**1. Introduction**

Sagittal spinal alignment is more strongly correlated than coronal spinal alignment to health-related quality of life (HRQOL) [1] even for mild spinal deformity, which can be an important barometer of health status for ordinary citizens. Sagittal spinal alignment deteriorates with age in community-dwelling older people [2–4]. In addition, an increase in sagittal vertical axis (SVA; anteriorization of the center of gravity line of the cervical spine base) is associated with a decrease in lumbar lordosis [5]. Age-related changes in lumbopelvic condition are known to affect sagittal spinal alignment. Two epidemiological studies conducted in different regions corroborated the finding of a characteristic gender difference in the process of spinal alignment change with aging. Specifically, alignment changes over time in males were prominent in the cervical spine region, while females predominantly displayed changes in the lumbo-pelvic area [3,4]. However, no clear evidence has been presented on the reasons for such phenomena. Spinal alignment can be affected by a variety of factors, including activity level and profession. Age-related cervical spondylosis may contribute to poor alignment of the cervical spine [6]. This study aimed to clarify the pathomechanism of sagittal cervical alignment changes in community-dwelling older residents.

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

#### *2.1. Creation of a Randomly Sampled Resident Cohort for Epidemiological Survey*

In the establishment of a new population study of Japanese people, we employed random sampling from the basic resident registry of a cooperating town to minimize selection bias and obtain a cohort representative of the general population. Residents between the age of 50 and 89 years were randomly sampled from the basic resident registry of a town to construct a 415-participant cohort termed "the Obuse study" cohort. "Obuse" is the name of the cooperating town located in the central inland area of Japan, with a population of approximately 10,000 people. The Obuse study is a comprehensive investigation on the locomotion health of community-dwelling older people. In the Obuse study cohort, 411 individuals who were able to stand unassisted and whose cervical spinal alignment could be measured were subjected to analysis. According to participant interview results, 21 subjects with a history of thoracolumbar spondylosis and five with a history of rheumatoid arthritis were included. As they were not in such a condition that would cause them to lose their standing balance, they were added to the analysis. Individuals with spinal instrumentation surgery were not included, and those with diagnosed illnesses that significantly altered balance, such as adult spinal deformity and Parkinson's disease, were excluded as well.

#### *2.2. X-ray Examination and Measurement of Spinal Alignment*

All participants underwent lateral X-ray photography for the measurement of sagittal spinal alignment parameters, including C2–C7 sagittal vertical axis (CSVA; the distance between a plumb line from the center of the C2 vertebral body and posterior superior corner of C7), C2–C7 cervical lordosis (CL; the angle between the C2 inferior endplate and C7 inferior endplate), T1 slope (T1S), and SVA. The average values of measurements by two board-certified spine surgeons and a trained staff member were used for each parameter. The inter-rater reliability of each parameter was as follows: 0.96 for CSVA, 0.88 for CL, 0.88 for T1S, and 0.95 for SVA. The presence of cervical spondylotic changes was also recorded. The two spine surgeons independently determined the presence or absence of spondylotic changes, with cases determined as having spondylosis by both raters being regarded as spondylotic (inter-rater reliability: 0.95). Osteophyte formation around the vertebral endplates with a loss of intervertebral disc height as well as osteophyte formation and osteosclerotic change of the articular facet joints were defined as spondylotic changes.

#### *2.3. HRQOL Assessments*

SF-8 ™ Health Survey measures were determined for all participants for HRQOL evaluation. Results were calculated and expressed as two summary scores: physical component summary (PCS) and mental component summary (MCS).

#### *2.4. Statistical Analysis*

We compared cervical sagittal spinal alignment parameters between spondylotic and non-spondylotic groups using linear regression models. The response variable was the alignment parameter and the explanatory variables were the presence of cervical spondylosis and age. The Pearson correlation coefficient between T1S minus CL, which is also known as the residual lordotic compensation for subcervical anterior tilting [7], and CSVA were assessed for each gender. We examined the correlation between cervical and subcervical alignment parameters following age adjustment for each gender. For other analyses, Welch's t-test was used to compare quantitative variables, and Fisher's exact test was used to compare qualitative variables. Statistical analyses were carried out using the statistical package R, version 3.4.3 (available at http://www.r-project.org accessed on 26 November 2021). The level of significance was set at *p* < 0.05.


