the array **c\_in** and become the values of outputs of an adder. Similarly, the results of computations from the very right column of the informational layer of array **byte::CellStruct** are transferred to array **out** that stores the results of pipeline computations. Double layer templates are presented in sheet **Rules.3do**. The templates named **ati** and **doi** are put in correspondence with the left and right sides of substitution command with the number **i**. The upper layer of template **ati** coincides with the left part of the substitution number **i**, while that of template **doi** coincides with the right part of that substitution. The left upper cell of the bottom layer of template **ati** contains number **i** of substitution command. The number is represented by a color. A color of the left bottom cell of the same layer coincides with that of those cells in the bottom layer of array **byte::CellStruct**, which provides its partition into blocks. All the other cells of the both templates are empty (diagonally crossed). The templates used in substitution commands of the procedure imitating clocking of CA are presented in sheet **Shifts.3do**. A cycle of a model execution is divided into the four stages. At each of them parallel substitution commands kept in the settings table are executed:

The operation of gates of a scheme is simulated at the first three stages of cycle. The data transfer between gates is simulated at the fourth stage. The cellular image and the settings table return to the initial ("unshifted") state at the end of a cycle.

Let us briefly present main procedures of simulation program. The description of parallel substitution commands is kept in procedure **mainProc**, while the shifts performed at the each stage of a cycle are defined in procedure **shiftImage**. The body of procedure **mainProc** contains operator **in** with parameter **byte::CellStruct** and eighteen bunches of **at-do**

operators. The parameters of operators **at** and **do** in the i-th bunch are the templates named **ati** and **doi** respectively. The shifts of image of the digital scheme with respect to settings layer and the interleaving of substitution commands is done in procedure **ShiftImage** by vector functional substitutions. Cellular arrays **byte::CellStruct** and **Count** listed in round brackets in the first operator **in** form a composition, which has the following meaning. The changes in array **byte::CellStruct** happen only when the unicellular array **Count** is in a certain state. For example, if the state of **Count** coincides with that of **st2**, the shift of the image of a digital scheme is done by one row of blocks down from its source placement. This shift is performed by the function **fShift** that uses the values of variables **x** and **y** from template **ShiftDown** in its operator **y:=x**. The operators **at-do** in the second operator **in** alter the state of **Count** in order to set phases of cycle.

#### *3.3.3. A transformation of CA into optoelectronic matrix*

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*3.3.2. CA simulation model implementing eight-bit adder*

sheets with all the graphic objects of the model.

kept in the settings table are executed:

even columns are swapped).

above the source image at the first stage;

 above the image shifted two cells up from the source one at the second stage; above the image shifted two cells down from the source one at the third stage;

table return to the initial ("unshifted") state at the end of a cycle.

 above the image shifted one cell down and one cell right from the source at the fourth stage (the command interleaving is done in the settings table during this stage: odd and

The operation of gates of a scheme is simulated at the first three stages of cycle. The data transfer between gates is simulated at the fourth stage. The cellular image and the settings

Let us briefly present main procedures of simulation program. The description of parallel substitution commands is kept in procedure **mainProc**, while the shifts performed at the each stage of a cycle are defined in procedure **shiftImage**. The body of procedure **mainProc** contains operator **in** with parameter **byte::CellStruct** and eighteen bunches of **at-do**

The screenshot of a window of this project is presented in Figure 8. This window contains

