### Citations

726 |
Mechanical Properties of Living Tissues
- Fung
- 1993
(Show Context)
Citation Context ...(∇u T )]=μ(D(u))D(u)+λ2[ ˙D(u)−(∇u)D(u)−D(u)(∇u T )] where λ1, λ2 are material constants that characterize the model. For a discussion on rheological properties of blood flow we refer, e.g., to [12], =-=[38]-=-, [39], [94], [57]. For a more thorough mathematical analysis of Oldroyb-B models see, e.g., [102], [4], [83], [68], [40], [41], [71]. h Us10 Alfio Quarteroni Figure 6. Velocity profiles computed in a... |

428 |
Numerical Approximation of Partial Differential Equations
- Quarteroni, Valli
- 1997
(Show Context)
Citation Context ... (7)–(12) (or that discussed above based on the one dimensional model (13) for the radial vessel deformation) poses many challenges. After space discretization (e.g. by the finite element method, see =-=[77]-=-) one obtains a coupled nonlinear algebraic system. Since the density of the structure is comparable to that of the fluid, the stability of numerical simulations of fluid-structure interactions relies... |

421 |
Domain Decomposition Methods for Partial Di®erential Equations
- Quarteroni, Valli
- 1999
(Show Context)
Citation Context ...re (10) is coupled with the projection step of the Navier–Stokes equations, and the stress continuity equation (12) is enforced. Another strategy is mutuated from domain decomposition techniques (see =-=[78]-=-) and is proposed in [24]. The global coupled problem (7)–(12) is reduced to a (generally nonlinear) interface equation, the so-called pseudo-differential Steklov–Poincaré equation, where the only unk... |

365 |
2002] The immersed boundary method
- Peskin
(Show Context)
Citation Context ... was introduced by Charles Peskin in his Ph.D thesis in 1972 in order to study the fluid dynamics of heart valves, and it was then extended to become a three-dimensional model of the whole heart (see =-=[73]-=- and the references therein). According to Peskin, “the philosophy of the immersed boundary method is to blur the distinction between fluid dynamics and elasticity”. This is accomplished by inserting ... |

138 |
A New Constitutive Framework for Arterial Wall Mechanics and a Comparative Study of Material Models
- Holzapfel, Gasser, et al.
(Show Context)
Citation Context ...ll has a very complex nature; devising an accurate model for its mechanical behavior is rather difficult. Its structure is indeed formed by many layers with different mechanical characteristics [38], =-=[48]-=-. The most important are the endothelium (of about 2 microns, with anti-adhesive function), the tunica intima (of 10 microns, made of connective tissue), the internal elastic lamina, of 2 microns,sCar... |

128 |
Mathematical principles of classical fluid mechanics. Handbuch der Physik (herausgegeben von
- Serrin
- 1959
(Show Context)
Citation Context ...ent), f is the specific body force (e.g., f =−ge3 where e3 represents the unit vector in the vertical direction and g the gravitational acceleration), while T is the Cauchy stress tensor (see [3] and =-=[86]-=-). The system (2),(3) can be closed by using a constitutive law that relates the Cauchy stress to kinematic quantities (velocity and pressure), and which is peculiar to the specific rheological behavi... |

121 |
Thermodynamic analysis of the permeability of biological membrane to non-electrolytes. Biochimica et Biophysica Acta
- Kedem, Katchalsky
- 1958
(Show Context)
Citation Context ...e flux of fluid (Jv) and the flux of chemicals (Js) between two solutions (denoted by i = 1, 2) separated by a semipermeable membrane across which concentrations and fluid pressure are different, see =-=[51]-=-, [50]. In the case of just one solute, denoting with δp = p1 −p2 and δc = c1 −c2 the driving forces across the membrane, the interface equations originally proposedsCardiovascular mathematics 27 by K... |

115 |
Mathematical Physiology
- Keener, Sneyd
- 2004
(Show Context)
Citation Context ...ected; on the other hand, a high arterial pressure would induce vascular diseases and heart overload. This regulation mechanism is called baroreflex effect and is described, for instance, in [49] and =-=[52]-=-. The elements of the feedback baroreceptor loop are a set of baroreceptors located in the carotid arteries and the aortic arch, which transmit impulses to the brain at a rate increasing with the arte... |

104 |
Biodynamics: circulation
- Fung
- 1984
(Show Context)
Citation Context ...)]=μ(D(u))D(u)+λ2[ ˙D(u)−(∇u)D(u)−D(u)(∇u T )] where λ1, λ2 are material constants that characterize the model. For a discussion on rheological properties of blood flow we refer, e.g., to [12], [38], =-=[39]-=-, [94], [57]. For a more thorough mathematical analysis of Oldroyb-B models see, e.g., [102], [4], [83], [68], [40], [41], [71]. h Us10 Alfio Quarteroni Figure 6. Velocity profiles computed in a carot... |

96 |
Added-mass effect in the design of partitioned algorithms for fluid-structure problems
- Causin, Gerbeau, et al.
- 2005
(Show Context)
Citation Context ...mes should be used as they would guarantee energy conservation (up to the dissipation terms) and therefore numerical stability. This is outlined on a simplified fluid-structure interaction problem in =-=[13]-=-, where implicit and staggered algorithms are analyzed by taking into account the so-called added-mass effect. In particular it is shown that numerical instabilities may occur when using loosely coupl... |

95 |
the Basic Equations of Fluid Mechanics
- Aris, Vectors
- 1989
(Show Context)
Citation Context ...al gradient), f is the specific body force (e.g., f =−ge3 where e3 represents the unit vector in the vertical direction and g the gravitational acceleration), while T is the Cauchy stress tensor (see =-=[3]-=- and [86]). The system (2),(3) can be closed by using a constitutive law that relates the Cauchy stress to kinematic quantities (velocity and pressure), and which is peculiar to the specific rheologic... |

83 |
Fluid structure interaction with large structural displacements
- Tallec, Mouro
- 2001
(Show Context)
Citation Context ... of the fluid, the stability of numerical simulations of fluid-structure interactions relies heavily on the accuracy in solving the nonlinear coupled problem at each time step [23], [59], [60], [70], =-=[88]-=-.s16 Alfio Quarteroni Ideally, implicit schemes should be used as they would guarantee energy conservation (up to the dissipation terms) and therefore numerical stability. This is outlined on a simpli... |

