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\n
1. Introduction
\n
The governing equation for the fluid flow is known as Navier-Stokes equation, which is however difficult to solve analytically; and therefore, a lot of numerical techniques have been proposed and developed. Nevertheless various complex flow phenomena such as turbulent flow, multi-phase flow, compressible flow, combustion, and phase change encountered in the fields of engineering would have still difficulties to circumvent even using both present computational resources and numerical techniques. The present chapter devotes not to elucidate such complex phenomena, but to introduce rather simplified fluid flow by using the finite difference method.
\n
One focuses on incompressible flows, in which physical properties such as the viscosity, the thermal conductivity, the specific heat are constant and even the fluid density is not a thermodynamic variable. This simplified assumption makes the fluid flow phenomena much easier to be handled and it is valid when the flow velocity is much slower than the sound velocity and/or the temperature difference in the fluid is small enough to consider the thermal expansion coefficient is independent to the temperature. The former situation is known the low Mach number approximation, while the latter one the Boussinesq approximation.
\n
Another simplification on the incompressible flows is the reduction of dimension due to the characteristic of similarity and periodicity. For the boundary layer flows such as the Blasius flow, the stagnation-point flow, and the von Kármán rotating disk flow have the similar solution where the flow transition from laminar to turbulence does not occur. In those cases, a combined dimensionless variable (similar variable) η is introduced and the velocity distribution can be only a function of η. While for the onset of instability such as the Rayleigh-Bénard convection, the Bénard-Marangoni convection, and the Taylor-Couette flow, the periodic characteristic of flow structure is observed. At the stage of onset of instability, the non-linear term is negligible and therefore the function of flow field is separated into the amplitude part and periodic part, respectively. This makes the effort on numerical analysis to reduce significantly and also to contribute the augmentation of accuracy of the results.
\n
This chapter consists of three main bodies. First, a numerical technique for solving the boundary value problem called the first Stokes problem or the Rayleigh problem [1] is introduced. The differential equation is transferred into an ordinary equation and it is solved by a finite difference method using the Jacobi method. Second, similar solution of natural convection heat transfer heated from a vertical plate with uniform heat flux is introduced together with the method how to obtain the system of ordinary differential equations. The obtained Nusselt numbers are compared with some previous studies. Third, for example, of the linear stability analysis, one shows that the HSMAC method can be applied to obtain the critical values for the onset of secondary flow such as the Taylor-Couette flow. The Eigen functions of flow and pressure fields are visualized.
\n
\n
\n
2. Unsteady flow due to sudden movement of the plate
\n
\n
2.1. Governing equations
\n
An infinite length plate is set in a stationary fluid as an initial condition. Let us consider the situation that the infinite length plate suddenly moves along its parallel direction at a constant speed uw. This problem was first solved by Stokes [2] in his famous treatment of the pendulum. Since Lord Rayleigh [3] also treated this flow, it is often called the Rayleigh problem in the literature. One takes that x is the plate movement direction and y is distance from the plate. Since the velocity component perpendicular to the plate v is zero, the momentum equation is simplified and is shown as a diffusion equation
Here, u is the velocity component parallel to the plate direction, t is the time, and ν is the kinematic viscosity. The boundary conditions for this partial differential equation are as follows:
In order to reduce the partial differential equation to an ordinary equation, the following dimensionless velocity \n\nU\n\n and the similar variable η are introduced
As a consequence, one needs to solve this boundary value problem. The theoretical solution can be easily obtained and expressed using the error function
2.2. Numerical method for solving the ordinary differential equation using finite difference method
\n
For numerical solution, it is necessary to define the range of η, as recognized from Figure 1, η = 4 is enough. Hence, the boundary condition shown below is used instead of Eq. (5)
As illustrated in Figure 2, in which vertical and horizontal axes are exchanged from Figure 1, one needs to obtain each value of dimensionless velocity numerically. The approximated velocity profile is expressed by connecting these values smoothly. For simplicity, the intervals between neighboring two points are the same and it is noted as \n\nΔη\n\n. When the second-order central difference method is used, Eq. (4) is as follows:
Here, \n\n\nη\ni\n\n=\n\n\ni\n−\n1\n\n\n\nΔη\n\n\n and αi and βi are coefficients determined by the number of grids. The boundary condition (7) is modified
This kind of tridiagonal matrix is often seen and can be solved by a direct numerical method, such as Tomas method. However, the rank of the matrix is usually extremely large and one introduces an iterative method for solving the king-size matrix.
\n
\n
\n
2.3. Iterative method for matrix solver
\n
In general, the rank of the matrix appearing in computational fluid dynamics (CFD) is large and iterative methods such as Jacobi, Gauss-Seidel, or successive over relaxation (SOR) methodare employed. In this subsection, the Jacobi method is explained. The matrix can be divided into three parts of lower, diagonal, and upper as follows:
In the Jacobi method, only the diagonal part is put in the left-hand side (n + 1 step), while the lower and upper parts are moved to the right-hand side (n step)
By using Eq. (9), Eq. (14) is computed repeatedly and then the value of each grid gradually converges to a certain solution. The Gauss-Seidel and SOR methods are known as the faster convergence method.
\n
\n
\n
\n
3. Similarity solution for natural convection heated from a vertical plate
\n
\n
3.1. Introduction
\n
In this section, let us consider the natural convection heat transfer for a vertical plate heated with uniform heat flux in the wide range of Prandtl number from zero to infinity. In order to explain the numerical method as how to solve the governing equations, one assumes that the flow and temperature fields formed in the vicinity of the heated plate have a similarity and then one introduces the finite difference method to obtain numerical results.
\n
\n
\n
3.2. Governing equations
\n
One assumes that the flow is incompressible laminar and boundary layer equations are used in this analysis. The governing equations with presuming the Boussinesq approximation are shown in Eqs. (15)–(17) together with the boundary condition (18). Here, one defines that x axis is in the vertical direction and its velocity component is \n\nu\n\n, and y axis is in the direction perpendicular to the vertical plate and its velocity component is \n\nv\n\n.
Here, β is the thermal expansion coefficient, g is the acceleration due to gravity, α is the thermal diffusivity, k is the thermal conductivity, and T is the temperature.
\n
\n
\n
3.3. Non-dimensionalization
\n
First, dimensionless variables, such as velocity and temperature, are set as follows using the unknown reference value denoted with subscripts a and b:
At the moment stage, \n\n\nx\na\n\n\n is recognized as the height of the vertical plate.
\n
Putting [3] = 0, and one obtains \n\n\nT\nb\n\n=\n\nT\n∞\n\n\n.Hence [7] becomes \n\nθ\n=\n0\n\n.