The sweep of a double layer cellular array **byte::CellStruct** is presented at sheet **Model.3do**. The upper layer containing the image of an eight-bit adder is presented at the left. The bottom layer is shown at the right. It contains a computer-aided representation of the settings table of an adder. The division of array layers into blocks is done by setting the cells of the bottom layer with both even coordinates into a state dedicated for this purpose. The numbers of substitution commands are represented by color in the settings table. The numbers of commands are distributed by the block cells as follows: the right and left top cells of block keep the numbers of the first and second commands respectively. The rest of cellular arrays shown in this window are auxiliary. Array **inp** keeps a set of input data. The columns of array **inp** are written in each cycle to the leftmost column of the informational layer of array **byte::CellStruct** using the array **c\_in** and become the values of outputs of an adder. Similarly, the results of computations from the very right column of the informational layer of array **byte::CellStruct** are transferred to array **out** that stores the results of pipeline computations. Double layer templates are presented in sheet **Rules.3do**. The templates named **ati** and **doi** are put in correspondence with the left and right sides of substitution command with the number **i**. The upper layer of template **ati** coincides with the left part of the substitution number **i**, while that of template **doi** coincides with the right part of that substitution. The left upper cell of the bottom layer of template **ati** contains number **i** of substitution command. The number is represented by a color. A color of the left bottom cell of the same layer coincides with that of those cells in the bottom layer of array **byte::CellStruct**, which provides its partition into blocks. All the other cells of the both templates are empty (diagonally crossed). The templates used in substitution commands of the procedure imitating clocking of CA are presented in sheet **Shifts.3do**. A cycle of a model execution is divided into the four stages. At each of them parallel substitution commands

Let us list those operations converting optical signals, which are to be carried out in an optoelectronic matrix to implement the above-mentioned CA. The operations have to provide the following for each block of CA: a) a comparison of the image of the left part of a command, whose number is written in the settings table, with the image of block in the image of a scheme, and b) if they coincide, replacement of the image of such block by the image of the right part of a command. Let us demonstrate that an execution of such operations is possible in a four layer matrix (called **S**). The images of left parts of substitution commands are kept in its first layer. The second layer contains the image of a digital scheme. The images of comparison schemes are in the third layer. The images of right parts of substitution commands are in the fourth layer. Matrix **S** is built using the basic gate rather schematically and without details of implementation. All the essential physical elements: modulators, photodetectors, memory cells are considered to have a size equal to one cell. The reasons for that are as follows: 1) matrix **S** built in such way can be easily turned into a data object when it is simulated, 2) the obtained matrix **S** has rather generalized form that makes possible to specify its versatile representations taking into consideration real sizes of its elements later, because these sizes are not known a priori and depend on physical principles of construction of the elements, technology, and the application domain.

The cells of informational layer of CA have three states. But the basic gate is binary. Thus, a transition must be done to binary encoding of the states of matrix **S**. For example, an encoding of white, gray and black cells presented in Figure 9 can be chosen.

**Figure 9.** Binary encoding of CA states

A white cell denotes a memory cell containing one, an opened modulator or an opened photodetector. A black cell denotes a memory cell containing zero, a closed modulator or a closed photodetector.

Let us commence the construction of matrix S using its second layer that contains an image of a digital scheme in a binary encoding. An image of each block in CA informational layer is composed of modulator states. Memory cells control the states of modulators (opened, closed). Assume that each cell has two outputs. Modulators are connected to both of them. Let us consider that each memory cell has two inputs, each of which is connected to a photodetector. Let us also assume that the signals from the inputs of a cell appear at its output with a fixed delay. A line of cells is composed of such elements. The first and second cells are modulators. The third cell is a memory cell. The fourth and fifth cells are photodetectors. A memory cell operates in two phases. If it contains one at the first phase (the phase of comparison), it opens the first modulator and closes the second one. And otherwise, it closes the first modulator and opens the second one. At the second phase (phase of recording) if the fourth photodetector is opened, and the fifth one is closed, one is written to memory cell. Otherwise, memory cell resets to zero.

**Figure 10.** Binary encoding of cell states in the second layer of optoelectronic matrix

An image of the second layer of matrix **S** when it is ready for the phase of comparison is obtained by replacing each cell in the information layer of CA by a group of cells according to the substitution rules in Figure 10. Thus, a block of optoelectronic matrix of size 10 4 cells composed of four lines is put in correspondence to each block of the informational layer of CA.

*Remark*. Gray cells are also used in the transition to binary encoding, but they denote "void", absence of any hardware.

