Showing papers in "International Journal for Numerical Methods in Biomedical Engineering in 2010"

Coupling strategies for biomedical fluid–structure interaction problems

Abstract: The coupling of lightweight and often thin-walled structures to fluids in an incompressible regime is a recurring theme in biomechanics. There are many fluid-structure interaction (FSI) solution schemes to address these kinds of problem, each one with its costs and benefits. Here, we attempt a comparison of the most important FSI schemes in the context of biomechanical problems, that is a comparison of different fixed-point schemes and a block preconditioned monolithic scheme. The emphasis of this study is on the numerical behavior of these FSI schemes to gain an understanding of their effectiveness in comparison with each other. To this end a simplified benchmark problem is studied to show its applicability for more involved biomechanical problems. Two such examples with patient-specific geometries are also discussed. The monolithic scheme proved to be much more efficient than the partitioned schemes in biomechanical problems

A computational strategy for prestressing patient‐specific biomechanical problems under finite deformation

Abstract: In simulation of biomechanical structures the patient-specific geometry of the object of interest is very often reconstructed from in vivo medical imaging such as CT scans. Such geometries therefore represent a deformed configuration stressed by typical in vivo conditions. Commonly, such structures are considered stress free in simulation. In this contribution we present and compare two methods to introduce a physically meaningful stress/strain state to the obtained geometry for simulations in the finite strain regime and demonstrate the necessity of such prestressing techniques. One method is based on an inverse design analysis to calculate a stress-free reference configuration. The other method developed here is based on a modified updated Lagrangian formulation. The formulation of both methods is provided in detail and implementation issues are discussed. Applicability and accurateness of both approaches are compared and evaluated utilizing an analytical aorta model and fully three-dimensional patient-specific abdominal aortic aneurysm structures in the finite strain regime.

Space-time finite element computation of arterial fluid-structure interactions with patient-specific data

Abstract: The stabilized space–time fluid–structure interaction (SSTFSI) technique developed by the team for advanced flow simulation and modeling is applied to the computation of arterial fluid–structure interaction (FSI) with patient-specific data. The SSTFSI technique is based on the deforming-spatial-domain/stabilized space–time formulation and is supplemented with a number of special techniques developed for arterial FSI. These include a recipe for pre-FSI computations that improve the convergence of the FSI computations, using an estimated zero-pressure arterial geometry, layers of refined fluid mechanics mesh near the arterial walls, and a special mapping technique for specifying the velocity profile at an inflow boundary with non-circular shape. In the test computations reported here, we focus on a patient-specific middle cerebral artery segment with aneurysm, where the arterial geometry is based on computed tomography images. Copyright © 2009 John Wiley & Sons, Ltd.

Computational model of whole blood exhibiting lateral platelet motion induced by red blood cells.

Abstract: An Immersed Boundary method is developed in which the fluid's motion is calculated using the lattice Boltzmann method. The method is applied to explore the experimentally-observed lateral redistribution of platelets and platelet-sized particles in concentrated suspensions of red blood cells undergoing channel flow. Simulations capture red-blood-cell-induced lateral platelet motion and the consequent development of a platelet concentration profile that includes an enhanced concentration within a few microns of the channel walls. In the simulations, the near-wall enhanced concentration develops within approximately 400 msec starting from a random distribution of red blood cells and a uniform distribution of platelet-sized particles.

An n-sided polygonal edge-based smoothed finite element method (nES-FEM) for solid mechanics

Abstract: SUMMARY An edge-based smoothed finite element method (ES-FEM) using triangular elements was recently proposed to improve the accuracy and convergence rate of the existing standard finite element method (FEM) for the elastic solid mechanics problems. In this paper the ES-FEM is further extended to a more general case, n-sided polygonal edge-based smoothed finite element method (nES-FEM), in which the problem domain can be discretized by a set of polygons, each with an arbitrary number of sides. The simple averaging point interpolation method is suggested to construct nES-FEM shape functions. In addition, a novel domain-based selective scheme of a combined nES/NS-FEM model is also proposed to avoid volumetric locking. Several numerical examples are investigated and the results of the nES-FEM are found to agree well with exact solutions and are much better than those of others existing methods. Copyright q 2010 John Wiley & Sons, Ltd.