\n
Putting [6] = 1, and one gets \n\n\n\nqy\na\n\n\nkT\na\n\n\n=\n1\n\n⇒\n\n\nT\na\n\n=\n\n\nqy\na\n\nk\n\n\n
\n
Putting [5] = 1, and one gets \n\n\n\nα\n\nx\na\n\n\n\n\n\ny\na\n\n2\n\n\nu\na\n\n\n\n=\n1\n\n⇒\n\n\ny\na\n\n=\n\n\n\n\nα\n\nx\na\n\n\n\nu\na\n\n\n\n\n1\n/\n2\n\n\n\n
Furthermore, one assumes that the velocity and temperature fields has a similarity along the direction of vertical plate, so one puts X = 1. These equations are useful for analyzing low Prandtl number cases and summarized as follows:
Figure 3 shows the numerical result for the various Prandtl number cases. The upper figures indicate the vertical velocity and lower ones the temperature. The left-hand side figures show the cases of Pr ≥ 1, while the right-hand side ones the cases of Pr ≤ 1
\n
Figure 3.
Vertical velocity and temperature distributions for various Prandtl numbers. The left-hand side indicates high Prandtl number cases while the right-hand side low Prandtl number cases.
\n
Table 1 shows the summary of the local Nusselt number for various Prandtl number cases together with the reference of Churchill and Ozoe for comparison [4]. The agreement is quite good except for the extreme cases such as Pr → 0 and ∞. In such extreme cases, a small amount of discrepancy exists. In this study, the boundary condition for Pr → 0
are used. Owing to this kind of special treatments for the boundary condition of such extreme cases, one can obtain accurate numerical results for the system of ordinary equations. The results between the solution of the present method and that of Le Fevre [5] for the case of constant temperature of heated wall are identical to each other. The value for Pr → ∞ is 0.5027 and that for Pr = 0 is 0.6004.
Local Nusselt number for various values of Prandtl number (the upper: present results, the lower: Churchill and Ozoe [4]).
\n
\n
\n
\n
4. Linear stability of Taylor-Couette flow
\n
\n
4.1. Governing equations
\n
In the text book of Chandrasekar [6], various examples of the linear stability analysis such as the Rayleigh-Bénard convection, the Taylor-Couette flow, and the Rayleigh-Taylor instability were studied extensively. More recently, Koschmieder [7] described the research focusing on the Bénard cells and the Taylor vortices. In this section, only the Taylor-Coette flow is considered. Figure 4 shows the schematic model considered for the Taylor-Couette flow. In this section, the fluid flow inside of the co-axial double cylindrical enclosure is assumed to be incompressible Newtonian, isothermal and axisymmetric. The gray part represents the computational domain. It is known that the stationary secondary flow is generated at a certain condition under the influence of centrifugal force due to the rotation of primary basic flow which is in azimuthal direction. The continuity of mass and momentum equations are shown in the cylindrical coordinate system as follows:
Here, it is indicated that r is the radial, θ is the azimuthal, and z is the axial components.
\n
\n
\n
4.2. Basic state and linearization
\n
The cylindrical enclosure is long enough to neglect the top and bottom ends. In that situation, the basic states for the azimuthal component of velocity and pressure are as follows:
Here, Ω1 is the angular velocity at the inner cylinder, Ω2 is the angular velocity at the outer cylinder, p is the pressure, ρ is the density, and g is the acceleration due to gravity. In order to derive disturbance equations for the linear stability, the three components of velocity and pressure are represented as a summation of basic state and infinitesimal disturbance as follows:
By considering the periodicity of the secondary flow which could be happened, each component of infinitesimal disturbance is assumed to be given in the following form. Here, a is the axial wavenumber (real number) and s is angular frequency (complex number)
In this section, it is assumed that S = 0. This indicates that the secondary flow caused by the centrifugal instability is stationary and it contains toroidal vortices. To deal with the simultaneous ordinary differential equations for the boundary value problem, a one-dimensional staggered grid system is employed as shown in Figure 5. All the equations are discretized by the fourth order central difference method with a given wavenumber k using the HSMAC method [8] during which \n\n\nRe\nΩ\n\n\n is obtained by the Newton method. The following equations are used for correction of the pressure and velocity simultaneously. Here, the subscript i indicates grid location, while the superscripts m and n indicate the iteration of the corrections for the convergence of Eq. (56) and the time step, respectively. The more detailed explanation can be found in the recent papers published by the present author [9, 10]
The staggered grids in the radius direction together with the points of each variable definition.
\n
Table 2 shows the computational results for various rotation speeds at η = 0.5. When μ > 0.25, the basic flow is always stable due to the Rayleigh’s criterion. The present results exhibit slightly smaller values of Taylor number than those of Chandrasekar. Figures 6 and 7 show the amplitude functions and Eigen functions, respectively, for the case of μ = 0 (the outer cylinder is stationary), and Figures 8 and 9 show the case of μ = −0.5 (the outer cylinder rotates with half angular velocity in opposite direction to the inside rotation).
Computational results and comparison with Chandrasekar (η = 0.5).
\n
Figure 6.
Amplitude functions (η = 0.5, μ = 0, k = 6.325).
\n
Figure 7.
Visualization of Eigen functions for two wavelengths (η = 0.5, μ = 0, k = 6.325). From left to right, Stokes stream function, azimuthal velocity, and pressure.
Visualization of Eigen functions for two wavelengths (η = 0.5, μ = −0.5, k = 9.602). From left to right, Stokes stream function, azimuthal velocity, and pressure.
\n
The simultaneous ordinary equations from (56) to (59) were divided into the real and imaginary parts. However, only four equations among the eight equations are necessary to solve in this problem because of the symmetricity and anti-symmetricity of the complex variables. In Figures 6 and 8, the real part of \n\n\nU\n˜\n\n,\n\nV\n˜\n\n,\n\nP\n˜\n\n\n and the imaginary part of \n\n\nW\n˜\n\n\n are shown. For the visualization shown in Figures 7 and 9, the Stokes stream function \n\nΨ\n\n is defined as follows:
Here, the subscripts \n\nℜ\n\n and \n\nℑ\n\n represent the real part and the imaginary part, respectively. The visualization of other variables, such as the azimuthal velocity and the pressure, are treated in the similar manner using the trigonometric functions.