82 |
On the coupling of 3d and 1d navier–stokes equations for flow problems
- Formaggia, Gerbeau, et al.
(Show Context)
Citation Context ...ery with reduced models, which are able to represent, although in a simplified way, the presence of the remaining part of the circulatory system. Techniques of this type has been used and analyzed in =-=[32]-=-, [33]. An account will be given in Section 4. Normally, on arterial sections like Ɣin and Ɣout only “averaged” data are available (mean velocity and mean pressure instead of a vector condition like t... |

81 |
The Mechanics of the Circulation
- Caro
- 1978
(Show Context)
Citation Context ...∇u)τ−τ(∇u T )]=μ(D(u))D(u)+λ2[ ˙D(u)−(∇u)D(u)−D(u)(∇u T )] where λ1, λ2 are material constants that characterize the model. For a discussion on rheological properties of blood flow we refer, e.g., to =-=[12]-=-, [38], [39], [94], [57]. For a more thorough mathematical analysis of Oldroyb-B models see, e.g., [102], [4], [83], [68], [40], [41], [71]. h Us10 Alfio Quarteroni Figure 6. Velocity profiles compute... |

79 | Method for the calculation of velocity, rate of flow and viscous drag in arteries when the pressure gradient is known - Womersley |

76 |
Numerical approximation of fluid-structure interaction problems with application to haemodynamics, Thèse de doctorat de l’École Polytechnique Fédérale de Lausanne
- Nobile
- 2001
(Show Context)
Citation Context ...o that of the fluid, the stability of numerical simulations of fluid-structure interactions relies heavily on the accuracy in solving the nonlinear coupled problem at each time step [23], [59], [60], =-=[70]-=-, [88].s16 Alfio Quarteroni Ideally, implicit schemes should be used as they would guarantee energy conservation (up to the dissipation terms) and therefore numerical stability. This is outlined on a ... |

52 |
An efficient solver for the fully coupled solution of large-displacement fluid–structure interaction problems
- Heil
- 2004
(Show Context)
Citation Context ...thods are slow, and in some cases may even fail to converge [70], [13], [25]. A more radical approach consists of using Newton based methods, owing to their potentially faster convergence [25], [29], =-=[46]-=-, [61]. However, since they demand the evaluation of the Jacobian associated to the fluid-solid coupled state equations, a critical step is the evaluation of the cross Jacobian [93], which expresses t... |

52 |
Mathematical modelling and numerical simulation of the cardiovascular system. Handbook of numerical analysis
- Quarteroni, Formaggia
- 2004
(Show Context)
Citation Context ... ˆ� s , (10) u = ˙η ◦ (L s ) −1 on Ɣ(t), (11) F s � s · ˆn s = J f T f · (F f ) −T · ˆn s on ˆƔ, (12) where ˆn s denotes the outward unit vector on ˆƔ, ∂ ∂t| ˆx represents theALE time derivative (see =-=[75]-=-) and H (.) denotes any continuous extension operator from ˆƔ to the fluid domain ˆ� f (for instance the harmonic extension, or else the extension by the linear elasticity operator). This coupled prob... |

49 |
A Newton method using exact Jacobians for solving fluidstructure coupling
- Fernández, Moubachir
- 2005
(Show Context)
Citation Context ...ese methods are slow, and in some cases may even fail to converge [70], [13], [25]. A more radical approach consists of using Newton based methods, owing to their potentially faster convergence [25], =-=[29]-=-, [46], [61]. However, since they demand the evaluation of the Jacobian associated to the fluid-solid coupled state equations, a critical step is the evaluation of the cross Jacobian [93], which expre... |

46 | A Quasi-Newton algorithm based on a reduced model for fluid-structure interaction problems in blood flows, ESAIM
- Gerbeau, Vidrascu
(Show Context)
Citation Context ... be made inexactly, either by resorting to finite difference approximation of derivatives (see, e.g., [93]), or by barely replacing the tangent operator of the coupled system with a simpler one [42], =-=[43]-=-. However, either approximation may seriously compromise the convergence rate. Acceleration techniques using Krylov spaces have been proposed in [26], [46], [62]. A Newton method with exact Jacobian h... |

44 |
Numerical treatment of defective boundary conditions for the Navier–Stokes equations
- Formaggia, Gerbeau, et al.
- 2002
(Show Context)
Citation Context ...lable data and, on the other hand, permit to formulate a mathematically well posed problem. In these notes we will not investigate this particular aspect, which is however illustrated and analyzed in =-=[34]-=-, [97], [98]. Now we will make some considerations on the behavior of blood flow. Most often, it is laminar. Characteristic values of the Reynolds number, Re = ρUL μ , where U is a representative mean... |

43 |
A biomechanical model of muscle contraction
- Bestel, Clément, et al.
(Show Context)
Citation Context ...alve is described by setting Q = 0 when Pa >Pv,Pa = Pv − RQ if Q>0. For more details about this model, see [37]. More sophisticated ODE models are available, such as the visco-elasto-plastic model in =-=[7]-=-. From a mathematical standpoint, a general representation of lumped parameters models is a Differential-Algebraic-Equations (DAE) system in the form dy dt = B(y, z,t) t ∈ (0,T] G(y, z) = 0 supplement... |

39 |
Veneziani A. Analysis of a geometrical multiscale model based on the coupling of PDE’s and ODE’s for blood flow simulations. SIAM Multiscale Modeling and Simulation
- Quarteroni
- 2003
(Show Context)
Citation Context ...ly well-posed mathematical problem. The analysis of the complete system is very difficult, though. Partial results are available on the coupling of 3D and 0D models, and of 1D and 0D, see [33], [32], =-=[81]-=-. An account is given in [37]. So far, we have described the heart ventricle functionality by a simple 0D model. Clearly, this is an overly simplified approach. In fact, the development of a mathemati... |

37 |
Multiscale modelling of the circulatory system: a preliminary analysis
- Formaggia, Nobile, et al.
- 1999
(Show Context)
Citation Context ...th reduced models, which are able to represent, although in a simplified way, the presence of the remaining part of the circulatory system. Techniques of this type has been used and analyzed in [32], =-=[33]-=-. An account will be given in Section 4. Normally, on arterial sections like Ɣin and Ɣout only “averaged” data are available (mean velocity and mean pressure instead of a vector condition like that in... |

35 | Fluid-structure algorithms based on Steklov-Poincaré operators
- Deparis, Discacciati, et al.
- 2006
(Show Context)
Citation Context ...he projection step of the Navier–Stokes equations, and the stress continuity equation (12) is enforced. Another strategy is mutuated from domain decomposition techniques (see [78]) and is proposed in =-=[24]-=-. The global coupled problem (7)–(12) is reduced to a (generally nonlinear) interface equation, the so-called pseudo-differential Steklov–Poincaré equation, where the only unknown is the displacement ... |