A meshless Total Lagrangian explicit dynamics algorithm for surgical simulation

Abstract: A method is presented for computing deformation of very soft tissue. The method is motivated by the need for simple, automatic model creation for real-time simulation. The method is meshless in the sense that deformation is calculated at nodes that are not part of an element mesh. Node placement is almost arbitrary. Fully geometrically nonlinear Total Lagrangian formulation is used. Geometric integration is performed over a regular background grid that does not conform to the simulation geometry. Explicit time integration is used via the central difference method. As an example the simple but fully nonlinear Neo-Hookean material model is employed. The results are compared with a finite element simulation to verify the usefulness of the method. Copyright © 2010 John Wiley & Sons, Ltd.

Comparison of High-Order Absorbing Boundary Conditions and Perfectly Matched Layers in the Frequency Domain

Abstract: The need for numerical schemes for wave problems in large and unbounded domains appears in various applications, including modeling of pressure waves in arteries and other problems in biomedical engineering. Two powerful methods to handle such problems via domain truncation are the use of high-order absorbing boundary conditions (ABCs) and perfectly matched layers (PMLs). A numerical study is presented to compare the performance of these two types of methods, for two-dimensional problems governed by the Helmholtz equation. The high-order ABCs employed here are of the Hagstrom–Warburton type; they are adapted and applied to the frequency domain for the first time. Four PMLs are examined, with linear, quadratic, constant and unbounded decay functions. Two planar configurations are considered: a waveguide and a quarter plane. In the latter case, special corner conditions are developed and used in conjunction with the ABC. One of the main conclusions from the ABC-PML comparison is that in the high-accuracy regime, the ABC scheme and the unbounded PML are equally effective. Copyright © 2010 John Wiley & Sons, Ltd.

Influence of wall thickness on fluid-structure interaction computations of cerebral aneurysms

Abstract: Fluid–structure interaction (FSI) analyses of cerebral aneurysm using patient-specific geometry with uniform and pathological aneurysmal wall thickness models are carried out. The objective is to assess the influence of the wall thickness on the FSI and hemodynamics in aneurysms. Two aneurysm models that were reconstructured based on CT images are used. The arterial wall thickness is set to 0.3 mm for the non-aneurysmal artery and to 0.05 mm for the aneurysmal wall based on experimental findings. Another set of aneurysm models with a uniform wall thickness of 0.3 mm for the entire model is used for comparison. The FSI simulations are carried out using the deforming-spatial-domain/stabilized space–time method with physiological inflow and pressure profiles. Computations with different aneurysmal wall thicknesses depict considerable differences in displacement, flow velocity and wall shear stress (WSS). The wall displacement for the pathological wall model is 61% larger than that of the uniform wall model. Consequently, the flow velocities in the aneurysm with the pathological wall model are lower, and that results in a 51% reduction in WSS on the aneurismal wall. Because low WSS on the aneurymal wall is linked to growth and rupture risk of aneurysm, the results suggest that using uniform wall thickness for the aneurysmal wall could underestimate risk in aneurysms. Copyright © 2009 John Wiley & Sons, Ltd.

Towards a comprehensive computational model for the respiratory system

Abstract: This paper is concerned with computational modeling of the respiratory system against the background of acute lung diseases and mechanical ventilation. Notionally, we divide the lung into two major subsystems, namely the conducting airways and the respiratory zone represented by lung parenchyma. Due to their respective complexity, both parts are themselves out of range for a direct numerical simulation resolving all relevant length scales. Therefore, we develop detailed individual models for parts of the subsystems as a basis for novel multi-scale approaches taking into account the unresolved parts appropriately. In the tracheo-bronchial region, CT-based geometries up to a maximum of approximately seven generations are employed in fluid-structure interaction simulations, considering not only airway wall deformability but also the influence of surrounding lung tissue. Physiological outflow boundary conditions are derived by considering the impedance of the unresolved parts of the lung in a fully coupled 3D-1D approach. In the respiratory zone, an ensemble of alveoli representing a single ventilatory unit is modeled considering not only soft tissue behavior but also the influence of the covering surfactant film. Novel nested multi-scale procedures are then employed to simulate the dynamic behavior of lung parenchyma as a whole and local alveolar ensembles simultaneously without resolving the alveolar micro-structure completely.