\n
\n
\n\n',keywords:"finite difference method, similar solution, boundary layer, linear stability analysis, HSMAC method",chapterPDFUrl:"https://cdn.intechopen.com/pdfs/58110.pdf",chapterXML:"https://mts.intechopen.com/source/xml/58110.xml",downloadPdfUrl:"/chapter/pdf-download/58110",previewPdfUrl:"/chapter/pdf-preview/58110",totalDownloads:475,totalViews:381,totalCrossrefCites:0,totalDimensionsCites:0,hasAltmetrics:0,dateSubmitted:"May 12th 2017",dateReviewed:"November 7th 2017",datePrePublished:"December 20th 2017",datePublished:"February 28th 2018",readingETA:"0",abstract:"The present chapter introduces incompressible Newtonian fluid flow and heat transfer by using the finite difference method. Since the solution of the Navier-Stokes equation is not simple because of its unsteady and multi-dimensional characteristic, the present chapter focuses on the simplified flows owing to the similarity or periodicity. As a first section, the first Stoke problem is considered numerically by introducing the finite difference method. In the second section, natural convection heat transfer heated from a vertical plate with uniform heat flux is introduced together with the method how to obtain the system of ordinary differential equations. In the third example, linear stability analysis for the onset of secondary flow during the Taylor-Couette flow is numerically treated using the HSMAC method.",reviewType:"peer-reviewed",bibtexUrl:"/chapter/bibtex/58110",risUrl:"/chapter/ris/58110",book:{slug:"finite-element-method-simulation-numerical-analysis-and-solution-techniques"},signatures:"Toshio Tagawa",authors:[{id:"210981",title:"Dr.",name:"Toshio",middleName:null,surname:"Tagawa",fullName:"Toshio Tagawa",slug:"toshio-tagawa",email:"tagawa-toshio@tmu.ac.jp",position:null,institution:{name:"Tokyo Metropolitan University",institutionURL:null,country:{name:"Japan"}}}],sections:[{id:"sec_1",title:"1. Introduction",level:"1"},{id:"sec_2",title:"2. Unsteady flow due to sudden movement of the plate",level:"1"},{id:"sec_2_2",title:"2.1. Governing equations",level:"2"},{id:"sec_3_2",title:"2.2. Numerical method for solving the ordinary differential equation using finite difference method",level:"2"},{id:"sec_4_2",title:"2.3. Iterative method for matrix solver",level:"2"},{id:"sec_6",title:"3. Similarity solution for natural convection heated from a vertical plate",level:"1"},{id:"sec_6_2",title:"3.1. Introduction",level:"2"},{id:"sec_7_2",title:"3.2. Governing equations",level:"2"},{id:"sec_8_2",title:"3.3. Non-dimensionalization",level:"2"},{id:"sec_9_2",title:"3.4. Numerical results",level:"2"},{id:"sec_11",title:"4. Linear stability of Taylor-Couette flow",level:"1"},{id:"sec_11_2",title:"4.1. Governing equations",level:"2"},{id:"sec_12_2",title:"4.2. Basic state and linearization",level:"2"},{id:"sec_13_2",title:"4.3. Linear stability analysis",level:"2"}],chapterReferences:[{id:"B1",body:'Schlichting H, Gersten K. Boundary Layer Theory. 8th Revised and Enlarged ed. Berlin: Springer; 1999\n'},{id:"B2",body:'Stokes GG. On the effect of the internal friction of fluids on the motion of pendulums. Transactions of the Cambridge Philosophical Society. 1856;9(Part II):8-106 or Collected Papers III\n'},{id:"B3",body:'Rayleigh L. On the motion of solid bodies through viscous liquids. Philosophical Magazine. 1911;21:697-711\n'},{id:"B4",body:'Churchill SW, Ozoe H. A correlation for laminar free convection from a vertical plate. Journal of Heat Transfer. 1973;95(4):540-541\n'},{id:"B5",body:'Le Fevre EJ. Laminar free convection from a vertical plane surface. In: Proceedings of the 9th International Congress of Applied Mechanics; Brussels; Vol. 4; 1956. pp. 168-174\n'},{id:"B6",body:'Chandrasekar S. Hydrodynamic and Hydromagnetic Stability. Oxford: Clarendon Press; 1961\n'},{id:"B7",body:'Koschmieder EL. Bénard cells and Taylor vortices. In: Cambridge Monographs on Mechanics and Applied Mathematics. United State of America: Cambridge University Press; 1993\n'},{id:"B8",body:'Hirt CW, Nichols BD, Romero NC. SOLA: A Numerical Solution Algorithm for Transient Fluid Flows. Los Alamos, New Mexico, United State of America: Los Alamos Scientific Laboratory of University of California. 1975. p. LA-5852\n'},{id:"B9",body:'Tagawa T, Egashira R. Fluid flow of a liquid metal in a cylinder driven by a rotating magnetic field. Transactions of the Japan Society of Mechanical Engineers, Part B. 2012;78(794):1680-1695\n'},{id:"B10",body:'Tagawa T. Numerical investigation of Bénard-Marangoni convection of paramagnetic liquid in annular layers. In: The 15th International Heat Transfer Conference; Kyoto, Japan; August 2014\n'}],footnotes:[],contributors:[{corresp:"yes",contributorFullName:"Toshio Tagawa",address:"tagawa-toshio@tmu.ac.jp",affiliation:'
Department of Aerospace Engineering, Tokyo Metropolitan University, Japan
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1. Introduction
Hemophilia is a disease that has a frequency of approximately 1 in 10,000 births. It has an X-linked transmission, and it consists in a bleeding disorder due to the deficiency of clotting factor VIII (hemophilia A) or factor IX (hemophilia B). Hemophilia is a genetic or acquired disease that leads to spontaneous and recurrent bleedings, which affect the joints and muscles, thus determining chronic damage to the cartilage which will lead to joint disease and hemophilic arthropathy.
There are two major types of hemophilia: type A and type B. These disorders are X-linked and consist in hemorrhages, resulting from diminished levels of clotting factors VIII and IX. Type A is 5–6 times more frequent than type B. This pathology affects in a symptomatic manner only male patients and is characterized by excessive bleeding, which is installed rather spontaneously or after minimal incidents, and is difficult to stop [1].
Hemophilia is a chronic condition that requires a substitution treatment with the defective factor. Its severity varies accordingly to the residual factor level. It is classified as severe (when the clotting factor activity is less than 1%), moderate (1–5%), and mild (6–40%).
If not treated hemophilic patients, especially those with very low clotting factor activity and severe disease, have recurrent disabling and life-threatening bleeding episodes. Using prophylactic factor therapy may diminish bleeding; therefore these novel therapies have changed the prognosis of hemophilic patients, providing increased life expectancy and better quality of life [2, 3, 4].
Even though hemophilic patients were initially thought to have a low incidence of atherothrombotic complications, it is now clear that atherothrombotic events occur.
Limited data suggest that hemophilia is not protective against atherosclerosis and thrombosis, but this theory is still to be studied in men with severe forms of hemophilia without other CVD risk factors, such as active HIV infection [5].
The most common manifestation of hemophilia is represented by bleeding. The severity of hemorrhages is correlated with the plasmatic level of clotting factors. Therefore, there are patients with mild or minor hemophilia that may not bleed excessively until they undergo a surgical intervention or after a trauma.
