*Article* **Loneliness, Complaining and Professional Burnout of Medical Personnel of Psychiatric Wards during COVID-19 Pandemic—Cross-Sectional Study**

**Edyta Karcz 1,\*, Agata Zdun-Ryzewska ˙ 2 and Agnieszka Zimmermann 3**

**Abstract:** Background: Professional burnout in the medical community has been present for a long time, also among mental health professionals. The aim of the study was to examine the links between loneliness, complaining and professional burnout among medical personnel in psychiatric care during a pandemic. Loneliness and complaining of the medical staff are not documented in the literature well enough. Methods: Oldenburg Burnout Questionnaire, the Loneliness Scale, the Complaint Questionnaire and author's questionnaire. The respondents: 265 medical employees doctors (19.2%), nurses (69.8%), paramedics (4.9%), medical caregivers (5.7%). Results: Loneliness and complaining are significant predictors of exhaustion. The model explains 18% of exhaustion variance. Loneliness, complaining and job seniority are also predictors of disengagement; the model allows to predict 10% of the variance of disengagement. Women are more prone to complain. Complaining significantly correlates with direct support from management. A high rate of loneliness correlates, in a statistically significant way, with worse work organization, less management support, worse atmosphere in the team and with more irresponsible attitudes of colleagues. Conclusions: Loneliness and complaining can be used to predict occupational burnout. Women and people without management support complain more often. Loneliness is connected with bad work organization and bad cooperation in a team.

**Keywords:** complaining; medical staff; psychiatric; loneliness; occupational burnout

#### **1. Introduction**

The speed and extent of the spread of the pandemic COVID-19 has caused health and life threats to medical professionals on an unprecedented scale [1]. Numerous studies conducted since the onset of the presence of the virus indicate many factors that are a source of stress for staff. These are, among others: fear for their own safety, the risk of infecting members of their family and loved ones, but also team members [2,3], anxiety about the availability of personal protective equipment, and lack of adequate support [3,4].

An element that significantly enhances the intensity of the impact of the above factors on the mental health of employees is the chronicity of the situation. Functioning in such difficult conditions for a long period of time poses a very high risk to both physical and mental health of all people, in particular health care employees, who are probably more than before exposed to the phenomenon of occupational burnout.

Professional burnout is a response to the long-term effects of interpersonal stressors at work [5] and a form of occupational tension resulting from the buildup of work-related stress [6]. Work burnout commonly understood as a syndrome consisting of exhaustion

**Citation:** Karcz, E.; Zdun-Ryzewska, ˙ A.; Zimmermann, A. Loneliness, Complaining and Professional Burnout of Medical Personnel of Psychiatric Wards during COVID-19 Pandemic—Cross-Sectional Study. *Healthcare* **2022**, *10*, 145. https:// doi.org/10.3390/healthcare10010145

Academic Editors: Alberto Modenese and Fabriziomaria Gobba

Received: 20 December 2021 Accepted: 11 January 2022 Published: 13 January 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

defined as a consequence of intense physical and mental stress and disengagement from work as a result of long-term stress at work [7]. Work burnout is one of the major problems among mental health care employees [8] also among mental health professionals. A recently published meta-analysis shows the presence of exhaustion in 40% of medical staff in this sector, while 19% could be described with low levels of personal accomplishment related to disengagement from work [9]. Due to the worldwide pandemic, those numbers will probably grow.

An element that is significantly related to burnout is loneliness. Loneliness occurs when people experience a sense of loneliness and when, regardless of the number of contacts, they begin to lack meaningful social relationships. This subjective feeling of loneliness depends more on the quality of the relationship. It is a kind of dissonance between real and desired social relations [10]. The current epidemic situation and the related need to maintain social distance has worsened interpersonal relations, thus limiting social support, which may also contribute to the growing feeling of loneliness.

The problem of the presence of loneliness in the professional life of medical employees is not described in detail in the literature. In the last few years, there have been studies on the existence of loneliness mainly among doctors, where the authors state that loneliness is common in the work of doctors and is associated with burnout [10]. In a study involving 401 family doctors, the incidence of loneliness was 44.9%. The analysis of the results showed that physicians who experienced a greater sense of loneliness more often reported at least one of the symptoms of occupational burnout [11]. In other studies, loneliness has been identified as one of the leading stressors in the work of nursing managers [12].

The most common intention of complaining people is experiencing a sense of relief by expressing dissatisfaction, which, as most people seem, should have a soothing effect on unpleasant emotional states [13]. However, there are reports linking the phenomenon of burnout and complaints. Burnout is not just complaint, it is a much more serious condition, but it might be related to complaining [14].

Nowadays, protecting the health of medical employees providing services in the field of psychiatric services requires a high priority. Without it, it will not be possible to help those in need. Working in extremely difficult conditions, in a sense of high risk, additionally reinforced by many stress factors, indicates an urgent need to provide mental support, which should be implemented both by the management of the entities and the external environment. An important element of it is social support, which is a significant work resource [15] and has a positive impact on mental health. Support from friends and coworkers can reduce burnout by mitigating loneliness [16]. Support should be organized in such a way that employees try to constructively discuss problems, avoiding negative forms of communication. Psychiatrists themselves report that factors of the work environment, more than personal factors, play a greater role in the development of burnout [17]. This clearly shows that employees expect effective labor resources. Loneliness is related to seniority. Doctors with more experience were less likely to see themselves as lonely [11]. The aim of our study was to look at the phenomenon of occupational burnout in connection with the loneliness and complaining.

We stated a hypothesis that loneliness and complaining contributed to burnout. We assumed that some of the staff experience the problem of burnout. In our study, we hypothesized that there was no association between burnout and sociodemographic variables.

Loneliness and complaints of medical personnel in psychiatric practice are not well documented in the literature. There is no evidence of whether, and if so how, they are related to burnout. This problem appears especially when hospitals are overloaded with COVID-19. Our study is an important attempt to establish the correlation between loneliness experienced by psychiatric employees and individual tendency to complain and professional burnout. Results of our research can provide a valuable guidance for management improving the work in case of the environment of psychiatric care professionals.

#### **2. Materials and Methods**

#### *2.1. Study Participants*

A total of 265 medical employees from two psychiatric hospitals in the Pomeranian Voivodeship participated in the study. These were: the Provincial Psychiatric Hospital in Gdansk and the Hospital for the Nervous and Mentally Ill in Starogard Gdanski. The management of the institutions obtained consent to conduct the study. The total number of health professionals working in the two hospitals included in the study was 860. In the first hospital, out of 265 medical workers, 93 people applied for the study, of which 11 questionnaires were rejected due to incomplete answers. In the second hospital, out of 595 medical employees, 207 employees expressed their willingness to participate in the study, 183 of whom were finally qualified. All employees working in the hospital wards took part in the study. A written invitation was forwarded to the ward managers and then given to the employees. Afterwards, we contacted the employees who expressed their willingness to participate in the survey. The questionnaires were left in each ward. Only those willing took part in the study. An invitation to participate in the study was enclosed with the questionnaire. The subject of the study and information on the anonymity of the participants were given. All the participants gave their informed consent to participate in the study.

