**2. Problem statements**

Nowadays food industry makes a significant contribution to national economy in many developing countries. Here in Ethiopia the economy depend on agricultural and which accounts 43.2% of gross domestic product (GDP) [7]. Also there is less contribution in an improvement of biscuit industry analyzed and waste minimization. There is different waste that are identified in six sigma (DMAIC) on NAS food Plc. Currently the company only uses 30% of its capacity and produce 3000 carton per day via 349 workers but it can produce 10,000 cartons with 1000 workers. As a result the value of waste ratio is 36.7%, this show non lean and can be categorized as a traditional company [8]. The defect of the company also calculated and defect per million are 67,308. This shows that the biscuit production of has a production capability with a failure of 67,308 every 1000,000 productions or equivalent to 6.73% loss and this indicates the production process still has a high failure rate. The other problem here is there are limited studies were conducted so far to implement waste minimization tools like six sigma, lean and MBNQA approach on Ethiopian food processing industries [9].

*Development of Integrated Lean Six Sigma-Baldrige Framework for Manufacturing Waste… DOI: http://dx.doi.org/10.5772/intechopen.95279*


**4. Conclusions**

Generally, there are many unexploited huge potentials from the etchedgraphene products, but the perspectives are bright. If these etching technologies are extended to other nanomaterials such as transition metal dichalcogenides (TMDs) or transition metal carbides, nitrides, and carbonitrides (MXenes), and black phosphorous [42], it will definitely achieve high-quality electronics and optoelectronics. Bandgap tuning for nanomaterials will significantly improve the on/off current ratio, photoresponsivity, quantum efficiency, conductivity and others. Layer-by-layer etching for multilayer materials by low-energy plasma technology (double mesh grids inserted for plasma apparatus such as chlorineradical ICP, neutral-beam ICP and ion beam ICP) with no physical damage would be the next research direction and can be applied to the other low-dimensional materials [28, 43] to achieve ultrahigh performance of electronic and optoelectronic devices [28, 43]. For instance, in the latest report in 2019, Kim et al. utilized a chlorine ICP innovative plasma apparatus that has no physical damage effect by inserting double mesh grids for cyclic ALE process on intrinsic multilayer MoS2 and successfully fabricated heterostructured photodetector with ultraresponsivity (~106 A/W) in the visible range [43].

**69**

**Author details**

South Korea

Phuong V. Pham1,2,3

University (SKKU), Suwon, South Korea

provided the original work is properly cited.

1 SKKU Advanced Institute of Nano Technology (SAINT), Sungkyunkwan

3 School of Information Science and Electronic Engineering, College of

Microelectronics, Zhejiang University, Hangzhou, China

\*Address all correspondence to<EMAIL_ADDRESS>
2 Center for Multidimensional Carbon Materials, Institute for Basic Science, Ulsan,

© 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,

*The New Etching Technologies of Graphene Surfaces DOI: http://dx.doi.org/10.5772/intechopen.92627*


Preface

Environment and energy are two of the most important issues facing humanity today. The textile industry consumes a considerable amount of energy and water during the manufacturing processes. Energy and water consumption is closely associated with environmental issues, because production also means environmental pollution and water and energy shortage. Environmental problems caused by the textile industry can be studied under four classes: air, water, solid waste pollution, and noise. Waste management for solving environmental problems is realized by the utilization of cleaner technologies, reuse, material recycling, material and energy recovery, storage without recycling, or disposal by burning.

In this book, the relationship between the textile industry and the environment is examined from four different viewpoints, for which the basis is the waste management steps specified above. Recycling of spinning mill wastes, ozone usage that provides less chemical and water utilization, reuse of treated water in the dyeing processes, and approaches in the treatment of waste waters of dyeing plants and finishing factories are solutions offered to reduce environmental pollution arising from textile production processes. On the other hand, application of phase change materials to textile materials is examined in one chapter. The possibility of utilizing textile materials to which phase change materials are applied, not only for comfort purposes but also as energy storage materials, means that technical textiles could be a solution for energy storage. Briefly, the relationship between the textile industry and the environment both as a source of and as a solution to pollution is mentioned in this book.

I thank all the authors who have contributed to this book and hope that it will be helpful to the readers.