The accurate diagnostic of hemophilia is mandatory for an optimal management. Hemophilia should be suspected in patients with early bruising in childhood, with excessive hemorrhages after trauma or surgical intervention, or in patients with spontaneous bleeding.
2. Principles of care
Patients with hemophilia need a complex therapeutical management. The most important aim is to administrate the deficient clotting factor so that bleedings are terminated or prevented. If an acute bleeding occurs, it is important to treat it in the first 2 hours.
In order to ease the appropriate management, all patients should carry upon them accessible identification information such as diagnosis, severity of bleeding disorder, type of treatment product that should be used, and contact information.
The patients with hemophilia should benefit from a comprehensive care treatment provided by a team of specialists. This type of care should increase the quality of life while reducing morbidity and mortality.
Hemophilic patients should benefit from fitness and physical activity therapy, in order to obtain normal neuromuscular development, coordination, healthy body weight, and appropriate self-esteem [6].
Adjunctive therapy should be provided consisting in physiotherapy, antifibrinolytic drugs, and certain COX-2 inhibitors in order to soothe the pain.
Prophylactic factor replacement therapy should be administrated so that bleeding and joint destruction is prevented, thus preserving a normal musculoskeletal function.
Surgery is required for complications related to hemophilia or for unrelated disease. The surgical treatment should be done in a comprehensive treatment center for hemophilia [7, 8].
3. Complications of hemophilia
In the majority of cases (90%), the bleeding episodes in hemophilic patients occur in the joints, thus leading to hemarthrosis. From all these bleedings, the most affected joints are the knees, elbows, and ankles. The affected articulation is usually swollen, held in flexion, the mobility being very restricted and painful.
If the deficient clotting factor is given quickly, the hemorrhages can be controlled, and the episode can benefit from conservative orthopedic treatment without long-term complications.
If the bleeding persists or if hemorrhages reoccur, the presence of blood in the joint may lead to apoptosis of the chondrocytes. When there is too much blood present, the synovial membrane will become hypertrophic as it tries to reabsorb the blood. From that moment a vicious circle of chronic synovitis develops thus leading to join destruction and to hemophilic arthropathy [9, 10] (Figure 1).
Figure 1.
Modifications of hemarthrosis in hemophilia [11].
The hypertrophic synovial membrane consists of villous formation with increased vascularization and chronic inflammatory process. Hemophilic children will have hypertrophic epiphyseal growth plates. This bone hypertrophy can determine length discrepancies and modifications in contour and angular deformities. Further destruction of the cartilage may appear if the inflammatory and hemorrhagic process is not controlled. When the synoviocytes are destroyed, they release lysosomal enzymes that promote further cartilage destruction and promote chronic inflammation. As the modifications progressively occur and the cartilage of the joint degrades, the joint function diminishes, and there are limited and painful movements [12, 13, 14].
The apparition of hemarthrosis is the most frequent and unfavorable clinical expression of a hemorrhage in a hemophilic patient; it has an incidence of 75%. It usually appears between 1 and 5 years; if it does occur after 10 years, it is usually due to a mitigated condition. The other symptoms that may appear are relapses. The trigger is represented by a trauma which is very frequently unnoticeable. The most affected joints are in a decreasing order as follows: knees (36%), ankle (30%), elbow (23%), hand (6%), shoulder (3%), and hip (2%) [15, 16].
Hemarthrosis usually affects only one joint, but sometimes the bleeding may be present in both joints, but the lesions are not symmetric. Relapses usually affect the same articulation. Each bleeding episode determines disorders of the joint, thus creating a predisposition for a relapse. The joint structures will weaken, the muscles become atrophic and develop fibrosis thus the join functionality becomes mechanics deficient. In order to bleed less, the synovial will become hypertrophic and will have an increased vascularization, and this mechanism will lead to a vicious circle. From this moment on, a chronic condition begins and is called “hemophilic arthropathy.” This complication advances slowly during time and induces severe modification of the joint with ankylosis. Some experimental studies have proven that a major hemarthrosis induces in the cavity of the joint a dense inflammatory process, while the local tissues change their color and become brownish as a result of the hemosiderin deposits that are due to the erythrocyte damage. The vessels become hyperplasic, thus creating brittle vessels, which are prone to bleeding, therefore inducing a vicious circle: bleeding-vascular hyperplasia-bleeding [11, 17, 18].
The surface of the articulation roughens and pannus is formed. The bone located in the subchondral region becomes dysmorphic. After 30 days the erosions present in the cartilage and bone are obvious.
Different studies have proven that the affected joints are an important factor in inducing cartilage destruction in hemophilic patients. Different authors showed that the presence of iron in the intra-articular blood induces molecular modifications that can offer an explanation for the cellular proliferation in the synovial membrane (synovitis).
Valentino et al. proved in an experimental study that the bleeding that results from a controlled trauma causes joint swelling, synovitis, and hemophilic arthropathy.
In order to alleviate these complications, substitutive treatment with deficient coagulation factor applied from a young age (primary prophylaxis) represents the best therapeutic conduct. Even though primary prophylaxy with the deficient clotting factor is given despite, some patients still have intra-articular hemorrhages, as a result of an insufficient dose of coagulation factor or due to a diminished adherence to the therapy, while other hemophilic patients may present sub-clinically manifested hemarthroses [19, 20].
If continuous prophylactic therapy with clotting factors is provided, the natural course of the arthropathy can be slowed down. One of the most threatening complications of the therapy with clotting factors is the apparition of alloantibodies that are directed against the exogenous molecules of clotting factor. This complication appears in one third of the patients, and it increases the likelihood to develop an uncontrolled bleeding [20, 21].
4. Emicizumab
There has been a new drug developed for the treatment of hemophilic patients. It is called emicizumab, and it is a recombinant antibody that brings activated factor IXa and factor X into an adequate conformation that will lead to the activation of factor X and therefore will mimic the cofactor function of factor VIIIa. A subcutaneous injection with emicizumab that is given once weekly proves to be an efficient method to prevent bleeding in the majority of type A hemophilic patients with inhibitors to factor VIII. Even more the prevention of bleeding has been observed in 66% of patients without inhibitors to factor VIII.
5. Moroctocog alfa
The administration of plasmatic factor VIII has better clinical results in type A hemophilic patients than the transfusion with plasma. The side effects are linked to viral infections transmission such as hepatitis B, C, or HIV; therefore it is better to use in clinical practice recombinant clotting factors that are associated with a diminished risk of viral transmission. In order to have safer products, there have been more modern generations of recombinant factor VIII (rFVIII) developed, the viral transmission being much lower with each new generation of compounds. The first generation had a human serum albumin in order to stabilize the product. The second-generation compounds have no albumin in their composition, but proteins from humans or animals were still allowed in the process of cell culture. The third-generation compounds have eliminated animal and human proteins, but contain murine monoclonal antibodies, which are still used for the purification of rFVIII. It was proven that the elimination of the middle portion (domain B) of the wild-type FVIII did not diminish the clotting activity. It was also shown that the full-length protein had similar effects. These findings helped to discover the recombinant FVIII with deletion of the B domain called moroctocog alfa [21, 22].