**Margherita Sisto \*, Domenico Ribatti and Sabrina Lisi**

Department of Basic Medical Sciences, Neurosciences and Sensory Organs (SMBNOS), Section of Human Anatomy and Histology, University of Bari "Aldo Moro", 70124 Bari, Italy<EMAIL_ADDRESS>(D.R<EMAIL_ADDRESS>(S.L.)

**\*** Correspondence<EMAIL_ADDRESS>Tel.: +39-080-547-8315; Fax: +39-080-547-8327

Received: 3 July 2020; Accepted: 28 August 2020; Published: 31 August 2020

**Abstract:** Sjögren's syndrome (SS) is a systemic autoimmune inflammatory disease with a poorly defined aetiology, which targets exocrine glands (particularly salivary and lachrymal glands), affecting the secretory function. Patients suffering from SS exhibit persistent xerostomia and keratoconjunctivitis sicca. It is now widely acknowledged that a chronic grade of inflammation plays a central role in the initiation, progression, and development of SS. Consistent with its key role in organizing inflammatory responses, numerous recent studies have shown involvement of the transcription factor nuclear factor κ (kappa)-light-chain-enhancer of activated B cells (NF-κB) in the development of this disease. Therefore, chronic inflammation is considered as a critical factor in the disease aetiology, offering hope for the development of new drugs for treatment. The purpose of this review is to describe the current knowledge about the NF-κB-mediated molecular events implicated in the pathogenesis of SS.

**Keywords:** Sjögren's syndrome; NF-κB; inflammation


**Author details**

Dimas Bagus Wiranatakusuma\*, Imamuddin Yuliadi and Ikhwan Victhori International Program for Islamic Economics and Finance, Faculty of Economics and Business, Department of Economics, Universitas Muhammadiyah Yogyakarta, Yogyakarta, Indonesia

\*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.

*Risk Analyses on Islamic Banks in Indonesia DOI: http://dx.doi.org/10.5772/intechopen.92245*


**4.1 Discussion of the obtained results**

According to **Table 2**, we construct the following graphs to assess the asymmetry in the muscles. The graph shows the results according to the angular values on the horizontal axis and the results according to the power values on the vertical axis (**Figure 8**). As can be seen from the graph, the muscle strengths in the right and left legs differ from each other at certain angular velocity values during abduction. At some angular velocity values, the muscle forces in the right and left legs are the same (30°/sec, 60°/sec, 180°/sec, 360°/sec), and these values indicate that there is no asymmetry. We do not take these prices into account. At different values of angular velocity, the asymmetry

**Figure 8.** *Abduction of the right and left leg (thigh).*

*Methods and Tools for Assessing Muscle Asymmetry in the Analysis of Electromyographic… DOI: http://dx.doi.org/10.5772/intechopen.103061*

#### **Figure 9.**

*Histogram for asymmetry assessment during right and left leg abduction.*

between the right and left foot is also different. At some values, the asymmetry is less noticeable (120°/sec, 210°/sec, 300°/sec, 330°/sec, 390°/sec, 450°/sec). At some values, there is a sharp asymmetry (90°/sec, 150°/sec, 240°/sec, 270°/sec).

The histogram of the results is shown in **Figure 9**.

#### **4.2 The result**

The minimum difference between right and left muscle strength is 5 W/kg, and the maximum difference is 30 W/kg. Given that the difference between these values is 25 W/kg, the difference in power values of 12 + 5, i.e. 17 W kg and below, in the assessment of asymmetry during abduction between the right and left arm is a natural asymmetry, and values above 17 W/kg it would be more correct to accept the existing asymmetry.