34 |
Existence for an unsteady fluid–structure interaction problem
- Grandmont, Maday
- 2000
(Show Context)
Citation Context ...ed forces, existence of regular solutions is proven in [44]. In the unsteady case, local solvability in time is proven in the simple case where the structure is a collection of rigid moving bodies in =-=[45]-=-. See also [27]. Formulations based on optimal control on simpler models have been investigated, e.g., in [55], [72], [66], [67], [103], [104]. As previously mentioned, simpler models than (10) can be... |

34 |
Modeling, Analysis and Control of Dynamic Elastic Multi-Link Structures
- Lagnese, Leugering, et al.
- 1994
(Show Context)
Citation Context ...ts (like in Figure 12, right) ensuring mass and energy conservation (see [75]). Its mathematical investigation would require the analysis of nonlinear hyperbolic systems on networks (see, e.g., [19], =-=[53]-=-). The resulting network of one dimensional hyperbolic models are very well suited to describe the propagation of waves (the pulse), a phenomenon generated by the interaction between blood flow and co... |

33 |
Hindered transport of large molecules in liquid-filled pores
- Deen
- 1987
(Show Context)
Citation Context ...d we will call them effective coefficients, denoted with LP,eff(ε1,ε2), �eff(ε1,ε2), seff(ε1,ε2) respectively. This theoretical characterization is a very challenging task, see e.g. [18], [89], [90], =-=[22]-=-. An approach that allows a direct estimation of the effective coefficients is proposed in [74]. To define the mathematical problems describing the mass transfer from the lumen to the arterial wall, w... |

31 |
A parallel solver for reaction-diffusion systems in computational electrocardiology
- Franzone, Pavarino
(Show Context)
Citation Context ...ations are proposed to relate material properties to tissue behavior. Cardiac tissue is made of discrete cells but it can be modeled as a continuum. For instance, the bidomain model (see, e.g., [17], =-=[16]-=-) consists of two interpenetrating domains that represent cells (intracellular domain) and the space surrounding the cells (extracellular domain). These two domains are assumed to co-exist at all poin... |

31 |
Mathematical and numerical models for transfer of low-density lipoproteins through the arterial wall: a new methodology for the model set up with applications to the study of disturbed lumenal flow
- Prosi, Zunino, et al.
(Show Context)
Citation Context ...) respectively. This theoretical characterization is a very challenging task, see e.g. [18], [89], [90], [22]. An approach that allows a direct estimation of the effective coefficients is proposed in =-=[74]-=-. To define the mathematical problems describing the mass transfer from the lumen to the arterial wall, we label with i = 1 the physical quantities associated with the free fluid and with i = 2 the on... |

30 |
Mathematical analysis of the quasilinear effects in a hyperbolic model blood flow through compliant axi-symmetric vessels
- Čanić, Kim
(Show Context)
Citation Context ...rent models can be obtained by choosing different pressure-area laws. Finally, KR is a parameter accounting for the viscosity of the fluid. For the analysis of the hyperbolic system (14) see [75] and =-=[10]-=-. In this simple (and most popular) one dimensional model the vessel mechanics is overly simplified. In practice, it is reduced to an algebraic relationship between thesCardiovascular mathematics 19 m... |

30 |
Mechanics and thermodynamics of transcapillary exchange,” in Handbook of Physiology The Cardiovascular SystemMicrocirculation
- Curry
- 1984
(Show Context)
Citation Context ... of each medium and we will call them effective coefficients, denoted with LP,eff(ε1,ε2), �eff(ε1,ε2), seff(ε1,ε2) respectively. This theoretical characterization is a very challenging task, see e.g. =-=[18]-=-, [89], [90], [22]. An approach that allows a direct estimation of the effective coefficients is proposed in [74]. To define the mathematical problems describing the mass transfer from the lumen to th... |

29 |
Simulating patterns of excitation, repolarization and action potential duration with cardiac Bidomain and Monodomain models
- Franzone, Pavarino, et al.
- 2005
(Show Context)
Citation Context ...ng equations are proposed to relate material properties to tissue behavior. Cardiac tissue is made of discrete cells but it can be modeled as a continuum. For instance, the bidomain model (see, e.g., =-=[17]-=-, [16]) consists of two interpenetrating domains that represent cells (intracellular domain) and the space surrounding the cells (extracellular domain). These two domains are assumed to co-exist at al... |

27 |
2001), Partitioned analysis schemes for the transient interaction of incompressible flows and nonlinear flexible structures
- Mok, Wall
(Show Context)
Citation Context ...en fluid and structure, common strategies rely on fixed point methods [14]. Several ad-hoc variants have been proposed, including steepest descent algorithms in [88], Aitkenlike acceleration formulas =-=[63]-=-, [64], and transpiration boundary conditions [23] to avoid the computation of the fluid matrices at each sub-iteration. Yet, in general, these methods are slow, and in some cases may even fail to con... |

26 |
Flow rate defective boundary conditions in haemodinamics simulations
- Veneziani, Vergara
- 2005
(Show Context)
Citation Context ...data and, on the other hand, permit to formulate a mathematically well posed problem. In these notes we will not investigate this particular aspect, which is however illustrated and analyzed in [34], =-=[97]-=-, [98]. Now we will make some considerations on the behavior of blood flow. Most often, it is laminar. Characteristic values of the Reynolds number, Re = ρUL μ , where U is a representative mean flow ... |

25 |
Accelerated iterative substructuring schemes for instationary fluid-structure interaction
- Mok, Wall, et al.
- 2001
(Show Context)
Citation Context ...id and structure, common strategies rely on fixed point methods [14]. Several ad-hoc variants have been proposed, including steepest descent algorithms in [88], Aitkenlike acceleration formulas [63], =-=[64]-=-, and transpiration boundary conditions [23] to avoid the computation of the fluid matrices at each sub-iteration. Yet, in general, these methods are slow, and in some cases may even fail to converge ... |

25 | Optimal control and shape optimization of aorto-coronaric bypass anastomoses - Quarteroni, Rozza - 2003 |

23 |
Design by Optimal Flow Control and Reduced Basis Techniques: Applications to Bypass
- Shape
- 2005
(Show Context)
Citation Context ...evising prosthetic devices by the help of shape optimization theory. In particular, shape optimization has been used for minimizing the downstream vorticity in coronary by-pass grafts (see [1], [76], =-=[85]-=-). These numerical investigations can help the surgeon in understanding how the different surgical solutions may affect blood circulation and guide the choice of the most appropriate procedure for a s... |