ReFacto® is a recombinant clotting factor VIII which has a B-domain deletion (moroctocog alfa). It has a molecular weight of about 170,000 Da and contains1438 amino acids.
ReFacto has a similar functionality as endogenous clotting factor VIII. When given to a patient with hemophilia, factor VIII will bind to the patient’s intrinsic von Willebrand factor. When activated factor VIII becomes a cofactor for activated factor IX, thus catalyzing the activation of factor X. The activated factor X will subsequently transform prothrombin in thrombin. The latter will transform fibrinogen in fibrin, thus forming the red clot. When giving substitution treatment, the levels of factor VIII increase, and the deficiency is temporarily corrected, thus leading to a diminishment in bleeding episodes [1, 23].
6. Personal clinical experience
We analyzed five patients with hemophilia type A, aged between 35 and 62 years. Two of them had a severe form of hemophilia with factor VIII less than 1%, while the other three had a moderate form with factor VIII ranging between 1 and 5%. All of them described intense pain as a result of functionally chronic knee arthropathies. Thus, the lesions had an indication of endoprosthesis and total knee repair. These orthopedic interventions were done by a multidisciplinary team, formed by hematologists, orthopedists, and intensive care staff (Figure 2).
Figure 2.
TKR for severe hemophilic osteoarthritis.
The orthopedic surgeries were realized after a rigorous hematological control, offered through the national protocol for hemophilia. Therefore, all patients received the necessary amount of substation therapy with clotting factor. During the surgery and in the postprocedural surveillance period, the patients had their blood count, hemostasis, and transfusion requirements very thoroughly assessed. Also, other postsurgical complications were routinely searched (Figure 3).
Figure 3.
(A–H) Severe axial deformity. Genu varum in severe hemophilic arthropathy. (A–B) Preoperative X-rays. (C–D) Severe genu varum clinically and radiologically. (E–F) Postoperative X-rays. (G–H) Clinical view of the knee with axis restored and wound healed.
The postsurgical evolution of these patients was favorable, with similar hemostatic profile as the non-hemophilic patients. Only one patient had increased bleeding times, as his clotting profile associated also a factor VII deficiency, thus requiring blood transfusion.
After the administration of Moroctocog alpha substitution treatment, all five patients had a normal clotting profile, thus requiring thromboprophylaxis with LMVH (enoxaparin) in order to prevent VTE. An important aspect to be noted refers to the fact that the amount of bleeding did not correlate with the levels of residual factor. Even more, we noted no differences regarding the volume of blood drained after the surgery between patients with moderate or severe hemophilia. The elderly patients had similar outcomes with young patients with favorable postoperative prognosis, consisting in diminishment of joint pain, improvement in functionality, and increased quality of life. We thus concluded that older age is not a contraindication for complex surgical intervention.
The systemic substitutive treatment was very efficient and normalized the clotting profile of the patients. Therefore, the surgical hemostasis was done without using topical agents such as bio surgical gels or foams. Even more the intrasurgical bleeding of these patients was similar with the hemorrhage seen in patients without the diagnosis of hemophilia. The monitorization of the clotting profile of the patients was thoroughly done by a hematologist trained in treating hemophilic patients requiring elective surgeries. The administration of the substitution therapy followed the guidelines described in the National Protocol of Hemophilia. The clotting profile was monitored daily, and the results showed a normal hemostasis after the administration of treatment. That is why we decided to give low-molecular-weight heparin in these patients, as the risk of thromboembolic events increased after the normalization of the hemostasis, due to the associated risk factors (age, sedentarism, obesity, cardiovascular disease). We chose to give enoxaparin once daily in a 1 mg/kg dose, and the clinical and paraclinical results were favorable.
7. Prophylaxy of thrombosis in hemophilic patients who undergo orthopedic surgeries
Pruthi et al. published a paper in 2000 regarding the use of thrombophylaxy in patients with hemophilia. They presented the case of a patient with moderate hemophilia B, who underwent treatment with factor IX concentrate in order to realize a total hip replacement for a hip fracture and developed venous thromboembolism in the operated limb after the intervention. The thrombophilia screening detected the presence of a heterozygous type of factor V Leiden mutation [24]. Therefore, the authors concluded that presurgical screening for thrombophilia is useful in hemophilic patients who had a previous history of VTE. Another research realized by Mannucci the same year suggested that all patients with thrombophilia should receive short-term therapy with LMWH if they are exposed to significant risks such as prolonged immobilization or surgery [25].
Later in 2004, Dargaud et al. suggested that hemophilic patients should not routinely receive thromboprophylaxis as there are not enough studies, but they also added that hemophilia per se does not protect against venous thromboembolism. The conclusion of this study was that specific cases with increased risk of thrombosis should receive therapy with LMWH [26]. In 2006 Butcher and Pasi reported the case of a patient with hemophilia A, who developed an episode of massive pulmonary embolism after major pelvic surgery. Thus, they concluded that thromboprophylaxis in selected hemophilic patients is very important [27].
Another research done by Uprichard et al. in 2012 included 13 patients with total kidney replacement, from which 11 had hemophilia B. They received mechanical thromboprophylaxis, and one also received pharmacological treatment. The results were satisfying as no patient suffered VTE [28].
In 2012, Uprichard et al. analyzed a series of 13 TKRs in 11 patients with hemophilia B, who received mechanical thromboprophylaxis, and 1 also received pharmacological thromboprophylaxis. No patients suffered VTE [29].
On the other hand, another study realized by Krekeler et al. in 2012 analyzed 105 interventions, 90 of them being major orthopedic surgeries and 15 minor surgeries. The authors did not find any case of VTE even though therapy with LWMH wasn’t given after the surgery. In the same year Ozelo arrived as the same conclusion as Butcher and Pasi. Another research from 2013 done by Berntorp stated that in case of elderly patients diagnosed with hemophilia or patients with von Willebrand disease, a rigorous assessment of the risk and benefit of thromboprophylaxis in the patients who underwent major orthopedic surgery should be realized.
Ozelo et al. proved that the use of graduated compression stockings and early mobilization is sufficient in preventing VTE in the majority of patients. Thus, the administration of anticlotting therapies should be taken into account just for patients that have strong additional risk factors for thrombosis. Contrary, patients with hemophilia treated with inhibitors should not receive pharmacological thromboprophylaxis. Patients with von Willebrand disease, who receive replacement therapy with factor concentrates and who underwent surgical procedures, should have a strict monitorization of FVIII plasma levels, and thrombophylaxy should be taken into account if there are other thrombotic risk factors [30, 31, 32].