The minimum difference between right and left muscle strength is 5 W/kg, and the maximum difference is 70 W/kg. Since the difference between these values is 65 W/kg, differences in muscle strength of 32 + 5, i.e. 37 W/kg and below, can be considered as a natural asymmetry, and differences in muscle strength greater than 37 W/kg can be considered as existing asymmetry.


**Meet the editor**

Dr. Mohsen Mhadhbi received his PhD degree in Chemistry from the Faculty of Sciences of Sfax, University of Sfax (Tunisia). Since 2011, he has been an Assistant Professor and a member of a research team at the Laboratory of Useful Materials, National Institute of Research and Physical-Chemical Analysis, University of Carthage (Tunisia), focusing on the synthesis and characteriza-

tion of nanomaterials for industrial responders (hydrogen storage, cutting tools, and biomedical applications). He served as a teacher in Inorganic Chemistry at different institutes in Tunisia and supervised several researchers in Materials Science. He has published works in national and international impacted journals and books. Dr. Mhadhbi is a member of different associations. He is also a reviewer and an editorial board member of different scientific journals and congresses.

Contents

**Preface VII**

Mohsen Mhadhbi

**Material 7**

**Materials 9**

Manish K. Rathod

Cheng Wang and Ye Zhu

**Section 1 An Introduction to Phase Change Material 1**

Chapter 1 **Introductory Chapter: Phase Change Material 3**

**Section 2 Experimental and Numerical Study of Phase Change**

Chapter 2 **Experimental and Numerical Studies on Phase Change**

**Section 3 Thermal Stability of Phase Change Material 35**

Chapter 3 **Phase Change Materials and Their Applications 37**

**Section 4 Latent Heat Thermal Energy Storage System 59**

Chapter 4 **Latent Heat Thermal Energy Storage System 61**

Chapter 5 **Thermodynamic Properties of the Polyols as Phase Change Materials for Thermal Energy Storage 83**

**Section 5 Applications of Phase Change Material 81**

Zhicheng Tan, Quan Shi and Xin Liu

Ponnuraj Stella Jesumathy


**2.2 KPI modeling**

### *2.2.1 KPI modeling issues*

The KPI modeling seems to be one of the most important actions closely related to KPI indicator processing and they have to indicate appropriate properties in order to be denoted as the good KPIs.

However, those properties may be seen as the first aspects concerned with KPI validation as well, while they night be postulated as follows [2].

However, the above-mentioned KPI indicator properties seem to be only one side concerned with KPI indicator modeling [15, 16].

**The second aspect** is closely related to KPI attributes postulated as KPI name, Type, Scale, Source, Owner, Threshold, and Hardness.

**The third aspect** is the performance indicator expression. It is "a mathematical statement over a performance indicator evaluated to a numerical, qualitative or Boolean value for a time point, for the organization, unit or agent. For example, P I27 ≤ 48h."

The **fourth aspect** concerned with KPI formalization is the performance indicator expression. It is "a mathematical statement over a performance indicator. The authors suggest specifying the required values of KPIs as constraints coming from goals. The authors claim that they integrate the performance view with the process, organization and agent-oriented views. However, there is no information about the process semantics used for modeling and no evidence about validation of the PI properties. In any case, the authors write about the process views of the real organizations, not about the abstract processes that are proposed [9, 15, 16].

#### *2.2.2 KPI modeling approaches and methods*

#### *<IP_ADDRESS> MetricM method*

The method MetricM [18] "is built upon and extends an enterprise modelling approach to benefit from he reuse of modelling concepts to provide relevant organizational context, including business objectives, organizational roles and responsibilities." The method can be adapted to any enterprise modeling approach. The modeling language.

MetricML used in MetricM "adds essential concepts to modelling performance indicators and semantics to key modelling concepts." The concept Indicator is used to present a KPI.