#### *2.2. Study Questionnaire*

The study was designed as a questionnaire survey and consisted of 4 sections with a total of 66 questions. The following is a detailed description of part of the questionnaire:

(1) Self-designed questionnaire—concerning socio-demographic data (gender, profession, work experience, education), and 6 questions concerning issues related to the organization of work during the pandemic of COVID-19 (assessment of the degree of organization of work in a team, assessment of team relations, the amount of support received from direct management, the amount of support received from the management of the facility and the degree to which teammates comply with the procedures and guidelines related to protecting health against COVID-19). The questionnaire consisted of 10 questions.

(2) The Oldenburg Burnout Questionnaire—OLBI is a tool that allows you to measure occupational burnout [7]. The questionnaire uses the two-factor concept of occupational burnout. The first factor is broadly defined exhaustion (taking into account its emotional, cognitive and physical components). Example of questions in this section are: "There are days when I feel tired before I arrive at work" or "During my work, I often feel emotionally drained". The second component is distance from work, called disengagement, for example, in a form of a statement such as: "I feel more and more engaged in my work" or "Lately, I tend to think less at work and do my job almost mechanically". The questionnaire consists of 16 questions. The questions were answered on a 4-point scale (1—I strongly agree, 2—I agree, 3—I disagree, 4—I strongly disagree) [18]. The questionnaire, both in its original and Polish version, is characterized by good psychometric properties. Cronbach's alpha coefficient was calculated to assess internal consistency of the questionnaire in our study. Cronbach's alpha was also good (α = 0.81).

(3) The De Jong Gierveld scale for measuring the sense of loneliness [19] and its Polish adaptation [20] allows to measure the perceived loneliness both in individual diagnosis and in scientific research. The scale contains a total of 11 items, most of which are formulated negatively, i.e., it allows to measure the dissatisfaction with social contacts (e.g., "I lack other people's company"), and some positively, i.e., it measures satisfaction with social contacts (e.g., "on friends whenever I need it "). The responses were rated on a 5-point scale (1—definitely yes, 2—yes, 3—neither yes nor no, 4—no, 5—definitely no). This questionnaire is also characterized by appropriate psychometric properties in both versions (original and adapted to Polish conditions). In this study, Cronbach's alpha for this scale could be described as satisfactory (α = 0.72).

(4) The questionnaire of the content of daily conversations (Complaint Questionnaire) was designed by Bogdan Wojciszke and Wiesław Baryła [13]. We received it from the

authors with permission to use it and their description of satisfactory psychometric characteristics. The Cronbach's alpha for this questionnaire in this study was also good, α = 0.89. The questionnaire consists of 29 items and allows to measure the tendency to complain by answering the questions about how often the respondents talk about the mentioned topics. Some of the topics presented are positive, e.g., in the question about the frequency of talking about human kindness. Most of them deal with topics that are commonly associated with complaining: increasing crime, the heartlessness of officials and human indifference. Responses were rated on a 5-point scale (1—never, 2—rarely, 3—sometimes, 4—often, 5 very often). The questionnaire produces one overall score that is an indicator of a person's propensity to generally complain.

#### *2.3. Statistical Methods*

All statistical analyses were performed with the Statistica 12.0 (StatSoft, Kraków, Poland). The study used parametric methods due to appropriate size of the study group, normal distribution of values and the continuous character of the variables. The Pearson correlation coefficient was used to measure the interrelationships between the variables. Differences between groups were tested using the Student's *t*-test or one-way analysis of variance. Regression analysis (multiple regression type) was also performed.

#### **3. Results**

The completed questionnaires were returned by 265 (88%) respondents. Our study included medical personnel who have direct and closest contact with the patient on a daily basis. The detailed division of respondents by occupation is as follows: doctors (19.2%), nurses (69.8%), paramedics (4.9%), medical caregivers (5.7%). Most of the participants were female (82%) with long professional experience. Almost 60% of the studied group had higher education. The socio-demographic characteristics of the group are presented in Table 1.

**Table 1.** Socio-demographic characteristics of the study group.

There were no statistically significant connections between the group of sociodemographic variables and occupational burnout. There were no significant statistical differences between men and women in terms of exhaustion (t = 1.93, *p* = 0.06, df = 262), also in terms of disengagement (t = −0.42, *p* = 0.67, df = 262). Additionally, in the area of education, no statistically significant differences were observed between the two main groups

in our study, one with higher and one with secondary education in terms of exhaustion (t = −0.84, *p* = 0.4, df = 262), or disengagement (t = −1.67, *p* = 0.09, df = 262). There were also no statistically significant differences in the context of exhaustion (F (5, 259) = 1.79, *p* = 0.11) and disengagement (F (5, 259) = 1.18, *p* = 0.32) between people working in different professions (doctor, nurse, paramedic, caregiver) within the unit of a psychiatric hospital.

The performed regression analysis (multiple regression type, all predictors entered simultaneously) allowed to obtain two statistically significant models, thanks to which it is possible to identify variables that are predictors of fatigue and disengagement. The regression model for exhaustion is presented in Table 2.

**Table 2.** Regression model for the exhaustion variable with significant predictors in the group of employees of psychiatric wards.

\* *p* ≤ 0.001.

Loneliness (β = 0.20, *p* < 0.001) and complaining (β = 0.35, *p* < 0.001) proved to be statistically significant predictors of exhaustion. Work experience was the only nonsignificant predictor of fatigue. The whole model is statistically significant (F (3.261) = 20.12, *p* < 0.00001) and allows explanation of about 18% of the exhaustion variance (adjusted R 2 = 0.178). The presence of a feeling of loneliness and complaining about many different topics allows us to predict severe exhaustion in psychiatric wards.

Another model containing predictors of disengagement is presented in Table 3.

**Table 3.** Regression model for the variable of disengagement with significant predictors in the group of employees of psychiatric wards.

\* *p* ≤ 0.01, \*\* *p* ≤ 0.001.

The model is also statistically significant (F (3.261) = 10.37, *p* < 0.001) and allows to predict approximately 10% of the variance of disengagement (adjusted R2 = 0.96). In this case, significant predictors of disengagement turned out to be work experience (β = −0.13, *p* < 0.001), also loneliness (β = 0.13, *p* = 0.01) and complaints (β = 0.25, *p* < 0.001). In this case, the feeling of loneliness and intense complaining also allow to predict the lack of commitment to work. In the case of this model, it is possible to predict the lack of commitment based on the length of service—the longer the employee's work experience, the smaller the chance of disengagement (employees with shorter work experience are less involved).