23 |
Finite element methods for fluid dynamics with moving boundaries and interfaces
- Tezduyar
- 2004
(Show Context)
Citation Context ...rgence [25], [29], [46], [61]. However, since they demand the evaluation of the Jacobian associated to the fluid-solid coupled state equations, a critical step is the evaluation of the cross Jacobian =-=[93]-=-, which expresses the sensitivity of the fluid state to solid motions. This evaluation can be made inexactly, either by resorting to finite difference approximation of derivatives (see, e.g., [93]), o... |

22 |
On the existence of strong solutions to a coupled fluid structure evolution problem
- Veiga
(Show Context)
Citation Context ...the elastic energy of the 1D vessel is controlled by the initial data and the source term (see [75]). A result of existence of strong solutions in the case of periodic conditions in space is given in =-=[5]-=-. The numerical solution of a coupled fluid-structure nonlinear problem like (7)–(12) (or that discussed above based on the one dimensional model (13) for the radial vessel deformation) poses many cha... |

22 | Partitioned strong coupling algorithms for fluid–structure interaction
- Matthies, Steindorf
- 2003
(Show Context)
Citation Context ...able to that of the fluid, the stability of numerical simulations of fluid-structure interactions relies heavily on the accuracy in solving the nonlinear coupled problem at each time step [23], [59], =-=[60]-=-, [70], [88].s16 Alfio Quarteroni Ideally, implicit schemes should be used as they would guarantee energy conservation (up to the dissipation terms) and therefore numerical stability. This is outlined... |

22 |
C.: Predictive medicine: computational techniques in therapeutic decision-making
- Taylor, Draney, et al.
- 1999
(Show Context)
Citation Context ...e outcome of alternative treatment plans for the individual patient can be foreseen by simulations, yielding a new paradigm of the clinical practice which is referred to as “predictive medicine” (see =-=[92]-=-). In this presentation we will address some of the most basic models that are used to describe blood flow dynamics in local arterial environments (Section 2) and to predict the vessel wall deformatio... |

20 |
Wave propagation in a model of the arterial circulation
- Wang, Parker
(Show Context)
Citation Context ...2 13 12 4 33 5 1 3 30 31 40 2 14 18 15 27 29 28 36 43 16 17 26 19 35 37 34 39 38 41 42 45 44 21 20 25 24 Figure 14. Arterial tree composed of a set of 55 straight vessels, described by 1D models (see =-=[100]-=-). On the right a pathological case, in which some of the vessels are supposed to be completely occluded. on the analogy with electric networks, where the flow rate is represented by the electric curr... |

19 |
Numerical analysis of axisymmetric flows and methods for fluid-structure interaction arising in blood flow simulation. PhD thesis, École Polytechnique Fédérale de Lausanne
- Deparis
- 2004
(Show Context)
Citation Context ... axial symmetry (which implies the further assumption of a straight axis) the dependence on θ is completely neglected. In this case, also the fluid would be described by a 2D axi-symmetric model (see =-=[25]-=-). The simplest models, called 1D models, are derived by making the same assumption on the wall thickness made for the shell model, yet starting from a 2D model. The structure will then be represented... |

19 |
Fluid-structure interaction in blood flows on geometries coming from medical imaging
- Gerbeau, Vidrascu, et al.
- 2005
(Show Context)
Citation Context ...on can be made inexactly, either by resorting to finite difference approximation of derivatives (see, e.g., [93]), or by barely replacing the tangent operator of the coupled system with a simpler one =-=[42]-=-, [43]. However, either approximation may seriously compromise the convergence rate. Acceleration techniques using Krylov spaces have been proposed in [26], [46], [62]. A Newton method with exact Jaco... |

19 | Mathematical and numerical modeling of solute dynamics in blood flow and arterial walls
- Quarteroni, Veneziani, et al.
(Show Context)
Citation Context ...). Besides their interest for bio-medical applications, (20) and (21) represent a difficult system of nonlinear partial differential equations whose analysis has been specifically addressed in [105], =-=[79]-=-, [80]. Irregularities in the flow field across the arterial wall influence the concentration distribution within the wall. Figure 18 displays the concentration contours in the wall of the two differe... |

18 | Partitioned but strongly coupled iteration schemes for nonlinear fluid–structure interaction. Computers and Structures 80: 1991–1999
- HG, Steindorf
- 2002
(Show Context)
Citation Context ...comparable to that of the fluid, the stability of numerical simulations of fluid-structure interactions relies heavily on the accuracy in solving the nonlinear coupled problem at each time step [23], =-=[59]-=-, [60], [70], [88].s16 Alfio Quarteroni Ideally, implicit schemes should be used as they would guarantee energy conservation (up to the dissipation terms) and therefore numerical stability. This is ou... |

16 |
ibzeqilibrium Thermo- dynamics in Biophysics
- KATCHALSKY, P
(Show Context)
Citation Context ... of fluid (Jv) and the flux of chemicals (Js) between two solutions (denoted by i = 1, 2) separated by a semipermeable membrane across which concentrations and fluid pressure are different, see [51], =-=[50]-=-. In the case of just one solute, denoting with δp = p1 −p2 and δc = c1 −c2 the driving forces across the membrane, the interface equations originally proposedsCardiovascular mathematics 27 by Kedem–K... |

16 |
Adaptive domain decomposition methods for advection-diffusion problems. In Modeling, mesh generation, and adaptive numerical methods for partial differential equations
- Carlenzoli, Quarteroni
- 1993
(Show Context)
Citation Context ...ides their interest for bio-medical applications, (20) and (21) represent a difficult system of nonlinear partial differential equations whose analysis has been specifically addressed in [105], [79], =-=[80]-=-. Irregularities in the flow field across the arterial wall influence the concentration distribution within the wall. Figure 18 displays the concentration contours in the wall of the two different wal... |

16 |
Endothelial albumin permeability is shear dependent, time dependent, and reversible
- Jo, Dull, et al.
- 1991
(Show Context)
Citation Context ...ch medium and we will call them effective coefficients, denoted with LP,eff(ε1,ε2), �eff(ε1,ε2), seff(ε1,ε2) respectively. This theoretical characterization is a very challenging task, see e.g. [18], =-=[89]-=-, [90], [22]. An approach that allows a direct estimation of the effective coefficients is proposed in [74]. To define the mathematical problems describing the mass transfer from the lumen to the arte... |