*Business Process Linguistic Modeling: Theory and Practice Part I: BPLM Strategy Creator DOI: http://dx.doi.org/10.5772/intechopen.95096*

The MetricML Indicator metatype is used for modeling its relations to other indicator types, to reference object types representing organizational context and to goal types [2].

### *<IP_ADDRESS> Attribute approach*

predictive models of future performance based on specified business objectives

The KPI modeling seems to be one of the most important actions closely related

However, those properties may be seen as the first aspects concerned with KPI

to KPI indicator processing and they have to indicate appropriate properties in

• KPI needs to be sensitive to changes of the business process state.

• KPI should be oriented to improvement, not to conformance to plans

However, the above-mentioned KPI indicator properties seem to be only one

**The second aspect** is closely related to KPI attributes postulated as KPI name,

**The third aspect** is the performance indicator expression. It is "a mathematical statement over a performance indicator evaluated to a numerical, qualitative or Boolean value for a time point, for the organization, unit or agent. For example,

The **fourth aspect** concerned with KPI formalization is the performance indicator expression. It is "a mathematical statement over a performance indicator. The authors suggest specifying the required values of KPIs as constraints coming from goals. The authors claim that they integrate the performance view with the process, organization and agent-oriented views. However, there is no information about the process semantics used for modeling and no evidence about validation of the PI properties. In any case, the authors write about the process views of the real organizations, not about the abstract processes that are proposed

The method MetricM [18] "is built upon and extends an enterprise modelling approach to benefit from he reuse of modelling concepts to provide relevant organizational context, including business objectives, organizational roles and responsibilities." The method can be adapted to any enterprise modeling approach. The

MetricML used in MetricM "adds essential concepts to modelling performance indicators and semantics to key modelling concepts." The concept Indicator is used

• KPI should be linear, (d) a KPI should be semantically reliable,

validation as well, while they night be postulated as follows [2].

and resource allocations [17].

order to be denoted as the good KPIs.

• KPI should be efficient,

P I27 ≤ 48h."

[9, 15, 16].

*<IP_ADDRESS> MetricM method*

modeling language.

to present a KPI.

**162**

• KPI should be in a quantifiable form.

*Operations Management - Emerging Trend in the Digital Era*

side concerned with KPI indicator modeling [15, 16].

Type, Scale, Source, Owner, Threshold, and Hardness.

*2.2.2 KPI modeling approaches and methods*

**2.2 KPI modeling**

*2.2.1 KPI modeling issues*

An alternative "attribute" approach conceptualizes performance indicator as (meta-) attribute of metatypes (e. g "average throughput time" of a business process type or "average number of employees" of an organizational unit type). Alternative approach for KPI modeling in our method is used. MetricM uses declarative models. The model of underlying processes needed for validation of KPI properties are not used in MetricM. The two approaches, presented above, build upon ideas of many earlier approaches to KPI modeling. The general tendency is to postpone the validation of the KPI properties to the moment when the process model of the organization is ready.

#### *<IP_ADDRESS> Semantics synchronous and asynchronous modeling*

However, the KPIs are defined at a different level of abstraction, namely at the tactical and strategic level, i.e. at the level of observable states of the system and the asynchronous modeling does not provide the right level of abstraction [15, 16].

The synchronous modeling semantics is based on the CSP parallel composition operator defined by Hoare [19]. The operator defines that an event from environment is accepted by the model if all processes of this model are able to accept it. Otherwise, the event is refused.

Although there were many applications of the CSP parallel composition operator in the architecture description languages [20] in programming languages [21] only after the extension of this operator for machines with data, made by McNeile [22] the operator became practical for business system modeling. The Protocol Modeling proposed in enables coping with complexity of business modeling. The reason is that the synchronous semantics decreases the data space of models.

#### *<IP_ADDRESS> KPI indicator linguistic modeling approach*

This approach is based on existence of linguistic sets, while they represent KPI modeling static aspects. However, there are many relations among those linguistic sets as well, while they are quantified via PBPL Equation [10, 11, 23, 24]. This approach is discussed in Section 4 in more details.