Modelling brain deformations for computer-integrated neurosurgery

Abstract: In this review paper we discuss Intelligent Systems for Medicine Laboratory's contributions to mathematical and numerical modelling of brain deformation behaviour for neurosurgical simulation and brain image registration. These processes can be reasonably described in purely mechanical terms, such as displacements, strains and stresses and therefore can be analysed using established methods of continuum mechanics. We advocate the use of fully non-linear theory of continuum mechanics. We discuss in some detail modelling geometry, boundary conditions, loading and material properties. We consider numerical problems such as the use of hexahedral and mixed hexahedral–tetrahedral meshes as well as meshless spatial discretization schemes. We advocate the use of total Lagrangian formulation of both finite element and meshless methods together with explicit time-stepping procedures. We support our recommendations and conclusions with two examples: computation of the reaction force acting on a biopsy needle, and computation of the brain shift for image registration. Copyright © 2009 John Wiley & Sons, Ltd.

Fluid–structure interactions of the mitral valve and left heart: Comprehensive strategies, past, present and future

Abstract: The remodeling that occurs after a posterolateral myocardial infarction can alter mitral valve function by creating conformational abnormalities in the mitral annulus and in the posteromedial papillary muscle, leading to mitral regurgitation (MR). It is generally assumed that this remodeling is caused by a volume load and is mediated by an increase in diastolic wall stress. Thus, mitral regurgitation can be both the cause and effect of an abnormal cardiac stress environment. Computational modeling of ischemic MR and its surgical correction is attractive because it enables an examination of whether a given intervention addresses the correction of regurgitation (fluid-flow) at the cost of abnormal tissue stress. This is significant because the negative effects of an increased wall stress due to the intervention will only be evident over time. However, a meaningful fluid-structure interaction model of the left heart is not trivial; it requires a careful characterization of the in-vivo cardiac geometry, tissue parameterization though inverse analysis, a robust coupled solver that handles collapsing Lagrangian interfaces, automatic grid-generation algorithms that are capable of accurately discretizing the cardiac geometry, innovations in image analysis, competent and efficient constitutive models and an understanding of the spatial organization of tissue microstructure. In this manuscript, we profile our work toward a comprehensive fluid-structure interaction model of the left heart by reviewing our early work, presenting our current work and laying out our future work in four broad categories: data collection, geometry, fluid-structure interaction and validation.

Application of the homotopy perturbation method for the Fokker–Planck equation

Abstract: In this paper, we will discuss the solution of an initial value problem of parabolic type. The main objective is to propose an alternative method of solution, one not based on finite difference or finite element or spectral methods. The aim of the present paper is to investigate the application of the Homotopy perturbation method (HPM) for solving the Fokker–Planck equation and some similar equations. This method is a powerful tool for solving various kinds of problems. Employing this technique, it is possible to find the exact solution or an approximate solution of the problem. The results show applicability, accuracy and efficiency of HPM in solving nonlinear differential equations. It is predicted that HPM can be widely applied in science and engineering problems. Copyright © 2008 John Wiley & Sons, Ltd.

Free vibration analysis of Timoshenko beams by DSC method

Abstract: Free vibration analysis of Timoshenko beams has been presented. Discrete singular convolution method is used for numerical solution of equation of motion of Timoshenko beam. Clamped, pinned and sliding boundary conditions and their combinations are taken into account. Typical results are presented for different parameters and boundary conditions. Numerical results are presented and compared with that available in the literature. It is shown that very good results are obtained. This method is very effective for the study of vibration problems of Timoshenko beam. Copyright © 2009 John Wiley & Sons, Ltd.

Fast Numerical Solutions of Patient-Specific Blood Flows in 3D Arterial Systems.