8. Conclusions
The best therapy for hemophilic patients consists in doing primary prophylaxy so joint bleeding and other complications are prevented. Even though orthopedic surgeries in these patients are associated with increased risk of complications such as infections and hemorrhages, they can increase significantly the joint mobility and life quality if they are realized in specialized centers with hematological support. Moroctocog alfa is an efficient substitutive treatment that manages to normalize the hemostatic profile of patients. Therefore, it is recommended to provide prophylactic antithrombotic therapy after the orthopedic interventions.
\n',keywords:"hemophilia, hemophilic arthropathy, orthopedic surgery, hemostasis, physiotherapy",chapterPDFUrl:"https://cdn.intechopen.com/pdfs/69819.pdf",chapterXML:"https://mts.intechopen.com/source/xml/69819.xml",downloadPdfUrl:"/chapter/pdf-download/69819",previewPdfUrl:"/chapter/pdf-preview/69819",totalDownloads:26,totalViews:0,totalCrossrefCites:0,dateSubmitted:"June 6th 2019",dateReviewed:"October 3rd 2019",datePrePublished:"October 30th 2019",datePublished:null,readingETA:"0",abstract:"Hemophilia is a genetic or acquired disease that leads to spontaneous and recurrent bleedings, which affect the joints and muscles, thus determining chronic damage to the cartilage which will lead to joint disease and hemophilic arthropathy. Even though hemophilic patients were initially thought to have a low incidence of atherothrombotic complications, it is now clear that atherothrombotic events occur. The administration of plasmatic factor VIII has better clinical results in type A hemophilic patients than the transfusion with plasma. We analyzed five patients with hemophilia type A, aged between 35 and 62 years. Two of them had a severe form of hemophilia with factor VIII less than 1%, while the other three had a moderate form with factor VIII ranging between 1 and 5%. The five patients underwent total knee repair interventions and received substitution treatment with clotting factors but also prophylactic anticoagulant treatment. The postsurgical evolution of these patients was favorable, with similar hemostatic profile as the non-hemophilic patients. Moroctocog alfa is an efficient substitutive treatment that manages to normalize the hemostatic profile of patients. Therefore, it is recommended to provide prophylactic antithrombotic therapy after the orthopedic interventions.",reviewType:"peer-reviewed",bibtexUrl:"/chapter/bibtex/69819",risUrl:"/chapter/ris/69819",signatures:"Oana-Viola Badulescu, Iris Bararu Bojan, Maria Vladeanu, Codruta Badescu, Andrei Bojan, Paul Dan Sirbu and Manuela Ciocoiu",book:{id:"8206",title:"Biosurgicals - The Next Frontier in Operative Approaches",subtitle:null,fullTitle:"Biosurgicals - The Next Frontier in Operative Approaches",slug:null,publishedDate:null,bookSignature:" Michael S. S Firstenberg and Dr. Stanislaw P. Stawicki",coverURL:"https://cdn.intechopen.com/books/images_new/8206.jpg",licenceType:"CC BY 3.0",editedByType:null,editors:[{id:"64343",title:null,name:"Michael S.",middleName:"S",surname:"Firstenberg",slug:"michael-s.-firstenberg",fullName:"Michael S. Firstenberg"}],productType:{id:"1",title:"Edited Volume",chapterContentType:"chapter",authoredCaption:"Edited by"}},authors:null,sections:[{id:"sec_1",title:"1. Introduction",level:"1"},{id:"sec_2",title:"2. Principles of care",level:"1"},{id:"sec_3",title:"3. Complications of hemophilia",level:"1"},{id:"sec_4",title:"4. Emicizumab",level:"1"},{id:"sec_5",title:"5. Moroctocog alfa",level:"1"},{id:"sec_6",title:"6. Personal clinical experience",level:"1"},{id:"sec_7",title:"7. Prophylaxy of thrombosis in hemophilic patients who undergo orthopedic surgeries",level:"1"},{id:"sec_8",title:"8. Conclusions",level:"1"}],chapterReferences:[{id:"B1",body:'Huth-Kühne A, Baudo F, Collins P, et al. International recommendations on the diagnosis and treatment of patients with acquired hemophilia A. Haematologica. 2009;94(4):566-575. DOI: 10.3324/haematol.2008.001743'},{id:"B2",body:'Collins PW, Hirsch S, Baglin TP, Dolan G, Hanley J, Makris M, et al. Acquired hemophilia a in the United Kingdom: A 2-year national surveillance study by the United Kingdom Haemophilia Centre Doctors’ Organisation. Blood. 2007;109:1870-1877'},{id:"B3",body:'Green D, Lechner K. A survey of 215 non-hemophilic patients with inhibitors to factor VIII. Thrombosis and Haemostasis. 1981;45:200-203'},{id:"B4",body:'Franchini M, Gandini G, Di Paolantonio T, Mariani G. Acquired hemophilia a: A concise review. American Journal of Hematology. 2005;80:55-63'},{id:"B5",body:'Sood SL, Cheng D, Ragni M, et al. A cross-sectional analysis of cardiovascular disease in the hemophilia population. Blood Advances. 2018;2(11):1325-1333. DOI: 10.1182/bloodadvances.2018018226'},{id:"B6",body:'Srivastava A, Brewer AK, Mauser-Bunschoten EP, Key NS, Kitchen S, Llinas A, et al. Treatment Guidelines Working Group on Behalf of the World Federation of Hemophilia. Guidelines for the Managment of Hemophilia. 2nd ed. Haemophilia. Jan 2013;19(1):e1-e47'},{id:"B7",body:'Jansen NW, Roosendal G, Bijlsmal JW, Degroot J, Lafeber FP. Exposure of human cartilage tissue to low concentrations of blood for a short period of time leads to prolonged cartilage damage: An in vitro study. Arthritis and Rheumatism. 2007;56:199-207. DOI: 10.1002/art.22304'},{id:"B8",body:'Valentino LA, Hakobyan N. Histological changes in murine haemophilic synovitis: A quantitative grading system to assess blood-induced synovitis. Haemophilia. 2006;12:654-662. DOI: 10.1111/j.1365-2516.2006.01348.x'},{id:"B9",body:'Valentino LA, Hakobyan N, Rodriguez N, Hoots WK. Pathogenesis of haemophilic synovitis: Experimental studies on blood-induced joint damage. Haemophilia. 2007;13(Suppl 3):10-13. DOI: 10.1111/j.1365-2516.2007.01534.x'},{id:"B10",body:'Bardas CA, Gabri JZ, Apostu D, Oltean-Dan D, Tomoaia G, Benea H. Functional results of different repair techniques for knee articular cartilage lesions. Revista de Chimie. 2018;69(11):3288-3291'},{id:"B11",body:'Lafeber FP, Miossec P, Valentino LA. Physiopathology of haemophilic arthropathy. Haemophilia. 