> **Dr. Ayşegül Körlü** Professor, Ege University, Engineering Faculty, Department of Textile Engineering, İzmir, Turkey

**1**

**Chapter 1**

**Abstract**

**1. Introduction**

Sustainable Production Methods

The textile industry is part of the industries that continuously harm the environment because of the high water consumption and the presence of various pollutants in the wastewater. Wastewater treatment is lacking or includes only physical treatment in underdeveloped and developing countries due to installation and operating costs of a treatment plant. As a result, a broad spectrum of hazardous and toxic substances, such as (azo) dyes, heavy metals, acids, soda, and aromatic hydrocarbons, pollute precious sources of clean water, in which untreated water is discharged. The main solution to this problem is to reduce the treatment cost. For this purpose, the process should be optimized to reduce the amount of water and chemicals. In this chapter, first studies on the reference document (BAT) referred by the European Council are reviewed. Minimizing production costs, obtaining high-quality products, and reducing the amount and the pollutant content of wastewater are complex problems that cannot be solved by the conventional optimization methods. Therefore, nonconventional optimization methods applied on the textile

processes are also reviewed from the latest studies in the literature.

**Keywords:** sustainability, BAT, optimization, metaheuristics, genetic algorithm

Textile industry is the foremost sector in terms of the discharged volume and the composition of the wastewater [1]. Most of the textile production processes, such as scouring, washing, dyeing, bleaching, sizing, and finishing, consume large volumes of fresh water and discharge large volumes of effluent which are generally with intense color, high concentration of organic compounds, and large variations in composition [2, 3]. Especially wet process, which has five main stages including pretreatment, dyeing, finishing, drying, and quality control, is the major part of the textile industry due to the long processing time and technical complexity [4]. Specific water consumption range is given as 10–645 L/kg product for the textile industry and 21–645 L/kg for the mills with finishing and dyeing processes in (ref BAT-EC). In another source, it is reported that the consumed amount of water could reach to 932 L/kg product depending on the fiber and applied technology [5–7]. In recent years, depleted resources, global warming, and climate change resulting in challenging regulations enforce manufacturing enterprises to give efforts to reduce the waste of the processes, which motivate firms for the sustainable (cleaner) production. Besides environmental considerations, the effective planning of the production is also obligatory to reduce the production costs to be able to compete with other manufacturers. Moreover, an empirical study built on the

in Textile Industry

*Miray Emreol Gönlügür*


*2.6. Resveratrol Quantification*

An exactly 0.5 mL sample was mixed with 0.5 mL polydatin (internal standard, 50 μM) in methanol and then added into 4 mL methanol under vortexing for 60 s. After the mixture was centrifuged at 15,000× *g* for 60 min, the supernatant was measured on the Alliance HPLC system equipped with a 2695 separation module and 2998 PDA detector (Waters, Milford, MA, USA). The mobile phase was a mixture of methanol and distilled water (50:50, *v*/*v*), the flow rate was 1 mL min−1, and the column temperature was 35 ◦C. Both *trans*-resveratrol and polydatin were analyzed at 306 nm [23].


**Abstract**

The concentration of dust particles in the incoming air has a significant effect on the performance of cyclone separators. In the proposed work, four particle concentrations (0.05, 0.1, 0.2 and 0.3 kg/kg) in the dust stream have been mathematically investigated using both one-way and two-way coupling. A fine grid is solved using the Large Eddy Simulations to capture the accurate physical phenomena. For vortices smaller than the grid size the Smagorinsky Lilly model with a Smagorinsky constant, Cs of 0.1 has been applied. The collection efficiencies of the four cases are presented and the differences between the one-way and two-way coupled simulation approaches are highlighted in the present study. The two-way coupled simulations show an increase in the collection efficiency from 62% to 70% on increasing the solid loadings from 0.05 to 0.3 with marginal increase in pressure drop of 4.8%.

**Keywords:** stairmand high-efficiency cyclone, computational fluid dynamics, large Eddy simulations, solid loadings, Eulerian-Lagrangian


**2. Literature Review**

Overtourism is an issue of interest for politicians, managers, researchers, and tourists. It is typically discussed in the context of sustainable development, and, specifically, sustainable tourism. Although the concept of sustainable development remains fairly ambiguous [7], it has been gradually implemented in various economic sectors, including tourism industry, where it has led to the idea of sustainable tourism.