#### **2.3 KPI indicator decomposition**

The KPI indicators are designed and closely related to core business processes implemented and operated at strategic management level and have a nature of so called initial and primary KPI indicators, which should be decomposed to secondary and tertiary KPI indicators. The secondary indicators are closely related to main BP management at tactic level and the tertiary KPI indicators are closely related to subordinated and elementary BP management at operational level. This approach to KPI indicator decomposition is discussed in Section 4. However, the KPI decomposition is closely related to business dashboard existence [13, 25, 26].

*A dashboard in business is a tool used to manage all the business information from a single point of access.* It helps managers and employees to keep track of the company's KPIs and utilizes business intelligence to help companies make data-driven decisions.

There are 4 general subtypes of dashboards: (a) Strategic - focused on long-term strategies and high-level metrics, (b) Operational - shows shorter time frames and operational processes. (c) Analytical - contains vast amounts of data created by analysts and (d) Tactical - used by mid-management to track performance.

**4.1 BPLM strategy creator – structure and functionality BPLM strategy**

*Business Process Linguistic Modeling: Theory and Practice Part I: BPLM Strategy Creator*

Any business is getting started by business mission statement and business objectives and adequate business process establishment. Those three categories create an integral part of any business strategy. However, before we determine a set of business quantitative and qualitative indicators, real possibilities should be known to apply our business results at an appropriate market area and collect initial information. Usually, the information is stored at different media and documents. However, we have to make a preliminary document content semantic analysis in order to gain a required information and this is an initial action, which should be done with the use of the proposed BPLM Strategy Creator. This type of the document semantic analysis enables providing the document categorization and show use which documents should create basis for processing of business strategy qualitative aspects. Furthermore, we are interested in those documents, which contain data closely related to business strategy quantitative aspects, which might be quantified via indicators denoted as key performance indicators (KPI indicators). However, they usually are not in that form and shape as we need. Therefore, we have to provide the second type of document analysis in order to extract required data – usually denoted as the initial data, which should inform us which products related to our business could be accepted by the market, in which quantity and quality and what about financial assets could be gained. This data type could create content of

Assetst]}. Because the data are of a linguist nature those

. This is only one side of the coin, while we to know what about

Costs (0)]} linguistic sets. The data represent the first BPLM Strategy crea-

Assetst *;* XTotfin

Costs ð Þ 0 *;* ½ � SAD ið Þ *;* j *;* ½ � HR ið Þ *;* j *;* ½ � TECH ið Þ *;* j

Costs ð Þ 0 ,

Assetst]}, contains data

Costs (0)]},

(1)

**creator – structure and functionality – qualitative view**

*4.1.1 Strategic management level*

*DOI: http://dx.doi.org/10.5772/intechopen.95096*

sets {[YTotfin

{[XTotmat

postulated

**165**

f g ½ � KPI 0ð Þ ¼ YTotfin

to material assets1

Assetst]}, {[YTotmat

sets are denoted as linguistic sets. The linguistic set {[YTotfin

mentioned output products and they are stored within {[XTotfin

closely related to financial assets and the linguistic set contains data closely related

tor output, which is called the **basic output** as well, while the financial costs play a role of principal importance, but are not sufficient for production getting started. We have to know what about customers will buy our products, what about human resources with required theoretical knowledge and practical skills, and what about production technological devices and tools are needed, as well. This types of data

quantifies potential customers denoted as mainframe customers, the linguistic set {[HR (i, j)]} quantifies mainframe human resources and the {[TECH (i, j)]} linguistic set quantifies mainframe production technological devices and tools. A qualifier "mainframe" indicates that the linguistic set content is not specified in more details. When adding that linguist sets to the above-mentioned basic output we get the **initial BPLM** Strategy creator output, while formula (1) might be

investments (financial costs) are needed in order to pro produce the above-

are being stored in further linguistic sets. The linguistic set {[SAD (i, j)]}

Assetst , YTotmat

which represent so called the **total initial KPI** indicators.