2008;14(Suppl 4):3-9. DOI: 10.1111/j.1365-2516.2008.01732.x'},{id:"B12",body:'Berea G, Balan G, Sandru V, Sîrbu PD. In vitro three dimensional scaffold-free construct of human adiposederived stem cells in coculture with endothelial cells and fibroblasts. Revista de Chimie. 2017;68(6):1341-1344'},{id:"B13",body:'Hooiveld MJ, Roosendaal G, Jacobs KM, Vianen ME, Van Den Berg HM, Bijlsma JW, et al. Initiation of degenerative joint damage by experimental bleeding combined with loading of the joint: A possible mechanism of hemophilic arthropathy. Arthritis and Rheumatism. 2004;50:2024-2031. DOI: 10.1002/ art.20284'},{id:"B14",body:'Hakobyan N, Kazarian T, Jabbar AA, Jabbar KJ, Valentino LA. Pathobiology of hemophilic synovitis I: Overexpression of mdm2 oncogene. Blood. 2004;104:2060-2064. DOI: 10.1182/blood-2003-12-4231'},{id:"B15",body:'Sîrbu PD, Petreus T, Munteanu FL, Pertea M, Lunca S, Poroch V, et al. Clinical experience with a macroporous synthetic bone substitute (eurocer) in the treatment of the patients with bone defects international conference on advancements of medicine and health care through technology. IFMBE Proceedings. 2011;36(5):358-368. DOI: 10.1007/978-3-642-22586-4_75'},{id:"B16",body:'Valentino LA, Hakobyan N, Kazarian T, Jabbar KJ, Jabbar AA. Experimental haemophilic synovitis: Rationale and development of a murine model of human factor VIII deficiency. Haemophilia. 2004;10:280-287. DOI: 10.1111/ j.1365-2516.2004.00899.x'},{id:"B17",body:'Nilsson IM, Berntorp E, Löfqvist T, Pettersson H. Twenty-five years’ experience of prophylactic treatment in severe haemophilia A and B. Journal of Internal Medicine. 1992;232:25-32. DOI: 10.1111/j.1365-2796.1992.tb00546.x'},{id:"B18",body:'Manco-Johnson MJ, Abshire TC, Shapiro AD, Riske B, Hacker MR, Kilcoyne R, et al. Prophylaxis versus episodic treatment to prevent joint disease in boys with severe hemophilia. The New England Journal of Medicine. 2007;357:535-544. DOI: 10.1056/NEJMoa067659'},{id:"B19",body:'Hilgartner MW. Current treatment of hemophilic arthropathy. Current Opinion in Pediatrics. 2002;14:46-49. DOI: 10.10 97/00008480-200202000-00008'},{id:"B20",body:'Rodriguez-Merchan EC. Aspects of current management: Orthopaedic surgery in haemophilia. Haemophilia. 2012;18:8-16. DOI: 10.1111/j.1365-2516.2011.02544.x'},{id:"B21",body:'Korth-Bradley J, Rupon J, Plotka A, Charnigo R, Rendo P. Assessment of relative bioavailability of moroctocog alfa and moroctocog alfa (AF-CC) in subjects with severe hemophilia A. Clinical and Translational Science. 2018;11(3):283-288. DOI: 10.1111/cts.12544'},{id:"B22",body:'Kelley B, Jankowski M, Booth J. An improved manufacturing process for Xyntha/ReFacto AF. Haemophilia. 2010;16:717-725'},{id:"B23",body:'Recht M et al. Clinical evaluation of moroctocog alfa (AF-CC), a new generation of B-domain deleted recombinant factor FVIII (BDDrFVIII) for the treatment of haemophilia A: Demonstration of safety, efficacy, and pharmacokinetic equivalence to full-length recombinant factor VIII. Haemophilia. 2009;15:869-880'},{id:"B24",body:'Pruthi RK, Heit JA, Green MM, Emiliusen LM, Nichols WL, Wilke JL, et al. Venous thromboembolism after hip fracture surgery in a patient with haemophilia B and factor V Arg506Gln (factor V Leiden). Haemophilia. 2000;6(6):631-634'},{id:"B25",body:'Santagostino E, Mannucci PM, Bianchi Bonomi A. Guidelines on replacement therapy for haemophilia and inherited coagulation disorders in Italy. Haemophilia. 2000;6(1):1-10'},{id:"B26",body:'Dargaud Y, Meunier S, Negrier C. Haemophilia and thrombophilia: An unexpected association. Haemophilia. 2004;10(4):319-326'},{id:"B27",body:'Butcher JH, Pasi KJ. Fatal postoperative pulmonary embolism in mild haemophilia. Haemophilia. 2006;12(2):179-182'},{id:"B28",body:'Uprichard J, Adamidou D, Goddard NJ, Mann HA, Yee TT. Factor IX replacement to cover total knee replacement surgery in haemophilia B: a single-centre experience, 2000-2010. Haemophilia. Jan 2012;18(1):46-49'},{id:"B29",body:'Adamidou D, Goddard NJ, Mann HA, Yee TT. Factor IX replacement to cover total knee replacement surgery in haemophilia B: A single-Centre experience, 2000-2010. Haemophilia. 2012;18(1):46-49'},{id:"B30",body:'Krekeler S, Alesci S, Miesbach W. Incidence of thromboembolic events after major operations in patients with haemophilia. Hämostaseologie. 2012;32(Suppl 1):S45-S47'},{id:"B31",body:'Ozelo MC. Surgery in patients with hemophilia: Is thromboprophylaxis mandatory? Thrombosis Research. 2012;130(Suppl 1):S23-S26. DOI: 10.1016/j.thromres.2012.08.265'},{id:"B32",body:'Lentz SR, Misgav M, Ozelo M, Salek SZ, Veljkovic D, Recht M, et al. Results from a large multinational clinical trial (guardian™1) using prophylactic treatment with turoctocog alfa in adolescent and adult patients with severe haemophilia a: Safety and efficacy. Haemophilia. 2013;19(5):691-697'}],footnotes:[],contributors:[{corresp:null,contributorFullName:"Oana-Viola Badulescu",address:null,affiliation:'
Department of Morphofunctional Sciences, University of Medicine and Pharmacy “Grigore T. Popa”, Romania
Department of Morphofunctional Sciences, University of Medicine and Pharmacy “Grigore T. Popa”, Romania
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The aim of the present analysis is to compare results of a cross-sectional and a cohort approach considering overall hospital admission and hospital admission due to cancer and circulatory disease. Register-based data were analysed for the period of 2006–2009. In the cross-sectional analysis, a multiple logistic regression model was conducted based on the year 2006, and cohort information from the same year onward up to 2009 was available for a Cox regression model. Social welfare compensated unemployment and both types of disease-specific hospital admission were associated to be statistically significant in the cross-sectional analysis. With regard to circulatory disease, the cohort approach suggests that social welfare compensated unemployment might lead to hospital admission due to the disease. Given the significant results in the cross-sectional analysis for hospital admission due to cancer, the unfound cohort effect might indicate a reverse causation suggesting that the disease caused joblessness, and finally social welfare compensated unemployment and not vice versa. Comparing different study designs