Further analysis involved establishing associations between loneliness and complaining and other variables. Significant statistical differences were revealed between women and men (t = 1.98, *p* = 0.04). Women (M = 2.86, SD = 0.57) are more likely to complain than men (M = 2.67, SD = 0.57). In case of this difference, we achieved Cohen's *d* = 0.33, which means that the effect size is small. Additionally, complaining correlates in a statistically significant way with direct support from management (the less support, the greater the complaint).

Loneliness turned out to be related to organizational and team variables. High loneliness correlates in a statistically significant way with worse organization of work, also less support from administration management, management, worse working atmosphere (team

relations) and surprisingly with more irresponsible attitudes of colleagues in relation to compliance with procedures and guidelines related to health protection against COVID-19. All results are presented in Table 4.

**Table 4.** Correlations between loneliness and complaining and organizational and interpersonal variables related to the syndrome (Pearson's correlation coefficient).

\* *p* < 0.05.

#### **4. Discussion**

Our research aims to examine the relationship between loneliness, complaining and lack of engagement, and to show their impact on burnout. We examined the relationships between socio-demographic variables (gender, occupation, seniority, education) and the phenomenon of occupational burnout. The analysis showed that these variables did not affect occupational burnout in the respondents. Gender was not significantly related to burnout. Confirmation of the lack of relationship between gender and the studied aspects can be found, among others, in the Bijari [21] and Dinibutun studies [22], which confirm the comparable level of burnout in both men and women. On the other hand, different results confirming the relationship between gender and exhaustion are given by Adam, who stated that women experienced higher emotional exhaustion [23], and Schadenhofer, who showed that gender had a different effect on the frequency of exhaustion [24]. Our study indicates that education did not affect exhaustion and lack of engagement, which is consistent with Oyefeso's research [25]. Tan presents a different position on the subject, explaining the result with probably higher responsibility at work [26].

This study found no correlation between occupation and exhaustion and lack of engagement. Different positions can be found in the literature. A study of 200 employees showed that burnout was worse in nurses than in physicians, with both nurses and physicians having a higher level of burnout compared to other employees [27]. Mental health professionals may be more at risk of burnout than colleagues in other fields [28]. A study of psychiatrists in Milan confirm this assumption. A total of 49% of respondents [29] obtained a high level of emotional exhaustion.

The results of the current study showed that loneliness and complaining were important predictors of exhaustion. An employee who experiences exhaustion begins to feel more and more lonely. They begin to isolate themselves from others, their workshop slowly deteriorates and their professional activities become more and more difficult. When there is no support in the immediate surroundings, the feeling of loneliness grows, leading to even greater exhaustion over time. Experiencing more and more discomfort, they begin to critically evaluate situations that have so far been positive or indifferent. Criticism increases. They begin to complain. The more tired they are, the more they complain. Loneliness in the workplace is noticed by colleagues and significantly affects the efficiency of work and relationships in the team by weakening social relationships in the group. Thus, loneliness leads to withdrawal and reduction in job productivity [30]. In process of time, a person experiencing loneliness begins to feel worse, which is a negative consequence of loneliness [31]. In their research, Killgore and colleagues show that loneliness is getting worse during the current pandemic [32].

The results of the study are confirmed in the Ofei-Dodoo research, which indicates the correlation of a high level of exhaustion with a sense of loneliness [10]. In another study, Rogers confirms the relationship between loneliness and burnout, indicating that higher levels of loneliness were significantly associated with higher burnout [16]. It should also

be remembered that the emotional exhaustion experienced by the employee will have an influence on their private life, over time impeding the fulfillment of Zhang's family tasks and roles [33].

Dinibutun, in his work, states that there is a significant difference in exhaustion between nurses and doctors [22]. It may be because of the nature of the job. It is the nurse who is closest to the patient, spending a lot of time with them in direct contact. When the patient is agitated, the nurse must act quickly, trying to ensure the safety of both herself and the patient. It is very difficult, it causes a lot of emotional tension and ultimately leads to exhaustion.

Complaining means focusing on the negative aspects of the surrounding reality; more importantly, communicating using such a pattern. In a long-term complaining process, it may happen that the subject of the complaint is anything for the sake of the idea of complaining.

An extremely important issue is the impact of the behavior of people experiencing burnout on the relationships in the team. This problem is highlighted in Maslach's research, emphasizing that employee burnout may have a negative impact on other team members; consequently, leading to their distance from work and worsening social relations in the team [5]. Therefore, both difficult emotions and a lack of commitment to work are spilled to some extent. It does not take a long-time perspective for the quality of care to deteriorate.

Loneliness is naturally associated with a tendency to withdraw. The employee starts to move away from others, communication and performance of tasks may deteriorate. The fact that we work as a team in hospitals may turn out to be beneficial in this case. You can quickly notice a person who starts to move away from the group. The first source of support for an employee may be a group of colleagues at work. They are important in providing support. The research of many authors indicates the important role of social support as an element preventing burnout. The support offered by both colleagues and friends is of great importance, as confirmed by their research by Aronsson [34] and Mohindra [2].

Patients with mental health problems may not be able to comply with a sanitary regime. Poor self-care capacity and insufficient insight are factors that significantly hinder cooperation in this regard [35]. Many of the existing rules must be changed. The long-term promotion of group activities of patients should be currently slowed down by proposing to keep social distance. The problem, however, is that this is the opposite course of action. According to Arango, we have never encouraged patients to distance themselves [35]. Studies of patients experiencing psychosis show that they badly need emotional support from their loved ones. This need is confirmed by 91% of respondents in the Lahera study [36]. Due to the pandemic, large visiting restrictions are, as it were, going against. Additionally, although patients, understanding the necessity to introduce restrictions, try to comply with them, it is very difficult for them because of the separation from their loved ones.

The presence of all these difficulties and their mutual penetration, strengthened in the pandemic era, with care for their own health and safety, causes employees to gradually show an increasing lack of commitment at work. The superior goal of helping the patient may turn out to be disastrous for the helper. Significant predictors of disengagement are seniority, loneliness and complaining. The length of the work experience allows to forecast the level of disengagement. Employees with longer experience show less disengagement. We can find confirmation of seniority in the literature, where younger people are more likely to be exhausted [25]. In other studies, the author shows that greater age and experience were associated with less burnout [37]. More experience goes hand in hand with more practice and some kind of distance, which can be important when dealing with minor problems and failures at work. Another analysis was to establish the links between loneliness and complaining and other variables. According to the results, women are more prone to complaining. This may be related to greater sensibility to stress [38]. Women are more sensitive. As mothers, they strive for the proper development of their children and the safety of the whole family. Bearing in mind that human resources are the most valuable

asset of an organization [39], management should make every effort to provide a supportive work environment. The key importance of support from the employer is mentioned by many authors in their research. Belfroid et al. emphasize the importance of the quick availability of a superior in a difficult situation [40]. In turn, Kang et al. emphasize the importance of clear communication in the process of supporting employees [41].