Abstract: The study of hemodynamics in arterial models constructed from patient-specific medical images requires the solution of the incompressible flow equations in geometries characterized by complex branching tubular structures. The main challenge with this kind of geometries is that the convergence rate of the pressure Poisson solver is dominated by the graph depth of the computational grid. This paper presents a deflated preconditioned conjugate gradients (DPCG) algorithm for accelerating the pressure Poisson solver. A subspace deflation technique is used to approximate the lowest eigenvalues along tubular domains. This methodology was tested with an idealized cylindrical model and three patient-specific models of cerebral arteries and aneurysms constructed from medical images. For these cases, the number of iterations decreased by up to a factor of 16, while the total CPU time was reduced by up to 4 times when compared with the standard PCG solver.

Solution of parabolic integro-differential equations arising in heat conduction in materials with memory via He's variational iteration technique

Abstract: In this work, we present the solution of some parabolic integro-differential equations, which naturally arise in many applications. He's variational iteration method is implemented to give the solution for this equation. This technique is based on the incorporation of a general Lagrange multiplier in the construction of correction functional for the equation. Application of variational iteration technique to this problem shows that it performs extremely well in terms of accuracy, efficiently, simplicity, stability and reliability. Copyright © 2008 John Wiley & Sons, Ltd.

Performance of a high-continuity finite element in three-dimensional elasticity

Abstract: We test the performance of a three-dimensional finite element, named HC3 , which generalizes the high-continuity (HC) finite element proposed by Aristodemo in 1985 for two-dimensional elastic problems. The HC3 finite element is based on a quadratic B-spline interpolation of the displacement field in three-dimensional linear elasticity. The main feature of this interpolation technique, which can be considered as a particular case of the Bezier interpolation, consists in its capability in reproducing displacement fields of 1 smoothness with a computational cost equivalent to a linear interpolation, i.e. with a single knot for each element. Copyright © 2008 John Wiley & Sons, Ltd.

Fluid–structure interaction methods in biological flows with special emphasis on heart valve dynamics

Abstract: There are numerous examples of fluid–structure interactions (FSIs) within the human body. In all cases, a computer model capable of simulating the phenomenon can aid in the understanding of organ function, failure, and implant design or improvement. In the current paper, two approaches are examined for use in simulating the FSI problem of the dynamics of tissue heart valves. Valve leaflets have nonlinear anisotropic material properties, and undergo complex deformation. Their motion affects—and is affected by—the surrounding blood. This two-way coupling necessitates a robust algorithm in order to overcome numerical stiffness, convergence challenges, and stability issues. A locally refined Cartesian mesh, sharp interface method has been developed for the fluid flow solution. In the structural domain, the valve leaflet is represented in a Lagrangian fashion and moves based on its experimentally determined material properties. In computing leaflet motion, the anisotropic, nonlinear material properties of the valve leaflet are incorporated using a finite element solver, which calculates the leaflet deformation and stresses based on the stress imparted by the surrounding fluid. Two FSI algorithms have been studied in the context of a sharp-interface Cartesian grid setting, and each has been validated with benchmark results. The two approaches are compared, and ultimately one is selected as most appropriate for simulating tissue heart valves. In the selected approach, a strongly coupled, partitioned method is used in which subiterations of the fluid and structure solutions are performed at each time step. During the subiterations, the leaflet motion is used as a boundary condition on the fluid, and the fluid stresses act as a boundary condition on the leaflet. In this way, continuity is ensured and two-way coupling is achieved. The selected approach has overcome the challenges faced by previous simulations reported in the literature, and a robust FSI solution is achieved using physiologic Reynolds numbers, realistic material properties, highly resolved grids, and a dynamic simulation. This approach has the advantage of handling both thin and volumetric embedded objects in a unified fashion, and of treating rigid and deformable structures in the same way, thus allowing a spectrum of potential applications. Copyright © 2009 John Wiley & Sons, Ltd.