allows for a better causal interpretation, which should be recommended in future quantitative social welfare analysis.",signatures:"Gabriele Berg-Beckhoff, Gabriel Gulis, Carsten Kronborg Bak and\nPernille Tanggaard Andersen",authors:[{id:"188461",title:"Dr.",name:"Gabriele",surname:"Berg-Beckhoff",fullName:"Gabriele Berg-Beckhoff",slug:"gabriele-berg-beckhoff",email:"gbergbeckhoff@health.sdu.dk"},{id:"188463",title:"Dr.",name:"Gabriel",surname:"Gulis",fullName:"Gabriel Gulis",slug:"gabriel-gulis",email:"GGulis@health.sdu.dk"},{id:"188465",title:"Dr.",name:"Carsten",surname:"Kronborg Bak",fullName:"Carsten Kronborg Bak",slug:"carsten-kronborg-bak",email:"CKR@ucn.dk"},{id:"188466",title:"Dr.",name:"Pernille",surname:"Tangaard Andersen",fullName:"Pernille Tangaard Andersen",slug:"pernille-tangaard-andersen",email:"ptandersen@health.sdu.dk"}],book:{title:"An Analysis of Contemporary Social Welfare Issues",slug:"an-analysis-of-contemporary-social-welfare-issues",productType:{id:"1",title:"Edited Volume"}}}],collaborators:[{id:"118227",title:"Dr.",name:"Rosario",surname:"Laratta",slug:"rosario-laratta",fullName:"Rosario Laratta",position:null,profilePictureURL:"https://mts.intechopen.com/storage/users/118227/images/2216_n.jpg",biography:'Rosario Laratta is an associate professor of social policy at the School of Governance Studies and the School of Global Governance, Meiji University, Tokyo, & an adjunct faculty at the iCLA (Yamanashi Gakuin University), ICU (International Christian University), Sophia University, Temple University, and recently Toyo University. Before his current appointments, he worked four years for the University of Tokyo. He earned a Postdoctorate in Politics from the University of Tokyo, a PhD and MA in Political Sociology from Warwick University (UK), a MA in Public Policy from Bocconi University, and a BA in Political Science from Calabria University. He is the author of many books such as “Nonprofit Organizations in England and Japan” (2012) and “Empirical Policy Research” (2013), and editor of “Social Welfare” (2012), \\"Social Enterprise\\" (2016), and \\"An Analysis of Contemporary Social Welfare Issues\\" (2016). He has also published over hundred articles, most of which are peer-reviewed papers on leading international journals, such as “Hand in Hand or Under the Thumb?” (Cambridge Journal of Social Policy and Society), “From Welfare State to Welfare Society” (International Journal of Social Welfare), and ““Ethical Climate and Accountability in Nonprofits: a comparative study between Japan and U.K” (Public Management Review). He currently acts as a regular reviewer for fifteen peer-reviewed international journals and as advisory board member for some of those. He is also member of a number of academic associations in Japan and abroad.',institutionString:null,institution:null},{id:"187695",title:"Ph.D. Student",name:"Clare",surname:"Cannon",slug:"clare-cannon",fullName:"Clare Cannon",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",biography:null,institutionString:null,institution:{name:"Tulane University",institutionURL:null,country:{name:"United States of America"}}},{id:"187879",title:"Dr.",name:"Auxiliadora",surname:"González Portillo",slug:"auxiliadora-gonzalez-portillo",fullName:"Auxiliadora González Portillo",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",biography:null,institutionString:null,institution:{name:"Loyola University Andalusia",institutionURL:null,country:{name:"Spain"}}},{id:"187933",title:"Dr.",name:"Fred",surname:"Buttell",slug:"fred-buttell",fullName:"Fred Buttell",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",biography:null,institutionString:null,institution:null},{id:"188289",title:"Prof.",name:"Sylvia",surname:"Kirchengast",slug:"sylvia-kirchengast",fullName:"Sylvia Kirchengast",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",biography:null,institutionString:null,institution:{name:"University of Vienna",institutionURL:null,country:{name:"Austria"}}},{id:"188461",title:"Dr.",name:"Gabriele",surname:"Berg-Beckhoff",slug:"gabriele-berg-beckhoff",fullName:"Gabriele Berg-Beckhoff",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",biography:null,institutionString:null,institution:{name:"University of Southern Denmark",institutionURL:null,country:{name:"Denmark"}}},{id:"188463",title:"Dr.",name:"Gabriel",surname:"Gulis",slug:"gabriel-gulis",fullName:"Gabriel Gulis",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",biography:null,institutionString:null,institution:null},{id:"188466",title:"Dr.",name:"Pernille",surname:"Tangaard Andersen",slug:"pernille-tangaard-andersen",fullName:"Pernille Tangaard Andersen",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",biography:null,institutionString:null,institution:null},{id:"189164",title:"Dr.",name:"Germán",surname:"Jaraíz Arroyo",slug:"german-jaraiz-arroyo",fullName:"Germán Jaraíz Arroyo",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",biography:null,institutionString:null,institution:null}]},generic:{page:{slug:"WIS-cost",title:"What Does It Cost?",intro:"
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\\n\\t
Bill and Melinda Gates Foundation
\\n\\t
Wellcome Trust
\\n\\t
National Institute of Health (NIH)
\\n\\t
National Science Foundation (NSF)
\\n\\t
National Institute of Standards and Technology (NIST)
We are currently in the process of collecting sponsorship. If you have any ideas or would like to help sponsor this ambitious program, we’d love to hear from you. Contact Dr. Anke Beck at anke@intechopen.com.
\n\n
All of our IntechOpen sponsors are in good company! The research in past IntechOpen books and chapters have been funded by:
\n\n
\n\t
European Commission
\n\t
Bill and Melinda Gates Foundation
\n\t
Wellcome Trust
\n\t
National Institute of Health (NIH)
\n\t
National Science Foundation (NSF)
\n\t
National Institute of Standards and Technology (NIST)
\n\t
Research Councils United Kingdom (RCUK)
\n\t
Foundation for Science and Technology (FCT)
\n\t
Chinese Academy of Sciences
\n\t
Natural Science Foundation of China (NSFC)
\n\t
German Research Foundation (DFG)
\n\t
Max Planck Institute
\n\t
Austrian Science Fund (FWF)
\n\t
Australian Research Council (ARC)
\n
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