A clear division of duties, application of procedures and compliance with the rules contribute to shaping a proper and safe atmosphere in the team. The support needs of employees are individual and depend on many factors. Nevertheless, employer support seems to be a key element in the fight against burnout.

Caring for a safe work environment includes various aspects, both physical, in the form of providing personal protective equipment, and emotional, in the form of supporting employees and paying attention to their needs [33]. The control also contributes to reducing tension, and thus burnout [42], as it allows obtaining substantive information on the tasks performed. Our analysis is confirmed by studies by other authors showing that a high level of support protects against exhaustion [34]. In times of a pandemic, concern for the psychological safety of employees becomes of particular importance. Wu, in his research, shows that if workers feel that they will be supported in case of a disaster, they will be more resilient [43]. Looking at this issue from the other side, it should be stated that if we do not provide support to employees, the degree of complaining and the feeling of loneliness will increase. Additionally, this can lead to leaving the profession. Interesting results on this topic were presented by Shah, who showed that among nurses who reported resignation from the profession due to burnout, a high percentage indicated a stressful work environment as the reason [44]. Our study has some limitations. One of the limitations of our study is that it was conducted on a small group of regional employees. The study covered the staff of psychiatric hospitals in the Pomeranian Voivodeship. In the future, it is worth extending the survey to at least the entire country to make comparisons with surveys carried out in other countries. Another limitation of the project is the fact that the study was carried out during a pandemic, i.e., a time when health care staff was particularly burdened. However, it seems to us that psychiatric staff will long struggle with overload, also in a post-pandemic society.

#### **5. Conclusions**

Our study shows that loneliness, complaining and disengagement are significant predictors of psychiatric staff exhaustion. It is very important to create a friendly work environment. Support should take into account both an individual and a team approach. Loneliness, complaining and disengagement may be changed by organizing team meetings and staff training sessions to create a community. Such meetings could be enriched with psychoeducational elements indicating the psychological consequences of complaining and various affirmation techniques. It is important that it is systematic and allows flexible adaptation to the employee. The management of the institutions should take into account the prevention of infodemia, taking care of the substantive and safe transmission of information. Strong leadership and a clear management structure are a protective factor in this case. Moreover, it is essential to systematically monitor the phenomenon of burnout in individual professional groups.

Our study shows that loneliness and complaining are important concepts that predict significant outcomes in the area of occupational burnout in mental health care employees. It is worth undertaking further research on this issue in order to better understand the various interactions between loneliness, complaining and burnout. The obtained results will allow for taking effective measures in the field of burnout prevention. Problems with recruiting and maintaining medical staff, present in most facilities for many years, require management to pay attention to the employee's satisfaction, health and job satisfaction. Professional activity means that we spend a significant part of our lives at work. Therefore, it is necessary to ensure that the time spent there is fully satisfactory for the employees, which will translate into the satisfaction of our customers.

**Author Contributions:** Conceptualization: E.K. and A.Z.-R.; writing—original draft preparation: E.K.; writing—review and editing: A.Z.-R. and A.Z. All authors have read and agreed to the published version of the manuscript.

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

**Institutional Review Board Statement:** The study was conducted after obtaining a positive opinion from the Independent Bioethical Committee for Scientific Research at the Medical University of Gdansk (NKBBN/133/2021) in the period from 10 March to 30 April 2021.

**Informed Consent Statement:** Informed consent was obtained from all subjects involved in the study.

**Data Availability Statement:** The datasets used and/or analyzed during the current study are available from the corresponding author on reasonable request.

**Acknowledgments:** The authors would like to thank all correspondents for participation in the study and completing the questionnaire.

**Conflicts of Interest:** The authors declare no conflicts or competing interest.

#### **References**


**Author details**

Eduarda Martiniano de Oliveira Silveira\*, Marcela Castro Nunes Santos Terra, Fausto Weimar Acerbi-Júnior and José Roberto Soares Scolforo Forest Science Department, Federal University of Lavras (UFLA), Lavras, Brazil

\*Address all correspondence to<EMAIL_ADDRESS>
© 2019 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


*Edited by Madhusmita Mishra*

Growing and Handling of Bacterial Cultures is a collection of reviewed and relevant research chapters, offering a comprehensive overview of recent developments in the field of Life Sciences. The book comprises single chapters authored by various researchers and edited by an expert active in the field. All chapters are complete in itself but united under a common research study topic. This publication aims at providing a thorough overview of the latest research efforts by international authors on Growing and Handling of Bacterial Cultures, and open new possible research paths for further novel developments.

Published in London, UK © 2019 IntechOpen © Sinhyu / iStock

Growing and Handling of Bacterial Cultures

Growing and Handling of

Bacterial Cultures

*Edited by Madhusmita Mishra*


**7. Gas chromatography**

GC and GC-MS have been widely used for quantitative and qualitative analysis of bile acids in different biological samples [10, 14, 37, 62-65]. In broad terms, GC works on the same principle as HPLC, however, in GC compounds are in gaseous form and an inert gas, like nitrogen or helium, is used for elution. The various compounds are resolved on the basis of their retention/elution behavior on the stationary phase of the column. There are two basic requirements for GC analysis, an appropriate column and derivatization of the compounds, to cause vaporization under the chromatographic conditions used [19].

Then, those techniques are limited by complex sample preparation, derivatization and most importantly, because requires the hydrolysis of conjugated bile acids into their free forms, prior to their analysis [66]; although GC-MS provides high sensitivity and resolution of isomeric bile acids, it is necessary to isolate and purify bile acids before analysis [14, 19].

44 Chromatography – The Most Versatile Method of Chemical Analysis

placing in a 120°C oven [60].

concentration range 50–75% (v/v).