The issue of sustainable tourism has been analysed by many researchers, both in the theoretical field [8–15] and in case studies aimed at illustrating its practical dimension [16–19]. Butler [10] presented sustainable tourism as "tourism which is developed and maintained in an area (community, environment) in such a manner and at such a scale that it remains viable over an infinite period and does not degrade or alter the environment (human and physical) in which it exists to such a degree that it prohibits the successful development and well-being of other activities and processes". Sustainable tourism is a way of organizing and managing the tourism industry [14,20,21] in which determining the acceptable level of tourist traffic growth is a very important assumption [14].

Having that in mind, one can observe not only an intensification of the effects of classical tourism dysfunctions but also the emergence of new, unfavourable consequences of tourist traffic mismanagement, including what is known as overtourism.

Though not a new phenomenon [22–27], overtourism has recently become a "buzzword", appearing in quite numerous scientific discourses, popular scientific presentations, or mass media, including news. Along with the growth of tourism popularity and hypermobility, the burning issue of "tourism saturation" [25] has emerged. This phenomenon is often discussed as it pertains to large urban agglomerations, such as Barcelona, Venice, or Berlin, whose residents openly protest against what they call "tourism flooding", "tourism invasion", or even "tourism pollution". In some tourist destinations, an unflattering atmosphere has aroused around tourists, which is referred to in scientific literature as "tourismophobia" [25,27,28].

Overtourism, now constituting a global problem [25], has been defined as "the impact of tourism on a destination, or parts thereof, that excessively influences perceived quality of life of citizens and/or quality of visitors experiences in a negative way" [29]. Milano et al. [26] define it as "the excessive growth of visitors leading to overcrowding in areas where residents suffer the consequences of temporary and seasonal tourism peaks, which have caused permanent changes to their lifestyles, denied access to amenities and damaged their general well-being".

Despite a quite agreed-upon approach to the definition framework, overtourism is a complex phenomenon [26] and it does not simply stand for the number of tourists visiting a particular destination but for the issue of tourist capacity [24]. Since the phenomenon of "overloved cities" results from short-sighted tourism policy and poor management focused on generating maximum possible income [30], it causes a number of annoying consequences, e.g., overcrowding, degradation of both cultural and nature sites, low quality of tourists' experience, residents' dissatisfaction due to the increase in the prices of services, apartments, and real estate, and gentrification of the cities [24].

In the scientific literature, the problem of overtourism has been described many times in the context of big cities and well-known tourist destinations. Besides the flagship examples of Barcelona, Venice, Florence, Amsterdam, and Berlin, the following cases have also been mentioned:

Implementing potential solutions for the consequences of overtourism is a complex task that requires long-term strategic planning. It has been noted that "there is a pressing need to set a sustainable roadmap for urban tourism and position the sector in the wider urban agenda" [29]. The United Nations World Tourism Organization (UNWTO) [29] has proposed 11 strategies that may help limit the overtourism consequences:

The elements of the strategies limiting the negative impact of overtourism indicated by UNWTO [29] are included in the conceptual assumptions of tourism development in Wrocław up to 2023 [1] in the following aspects: the city tourist mission, strategic areas of tourism development and expectations of stakeholders, as well as the adopted strategic and operational objectives together with selected activities.

According to Séraphin et al. [27], branding is a very important tool to prevent the effects of overtourism by creating the desired image of a given tourist destination, e.g., by "appealing to target audience's emotional aspirations" or educating tourists [27]. The question arises as to how many destination marketing organisations use this educative function of branding to induce desired behaviours in tourists. What exactly would its efficiency depend on [34–40]?

Kruczek [24] indicates that overtourism is a "side effect" of mass tourism, affecting mostly (but not only) local communities and the natural environment. The need to move away from traditional mass tourism has been reflected in the demands for a paradigm change from the so-called 3S tourism (Sun, Sand, Sea) to 3E tourism (Entertainment, Excitement, Education) (e.g., [41]), bringing about sustainable tourism (e.g., [8,14]), various forms of alternative tourism [42,43], or ecotourism [44,45].

The greening of mass tourism [46,47] and the large-scale promotion of sustainable forms of travelling can prove to be effective ways not only to avoid the effects of overtourism but also to implement a more sustainable policy in cities, to improve the quality of life of host communities, and to raise the quality of the tourism experience.

The approach selection and strategy clarification require determination of whether overtourism is only a potential threat to a given area (destination) or a reality already. In the former case, preventive strategies should be pursued to inhibit any imbalances; in the latter situation, strategies to mitigate or eliminate the adverse effects of overtourism are essential. In any case, it is necessary to provide a diagnosis, preferably through repeated direct research in a particular location. This requires ongoing research and observation in places at risk of or already affected by overtourism, especially from the perspective of parties concerned with the phenomenon. The aim is to properly recognize the expectations and feedback of residents, the tourist industry, local authorities, and tourists themselves.