Let us perform a partition into blocks that have the same sizes and placement as in the rest of matrix layers.

Let us construct the first layer of matrix **S**. Unlike lines of cells form the second layer, the cell number four contains a memory cell and the fifth cell is gray. A memory cell is connected to modulators just as the memory cell occupying the third cell. The basis for setup of the first layer is the settings table of the control layer of CA. The setting of layer starts with encoding of its E-partition, i.e. the cells in columns 3 and 8 of the layer are set in such a way that the image formed by the states of modulators would coincide with the left part of that command, whose number is written first in the cell with exactly the same placement in the settings table of CA. The encoding for O-partition is embedded into the encoding of the layer that was just obtained. For this purpose binary codes set into correspondence to white, gray and black cells of the left part of the second command are written into the fourth column just as it is done for the cells of the third column in Figure 10.

The third layer of the matrix is constructed as follows. Black cells of a single block in the columns 1, 2, 6, 7 denote closed photodetectors. Black cells in the columns 4, 5, 9, 10 denote closed modulators. The rest of columns are empty. They are composed of gray cells. Pairs of photodetectors in rows 1, 2 and 3, 4 of the columns 1, 2 and 6, 7 are connected by OR scheme (parallel). Then all the OR schemes formed by pairs of photodetectors are connected sequentially forming AND scheme. A parallel assembly of all modulators of a block is connected as its load. The scheme obtained in the third layer allows to detect the situation when the images of blocks coded by the states of modulators located in the first and second layer one below another coincide, and in the case of full coincidence to prepare a substitution of the image of block of the second layer by the right part of command kept in the fourth layer.

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layer of CA.

of matrix layers.

absence of any hardware.

Let us commence the construction of matrix S using its second layer that contains an image of a digital scheme in a binary encoding. An image of each block in CA informational layer is composed of modulator states. Memory cells control the states of modulators (opened, closed). Assume that each cell has two outputs. Modulators are connected to both of them. Let us consider that each memory cell has two inputs, each of which is connected to a photodetector. Let us also assume that the signals from the inputs of a cell appear at its output with a fixed delay. A line of cells is composed of such elements. The first and second cells are modulators. The third cell is a memory cell. The fourth and fifth cells are photodetectors. A memory cell operates in two phases. If it contains one at the first phase (the phase of comparison), it opens the first modulator and closes the second one. And otherwise, it closes the first modulator and opens the second one. At the second phase (phase of recording) if the fourth photodetector is opened, and the fifth one is closed, one is

written to memory cell. Otherwise, memory cell resets to zero.

**Figure 10.** Binary encoding of cell states in the second layer of optoelectronic matrix

column just as it is done for the cells of the third column in Figure 10.

An image of the second layer of matrix **S** when it is ready for the phase of comparison is obtained by replacing each cell in the information layer of CA by a group of cells according to the substitution rules in Figure 10. Thus, a block of optoelectronic matrix of size 10 4 cells composed of four lines is put in correspondence to each block of the informational

*Remark*. Gray cells are also used in the transition to binary encoding, but they denote "void",

Let us perform a partition into blocks that have the same sizes and placement as in the rest

Let us construct the first layer of matrix **S**. Unlike lines of cells form the second layer, the cell number four contains a memory cell and the fifth cell is gray. A memory cell is connected to modulators just as the memory cell occupying the third cell. The basis for setup of the first layer is the settings table of the control layer of CA. The setting of layer starts with encoding of its E-partition, i.e. the cells in columns 3 and 8 of the layer are set in such a way that the image formed by the states of modulators would coincide with the left part of that command, whose number is written first in the cell with exactly the same placement in the settings table of CA. The encoding for O-partition is embedded into the encoding of the layer that was just obtained. For this purpose binary codes set into correspondence to white, gray and black cells of the left part of the second command are written into the fourth

The third layer of the matrix is constructed as follows. Black cells of a single block in the columns 1, 2, 6, 7 denote closed photodetectors. Black cells in the columns 4, 5, 9, 10 denote The construction of the fourth layer can be done in two stages. First, a layer that is exactly the same as the first one for the right parts of commands is built. Then the columns in each block are transposed in the following order: 5, 4, 3, 1, 2, 10, 9, 8, 6, 7.