Simulation of fluid-structure interaction with the interface artificial compressibility method

Abstract: Partitioned fluid–structure interaction simulations of the arterial system are difficult due to the incompressibility of the fluid and the shape of the domain. The interface artificial compressibility (IAC) method mitigates the incompressibility constraint by adding a source term to the continuity equation in the fluid domain adjacent to the fluid–structure interface. This source term imitates the effect of the structure's displacement as a result of the fluid pressure and disappears when the coupling iterations have converged. The IAC method requires a small modification of the flow solver but not of the black-box structural solver and it outperforms a partitioned quasi-Newton coupling of the two black-box solvers in a simulation of a carotid bifurcation. Copyright © 2009 John Wiley & Sons, Ltd.

Numerical framework for patient‐specific computational modelling of vascular tissue

Abstract: Accurate determination of the biomechanical implications of vascular surgeries or pathologies on patients requires developing patient-specific models of the organ or vessel under consideration. In this regard, combining the development of advanced constitutive laws that mimic the behaviour of the vascular tissue with advanced computer analysis and medical imaging techniques provides a powerful tool for modelling vascular tissues on a patient-specific basis. A framework for developing patient-specific models of blood vessel geometries obtained from medical imaging techniques is presented. The multiplicative decomposition of the deformation gradient tensor is intensively combined with the finite element method in order to account for the residual stress present on those geometries. In addition, an algorithm to compensate the mismatching effect of the load on the medical images is also discussed. Hence, a residually stressed and geometrically consistent model of the patient is obtained. The general framework is demonstrated in a realistic geometry of a carotid bifurcation. The example presented in this work shows that the incorporation of the residual stress dramatically affects the circumferential stress field, homogenizing the distribution and reducing the stress gradient. It also demonstrates that not accounting for the residual stress on a patient-specific geometry can lead to a completely different deformed configurations. Copyright © 2009 John Wiley & Sons, Ltd.

Remarks on some properties of conic yield restrictions in limit analysis

Abstract: A major difficulty when applying the kinematic theorem in limit analysis is the derivation of expressions of the dissipation functions and the set of plastically admissible strains At present, no standard methodology exists Here, it is shown that they can be readily obtained, provided that the yield restriction can be rewritten as an intersection of cones, and that the expression defining the dual cones is available This is always possible for the case of self-dual cones and some other classes, and covers many of the well-known criteria Therefore, a difficult obstacle with respect to the use of the kinematic theorem in conjunction with any numerical method can be overcome The methodology is illustrated by giving the expressions of the dissipation functions for various conic yield restrictions A special emphasis is given on upper bound finite element limit analysis Taking advantage of duality in conic programming, we can obtain the dual problem, where knowledge of the dual cone is not necessary Therefore, this formulation is feasible for any cone Finally, it is interesting that the form of the dual problem, for varying yield strength within the finite element, differs from that presented in other papers

The method of particular solutions for solving scalar wave equations

Abstract: A standard approach for solving 2D scalar wave propagation problems is presented with the use of the method of particular solutions (MPS). Motivated by the method of fundamental solutions for solving homogeneous equations, we propose a similar approach using the MPS for solving linear inhomogeneous differential equations without the need of finding the homogeneous solution. The wave equations are analyzed in the Laplace transformed domain and the Durbin inversion method is used to determine the solutions in the time domain. To demonstrate the effectiveness and simplicity of the new approach, three numerical examples have been given with excellent accuracy. Copyright © 2009 John Wiley & Sons, Ltd.

Assessment of smoothed point interpolation methods for elastic mechanics

Abstract: A generalized gradient smoothing technique and a smoothed bilinear form of Galerkin weak form have been recently proposed by Liu et al. to create a wide class of efficient smoothed point interpolation methods (PIMs) using the background mesh of triangular cells. In these methods, displacement fields are constructed by polynomial or radial basis shape functions and strains are smoothed over the smoothed domain associated with the nodes or the edges of the triangular cells. This paper summarizes and assesses bound property, convergence rate and computational efficiency for these methods. It is found that: (1) the incorporation of the PIMs with the node-based strain smoothing operation allows us to obtain an upper bound to the exact solution in the strain energy; (2) the incorporation of the PIMs with the edge-based strain smoothing operation using triangular background mesh can produce a solution of ‘ultra-accuracy’ and ‘super-convergence’; (3) the edge-based strain smoothing operation together with the linear interpolation can provide better computational efficiency compared with other smoothed PIMs and the finite element method when the same triangular mesh is used. These conclusions have been examined and confirmed by intensive examples. Copyright © 2009 John Wiley & Sons, Ltd.