The presented paper is based on such research, which reveals the opinions of key experts, people working for the benefit of tourism, and residents, i.e., important groups of stakeholders in tourism development.

Wrocław is conveniently located in terms of tourist traffic routes and transport connections, has an interesting past, a wealth of unique monuments of history, and recognized tourist attractions. It is also a place of important events and meetings. These are among the reasons why Wrocław is one of the Polish centres attracting tourists from various countries; it is estimated that the city is visited by more than 5 million people each year [2]. It should be noted that no studies on threats of overtourism have been carried out in Wrocław so far; therefore, the survey undertaken here (limited to a specific group of respondents, treated as experts) may be considered as the first approach to diagnosing the overtourism problem.


**1. Introduction**

218 Pulmonary Embolism

Nance JW Jr, et al. (2011). Optimization of contrast material delivery for dual-energy

Patel S, et al. (2003). Pulmonary embolism: optimization of small pulmonary artery

Remy-Jardin M, et al. (2007). Management of suspected acute pulmonary embolism in the

Schoepf UJ, et al. (2000). Pulmonary embolism: comprehensive diagnosis by using electron-

Schenzle JC, et al. (2010). Dual energy CT of the chest—How about the dose? Invest Radiol

Thieme SF, et al. (2010). Dual-energy lung perfusion computed tomography: a novel pulmonary functional imaging method. Semin Ultrasound CT MR 31(4):301-308. Thieme SF, et al. (2008). Dual energy CT for the assessment of lung perfusion—correlation to

Thieme SF, et al. (2009). Dual-energy CT for the assessment of contrast material distribution in the pulmonary parenchyma. AJR Am J Roentgenol ;193(1):144-149. Wildberger JE, et al. (2001). Multi-slice CT for visualization of pulmonary embolism using

Wildberger JE,et al. (2005). Multislice computed tomography perfusion imaging for

Zhang LJ, et al. (2009). Detection of pulmonary embolism by dual energy CT:correlation

Zhang LJ, et al. (2009). Detection of pulmonary embolism using dual-energy computed

Zhang LJ, et al. (2009). Detection of pulmonary embolism by dual energy CT: an

visualization of acute pulmonary embolism: animal experience. Eur Radiol

with perfusion scintigraphy and histopathological findings in rabbits. Eur Radiol

tomography and correlation with cardiovascular measurements: a preliminary

Tapson VF. (2008). Acute pulmonary embolism. N Engl J Med 358(10):1037–1052.

perfusion weighted color maps. Rofo 173(4):289–294.

experimental study in rabbits. Radiology 252(1):61–70.

pulmonary embolism. Invest Radiol May 13. [Epub ahead of print]. Pontana F, et al. (2008). Lung perfusion with dual-energy multidetector-row CT (MDCT):

visualization at multidetector row CT. Radiology 227(2):455–460.

patients. Acad Radiol 15(12):1494–1504.

scintigraphy. Eur J Radiol 68(3):369–74.

245(2):315–29.

45(6): 64-71.

15(7):1378–1386

19(12): 2844–2854.

study. Acta Radiol 50(8):892–901

Radiology 217(3):693–700.

computed tomography pulmonary angiography in patients with suspected

feasibility for the evaluation of acute pulmonary embolism in 117 consecutive

era of CT angiography: a statement from the Fleischner Society. Radiology

beam CT for detection of emboli and assessment of pulmonary blood flow.

When anticoagulants are contraindicated for the venous thromboembolism therapy and thromboembolism recurs, a vena cava filter is inserted percutaneously into a major vein in order to prevent blood clots from entering the lungs (Ando & Kuribayashi, 2000; Streiff, 2000) (Fig. 1). The inferior vena cava filter is a mesh structure designed to capture blood clots while not impeding blood flow. This filter is inserted using an introducer catheter from either the femoral or jugular vein and is fixed by a hook attached to the tip of a wire. Several filters have been designed to lyse captured clots.

Fig. 1. Placement of the inferior vena cava filter.