**7. Gas chromatography**

separated taurine and glycineconjugated standard bile acids. In [21], authors reported 15

In [59] they reported two solvent systems. The first one (isopropanol:glacial acetic acid, 93:7 v/v) allows separation of free bile acids, glycine conjugates and taurine conjugates from one another, and a second solvent system consisting of hexane:methylethylketone:glacial acetic acid, 56:36:8 v/v (Petcoff's solution), for the separation of the four free bile acids found in human bile. Authors in [48] used a TLC methodology to identify the fecal bile acid patterns in several carnivore species; plates were developed in a paper-lined, equilibrated bath containing Petcoff´s solution. After air drying, plates were visualized by spraying with a solution of acetic acid:sulphuric acid:anisaldehyde 50:1:0.5 (v/v) as revealing agent, and

On the other hand, as cited in [33], they developed plates in Petcoff´s solution and then visualized with a 50:1:0.5 v/v solution of acetic acid:sulfuric acid:p-anisaldehyde to identify bile acids from grizzly and black bear feces. In [35] they used used a developing bath of Petcoff's solution to run the plates and they visualized bile acid bands by spraying the plates with 50% v/v sulfuric acid, which allowed them to observe spot colors in cougar and jaguar feces [3]. Sulfuric acid was also present in our visualizing agent. [61] reported a method to separate standard bile acids consisting of a reversed thin-layer chromatography using a mixture of metanol:water as the solvent system, in the

In [6] they reported a TLC method to determine the fecal bile acid patterns in carnivore feces. It consisted of an alkaline extraction to purify the bile acids from other lipophilic steroidal compounds; plates were eluted with Petcoff's solution and developed with a

From our results, and because TLC of fecal bile acids has proved to offer robust data to establish habitat use and to study food habits of some sympatric mammal species [6, 36], we assume that this technique would also be useful for future ecological studies in Xenarthra and in other species. Considering the scarcity of available information about some ecological and biological aspects of Xenarthra, these results, the first ones on the application of TLC for the identification of their feces, could be very important for future studies about the

GC and GC-MS have been widely used for quantitative and qualitative analysis of bile acids in different biological samples [10, 14, 37, 62-65]. In broad terms, GC works on the same principle as HPLC, however, in GC compounds are in gaseous form and an inert gas, like nitrogen or helium, is used for elution. The various compounds are resolved on the basis of their retention/elution behavior on the stationary phase of the column. There are two basic requirements for GC analysis, an appropriate column and derivatization of the compounds,

mixture of glacial acetic acid, water, sulfuric acid and 3,4-dimethoxybenzaldehyde.

conservation, distribution and eco-physiology of this group.

to cause vaporization under the chromatographic conditions used [19].

solvent systems to separate bile acids, being the most efficient the acidic one.

Bile acids are present in unconjugated and/or conjugated form in biological fluids. They range from 1-2 µg/ml in plasma and urine to significant amounts in the intestinal content and as much as 10 mg/ml in the gallbladder bile. Bile acids are present in association with proteins, sterols and their esters, free or esterified fatty acids, bile pigments and watersoluble small molecules, which must be either removed before chromatography or the chromatographic conditions should be such that these compounds do not interfere in bile acid analysis. Since bile acids are present mainly as glycine or taurine conjugate in plasma and bile, unconjugated in feces and unconjugated as well as conjugated with glycine, taurine, glucuronic acid and sulfuric acid in the urine, the methods for isolation of bile acids from these sources need to be appropriately modified [19].

However, a major difficulty in quantitative analysis of fecal bile acids is their strong binding with the bacterial debris in the stool, and quantitative extraction is difficult. Stool contains bile acids, neutral sterols, cholesterol and its bacterial metabolites, plant sterols and their bacterial metabolites and fatty acids, which need to be removed before GC. Since fatty acids are less strongly retained on the capillary columns, bile acids can usually be quantitated in their presence.

For GC fecal bile acid analysis, several methods have been reported and most of them are quite complex [23, 62, 67].

In [68] they used continuous soxhlet extraction of aliquots of stool using chloroform and methanol. Extracts were derivatized and the methyl esters obtained were subjected to preparative TLC, respective bands were eluted and prepared for GC. On the other hand, in [23] they did a similar procedure but with tedious and longer steps. In alternate methods, bile acids from feces have been extracted with ammoniacal alcohol, methanol-hydrochloric acid, acetic acid-toluene, after removal of neutral sterols [23, 67].

In [19] they digested fecal samples with internal standard, extracted neutral sterols by repeated extractions, extracted bile acids with ethyl acetate, remove mineral acid and the residue was subjected to methyl ester formation; part of the aliquot was used for GC after trimethylsilylation. However, this method was not applicable to samples which contained conjugated bile acids.

Since the basic requirement for GC is that the compounds are in gaseous form at the column temperature, it is necessary to derivatize the polar functional groups. The carboxyl group in bile acids is often converted into the methyl ester. In addition, other bile acid esters have been used for GC, such as ethyl, n-propyl, isobutyl and n-butyl esters. Moreover, other derivatizations are common: of the hydroxyl group or the oxo group.


*Edited by Rakesh Sharma*

"Functional Magnetic Resonance Imaging - Advanced Neuroimaging Applications" is a concise book on applied methods of fMRI used in assessment of cognitive functions in brain and neuropsychological evaluation using motor-sensory activities, language, orthographic disabilities in children. The book will serve the purpose of applied neuropsychological evaluation methods in neuropsychological research projects, as well as relatively experienced psychologists and neuroscientists. Chapters are arranged in the order of basic concepts of fMRI and physiological basis of fMRI after event-related stimulus in first two chapters followed by new concepts of fMRI applied in constraint-induced movement therapy; reliability analysis; refractory SMA epilepsy; consciousness states; rule-guided behavioral analysis; orthographic frequency neighbor analysis for phonological activation; and quantitative multimodal spectroscopic fMRI to evaluate different neuropsychological states.

ISBN 978-953-51-0541-1

Functional Magnetic Resonance Imaging - Advanced Neuroimaging Applications

Photo by LeventKonuk / iStock

## Functional Magnetic Resonance Imaging Advanced Neuroimaging Applications

*Edited by Rakesh Sharma*

**FUNCTIONAL MAGNETIC**

**RESONANCE IMAGING –**

**ADVANCED**

**NEUROIMAGING**

**APPLICATIONS**

Edited by **Rakesh Sharma**


**1. Introduction**

Diesel engines find widespread applications in many industries, including transportation, agriculture, and power generation, among others. Soot and NOx emissions, which are products of fuel combustion in these engines, pose a threat to the environment and the health of living organisms. Over the years, strict global regulations have been set to reduce the negative impact of such emissions. These stringent legislations require manufacturers to design cleaner and more e fficient engines [1,2]. Many technologies, such as diesel particulate filters (DPFs) [1] and selective catalytic reduction (SCR) [3], have been developed to reduce emissions from diesel engines. In addition, controlling the combustion process (e.g., by using low-temperature combustion (LTC) [2], homogeneous charge compression ignition (HCCI) [4], reactivity-controlled compression ignition (RCCI) [5], and premixed charge compression ignition (PCCI)) have also attracted significant research interest [2]. Research on the fuel mixing process for preparing diesel combustion components in cylinders through e ffective injection rate adjustment is an important consideration. In this study, we only consider injection rate adjustment in the fuel injection system without changing the air intake and other contexts of the

system; thus, this study does not modify the existing injection system too greatly. This is due to the significant influence of the air–fuel mixing process on combustion e fficiency and exhaust emissions in diesel engines.