15 | Acceleration of a fixed point algorithm for a fluid-structure interaction using transpiration condition
- Deparis, Fernandez, et al.
(Show Context)
Citation Context ...re is comparable to that of the fluid, the stability of numerical simulations of fluid-structure interactions relies heavily on the accuracy in solving the nonlinear coupled problem at each time step =-=[23]-=-, [59], [60], [70], [88].s16 Alfio Quarteroni Ideally, implicit schemes should be used as they would guarantee energy conservation (up to the dissipation terms) and therefore numerical stability. This... |

15 |
Further existence results for classical solutions of the equations of a second-grade fluid
- Galdi, Sequeira
- 1994
(Show Context)
Citation Context ... a discussion on rheological properties of blood flow we refer, e.g., to [12], [38], [39], [94], [57]. For a more thorough mathematical analysis of Oldroyb-B models see, e.g., [102], [4], [83], [68], =-=[40]-=-, [41], [71]. h Us10 Alfio Quarteroni Figure 6. Velocity profiles computed in a carotid bifurcation during systole and diastole (courtesy of M. Prosi). 3. Mathematical models for local blood-flow dyna... |

14 |
Reduced and multiscale models for the human cardiovascular system
- Formaggia, Veneziani
(Show Context)
Citation Context ... to the vascular compliance is here represented by means of capacitances. Similarly, inductances and resistances represent the inertial terms and the effect of blood viscosity, respectively (see e.g. =-=[37]-=- and references therein). Figure 15 illustrates different electrical schemes that may be used to describe blood flow in a passive compartment. Exploiting the same analogy, it is also possible to devis... |

14 |
An interface Newton-Krylov solver for fluidstructure interaction
- Michler, Brummelen, et al.
- 2005
(Show Context)
Citation Context ...oupled system with a simpler one [42], [43]. However, either approximation may seriously compromise the convergence rate. Acceleration techniques using Krylov spaces have been proposed in [26], [46], =-=[62]-=-. A Newton method with exact Jacobian has been investigated both mathematically and numerically in [29]. Methods based on a fractional-step solution of the coupled system are proposed in [30]. In this... |

13 |
An approximate method for solving incompressible NavierStokes problems with flow rate conditions
- Veneziani, Vergara
(Show Context)
Citation Context ...nd, on the other hand, permit to formulate a mathematically well posed problem. In these notes we will not investigate this particular aspect, which is however illustrated and analyzed in [34], [97], =-=[98]-=-. Now we will make some considerations on the behavior of blood flow. Most often, it is laminar. Characteristic values of the Reynolds number, Re = ρUL μ , where U is a representative mean flow veloci... |

12 |
A director theory approach for modeling blood flow in the arterial system: an alternative to classical 1d models
- Robertson, Sequeira
(Show Context)
Citation Context ... tapering and curvature (the latter cannot be neglected in arterial vessels such as the coronaries, the aortic arch, etc.). The model becomes fairly more involved, an account is given, e.g., in [54], =-=[84]-=-. At some extent, the arterial system in its entirety can be regarded as a network 0 uz A L z Figure 12. Left: Representation of an arterial cylindrical segment. Right: Sketch of a bifurcation of 1D p... |

11 |
On the computational efficiency and implementation of block-iterative algorithms for nonlinear coupled problems
- Cervera, Codina, et al.
- 1996
(Show Context)
Citation Context ...t numerical instabilities may occur when using loosely coupled time-advancing schemes. To account for the nonlinear coupling between fluid and structure, common strategies rely on fixed point methods =-=[14]-=-. Several ad-hoc variants have been proposed, including steepest descent algorithms in [88], Aitkenlike acceleration formulas [63], [64], and transpiration boundary conditions [23] to avoid the comput... |

11 |
Modeling and simulation in medicine and the life sciences
- Hoppensteadt, Peskin
- 2002
(Show Context)
Citation Context ...ously affected; on the other hand, a high arterial pressure would induce vascular diseases and heart overload. This regulation mechanism is called baroreflex effect and is described, for instance, in =-=[49]-=- and [52]. The elements of the feedback baroreceptor loop are a set of baroreceptors located in the carotid arteries and the aortic arch, which transmit impulses to the brain at a rate increasing with... |

11 | Fluid-structure interaction boundary conditions by artificial compressibility - Raback, Ruokolainen, et al. - 2001 |

10 |
Shape design in aorto-coronaric bypass anastomoses using perturbation theory
- Agoshkov, Quarteroni, et al.
- 2006
(Show Context)
Citation Context ...s, or for devising prosthetic devices by the help of shape optimization theory. In particular, shape optimization has been used for minimizing the downstream vorticity in coronary by-pass grafts (see =-=[1]-=-, [76], [85]). These numerical investigations can help the surgeon in understanding how the different surgical solutions may affect blood circulation and guide the choice of the most appropriate proce... |

10 |
The distribution of labeled low-density lipoprotein across the rabbit thoracic aorta in vivo. Atherosclerosis 28
- Bratzler, Chisolm, et al.
(Show Context)
Citation Context ...iate conditions for the volume flux (Jv) and the mass flux (Js) are assumed: ul · nl = Jv on Ɣ, (−Dl∇cl + ulcl) · nl = Js on Ɣ. In this case the values of Jv and Js are provided by experimental data (=-=[8]-=-, [99], [95], [91]). More realistic models are the fluid-wall model and the multilayer model, both requiring suitable matching conditions describing the flux of fluid (Jv) and the flux of chemicals (J... |

10 |
Approximate controllability of a hydro-elastic coupled system
- Lions, Zuazua
- 1995
(Show Context)
Citation Context ...s proven in the simple case where the structure is a collection of rigid moving bodies in [45]. See also [27]. Formulations based on optimal control on simpler models have been investigated, e.g., in =-=[55]-=-, [72], [66], [67], [103], [104]. As previously mentioned, simpler models than (10) can be adopted to describe the vessel deformation. Of special interest are models based on a single spatial coordina... |

10 |
Multiscale computational modelling of the heart
- Smith, Nickerson, et al.
(Show Context)
Citation Context ...x ∈ ˆ� s ,t > 0. Both the Eulerian and the Lagrangian variables are employed. The development of a global cardiac model using finite elements for finite deformation mechanics equations is proposed in =-=[87]-=-. An anatomically based description using finite element shape functions is given, then governing equations are proposed to relate material properties to tissue behavior. Cardiac tissue is made of dis... |

9 |
On the asymptotic behaviour of anisotropic energies arising in the cardiac biodomain model
- Ambrosio, Franzone, et al.
(Show Context)
Citation Context ...mathematical viewpoint, this macroscopic representation of the cardiac tissue by a reaction-diffusion system of partial differential equations can be rigorously derived by a homogeneization procedure =-=[2]-=-, [6]. The development of realistic models for heart functioning is however far from being achieved, due to the tremendous complexity of this physical system and the induced computational complexity o... |