Ideally, the filter should capture blood clots efficiently while not impeding the blood flow. Moreover, the filter should not move in the blood vessel after deployment and should pass smoothly through the slim introducer catheter. Although insertion appears to be a safe and effective method by which to prevent the recurrence of pulmonary embolism, patients in whom the filter has become tilted may experience pulmonary embolism recurrence because of a decrease in the thrombus-trapping performance of the filter (Nara et al., 1995; Rogers et

Numerical Analysis of the Mechanical Properties of a Vena Cava Filter 221

1991). The total length of the GF is 47 mm (Greenfield et al., 1991).  The over-the-wire filter has a head with a small hole and inserted over the guidewire to optimize

This model of the filter is constructed with viscoelastic springs and *n* segments for the dynamic deformation of a flexible structure. The viscoelastic springs express the bending and torsional stiffness of the wire. The motion of the filter model is represented by the

> T ( ) ( , ) ( ) - ( - )- r i o w *n*

where *q* is the joint displacement vector, *q*o is the joint displacement vector when no load is applied, *M*(*q*) is the inertia matrix, *Vqq* (, ) is the centrifugal force (Coriolis force), *F*i is contact force vector of each segment (*i*), and *K* and *D*w are elastic and viscous coefficients of a mobile joint, respectively. The second and third terms of the right-hand side in this equation correspond to the viscoelastic forces of a mobile joint. The head and the wire of the filter consist of one and three segments (diameter: 2*R*w, length: *L*w), respectively. Each segment of the wire has a mobile joint in the center. The elastic coefficient of the mobile joint (*K*) with respect to bending resistance (*K*wx) and torsional resistance (*K*wz) are approximated

 *K*wx = *E*w*I*x/*L*w (2)

 *K*wz = *G*w*I*p/*L*w (3) where *E*w and *G*w are Young's modulus and the modulus of transverse elasticity of the wire of the filter, respectively, *I*x and *I*p are the area moment of inertia and the polar moment of

*M qq Vqq q Kq q q* + = *J F D* (1)

*i*

the alignment of the filter with the inferior vena cava (Kinney et al., 1997).

Fig. 2. The Greenfield inferior vena cava filter.

Newton-Euler equations of motion as follows:

as follows (Yamamura et al., 2003):

al., 1998). In order to satisfy these requirements, several types of filters, such as permanent, temporary, and retrievable filters, have been proposed. For example, several types of vena cava filters, such as Greenfield filter, Vena Tech filter, Bird's nest filter, Simon-Nitinol filter, TrapEase filter, Günther tulip filter, Antheor filter, Neuhaus protect filter, and Recovery-Nitinol filter, have been developed (Ando & Kuribayashi, 2000; Boston Scientific, 2007; Greenfield et al., 1990, 1991; Kinney et al., 1997; Nara et al., 1995; Rogers et al., 1998; Streiff, 2000; Swaminathan et al., 2006). However, there are few quantitative data on the mechanical properties of these filters. In particular, although Swaminathan reported the blood clot capturing efficiency from the viewpoint of computational fluid dynamics (Swaminathan et al., 2006), there are few quantitative data concerning, for example, the ease of filter delivery. Therefore, in the present study, we evaluated through numerical analysis the mechanical properties of a Greenfield filter deployed into a vein. In particular, since the filter expands rapidly, the surgeon cannot perceive the expanding motion or the transition of the contact force applied to the blood vessel wall. Therefore, a complete understanding of the mechanical properties of the filters must be determined on not only input from doctors but also on the results of numerical analysis regarding the expansion. These methods are expected to be useful for analyzing the structure of filters and may help to guide the design

of new filters. Based on the above considerations, we herein evaluate by numerical analysis the dynamic motion of a deployed filter using the evaluation standard of the incline and misalignment between the filter and the blood vessel. First, we evaluated whether the filter tilts when the catheter tilts or is misaligned or when the filter cannot expand. Second, we evaluated the migration of the deployed filter under a constant force.

#### **2. Methods**

Catheters and guidewires are used in the treatment of infarctions and aneurysms. In a previous study, in order to make intravascular treatment safer, we developed a computerbased surgical simulation system in order to simulate a catheter placed inside blood vessels for treatment of the brain (Takashima et al., 2006, 2007b, 2009). In the present study, we applied the simulation methods for the guidewire to the inferior vena cava filter because both the guidewire and the inferior vena cava filter are flexible structures. Using a similar model, we can easily combine the filter model with our catheter simulator. Actually, a catheter simulator has been developed as a training environment for inferior vena cava filter placement (Hahn et al., 1998). Ease of percutaneous filter delivery provides numerous advantages to both doctors and patients, including improved operational efficiency and reduced cost. Therefore, it is important that the filter be easy to use in combination with a catheter.