XTotmat

1 How many pieces of the actual output products could be produced.

**A strategic dashboard** is a reporting tool for monitoring the long-term company strategy with the help of critical success factors. They're usually complex in their creation, provide an enterprise-wide impact to a business and are mainly used by senior-level management [27–29].

**An analytical dashboard** is a type of dashboard that contains a vast amount of data created and used. They supply a business with a comprehensive overview of data, with middle management being a crucial part of its usage.

**A tactical dashboard** is utilized in the analysis and monitoring of processes conducted by mid-level management, emphasizing the analysis.

Then an organization effectively tracks the performance of a company's goal and delivers analytic recommendations for future strategies [30].


Section 2 Inverse Problem

**Chapter 6**

**Abstract**

proposed method.

**1. Introduction**

ent application in mind [1–15].

discussion on some numerical aspects.

**105**

A Numerical Approach to Solving

Levenberg-Marquardt Algorithm

This chapter is intended to provide a numerical algorithm involving the combined use of the Levenberg-Marquardt algorithm and the Galerkin finite element method for estimating the diffusion coefficient in an inverse heat conduction problem (IHCP). In the present study, the functional form of the diffusion coefficient is an unknown priori. The unknown diffusion coefficient is approximated by the polynomial form and the present numerical algorithm is employed to find the solution. Numerical experiments are presented to show the efficiency of the

**Keywords:** parabolic equation, inverse problem, Levenberg-Marquardt

The numerical solution of the inverse heat conduction problem (IHCP) requires

to determine diffusion coefficient from an additional information. Inverse heat conduction problems have many applications in various branches of science and engineering, mechanical and chemical engineers, mathematicians and specialists in many other sciences branches are interested in inverse problems, each with differ-

In this work, we propose an algorithm for numerical solving an inverse heat conduction problem. The algorithm is based on the Galerkin finite element method and Levenberg-Marquardt algorithm [16–17] in conjunction with the least-squares scheme. It is assumed that no prior information is available on the functional form of the unknown diffusion coefficient in the present study, thus, it is classified as the function estimation in inverse calculation. Run the numerical algorithm to solve the unknown diffusion coefficient which is approximated by the polynomial form. The Levenberg-Marquardt optimization is adopted to modify the estimated values.

The plan of this paper is as follows: in Section 2, we formulate a one-dimensional IHCP. In Section 3, the numerical algorithm is derived. Calculation of sensitivity coefficients will be discussed in Section 4. In order to discuss on some numerical aspects, two examples are given in Section 5. Section 6 ends this paper with a brief

an Inverse Heat Conduction

*Tao Min, Xing Chen, Yao Sun and Qiang Huang*

Problem Using the


Though the above equations are presented for calculations along the ГХ direction, the corresponding formula for ГM direction can be similarly transcribed. Due to the obvious link between the bulk (shear) modulus and monopolar (quadrupolar) resonance, it is more convenient to introduce κ eff 11 12 = + ( ) CC2 and ( ) 11 12 2 μ*eff* = − *C C* as effective elastic bulk modulus and shear modulus. The results for κ *eff* and μ*eff* evaluated from the relevant eigenstates are plotted in Figs. 11(d) and 11(e). In the lower negative band, κ *eff* is positive and finite, while μ*eff* is negative and diverges at the Г point, which is in accordance with the quadrupolar resonance. In the higher negative band, μ*eff* is positive and finite, while κ *eff* is negative and diverges at the Г point, which is induced by the monopolar resonance.