8 |
Introduction to Linear Shell Theory, Gauthier-Villars, illustrated edition edition
- Ciarlet
- 1998
(Show Context)
Citation Context ...rst case we exploit the fact that the effective wall thickness is relatively small to reduce the whole structure to a surface. A rigorous mathematical derivation (for the linear case) may be found in =-=[15]-=-. In the second case we neglect the variations ofs12 Alfio Quarteroni Median Line Local Coordinate Basis R er θ ez eθ Axial Section Plane Figure 8. A model of a “realistic” section of an artery with t... |

8 |
Controllability of tree-shaped networks of vibrating strings
- Dáger, Zuazua
(Show Context)
Citation Context ...n points (like in Figure 12, right) ensuring mass and energy conservation (see [75]). Its mathematical investigation would require the analysis of nonlinear hyperbolic systems on networks (see, e.g., =-=[19]-=-, [53]). The resulting network of one dimensional hyperbolic models are very well suited to describe the propagation of waves (the pulse), a phenomenon generated by the interaction between blood flow ... |

8 |
Multiscale analysis of thermoregulation in the human microvascular system
- Deuflhard, Hochmuth
(Show Context)
Citation Context ...ure variation may be relevant in some particular context, for instance in the hyperthermia treatment, where some drugs are activated through an artificial localized increase in temperature (see [47], =-=[28]-=-). Temperature may also have a notable influence on blood properties, in particular on blood viscosity. Yet, this aspect is relevant only in the flow through very small arterioles/veins and in the cap... |

8 |
Existence of a three-dimensional steady state fluid-structure interaction problem
- Grandmont
- 2002
(Show Context)
Citation Context ...a complete mathematical analysis of the coupled fluid-structure problem (7)–(12) is not available yet. In the steady case, for small enough applied forces, existence of regular solutions is proven in =-=[44]-=-. In the unsteady case, local solvability in time is proven in the simple case where the structure is a collection of rigid moving bodies in [45]. See also [27]. Formulations based on optimal control ... |

8 |
Viscoelastic properties of blood and blood analogs, in
- Thurston
- 1996
(Show Context)
Citation Context ...(u))D(u)+λ2[ ˙D(u)−(∇u)D(u)−D(u)(∇u T )] where λ1, λ2 are material constants that characterize the model. For a discussion on rheological properties of blood flow we refer, e.g., to [12], [38], [39], =-=[94]-=-, [57]. For a more thorough mathematical analysis of Oldroyb-B models see, e.g., [102], [4], [83], [68], [40], [41], [71]. h Us10 Alfio Quarteroni Figure 6. Velocity profiles computed in a carotid bif... |

7 |
Convergence of front propagation for anisotropic bistable reaction-diffusion equations, Asymptot. Anal
- Bellettini, Franzone, et al.
- 1997
(Show Context)
Citation Context ...matical viewpoint, this macroscopic representation of the cardiac tissue by a reaction-diffusion system of partial differential equations can be rigorously derived by a homogeneization procedure [2], =-=[6]-=-. The development of realistic models for heart functioning is however far from being achieved, due to the tremendous complexity of this physical system and the induced computational complexity of the... |

7 | One dimensional models for blood flow in arteries
- Formaggia, Lamponi, et al.
- 2003
(Show Context)
Citation Context ...between pressure and vessel area is governed by a differential equation. Yet, it is still possible, at a price of some simplifications, to recover again a system of two partial differential equations =-=[35]-=-, [33]. By so doing, the wall inertia introduces an additional dispersive term, while viscoelasticity contributes with a dissipation term. The treatment of these additional terms is problematic as fur... |

7 | Multiscale analysis for the bio-heat-transfer equation – the nonisolated case
- Hochmuth, Deuflhard
- 2004
(Show Context)
Citation Context ...mperature variation may be relevant in some particular context, for instance in the hyperthermia treatment, where some drugs are activated through an artificial localized increase in temperature (see =-=[47]-=-, [28]). Temperature may also have a notable influence on blood properties, in particular on blood viscosity. Yet, this aspect is relevant only in the flow through very small arterioles/veins and in t... |

7 |
Numerical efficiency of different partitioned methods for fluid-structure interaction
- Matthies, Steindorf
(Show Context)
Citation Context ...are slow, and in some cases may even fail to converge [70], [13], [25]. A more radical approach consists of using Newton based methods, owing to their potentially faster convergence [25], [29], [46], =-=[61]-=-. However, since they demand the evaluation of the Jacobian associated to the fluid-solid coupled state equations, a critical step is the evaluation of the cross Jacobian [93], which expresses the sen... |

7 |
Flow of an Oldroyd-B fluid due to a stretching sheet in the presence of a free stream velocity
- Bhatnagar, Gupta, et al.
- 1995
(Show Context)
Citation Context ...e model. For a discussion on rheological properties of blood flow we refer, e.g., to [12], [38], [39], [94], [57]. For a more thorough mathematical analysis of Oldroyb-B models see, e.g., [102], [4], =-=[83]-=-, [68], [40], [41], [71]. h Us10 Alfio Quarteroni Figure 6. Velocity profiles computed in a carotid bifurcation during systole and diastole (courtesy of M. Prosi). 3. Mathematical models for local blo... |

6 | Approximate controllability for a linear model of fluid structure interaction
- Osses, Puel
- 1999
(Show Context)
Citation Context ...en in the simple case where the structure is a collection of rigid moving bodies in [45]. See also [27]. Formulations based on optimal control on simpler models have been investigated, e.g., in [55], =-=[72]-=-, [66], [67], [103], [104]. As previously mentioned, simpler models than (10) can be adopted to describe the vessel deformation. Of special interest are models based on a single spatial coordinate, th... |

5 |
Strong steady solutions for a generalized Oldroyd-B model with shear-dependent viscosity in a bounded domain
- Arada, Sequeira
(Show Context)
Citation Context ...ze the model. For a discussion on rheological properties of blood flow we refer, e.g., to [12], [38], [39], [94], [57]. For a more thorough mathematical analysis of Oldroyb-B models see, e.g., [102], =-=[4]-=-, [83], [68], [40], [41], [71]. h Us10 Alfio Quarteroni Figure 6. Velocity profiles computed in a carotid bifurcation during systole and diastole (courtesy of M. Prosi). 3. Mathematical models for loc... |