Nonlinear quasi‐static finite element formulations for viscoelastic Euler–Bernoulli and Timoshenko beams

Abstract: Weak form finite element models for the nonlinear quasi-static bending and extension of initially straight viscoelastic Euler–Bernoulli and Timoshenko beams are developed using the principle of virtual work. The mechanical properties of the beams are considered to be linear viscoelastic. However, large transverse displacements, moderate rotations and small strains are allowed by retaining the von Karman strain components of the Green–Lagrange strain tensor in the formulation. The fully discretized finite element equations are developed using the trapezoidal rule in conjunction with a two-point recurrence relation. The resulting finite element equations, therefore, necessitate data storage from the previous time step only, and not the entire deformation history. Membrane locking is eliminated from the Euler–Bernoulli formulation through the use of selective reduced Gauss–Legendre quadrature. Membrane and shear locking are both circumvented in the Timoshenko beam finite element by employing a family of high-order Lagrange polynomials. A Newton–Raphson iterative scheme is used to solve the nonlinear finite element equations. Copyright © 2009 John Wiley & Sons, Ltd.

Variational iteration method for modified Camassa-Holm and Degasperis-Procesi equations

Abstract: In this paper, He's variational iteration method (VIM) is employed successfully for solving modified Camassa–Holm and Degasperis–Procesi equations. In this method, the solution is calculated in the form of a convergent series with an easily computable component. This approach does not need linearization, weak nonlinearity assumptions or the perturbation theory. The results show applicability, accuracy and efficiency of VIM in solving nonlinear differential equations with fully nonlinear dispersion term. It is predicted that VIM can be widely applied in science and engineering problems. Copyright © 2008 John Wiley & Sons, Ltd.

A three-dimensional particle simulation of the formation and collapse of a primary thrombus

Abstract: This report presents a technique based on the particle method to simulate the process of thrombogenesis while considering platelet aggregation under the influence of fluid dynamics. In the employed particle method, the blood region was discretized by particles that were assumed to have the characteristics of plasma and platelets. The moving particle semi-implicit (MPS) method developed for incompressible viscous flow was applied to the flow of plasma and platelets. Adhesion of platelets to the injured vessel wall was expressed by a spring force acting between them. The same modeling was applied for the aggregation of platelets. Three-dimensional computer simulation of thrombogenesis was performed in a rectangular flow channel under the condition of Re=0.02. We demonstrated that the proposed method can simulate the formation and destruction of a thrombus with the inclusion of feedback reactions of thrombus development and flow. The results revealed that the growth rate of a thrombus, its height, and time required from the beginning of thrombus formation to its collapse vary according to the flow rate, indicating that flow dynamics plays an important role in regulating the development of a primary thrombus. Copyright © 2010 John Wiley & Sons, Ltd.

Assessing the influence of heart rate in local hemodynamics through coupled 3D-1D-0D models

Abstract: In this study, a coupled dimensionally-heterogeneous model of the systemic circulation is applied in order to study computationally the influence of the heart rate in the local hemodynamics. This is achieved by using a 3D-1D-0D model of the whole arterial tree accounting for: details of the local blood flow in the vessel of interest through 3D models, the wave propagation phenomena in the larger arteries by means of 1D models and, the peripheral microvascular beds via 0D models. Two applications are presented which aim at assessing the influence of the global setting of the vascular network on the local hemodynamics. In the first example, the hemodynamics in a patient-specific model of the abdominal aorta is studied for two different systemic scenarios corresponding to different resting heart rates. In the second example, the blood flow in a standardized model of the carotid artery is analyzed for different heart rates including the resting state and several other exercise regimes. Copyright © 2010 John Wiley & Sons, Ltd.