A fragment of matrix **S** presented in Figure 11 illustrates the procedure described above. The fragment is built for such a block of CA, whose settings table has a cell that contains the numbers of substitution commands 7, 4. The fragment is in such a state when E-shift is done and it appeared that the image of the block in the informational layer of CA coincides with the image of left part of substitution command number 7. A polarized light comes perpendicularly to the first and last layers of the matrix, respectively, from above and from below. The phase of comparison of images of blocks in the layers 1 and 2 of matrix **S** and detection of their coincidence is shown in Figure 11, a. The modulators in columns 4, 5 and 9, 10 are opened. The phase of writing new states of memory cells of the second layer using photodetectors connected to their inputs is depicted in Figure 11, b.

**Figure 11.** A fragment of the matrix *S*: a - detection of matching images, b - the phase of setting of new cell states in the second layer.

After a certain fixed delay, memory cells of the second layer set new states for modulators on their outputs. A fixed delay can be implemented, for example, by division of a memory cell into two elements: main and buffer. Modulators are connected to the outputs of the

main buffer. Photodetectors are connected to the inputs of a buffer element. One cycle of state transition from a buffer element to a main one serves as a delay. Then the next shift of the image of a digital scheme is performed and the phase of comparison of image blocks can be done again.

It can be stated that CA turns into a simple homogeneous optoelectronic matrix **S**. It is a device that consists of four layers, which contain microscopic passive sources of light (optoelectronic modulators) and light detectors, forming a regular flat structure. The control of light sources and detectors is performed using electronic memory cells. Memory cells form a 2D shift register in order to provide setup of memory cells for storing the image of a scheme and alternation of commands. The obtained matrix is reconfigurable. It can be setup to imitate any combinatory scheme. The logical operations in the matrix (a comparison of the two codes and writing a code to memory) are preformed optically and their corresponding electronic gates simply do not exist. The proposed matrix has high performance. Indeed, after the pipeline has entered in the steady state, each next result is produced on the outputs of the matrix in each cycle.


*3.1. Materials*

Lipid POPC (1-palmitoyl-2-oleoyl-glycero-3-phosphocholine) was purchased from Avanti Polar Lipids (Alabaster, AL, USA). Fluorescent probe Atto488-DOPE was purchased from Atto-Tech (Siegen, Germany). Peptides β-Amyloid 1–40 and β-Amyloid 1–42 (Human) were purchased from Sigma-Aldrich (Pozna ´n, Poland). Labelled peptide β-Amyloid 1-40-TAMRA was purchased from Eurogentec (Seraing, Belgium). Detergent DOTM (Decyl-B-D-1-Thiomaltopyranoside) was purchased from Sigma Aldrich. Bio-Beads SM-2 were purchased from Bio-Rad (Warszawa, Poland). PBS tablets were purchased from VWR (Gda ´nsk, Poland).

#### *3.2. Preparation of Giant Unilamellar Vesicles (GUVs)*

A modified electroformation method was used to enable the incorporation of Aβ peptides [39]. Briefly, 20 μL of chosen lipid and detergent mixture in chloroform were deposited in small quantities (as 2 μL droplets) onto platinum electrodes. The concentration of lipid POPC was 1 mg/mL, while the concentration of DOTM detergent was calculated so that its final concentration in the electroformation chamber was equal to 75 μM. Two electrodes were set parallel to one another at a distance of 5 mm. The electrodes were kept for 1 h under reduced pressure to remove traces of organic solvents. Next, the electrodes were immersed in 400 mM sucrose solution. This was followed by applying AC voltage to electrodes with 1 Hz frequency and 1 V amplitude. The voltage was increased by 1 V every hour up to 4 V [40]. After the electroformation, chambers were left for 1 h without an electrical field applied to allow the descent of vesicles from electrodes. This was followed by buffer exchange and peptide incorporation. Drops of GUVs solution (50 μL) were transferred to 100 μL of 1.5 × PBS solution with 75 μM DOTM. The peptides were dissolved in 1% NH4OH solution and sonicated for 30 s. This was followed by the addition of 5× PBS buffer to obtain 1× PBS. The peptides were added to GUVs/PBS solution in such quantity to obtain 10 m% with respect to lipids and incubated for 12 h