#### **2.1 Filter model**

In the present study, we used a Greenfield filter (GF) constructed of titanium (Fig. 2) (Ando & Kuribayashi, 2000; Boston Scientific, 2007; Greenfield et al., 1990, 1991; Kinney et al., 1997; Nara et al., 1995; Rogers et al., 1998; Streiff, 2000; Swaminathan et al., 2006). This permanent filter is commonly used in Japan. The GF is constructed of either titanium or stainless steel and come in various shapes. The GF used herein is cone-shaped and consists of six wires connected to a head. The diameter of the wires is 0.45 mm (Swaminathan et al., 2006), and each leg has a "zigzag" pattern. The bottom diameter of the cone is 38 mm (Greenfield et al.,

al., 1998). In order to satisfy these requirements, several types of filters, such as permanent, temporary, and retrievable filters, have been proposed. For example, several types of vena cava filters, such as Greenfield filter, Vena Tech filter, Bird's nest filter, Simon-Nitinol filter, TrapEase filter, Günther tulip filter, Antheor filter, Neuhaus protect filter, and Recovery-Nitinol filter, have been developed (Ando & Kuribayashi, 2000; Boston Scientific, 2007; Greenfield et al., 1990, 1991; Kinney et al., 1997; Nara et al., 1995; Rogers et al., 1998; Streiff, 2000; Swaminathan et al., 2006). However, there are few quantitative data on the mechanical properties of these filters. In particular, although Swaminathan reported the blood clot capturing efficiency from the viewpoint of computational fluid dynamics (Swaminathan et al., 2006), there are few quantitative data concerning, for example, the ease of filter delivery. Therefore, in the present study, we evaluated through numerical analysis the mechanical properties of a Greenfield filter deployed into a vein. In particular, since the filter expands rapidly, the surgeon cannot perceive the expanding motion or the transition of the contact force applied to the blood vessel wall. Therefore, a complete understanding of the mechanical properties of the filters must be determined on not only input from doctors but also on the results of numerical analysis regarding the expansion. These methods are expected to be useful for analyzing the structure of filters and may help to guide the design

Based on the above considerations, we herein evaluate by numerical analysis the dynamic motion of a deployed filter using the evaluation standard of the incline and misalignment between the filter and the blood vessel. First, we evaluated whether the filter tilts when the catheter tilts or is misaligned or when the filter cannot expand. Second, we evaluated the

Catheters and guidewires are used in the treatment of infarctions and aneurysms. In a previous study, in order to make intravascular treatment safer, we developed a computerbased surgical simulation system in order to simulate a catheter placed inside blood vessels for treatment of the brain (Takashima et al., 2006, 2007b, 2009). In the present study, we applied the simulation methods for the guidewire to the inferior vena cava filter because both the guidewire and the inferior vena cava filter are flexible structures. Using a similar model, we can easily combine the filter model with our catheter simulator. Actually, a catheter simulator has been developed as a training environment for inferior vena cava filter placement (Hahn et al., 1998). Ease of percutaneous filter delivery provides numerous advantages to both doctors and patients, including improved operational efficiency and reduced cost. Therefore, it is important that the filter be easy to use in combination with a

In the present study, we used a Greenfield filter (GF) constructed of titanium (Fig. 2) (Ando & Kuribayashi, 2000; Boston Scientific, 2007; Greenfield et al., 1990, 1991; Kinney et al., 1997; Nara et al., 1995; Rogers et al., 1998; Streiff, 2000; Swaminathan et al., 2006). This permanent filter is commonly used in Japan. The GF is constructed of either titanium or stainless steel and come in various shapes. The GF used herein is cone-shaped and consists of six wires connected to a head. The diameter of the wires is 0.45 mm (Swaminathan et al., 2006), and each leg has a "zigzag" pattern. The bottom diameter of the cone is 38 mm (Greenfield et al.,

migration of the deployed filter under a constant force.

of new filters.

**2. Methods**

catheter.

**2.1 Filter model**

1991). The total length of the GF is 47 mm (Greenfield et al., 1991).

Fig. 2. The Greenfield inferior vena cava filter.