The latest developments in fuel injection strategy e fficiency tend to focus on the injection rate to increase fuel mixing e fficiency and reduce emissions. Notably, the combustion time will be shorter for cases with high initial injection rates. Generally, a high initial injection rate will result in better atomization and air entrainment. The duration of combustion decreases as the mixture of air and fuel improves, meaning that combustion occurs faster. Conversely, under a low initial injection rate, the initial atomization of the fuel and premixing are not good. The slow initial injection fuel droplets will combine with faster fuel droplets, which will result in a larger droplet size that yields a poor spray breakup. The combustion period will then be longer as more time is required to inject the fuel to atomize and evaporate it for combustion. In the past, researchers were interested in investigating the injection rates to improve fuel injection strategies. Juneja et al. [6] noted that increasing the injection rate after a previous injection is su fficient to increase the collision frequency and formation of large droplets, resulting in high momentum and greater penetration. Liu et al. [7] found that a higher peak injection rate yielded a higher spray tip penetration, peak entrainment rate, and entrainment rate after the end of injection (EOI). In addition, Arsie et al. [8] suggested that the start of injection is the main parameter that a ffects the impingement phenomenon, whereas Kun Lin Tay et al. [9] found that the start of combustion for each rate shape is di fferent, although the injection duration and start of injection are same due to the start of pressure rise in each case. The peak in-cylinder pressures are higher when the start of combustion is advanced due to the injection rate shaping. The combustion duration will be shorter with a higher initial injection velocity. Apart from that, the results from numerical study on the effects of boot injection rate shapes by co-workers of Balaji Mohan and Kun Lin Tay [10–12], showed that NOx decreased but large soot particles occur due to low injection velocity and narrow soot distribution when the main injection velocity is higher [11]. Dezhi Zhou et al. [12] found that higher boot injection velocity and shorter boot injection duration resulted in shorter ignition delay and more fuel burning at the premixed combustion stage. This suggests that a higher injection pressure will often lead to a better spraying process, that this is one of the most e ffective ways to meet the e fficiency requirements, and that this process has a potential benefit in diesel engine performance [13–15]. Agarwal et al. [16] found that increasing the injection pressure reduces the number and mass of particles and increases the diesel spray velocity, which improves the atomization and evaporation process. In addition, Shuai et al. [17] applied a numerical simulation to examine the e ffects of injection time and injection rate shape on the performance and exhaust emissions of compression ignition engines. The authors found that CO, UHC, and soot emissions can be reduced by using rectangular-type and boot-type rate shapes instead of other types. Based on these previous studies, the injection rate is clearly an important parameter that requires more attention. Injection rate parameters, such as injection velocity, injection mass quantity, and injection duration, have a significant influence on the fuel mixing and combustion process [18]. Many of these investigations considered how the diesel spray mixing process behavior can increase mixing e fficiency by studying the e ffect of the injection rate shape. Attempts to increase fuel mixing efficiency by determining the injection rate shape remain unsatisfactory. Although there have been extensive studies in the past on the influence of injection rates, most of these studies were interested in investigating the influence of injection rates on combustion e fficiency and engine emissions [9–12,17]. Few studies have investigated the influence of injection rates on spray mixing behavior.

Based on our previous study [19], we examined the spray mixing characteristics under di fferent injection rate shapes using a modified one-dimensional spray model. This one-dimensional spray model can analyze the spray penetration, entrainment rate, and velocity over a cross-sectional area, as well as the equivalence ratio distributed along with the spray's axial distance. This model does not consider breakup and evaporation. Instead, it reveals general information on both the liquid and the vapor. The fuel and air are assumed to be immediately mixed uniformly, so turbulent mixing cannot be analyzed in detail. A 3D-CFD model is better for researching a spray that includes two-phase flow characteristics.

Creating a spray model using CFD has become an e ffective way to study diesel spray to analyze the mechanism of fuel–air mixing and atomization. The results of many previous studies on creating a spray model using CFD show that the various parameters of fuel injection can be e fficiently monitored and predicted [20–22]. Nevertheless, there are few studies on the injection rate shape's e ffects on spray mixing. Unlike a quasi-steady-state spray, it is di fficult to obtain clear spray images that include liquid and vapor information under varying injection rates, so there is a lack of experimental data to validate the 3D-CFD spray model with varying injection rates. Consequently, most numerical studies focus on the e ffects of injection rates on combustion processes and do not o ffer an in-depth understanding of the spray behaviors under di fferent injection rates.

The objective of the current study is to analyze the e ffect of di fferent injection rate shapes on the diesel mixing process using a numerical modeling method. In this work, the "CONVERGE" CFD code was adopted for a constant-volume combustion chamber with a single hole injector, particularly to study the spray breakup and spray mixing behavior. Validation of the model results involved a comparison of the spray shape and spray penetration with the experimental data from previous researchers of the Sandia National Laboratory, taken from the ECN website [23]. We found that the modified CFD spray model can predict spray behavior. Four injection rate shapes were used to analyze the e ffects of injection rate shapes on diesel spray mixing behavior to understand the mixing process in-depth, including the microscopic spray characteristics, evaporation process, and mixture properties. The results of this study are expected to provide useful insights for developing an e ffective fuel injection rate design for future diesel engines.


**Abstract**

Changing lifestyle and sedentary schedule have led to the substantial increase in major noncommunicable diseases (NCDs) such as cardiac problems, cancers, diabetes, psychiatric disorders, and chronic respiratory diseases. Recent times have shown increased trends in incidence as well as prevalence of renal diseases. Hemodialysis is the most opted treatment modality for the patients of chronic renal diseases. Hence, the aim of the current chapter is to address the effect of renal diseases and its treatment on oral health. An extensive literature search from the year 2000 till 2015 was conducted to assess the effect of hemodialysis and renal diseases on various clinical parameters associated with oral health like dental caries, periodontal diseases, prevalence of calculus, etc. The literature review revealed that the dental health is compromised in the patients undergoing hemodialysis therapy. The oral healthrelated parameters get worsened with increasing duration of hemodialysis as well. The primary reason behind the debilitated periodontal condition among the patients may be attributed to the neglect of proper oral hygiene practices by the patient as they are preoccupied by more time-consuming and life-threatening kidney disease. A strong relation between oral health and hemodialysis has been observed. There is a need for further interdisciplinary research with emphasis on preventive dental treatment for the patients undergoing hemodialysis ensuring optimum outcome.