at room temperature. After that, DOTM removal was carried out using BioBeads in two batches. More detailed verification of Aβ monomers incorporation in GUVs can be found in Supporting Information in Section 2 Figures S2–S9.

#### *3.3. Confocal Microscopy Imaging and Acquisition*

A Cell Observer SD spinning disk confocal microscope (Zeiss, Jena, Germany) equipped with a Plan-Apochromat 100×/1.46 oil immersion objective (Zeiss) was used for vesicle recording. 512 × 512 pixels images were recorded with an EMCCD camera (Rolera, QImaging, British Columbia, Canada) using 2 × 2 binning with 0.133 μm pixel size with a video integration time of 30 ms. At least 5000 images were recorded for each vesicle. Samples were illuminated with 488 nm laser and emitted light passed through 527/54 filter. All samples were measured at 23 ± 1 ◦C. All measurements have been performed in a dedicated PTFE observation chamber with 300 μm height to reduce the effect of uncontrolled vesicle movements. The value of the depth of focus was equal to 0.85 μm. To enhance the quality of analysis the radius of a vesicle was calculated for each image. In case the change of radius was considered as an outliner, the image in the series was discarded from further analysis. It occurred due to misdetection caused by noise or other reasons described in previous work [41].

#### *3.4. Flicker-Noise Spectroscopy Analysis*

The flicker-noise spectroscopy technique is based on the analysis of a vesicle shape fluctuations over time. It is used to determine the bending rigidity coefficient from those fluctuations using the Helfrich's theory. Measurements were performed following our established protocol [41]. Briefly, the membrane fluctuation spectrum was extracted from every single recorded image of the same lipid vesicle using custom software. To calculate the bending rigidity coefficient from a set of time-lapsed two-dimensional images a correlation with three-dimensional membrane elasticity model was established. This was achieved by means of the angular autocorrelation function. The bending rigidity coefficient κ and membrane tension σ can be determined using two approaches, namely the statistical [41,42] and the average-based approach [41,43]. While the average-based approach might seem more straightforward, the main advantage of the statistical one is the histograms that show the characteristics of vesicle fluctuations and are in agreement with the model.

#### *3.5. Molecular Dynamics Simulations*

Molecular dynamics (MD) has been effectively used as a tool for studies of Aβ structures [44]. However, due to a high computational cost, many of these studies are performed on shorter Aβ segments in order to decrease the system size. Nevertheless, the MD simulations are used to study Aβ structures such as peptides [45], dimers [46] and oligomers [47]. In our work, we adopted a structure of Aβ peptides presented by Crescenzi et al. [48]. The full-atomistic MD simulation was performed using NAMD 2.9 [49] software with CHARMM36 united-atom force field [50] under NPT conditions (constant: Number of particles, Pressure and Temperature). Two different types of simulation were carried out, namely peptide incorporation on planar bilayer simulations and lipid vesicle simulation.

For peptides on planar bilayer simulations: a planar POPC membrane system consisting of 200 lipid molecules (100 on each of leaflets) was used. To determine peptide docking in the bilayer, several simulations were performed with various placement of the investigated peptide on the bilayer. The simulation was run till the peptide was incorporated into the bilayer and remained incorporated for at least 30 ns or it was not incorporated into the bilayer. Successful simulations for Aβ-40, Aβ-42, and Aβ-40 TAMRA were carried out for 62, 46, and 51 ns, respectively. The obtained stable position of the investigated peptide in the bilayer was later used for its manual incorporation in the vesicle system. More detailed information about systems setup and properties is presented in Supporting Information in Section 3 Figures S10–S15.