This model of the filter is constructed with viscoelastic springs and *n* segments for the dynamic deformation of a flexible structure. The viscoelastic springs express the bending and torsional stiffness of the wire. The motion of the filter model is represented by the Newton-Euler equations of motion as follows:

$$\mathbf{M}(\boldsymbol{q})\ddot{\boldsymbol{q}} + \mathbf{V}(\boldsymbol{q}, \dot{\boldsymbol{q}}) = \sum\_{i}^{n} \mathbf{J}\_{\rm r}^{\rm T}(\boldsymbol{q}) \mathbf{F}\_{i} \cdot \mathbf{K}(\boldsymbol{q} \cdot \boldsymbol{q}\_{\rm o}) \cdot \boldsymbol{D}\_{\rm w} \dot{\boldsymbol{q}} \tag{1}$$

where *q* is the joint displacement vector, *q*o is the joint displacement vector when no load is applied, *M*(*q*) is the inertia matrix, *Vqq* (, ) is the centrifugal force (Coriolis force), *F*i is contact force vector of each segment (*i*), and *K* and *D*w are elastic and viscous coefficients of a mobile joint, respectively. The second and third terms of the right-hand side in this equation correspond to the viscoelastic forces of a mobile joint. The head and the wire of the filter consist of one and three segments (diameter: 2*R*w, length: *L*w), respectively. Each segment of the wire has a mobile joint in the center. The elastic coefficient of the mobile joint (*K*) with respect to bending resistance (*K*wx) and torsional resistance (*K*wz) are approximated as follows (Yamamura et al., 2003):

$$K\_{\rm wrx} = E\_{\rm w} I\_{\rm x} / L\_{\rm w} \tag{2}$$

$$K\_{\rm wxz} = C\_{\rm pw} I\_{\rm p} / L\_{\rm w} \tag{3}$$

where *E*w and *G*w are Young's modulus and the modulus of transverse elasticity of the wire of the filter, respectively, *I*x and *I*p are the area moment of inertia and the polar moment of

Numerical Analysis of the Mechanical Properties of a Vena Cava Filter 223

The simulation models used in the present study are shown in Fig. 4. The centerline of the

blood vessel is along the *z*-axis.

Fig. 3. Dimensions of the filter model (unit: mm).

**2.3 Calculation of contact force**

Fig. 4. Simulation model (vena cava filter, catheter, and blood vessel).

circumferential direction of the cross-section (*f*ri). *f*ni is expressed as follows:

each joint and nearest point on the central curve of the blood vessel.

In order to determine whether contact occurs between the filter and the vessel, the distances between the joints and the tip of the filter model (*p*i) and the centerline of the vessel, were calculated. Considering the clearance of the filter and the blood vessel, we calculated the contact force according to the distance. Here, *F*i is decomposed into three components along the centerline of the blood vessel (*f*ti), the normal direction to the centerline (*f*ni), and the

 *f*ni = −*K*v(|*l*i|+*R*w−*R*v)3/2 *l*i/| *l*i| (7) where *K*v is the elastic coefficient of vessel deformation and *l*i is the distance vector between

inertia of area, respectively. In the present study, since the wire is a rod (radius: *R*w), *K*wx and *I*p are expressed as follows:

$$K\_{\rm wx} = \rm \rm \rm \rm \rm \, \_{m} \rm \, R\_{\rm w} \rm \, ^{4} / \, L\_{\rm w} \tag{4}$$

$$I\_{\mathbf{p}} = \mathbf{2} I\_{\mathbf{x}} \tag{5}$$

Assuming an isotropic material, *G*w is expressed using Poisson's ratio (*ν*) as follows:

$$G\_{\rm w} = E\_{\rm w} / \mathcal{D} (1 + \nu) \tag{6}$$

In the present study, *ν* = 0.3 (Petrini et al., 2005).