Modeling and simulation of bioheat transfer in the human eye using the 3D alpha finite element method (αFEM)

Abstract: Computational modeling is an effective tool for the detection of eye abnormalities and a valuable assistant to hyperthermia treatments. In all these diagnoses and treatments, predicting the temperature distribution accurately is very important. However, the standard finite element method (FEM) currently used for such purposes has strong reliance on element meshes and the discretized system exhibits the so-called ‘overly stiff’ behavior. To overcome this shortcoming, this paper formulates an alpha finite element method (αFEM) to compute two-dimensional (2D) and three-dimensional (3D) bioheat transfer in the human eyes. The αFEM can produce much more accurate results using triangular (2D) and tetrahedron (3D) elements that can be generated automatically for complicated domains and hence is particularly suited for modeling human eyes. In the αFEM, a scaling factor α∈[0, 1] is introduced to combine the ‘overly stiff’ FEM model and ‘overly soft’ node-based finite element method (NS-FEM) model. With a properly chosen α, the αFEM can produce models with very ‘close-to-exact’ stiffness of the continuous system. Numerical results have shown that the present method gives much more accurate results compared with the standard FEM and the NS-FEM. Copyright © 2010 John Wiley & Sons, Ltd.

A computational method for identifying a spacewise‐dependent heat source

Abstract: In this paper, we consider a finite difference approximation to an inverse problem of determining a spacewise-dependent heat source in the parabolic heat equation using the usual conditions of the direct problem and information from one supplementary temperature measurement at a given instant of time. Since the resulting matrix equation is ill-conditioned, a regularized solution is obtained by employing the truncated singular value decomposition to solve the matrix equation arising from the finite difference method, with the optimal regularization parameter determined by the generalized cross-validation criterion. The effectiveness of the proposed numerical scheme is illustrated by several continuous and discontinuous numerical examples. Copyright (C) 2008 John Wiley & Sons, Ltd.

Computational modeling of electrocardiograms: A finite element approach toward cardiac excitation

Abstract: The objective of this work is the computational simulation of a patient-specific electrocardiogram (EKG) using a novel, robust, efficient, and modular finite element-based simulation tool for cardiac electrophysiology. We apply a two-variable approach in terms of a fast action potential and a slow recovery variable, whereby the latter phenomenologically summarizes the concentration of ionic currents. The underlying algorithm is based on a staggered solution scheme in which the action potential is introduced globally as nodal degree of freedom, while the recovery variable is treated locally as internal variable on the integration point level. We introduce an unconditionally stable implicit backward Euler scheme to integrate the evolution equations for both variables in time, and an incremental iterative Newton–Raphson scheme to solve the resulting nonlinear system of equations. In a straightforward post-processing step, we calculate the flux of the action potential and integrate it over the entire domain to obtain the heart vector. The projection of the heart vector onto six pre-defined directions in space defines a six-lead EKG. We illustrate its generation in terms of a magnetic resonance-based patient-specific heart geometry and discuss the clinical implications of the computational electrocardiography. Copyright © 2009 John Wiley & Sons, Ltd.

Creep analysis of high concrete‐faced rockfill dam

Abstract: The focus of the present study of a concrete-faced rockfill dam (CFRD) is the time-dependent deformation problem of rockfill, especially under a high confining pressure. In this paper, a new creep constitutive model for rockfill is introduced. A numerical realization step and algorithm applied to the analysis using the general finite element method is also presented for the creep model. The numerical simulation result of the creep model is compared with data from a laboratory triaxial creep test. It is concluded that the creep model can describe the real creep characteristics and mechanical behavior of rockfill. In studying the stress and deformation behavior of the high rockfill dam, and considering the creep effect, the creep model is applied in performing creep analysis of the Shuibuya CFRD with 200 m high in China, now the highest constructed CFRD in the world. In comparing the creep numerical simulation results with those of previous analyses that did not consider the creep effect, the deformation of the dam exhibits an evident increment, and the rockfill creep has an obvious influence on the deformation and stress of the concrete-face slab. The prediction of the final maximum settlement was 2.09 m for the Shuibuya Dam, with the rockfill creep effect in accord with the creep parameters of the triaxial creep test. Copyright © 2009 John Wiley & Sons, Ltd.