For lipid vesicle simulations: a POPC vesicle was modelled as a liposome of 20 nm radius both sides hydrated with TIP3P water molecules, giving a final simulation box of 30 nm3. The vesicle system was selected over the planar system, as it differs in curvature, which can significantly change attached peptide's behavior [51]. Furthermore, we showed that, in some cases, results from vesicles systems agreed with the experimental data, while for the planar system results were completely different [25]. Three-dimensional periodic boundary conditions were applied to deal with potential energy disruption due to the origin cell discontinuity. The vesicle system was created using a custom script in Matlab. Starting APL was set as 68.1 on average [52], but was corrected accounting for the effect of vesicle's curvature. The APL value was multiplied by 0.95 for the inner and by 1.05 for the outer leaflets, respectively. The vesicle system was equilibrated prior to the addition of Aβ peptides for 100 ns. This was followed by peptide incorporation, which was done using a custom script. Peptides were equally distributed on the vesicle, merged with the liposome system and solvated. After peptide incorporation vesicles were equilibrated for additional 20 ns, followed by running for at least 10 ns and then analyzed. To determine the stable equilibration time-point, six selected parameters (vesicle radius, the thickness of lipid bilayer, mean values and standard deviations of both inner and outer leaflets) were continuously monitored. More detailed information about systems setup and properties is presented in Supporting Information in Section 4 Figures S16–S18.

For pressure wave propagation simulations: simulations were performed according to the established procedure [53,54]. Specifically, the planar system with incorporated β peptides was multiplied 4 times with an additional water slab in Z-axis. After equilibration of the membrane system was switched from NPT to NVE (constant: Number of particles, Volume and Energy) conditions. The pressure wave was modelled as the momentum change of water particles in Z-axis by averaged velocity Δvz defined by Equation (1), where I is pressure impulse, A denotes the area of changed water particles, m the mass of water, and N the number of changed water particles.

$$
\Delta v\_{\overline{z}} = \frac{l \cdot A}{m \cdot N} \tag{1}
$$

The simulated pressure wave was equal to 10 μN/m2·s (1 mPa·s). An evolution of bilayer bending and return to equilibrium was investigated. The position of phosphorus atoms was used to bin membrane position in the OX plane. The obtained bending characteristic of membrane was fitted with the sine function to parametrize the system's behavior and evolution in time.

#### *3.6. Determination of Bending Rigidity Coefficient in MD*

To determine the bending rigidity of model lipid vesicles, we adopted an algorithm originally developed by Braun & Sachs [25,55]. It has an advantage over other approaches [56–58] as it determines mechanical properties based on fluctuations of the bilayer within the vesicle, which can be different than for planar lipids [25]. In short, each lipid is described by a vector spreading from the head (phosphorus atom) up to tail position (midpoint of both 16th carbon atoms in each of tails). This is followed by the discrete surface representation *θ*, *ϕ* using a grid. For each time-point, the surface of fluctuations is established by detecting of fitted sphere's origin point, converting bilayer fluctuations into spherical coordinates and subtracting the radius value. Finally, the average of both inner and outer leaflets fluctuations is calculated. This is followed by spectral harmonics analysis (SPHA) for calculated fluctuations. Eventually, the Helfrich's approach is used by establishing spherical harmonic coefficients *alm*. The obtained *alm* undulation power spectrum can be interpreted according to the Helfrich continuum model for undulations on a sphere with vanishing spontaneous curvature.