**Keywords:** hemodialysis, dental health, duration of dialysis, kidney diseases


**1. Introduction**

Humanoid robot is a complex machine with a series of joint and links. Biped motion asserts surpass advantage than the others due to flexibility and good adaption when moving on unpredictable surface. Difference from human beings, the humanoid robots have a limitation of structure and number of degree of freedom. Moreover, legged walking behavior requires an action of many active joints and is much more challenge in synthetic gait to keep balance. To solve this matter, the traditional approaches consider that ensuring Zero Moment Point within support polygon is important key. For example, Firstly, states of art is the works of Kajita [1–3] with the Linear Inverted Pendulum Model. Recently, Monje et al. [4] integrated the dynamic steadiness while moving in real time. Samadi and Moghadam-Fard [5] applied Gravity Compensated Inverted Pendulum Mode (GCIPM) with proposing that trajectory of ZMP is created by a first-order function. Kai Hu et al. [6] designed Compensative Zero-Moment Point Trajectory from the reference ZMP to decrease the effect of disturbances. Likewise, Yang et al. [7] presented bivariatestability-margin-based control model to compensate zero moment point and modeling error, opposition-based learning algorithm is applied to generated gait pattern.

In the other direction, a number of researchers concentrate on central pattern generator (CPG)-based walking. Alongside the very common studies in [8–10], we can mention some up-to-date prominent instances such that JimmyOr [11] proposed an approach based on combination of CPG and ZMP to control spine motion, it is promising way to enable natural walk of the robot. Wei Li et al. [12] developed a mechanism to generate muscle forces for biped motion, this method designed a feedback controller which is formed by a dynamic neural network with CPGs.

A optimization-based approach considering stability and walking speed was introduced by Goswami Dip et al. [13]. Likewise, In-sik Lim et al. [14] addressed a gait generation technique for legged walking up and down stairs, in which, genetic algorithm and the human motion data were used to produce the optimal trajectory. Newly, Ho Pham Huy Anh and Tran Thien Huan [15] optimized walking gait by modified Jaya optimization algorithm.

Other scholars are interested in model-predictive methods. For example, Zamparelli [16] et al. designed a stable model predictive control to generate CoM trajectory for the robot on uneven surface. Scianca [17] presented a prediction model with stability constraints. Hildebrandt et al. [18] proposed a model-predictive approach for generating walking gait of the robots with redundant kinematic design.

In this chapter, we proposed a novel gait generation method, in which, trigonometric function with randomized coefficients is used to produce trial gait data for conducting simulation. The result is collected to build approximation function of output: rotation angle value, lateral and walking distance. Then, we designed an optimization problem with constraints and applied an improve differential algorithm for solving it. Optimal coefficients is returned to trigonometric function and define it exactly. By setting up cycle time, walking gait data will be generated by explicit trigonometric function and can be used for reference data in control.

Next part of this chapter is organized into five divisions: The first section introduces the subject of this research named Kondo KHR-3. The second section assigns gait functions to actuator joints. Thirdly, optimization problem with constraint is built to optimize gait trajectory. The novel differential evolution algorithm with Gauss distribution is developed in Section 4 to solve optimization problem. Section 5 includes results and discussions. The final section summarizes achievements of this research.

### **2. Biped model of Kondo**

#### **2.1 Physical configuration**

The subject is presented in this chapter which is based on a humanoid robot named Kondo KHR-3 as depicted in **Figure 1a**. This robot consists of 22 degrees of freedom (DoF) However, we concentrated on lower body with 10 DoFs, in which 5 is the number of DoFs for each leg. The linkage configuration is shown in **Figure 1b**, where *θ*, *d*, *m* are rotation angle, length and weight of each link, respectively. Specially, the weigh of upper body is represented by *mo*. The structure parameters of the robot are described in **Table 1**.

based foot design to reduce weight and energy consumption, this research is specially meaningful for biped robot with limited physical parameters [26]. Our research presents a foot structure as shown in **Figure 2**, which is a combination of proposals mentioned in two papers [23, 26]. This sketch is built based on the following considerations: Firstly, all external forces acting on foot is at three areas consisting of heel, tip and big toe. Secondly, a passive toe joint mechanism with spring is applied to reduce impact of ground reaction force on foot. The material of

**Parameters Value** *do* 90.6 (mm) *d*1 38.5 (mm) *d*2 66.5 (mm) *d*3 62 (mm) *d*4 66 (mm) *d*5 168 (mm) *mo* 999.4 (g) *m*11,12 14 (g) *m*21,22 100 (g) *m*31,32 65 (g) *m*41,42 71.3 (g)

*Applying Improve Differential Evolution Algorithm for Solving Gait Generation Problem…*

Review on previous papers, we witness an arm swing mechanism which has been introduced and modeled using Adams in [27] as shown in **Figure 3**, the shoulder joint

is linked to the hip joint by two linear springs. This mechanism is expected to generate the reaction moment from the arms to the trunk which eliminates ground reaction torque [28]. It makes the robot stable in motion. Our research applies this structure for the robot and characteristic parameters of the linear spring are stiffness

foot is ABS plastic and design parameters are described in **Table 2a**.

of 0.8 ð Þ *newton=mm* and damping of 0.008 ð Þ *newton: sec =mm* .

**2.3 Arm swing mechanism**

*Structure parameters of humanoid robot.*

**Figure 1.**

**Table 1.**

**43**

*Biped of Kondo: a) real robot; b) linkage model.*

*DOI: http://dx.doi.org/10.5772/intechopen.98085*

#### **2.2 Foot structure with toe mechanism**

Review on the works of foot structure for humanoid robots, we can list very old papers such as [19–21]. Recently, Sadedel et al. proposed a passive toe design. This mechanism improves energy efficiency of ankle and knee joints [22]. Likewise, Nerakae and Hasegawa simulated human-like foot structure which consist of big and tip toe to enhance biped walking gait in toe-off period [23]. In the other direction, Magistris et al. studied soft sole to minimize effect of the ground reaction force on stability during heel-strike period [24]. In [25], Daichi developed topology*Applying Improve Differential Evolution Algorithm for Solving Gait Generation Problem… DOI: http://dx.doi.org/10.5772/intechopen.98085*

**Figure 1.** *Biped of Kondo: a) real robot; b) linkage model.*

#### **Table 1.**

can mention some up-to-date prominent instances such that JimmyOr [11] proposed an approach based on combination of CPG and ZMP to control spine motion, it is promising way to enable natural walk of the robot. Wei Li et al. [12] developed a mechanism to generate muscle forces for biped motion, this method designed a feedback controller which is formed by a dynamic neural network with CPGs. A optimization-based approach considering stability and walking speed was introduced by Goswami Dip et al. [13]. Likewise, In-sik Lim et al. [14] addressed a gait generation technique for legged walking up and down stairs, in which, genetic algorithm and the human motion data were used to produce the optimal trajectory. Newly, Ho Pham Huy Anh and Tran Thien Huan [15] optimized walking gait by

Other scholars are interested in model-predictive methods. For example, Zamparelli [16] et al. designed a stable model predictive control to generate CoM trajectory for the robot on uneven surface. Scianca [17] presented a prediction model with stability constraints. Hildebrandt et al. [18] proposed a model-predictive approach for generating walking gait of the robots with redundant kinematic design. In this chapter, we proposed a novel gait generation method, in which, trigonometric function with randomized coefficients is used to produce trial gait data for conducting simulation. The result is collected to build approximation function of output: rotation angle value, lateral and walking distance. Then, we designed an optimization problem with constraints and applied an improve differential algorithm for solving it. Optimal coefficients is returned to trigonometric function and define it exactly. By setting up cycle time, walking gait data will be generated by explicit trigonometric function and can be used for reference data in control.