5 |
Interactions fluide structure en grands déplacements. Résolution numérique et application aux composants hydrauliques automobiles
- Mouro
- 1996
(Show Context)
Citation Context ...inal problem, in such a way that the solution is obtained through a sequence of independent solves involving each subproblem separately. A preliminary approach in this direction can be found in [88], =-=[65]-=-, where the coupling between Stokes equations and a linearized shell model is considered. The analysis of the Steklov–Poincaré operators associated to the fluid and shell models is developed, and a Ri... |

4 |
Computational study on LDL transfer from flowing blood to arterial walls
- Wada, Karino
(Show Context)
Citation Context ...conditions for the volume flux (Jv) and the mass flux (Js) are assumed: ul · nl = Jv on Ɣ, (−Dl∇cl + ulcl) · nl = Js on Ɣ. In this case the values of Jv and Js are provided by experimental data ([8], =-=[99]-=-, [95], [91]). More realistic models are the fluid-wall model and the multilayer model, both requiring suitable matching conditions describing the flux of fluid (Jv) and the flux of chemicals (Js) bet... |

3 |
A dynamic preconditioner for Newton-Krylov algorithm. Application to fluid structure interaction
- Deparis, Gerbeau, et al.
- 2004
(Show Context)
Citation Context ...tor of the coupled system with a simpler one [42], [43]. However, either approximation may seriously compromise the convergence rate. Acceleration techniques using Krylov spaces have been proposed in =-=[26]-=-, [46], [62]. A Newton method with exact Jacobian has been investigated both mathematically and numerically in [29]. Methods based on a fractional-step solution of the coupled system are proposed in [... |

3 |
The circulatory system: from case studies to mathematical modeling
- Formaggia, Quarteroni, et al.
- 2006
(Show Context)
Citation Context ...tom the case where the prosthesis is stiffer. The presence of a strong back-reflection in the latter case is evident. When the reflected wave reaches the �2 �1 �3s20 Alfio Quarteroni Figure 13. (from =-=[36]-=-). Snapshots of the simulation of a vascular bifurcation with a prosthesis, carried out with a 1D model. The three pictures in the top row illustrate the case of a prosthesis softer than the arterial ... |

3 |
Slow motion of a body in a fluid of second grade
- Galdi, Rajagopal
- 1997
(Show Context)
Citation Context ...cussion on rheological properties of blood flow we refer, e.g., to [12], [38], [39], [94], [57]. For a more thorough mathematical analysis of Oldroyb-B models see, e.g., [102], [4], [83], [68], [40], =-=[41]-=-, [71]. h Us10 Alfio Quarteroni Figure 6. Velocity profiles computed in a carotid bifurcation during systole and diastole (courtesy of M. Prosi). 3. Mathematical models for local blood-flow dynamics i... |

3 |
One dimensional and Multiscale Models for Blood Flow Circulation
- Lamponi
- 2004
(Show Context)
Citation Context ...nt for tapering and curvature (the latter cannot be neglected in arterial vessels such as the coronaries, the aortic arch, etc.). The model becomes fairly more involved, an account is given, e.g., in =-=[54]-=-, [84]. At some extent, the arterial system in its entirety can be regarded as a network 0 uz A L z Figure 12. Left: Representation of an arterial cylindrical segment. Right: Sketch of a bifurcation o... |

3 |
A study on the constitutive equation of blood
- Luo, Kuang
- 1992
(Show Context)
Citation Context ...u)+λ2[ ˙D(u)−(∇u)D(u)−D(u)(∇u T )] where λ1, λ2 are material constants that characterize the model. For a discussion on rheological properties of blood flow we refer, e.g., to [12], [38], [39], [94], =-=[57]-=-. For a more thorough mathematical analysis of Oldroyb-B models see, e.g., [102], [4], [83], [68], [40], [41], [71]. h Us10 Alfio Quarteroni Figure 6. Velocity profiles computed in a carotid bifurcati... |

3 |
Sensitivity and approximation of coupled fluid-structure equations by virtual control method
- Murea, Vázquez
(Show Context)
Citation Context ...the simple case where the structure is a collection of rigid moving bodies in [45]. See also [27]. Formulations based on optimal control on simpler models have been investigated, e.g., in [55], [72], =-=[66]-=-, [67], [103], [104]. As previously mentioned, simpler models than (10) can be adopted to describe the vessel deformation. Of special interest are models based on a single spatial coordinate, the one ... |

3 |
Steady flows of Jeffrey-Hamel type from the half plane into an infinite channel. Linearization on a symmetric solution
- Nazarov, Sequeira, et al.
(Show Context)
Citation Context ...l. For a discussion on rheological properties of blood flow we refer, e.g., to [12], [38], [39], [94], [57]. For a more thorough mathematical analysis of Oldroyb-B models see, e.g., [102], [4], [83], =-=[68]-=-, [40], [41], [71]. h Us10 Alfio Quarteroni Figure 6. Velocity profiles computed in a carotid bifurcation during systole and diastole (courtesy of M. Prosi). 3. Mathematical models for local blood-flo... |

3 |
Steady motions of viscoelastic fluids in 3-D exterior domains – existence, uniqueness and asymptotic behaviour, Arch Rational Mech Anal 149
- Novotný, Sequeira, et al.
- 1999
(Show Context)
Citation Context ...n on rheological properties of blood flow we refer, e.g., to [12], [38], [39], [94], [57]. For a more thorough mathematical analysis of Oldroyb-B models see, e.g., [102], [4], [83], [68], [40], [41], =-=[71]-=-. h Us10 Alfio Quarteroni Figure 6. Velocity profiles computed in a carotid bifurcation during systole and diastole (courtesy of M. Prosi). 3. Mathematical models for local blood-flow dynamics in comp... |

2 |
Atheroslerosis an dlate closure of aortocpronary saphenous vein grafts; sequential angiographic studies at 2 weeks, 1 year, 5-7 year and 10-12 years after surgery
- Campeau, Enjalbert, et al.
- 1983
(Show Context)
Citation Context ...e to treat coronary artery and peripheral vascular diseases. Nonetheless, over 50% of coronary artery bypass grafts fail within 10 years and more than 25% of infra-inguinal grafts within 5 years (see =-=[9]-=-, [31], [96]). The principal cause is neo-intimal hyperplasia that may degenerate in atherosclerosis. A better understanding of local haemodynamics, like the detection of regions of low wall shear str... |

2 |
Atheroma and arterial wall shear stress. Observations, correlation and proposal of a shear dependent mass transfer mechanism for atherogenesis
- Caro, Fitz-Gerald, et al.
- 1971
(Show Context)
Citation Context ...ng of local haemodynamics, like the detection of regions of low wall shear stress and of high residence time for blood particles, is of utmost importance to assess its correlation with atherogenesis (=-=[11]-=-). The vascular system is highly complex and able to regulate itself: an excessive decrease in blood pressure will cause the smaller arteries (the arterioles) to contract and the heart rate to increas... |