The parameters and dimensions of the filter model are shown in Table 1 and Fig. 3, respectively. In this table, subscripts *w* and *h* indicate the parameters of the wire and the head, respectively. Here, *K*wx and *K*wz are obtained by substituting *R*w and *E*w in Table 1 into Eqs. (2) and (3). Assuming a fixed joint, the values of the joints between the wire and the head are 100 times as large as those obtained using Eqs. (2) and (3). The recurved hook is set at an angle of 80° (Greenfield et al., 1991). The actual leg hook consists of a twisted and complicated structure in order to avoid migration of the filter after deployment or penetration of the vein (Greenfield et al., 1990, 1991) (Fig. 2). However, since the penetration of the vein was not evaluated in the present study, the bending number of the hook is one. The change of the bending angle is equal to the change of *q*o, as shown in Eq. (1). In a manner similar to the catheter simulator (Takashima et al., 2006, 2007b, 2009), the viscous term for each movable joint was considered in terms of *D*w. Since we cannot measure the exact values, we assumed *D*w to be smaller than *K*wx and *K*wz. We neglected the "zigzag" pattern and the slight flare of the wire. In the design of the titanium GF, the addition of a slight flare to the legs was made in order to facilitate discharge from the carrier without leg crossing, particularly from the jugular direction where the legs discharge first (Greenfield et al., 1990).

Table 1. Parameters of the filter model used in simulation.

#### **2.2 Blood vessel model**

The vessel is a circular elastic cylinder defined by a centerline and a radius (*R*v). The centerlines are represented by numerical data. The position of the centerline of the vessel is constant. The contact forces between the filter and the vessel are calculated according to the stiffness and the friction of the vessel wall. The friction force are derived from the fixation of the hook. Moreover, the diameter of the blood vessel (2*R*v) is assumed to be 20 mm, which is similar to Swaminathan (Swaminathan et al., 2006). In the instructions for the use of the GF (Boston Scientific, 2007), the maximum diameter of the inferior vena into which the filter can be deployed is 28 mm.

inertia of area, respectively. In the present study, since the wire is a rod (radius: *R*w), *K*wx and

 *K*wx = π*E*w*R*w4/*L*w (4)

 *I*p = 2*I*x (5)

 *G*w = *E*w/2(1+*ν*) (6)

The parameters and dimensions of the filter model are shown in Table 1 and Fig. 3, respectively. In this table, subscripts *w* and *h* indicate the parameters of the wire and the head, respectively. Here, *K*wx and *K*wz are obtained by substituting *R*w and *E*w in Table 1 into Eqs. (2) and (3). Assuming a fixed joint, the values of the joints between the wire and the head are 100 times as large as those obtained using Eqs. (2) and (3). The recurved hook is set at an angle of 80° (Greenfield et al., 1991). The actual leg hook consists of a twisted and complicated structure in order to avoid migration of the filter after deployment or penetration of the vein (Greenfield et al., 1990, 1991) (Fig. 2). However, since the penetration of the vein was not evaluated in the present study, the bending number of the hook is one. The change of the bending angle is equal to the change of *q*o, as shown in Eq. (1). In a manner similar to the catheter simulator (Takashima et al., 2006, 2007b, 2009), the viscous term for each movable joint was considered in terms of *D*w. Since we cannot measure the exact values, we assumed *D*w to be smaller than *K*wx and *K*wz. We neglected the "zigzag" pattern and the slight flare of the wire. In the design of the titanium GF, the addition of a slight flare to the legs was made in order to facilitate discharge from the carrier without leg crossing, particularly from the jugular direction where the legs

> *R*w (mm) 0.225 *R*h (mm) 0.875 *E*w (GPa) 22 Density (g/cm3) 5.3 *D*w (N·m·s/rad) 0.005 *L*w (mm) 4, 43 *L*h (mm) 2 *n* 25

The vessel is a circular elastic cylinder defined by a centerline and a radius (*R*v). The centerlines are represented by numerical data. The position of the centerline of the vessel is constant. The contact forces between the filter and the vessel are calculated according to the stiffness and the friction of the vessel wall. The friction force are derived from the fixation of the hook. Moreover, the diameter of the blood vessel (2*R*v) is assumed to be 20 mm, which is similar to Swaminathan (Swaminathan et al., 2006). In the instructions for the use of the GF (Boston Scientific, 2007), the maximum diameter of the inferior vena into which the filter can

Assuming an isotropic material, *G*w is expressed using Poisson's ratio (*ν*) as follows:

*I*p are expressed as follows:

In the present study, *ν* = 0.3 (Petrini et al., 2005).

discharge first (Greenfield et al., 1990).

**2.2 Blood vessel model**

be deployed is 28 mm.

Table 1. Parameters of the filter model used in simulation.

The simulation models used in the present study are shown in Fig. 4. The centerline of the blood vessel is along the *z*-axis.

Fig. 3. Dimensions of the filter model (unit: mm).

Fig. 4. Simulation model (vena cava filter, catheter, and blood vessel).