Knowing the effective moduli, the corresponding dispersion relations can be calculated by using Christoffel's equation. Along the ГХ direction, compressional wave and shear wave velocities are given by by *C*11 ρ and *C*44 ρ , respectively; whereas along the ГМ direction the compressional and shear wave velocities are (*CC C* 11 12 44 + + 2 2 )( ) ρ and ( )( ) 11 12 *C C*− 2ρ . The effective medium results show that the lower negative band supports a longitudinal (transverse) wave along ГХ (ГM) direction, whereas the upper negative band only allows longitudinal wave in both ГХ and ГM directions. The corresponding results obtained from the EMT are also plotted in Fig. 11(a) by crosses. Excellent agreements between the finite element results and the EMT prediction are found.

#### **6. Some intriguing properties of elastic metamaterials**

Like their EM and acoustic counterparts, elastic metamaterials have shown many intriguing wave transport properties. For example, the total mode conversion and the super-anisotropy are two of them. The total mode conversion can completely convert the incident transverse (longitudinal) wave into a refracted longitudinal (transverse) wave. It is an analogue of the Brewster angle in the EM case (for example, Jackson, 1999), but in a much more stringent and complex manner. It only occurs on the interface between a normal solid and an elastic metamaterial with negative refractive index (Wu et al. 2011). The super-anisotropic behavior has been demonstrated in Section 5.2. Also shown there is the property of sustaining only a longitudinal wave at certain frequencies, which is so-called "fluid-like" solids, blurring the distinction between solids and fluids (Lai et al., 2011).

Effective Medium Theories and Symmetry Properties of Elastic Metamaterials 165

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#### **7. Conclusion**

In this chapter, the effective medium properties of 2D elastic metamaterials have been reviewed. Unlike EM or acoustic metamaterials, the elastic metamaterial is in general anisotropic unless the lattice structure is a hexagon with isotropic scatterers. For the isotropic elastic metamaterial, the EMT may be derived from CPA. For the anisotropic metamaterial, the EMT may be obtained from the MST in conjunction with Christoffel's equation, or from the integration of eigenfields on the boundaries. EMT could greatly facilitate the design of new elastic metamaterials, such as rubber-coated water cylinder embedded in foam which gives rise to large negative bands for shear waves and a multimass locally resonant structure which results in both negative bands for longitudinal waves and super-anisotropic negative bands.

Elastic metamaterial opens a new research area. The experimental realization would be much more challenging and exciting. The generalization of EMT as well as the symmetry property to more complex lattice structures, such as rectangular lattices, would also be of interest as it will introduce even stronger anisotropy. Meanwhile, finding an EMT that can also treat the rotational modes is a challenging task. Such modes are normally excited at lower frequencies and form flat bands in the band structures.

#### **8. Acknowledgments**

The relevant work was supported by Hong Kong RGC Grant No. 605008, and start-up packages from KAUST and Soochow University.

#### **9. References**

In this chapter, the effective medium properties of 2D elastic metamaterials have been reviewed. Unlike EM or acoustic metamaterials, the elastic metamaterial is in general anisotropic unless the lattice structure is a hexagon with isotropic scatterers. For the isotropic elastic metamaterial, the EMT may be derived from CPA. For the anisotropic metamaterial, the EMT may be obtained from the MST in conjunction with Christoffel's equation, or from the integration of eigenfields on the boundaries. EMT could greatly facilitate the design of new elastic metamaterials, such as rubber-coated water cylinder embedded in foam which gives rise to large negative bands for shear waves and a multimass locally resonant structure which results in both negative bands for longitudinal waves

Elastic metamaterial opens a new research area. The experimental realization would be much more challenging and exciting. The generalization of EMT as well as the symmetry property to more complex lattice structures, such as rectangular lattices, would also be of interest as it will introduce even stronger anisotropy. Meanwhile, finding an EMT that can also treat the rotational modes is a challenging task. Such modes are normally excited at

The relevant work was supported by Hong Kong RGC Grant No. 605008, and start-up

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**7. Conclusion**

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**Section 2**

**The Performance of Metamaterials**


**Author details**

Elisabeth Resch and Bernhard Resch *Research Unit for Neonatal Infectious Diseases and Epidemiology, Division of Neonatology, Department of Pediatrics, Medical University of Graz, Austria*