2 |
Mathematical modelling of the cardiovascular system and skeletal muscle interaction during exercice, ESAIM-Proceedings, Eric Cancès and J-F
- D’Angelo
(Show Context)
Citation Context ...avy exercise. Chemoreflex and baroreflex effects can be included in the differential models presented so far through another coupled ODE system that models these feedback mechanisms (see, e.g., [21], =-=[20]-=- and the references therein). Cs Qa Ca Ra Qs Pas24 Alfio Quarteroni Being able to adopt equations in different geometrical dimensions (3D, 1D and 0D, as we have illustrated thus far) provides tremendo... |

2 |
Reduced model for coupling of axisymmetric Navier-Stokes equations with a reaction-diffusion model for concentration, EPFL-IACS report 02.2006, submitted
- D’Angelo, Milisic
(Show Context)
Citation Context ...ing heavy exercise. Chemoreflex and baroreflex effects can be included in the differential models presented so far through another coupled ODE system that models these feedback mechanisms (see, e.g., =-=[21]-=-, [20] and the references therein). Cs Qa Ca Ra Qs Pas24 Alfio Quarteroni Being able to adopt equations in different geometrical dimensions (3D, 1D and 0D, as we have illustrated thus far) provides tr... |

2 |
Existence of a weak solutions for a model of fluid-rigid structure interaction, Archive Ration
- Desjardins, Esteban
- 1999
(Show Context)
Citation Context ...tence of regular solutions is proven in [44]. In the unsteady case, local solvability in time is proven in the simple case where the structure is a collection of rigid moving bodies in [45]. See also =-=[27]-=-. Formulations based on optimal control on simpler models have been investigated, e.g., in [55], [72], [66], [67], [103], [104]. As previously mentioned, simpler models than (10) can be adopted to des... |

2 |
A projection semin-implicit scheme for the coupling of an eleastic structure with an incompressible fluid. INRIA Rapport de Recherche
- Fernandez, Gerbeau, et al.
(Show Context)
Citation Context ...], [46], [62]. A Newton method with exact Jacobian has been investigated both mathematically and numerically in [29]. Methods based on a fractional-step solution of the coupled system are proposed in =-=[30]-=-. In this case, the coupling conditions (11) and (12) are not exactly enforced. The diffusion term of the momentum equations are advanced first from the time step t n to t n+1 = t n + δt (δt > 0 being... |

2 |
Coronary bypass fate: long-term angiographic study
- Fitzgibbon, Kafka, et al.
- 1991
(Show Context)
Citation Context ...treat coronary artery and peripheral vascular diseases. Nonetheless, over 50% of coronary artery bypass grafts fail within 10 years and more than 25% of infra-inguinal grafts within 5 years (see [9], =-=[31]-=-, [96]). The principal cause is neo-intimal hyperplasia that may degenerate in atherosclerosis. A better understanding of local haemodynamics, like the detection of regions of low wall shear stress an... |

2 | Experimental set-up and numerical simulations of intravenous gas transfer devices - Mallabiabarrena - 2003 |

2 |
Optimal control approach for the fluid-structure interaction problems
- Murea
- 2001
(Show Context)
Citation Context ...mple case where the structure is a collection of rigid moving bodies in [45]. See also [27]. Formulations based on optimal control on simpler models have been investigated, e.g., in [55], [72], [66], =-=[67]-=-, [103], [104]. As previously mentioned, simpler models than (10) can be adopted to describe the vessel deformation. Of special interest are models based on a single spatial coordinate, the one along ... |

2 |
Modelling interstitial flow through arterial media
- Wang, Tarbell
- 1995
(Show Context)
Citation Context ...ium and we will call them effective coefficients, denoted with LP,eff(ε1,ε2), �eff(ε1,ε2), seff(ε1,ε2) respectively. This theoretical characterization is a very challenging task, see e.g. [18], [89], =-=[90]-=-, [22]. An approach that allows a direct estimation of the effective coefficients is proposed in [74]. To define the mathematical problems describing the mass transfer from the lumen to the arterial w... |

2 |
The effect of varying albumin concentration and hydrostatic pressure on hydraulic conductivity of the Rabbit common carotid artery
- Tarbell, Lever, et al.
- 1988
(Show Context)
Citation Context ...or the volume flux (Jv) and the mass flux (Js) are assumed: ul · nl = Jv on Ɣ, (−Dl∇cl + ulcl) · nl = Js on Ɣ. In this case the values of Jv and Js are provided by experimental data ([8], [99], [95], =-=[91]-=-). More realistic models are the fluid-wall model and the multilayer model, both requiring suitable matching conditions describing the flux of fluid (Jv) and the flux of chemicals (Js) between two sol... |

2 |
Measurement of endothelial permeability to I-low density lipoproteins in rabbit arteries by use of en face preparations
- Truskey, Roberts, et al.
- 1992
(Show Context)
Citation Context ...ions for the volume flux (Jv) and the mass flux (Js) are assumed: ul · nl = Jv on Ɣ, (−Dl∇cl + ulcl) · nl = Js on Ɣ. In this case the values of Jv and Js are provided by experimental data ([8], [99], =-=[95]-=-, [91]). More realistic models are the fluid-wall model and the multilayer model, both requiring suitable matching conditions describing the flux of fluid (Jv) and the flux of chemicals (Js) between t... |

1 |
Mc Donald’s Blood Flow in Arteries. Third edition
- Nichols, O’Rourke
- 1990
(Show Context)
Citation Context ...chemes that may be used to describe blood flow in a passive compartment. Exploiting the same analogy, it is also possible to devise a lumped parameter representation of the heart. Since, as stated in =-=[69]-=-, Chapter 13, left ventricle and arterial circulation represent two mechanical units that are joined together to form a coupled biological system, we need to couple the 1D model with a model of the he... |

1 |
Infra-inguinal vein graft stenosis. Br.J.Surg.80
- Varty, Allen, et al.
- 1993
(Show Context)
Citation Context ...coronary artery and peripheral vascular diseases. Nonetheless, over 50% of coronary artery bypass grafts fail within 10 years and more than 25% of infra-inguinal grafts within 5 years (see [9], [31], =-=[96]-=-). The principal cause is neo-intimal hyperplasia that may degenerate in atherosclerosis. A better understanding of local haemodynamics, like the detection of regions of low wall shear stress and of h... |