#### *3.7. Determination of Basic Structural Parameters*

Additionally, basic structural parameters were determined from performed MD simulations to establish the effect of Aβ peptides incorporation. These include membrane thickness, area per lipid and vesicle density profiles. For each frame position a sphere fit to phosphorus atoms in inner leaflet, in outer leaflet and to both was done in order to obtain radius for inner leaflet, for outer leaflet and for whole vesicle, respectively. Membrane thickness is calculated as a difference between the radius of outer and inner layers. The area per lipid for the whole vesicle was calculated according to Equation (2) using Braun and Sachs approach [55].

$$ALP\_{\text{vesicle}} = \frac{4\pi r\_{\text{resicle}}^2}{\frac{1}{2}(n\_{L,inner} + n\_{L,outer})} \tag{2}$$

To determine density vesicle profiles, three crucial zones of each vesicle area were selected: Head-groups, Carbonyl-Glycerol, and Acyl-Chain, respectively. The distance from radius was calculated for each particle and then histogrammed. Obtained results were followed by the normal distribution fit.


*Edited by Hammad Khalil*

This book covers recent developments in the field of functional calculus. Calculus is the elementary subject of applied analysis and its study provides a rich variety of functions and their behavior. The book brings together a range of different but related concepts from across the wide spectrum of the concept of calculus.

ISBN 978-1-80356-332-9

Functional Calculus - Recent Advances and Development

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**Author details**

areas are lack of over 160 horse powers tractors for soil preparation. Less than 30 cm of plow results in shallow root system and weak soil water-holding capacity, which leads to suffer

Over fertilization not only increases the production cost, but also leads to low fertilizer utilization efficiency. It is reported that applications of N, P, and K are over 70, 50, and 30%, respec-

Cultivars (ROC10, ROC16, and ROC20) from Taiwan Sugar Co-operation were grown in more than 70% of the total sugarcane plantation area, while varieties bred in mainland China were less than 30% in the past 30 years. ROC 22 has been planting more than 50% of sugarcane growing area in China over 20 years. This variety is becoming more susceptible to smut and cold, and poor ratooning ability. Especially, after continuous cultivation of ROC22 in the same fields, the soils have accumulated considerable amounts of smut pathogens. That is why healthy seed cane application for ROC22 does not give expected good results in sugarcane production. Finally, the sugarcane ratooning is limited to 1 or 2 years in China, when

Sugarcane production often suffers from the biotic and abiotic stress in China [35, 36]. For example, the frost in 1998–1999 and the drought in 2005–2006 caused serious damage to sugar production. Sugarcane smut, Pokkah Boeng, ratoon stunting, mosaic, and other diseases caused more than a 20% reduction in production. Borers and soil-borne pests (e.g., *Dorysthenes granulosus*, grub) were found in over 60% of sugarcane plantations, which caused the loss of

CY 2016 is the first year of China's governmental five-year plan (2016–2020) to boost sugar production. The plan's target is to raise annual sugar production to 15 MMT by 2020, when consumption is forecast to reach 18 MMT. The plan also implies the government's intention to gradually reduce imports. Sugar production needs to increase more than 10% annually from 2016 to 2020 in order to meet these challenging policy targets. The government has stated that it will provide subsidies and financial support to farmers to increase yields and reverse declines in sugarcane acreage. The Guangxi government has already started providing subsidies of \$5625 per hectares for seeds to sugarcane farmers, farm machinery, mulching film, and fertilizer. The goal is to reach 333,300 ha of "double-high" (high in sugar content and yield) sugarcane. "Double-high" production is classified as a yield of at least 120 MT per hectare and sugar content at 14% or more by constructing the sugarcane production base for optimization of cultivars, mechanization of production, modernization of water conservancy, and operation at large scale [37]. Currently, in Guangxi province, sugarcane production is

from drought and lodging.

64 Sugarcane - Technology and Research

tively, of sugarcane requirements [34].

**6.3. Simplification of commercial cultivar**

compared to Brazil where the production cycle is over 5 years.

**6.4. Frequent stresses on sugarcane production**

**6.5. Prospect and solutions of Chinese industry**

sugar content of over 0.5%.

**6.2. Over-fertilization**

Muqing Zhang\* and Muralidharan Govindaraju

\*Address all correspondence to<EMAIL_ADDRESS>
College of Agriculture Science, Guangxi University, Nanning, China