Next part of this chapter is organized into five divisions: The first section introduces the subject of this research named Kondo KHR-3. The second section assigns gait functions to actuator joints. Thirdly, optimization problem with constraint is built to optimize gait trajectory. The novel differential evolution algorithm with Gauss distribution is developed in Section 4 to solve optimization problem. Section 5 includes results and discussions. The final section summarizes achievements of

The subject is presented in this chapter which is based on a humanoid robot named Kondo KHR-3 as depicted in **Figure 1a**. This robot consists of 22 degrees of freedom (DoF) However, we concentrated on lower body with 10 DoFs, in which 5 is the number of DoFs for each leg. The linkage configuration is shown in **Figure 1b**, where *θ*, *d*, *m* are rotation angle, length and weight of each link, respectively. Specially, the weigh of upper body is represented by *mo*. The structure parameters

Review on the works of foot structure for humanoid robots, we can list very old papers such as [19–21]. Recently, Sadedel et al. proposed a passive toe design. This mechanism improves energy efficiency of ankle and knee joints [22]. Likewise, Nerakae and Hasegawa simulated human-like foot structure which consist of big and tip toe to enhance biped walking gait in toe-off period [23]. In the other direction, Magistris et al. studied soft sole to minimize effect of the ground reaction force on stability during heel-strike period [24]. In [25], Daichi developed topology-

modified Jaya optimization algorithm.

*Robotics Software Design and Engineering*

this research.

**42**

**2. Biped model of Kondo**

**2.1 Physical configuration**

of the robot are described in **Table 1**.

**2.2 Foot structure with toe mechanism**

*Structure parameters of humanoid robot.*

based foot design to reduce weight and energy consumption, this research is specially meaningful for biped robot with limited physical parameters [26]. Our research presents a foot structure as shown in **Figure 2**, which is a combination of proposals mentioned in two papers [23, 26]. This sketch is built based on the following considerations: Firstly, all external forces acting on foot is at three areas consisting of heel, tip and big toe. Secondly, a passive toe joint mechanism with spring is applied to reduce impact of ground reaction force on foot. The material of foot is ABS plastic and design parameters are described in **Table 2a**.

#### **2.3 Arm swing mechanism**

Review on previous papers, we witness an arm swing mechanism which has been introduced and modeled using Adams in [27] as shown in **Figure 3**, the shoulder joint is linked to the hip joint by two linear springs. This mechanism is expected to generate the reaction moment from the arms to the trunk which eliminates ground reaction torque [28]. It makes the robot stable in motion. Our research applies this structure for the robot and characteristic parameters of the linear spring are stiffness of 0.8 ð Þ *newton=mm* and damping of 0.008 ð Þ *newton: sec =mm* .

Where *θi* is the angle assigned to joint *i*, *ai*, *bi*,*ci*, *di* are coefficients; *t*, *i* are time

0; *t* ¼ 0 *or t*≥3*:*6 �1*:*5; *t* ¼ 0*:*3&*t* ¼ 3*:*3 *θ*1ð Þ*t* ; 0*:*3 <*t*< 3*:*3

0; *t*≤0*:*3 *or t*≥ 3*:*6 *θ*2ð Þ *t* þ 0*:*6 ; 0*:*3<*t*< 3*:*3 15; *t* ¼ 3*:*3

0; *t*≤0*:*3 *or t* ≥3*:*6 *θ*3ð Þ *t* þ 0*:*6 ; 0*:*3<*t* <3*:*3 30; *t* ¼ 3*:*3

0; *t*≤0*:*3 *or t* ≥3*:*6 *θ*4ð Þ *t* þ 0*:*6 ; 0*:*3<*t* <3*:*3 15; *t* ¼ 3*:*3

0; *t* ¼ 0 *or t*≥ 3*:*3

0; *t* ¼ 0 *or t*≥ 3*:*3

0; *t* ¼ 0 *or t*≥ 3*:*3

15; *t* ¼ 0*:*3 *θ*2ð Þ*t* ; 0*:*3<*t*< 3*:*3

30; *t* ¼ 0*:*3 *θ*3ð Þ*t* ; 0*:*3<*t*< 3*:*3

15; *t* ¼ 0*:*3 *θ*4ð Þ*t* ; 0*:*3<*t*< 3*:*3

Response surface model (RSM) is a mathematical model which is used for an approximation of stochastic process and is firstly introduced by Box and Wilson [27]. Our research adopts 3*rd*-order RSM to predict output value of simulation such as lateral and walking distance, rotation angle. The expression of 3*rd*-order RSM is

*cpiix*2

Where *n* is a design variable number, *n* = 16, *xi* is a design variable, and *ap*, *bp*, *cp*, *dp* are the coefficients of terms. Number of sampling for initialization is calculated by

*ii* þ X*n ij i*ð Þ <*j* *cpijxix j* þX*n*

*i*¼1

*dpiix*3

*ii:* (9)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

and index of joint, respectively; *ω* is an angular velocity, *ω* = 5.236 (*rad=s*)

*Applying Improve Differential Evolution Algorithm for Solving Gait Generation Problem…*

*θ*1 ¼

8 ><

>:

8 ><

>:

8 ><

>:

8 ><

>:

8 ><

>:

8 ><

>:

*θ*5 ¼

*θ*6 ¼

*θ*7 ¼

**4. Optimization problem with predictive function**

**4.1 Response surface methodology**

*P x* ~ð Þ¼ *apo* þX*n*

*i*¼1

*bpixi* þX*n*

*i*¼1

displayed by Eq. (9).

Eq. 10.

**45**

*θ*2 ¼

*DOI: http://dx.doi.org/10.5772/intechopen.98085*

*θ*3 ¼

*θ*4 ¼

8 ><

>:

**Figure 2.** *Novel foot design.*

**Figure 3.** *Principle of arm swing: a) mechanism with linear spring; b) integration in simulation model.*


**Author details**

Asma Mohammed Bahurmoz King Abdulaziz University, Jeddah, Saudi Arabia

\*Address all correspondence to<EMAIL_ADDRESS>
© 2020 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

*Measuring Corporate Social Responsibility Performance: A Comprehensive AHP Based Index DOI: http://dx.doi.org/10.5772/intechopen.94463*