A comparative computational study of blood flow through prosthetic heart valves using the finite element method

The steady flow of blood through three common types of prosthetic heart valves was simulated numerically using the finite element method. The velocity, pressure and stress fields were obtained for the disk-type, tilting-disk and ball-type prosthetic heart valves in aortic position, for increasing Reynolds numbers up to 900, 1500 and 2000 respectively. Computer graphics of calculated velocities are presented, showing in detail the accelerated flow, recirculation and stagnation areas developed in the prosthesis. Maximum wall shear stresses were found at 0.5, 1.4, and 1.2 diameters from the sewing ring downstream for the disk, tilting-disk and ball valves being the values of 55, 18 and 33 dyn cm-2 respectively. In the vicinity of the occluder, maximum shear stresses of 38, 30 and 47 dyn cm-2 respectively were computed. The flow characteristics and performance for each valve are compared, the results are presented in terms of energy loss and maximum shear stress. The velocity and stress fields are compared with in vitro evaluations found in the literature.     

Physiologically based boundary conditions in finite element modelling

Finite element analysis has been used extensively in the study of bone loading and implant performance, such as in the femur. The boundary conditions applied vary widely, generally producing excessive femoral deformation, and although it has been shown that the muscle forces influence femoral deflections and loading, little consideration has been given to the displacement constraints. It is hypothesised that careful application of physiologically based constraints can produce physiological deformation, and therefore straining, of the femur. Joint contact forces and a complete set of muscle forces were calculated based on the geometry of the Standardised Femur using previously validated musculoskeletal models. Five boundary condition cases were applied to a finite element model of the Standardised Femur: (A) diaphyseally constrained with hip contact and abductor forces; (B) case A plus vasti forces; (C) case A with complete set of muscle forces; (D) distally constrained with all muscle forces; (E) physiological constraints with all muscle forces. It was seen that only the physiological boundary conditions, case E, produced physiological deflections (< 2.0mm) of the femoral head in both the coronal and sagittal planes, which resulted in minimal reaction forces at the constrained nodes. Strains in the mid-diaphysis varied by up to 600 micro-strain under walking loads and 1000 micro-strain under stair climbing loads. The mode of loading, as indicated by the strain profiles on the cortex also varied substantially under these boundary conditions, which has important consequences for studies that examine localised bone loading such as fracture or bone remodelling simulations.     

Three-dimensional finite element modelling of muscle forces during mastication

This paper presents a three-dimensional finite element model of human mastication. Specifically, an anatomically realistic model of the masseter muscles and associated bones is used to investigate the dynamics of chewing. A motion capture system is used to track the jaw motion of a subject chewing standard foods. The three-dimensional nonlinear deformation of the masseter muscles are calculated via the finite element method, using the jaw motion data as boundary conditions. Motion-driven muscle activation patterns and a transversely isotropic material law, defined in a muscle-fibre coordinate system, are used in the calculations. Time-force relationships are presented and analysed with respect to different tasks during mastication, e.g. opening, closing, and biting, and are also compared to a more traditional one-dimensional model. The results strongly suggest that, due to the complex arrangement of muscle force directions, modelling skeletal muscles as conventional one-dimensional lines of action might introduce a significant source of error.     

Statistical finite element method for real-time tissue mechanics analysis

The finite element (FE) method can accurately calculate tissue deformation. However, its low speed renders it ineffective for many biomedical applications involving real-time data processing. To accelerate FE analysis, we introduce a novel tissue mechanics simulation technique. This technique is suitable for real-time estimation of tissue deformation of specific organs, which is required in computer-aided diagnostic or therapeutic procedures. In this method, principal component analysis is used to describe each organ shape and its corresponding FE field for a pool of patients by a small number of weight factors. A mapping function is developed to relate the parameters of organ shape to their FE field counterpart. We show that irrespective of the complexity of the tissue's constitutive law or its loading conditions, the proposed technique is highly accurate and fast in estimating the FE field. Average deformation errors of less than 2% demonstrate the accuracy of the proposed technique.     

Multi-scale analysis of optic chiasmal compression by finite element modelling

The precise mechanism of bitemporal hemianopia (a type of partial visual field defect) is still not clear. Previous work has investigated this problem by studying the biomechanics of chiasmal compression caused by a pituitary tumour growing up from below the optic chiasm. A multi-scale analysis was performed using finite element models to examine both the macro-scale behaviour of the chiasm and the micro-scale interactions of the nerve fibres within it using representative volume elements. Possible effects of large deflection and non-linear material properties were incorporated. Strain distributions in the optic chiasm and optic nerve fibres were obtained from these models. The results of the chiasmal model agreed well with the limited experimental results available, indicating that the finite element modelling can be a useful tool for analysing chiasmal compression. Simulation results showed that the strain distribution in nasal (crossed) nerve fibres was much more nonuniform and locally higher than in temporal (uncrossed) nerve fibres. This strain difference between nasal and temporal nerve fibres may account for the phenomenon of bitemporal hemianopia.     

Finite element modelling of polymethylmethacrylate flow through cancellous bone

A mathematical model based on the Finite Element Method is developed to simulate the non-linear flow of acrylic bone cement through cancellous bone. The cancellous bone bed is modelled as a bed of parallel capillaries filled with equal spaced toroidal trabeculae. By manipulating the relative size of the torus and the capillary, the flow within bone of varying porosity is simulated. An apparent permeability based on the volume weighted average viscosity and Darcy's law is developed to describe the flow of the acrylic through the cancellous bone bed. The model predicts a cancellous bone permeability of 5.6 x 10(-9)-8.3 x 10(-9) m2 for linear flow. The non-linear behavior of the acrylic cement results in an increase of apparent permeability when compared to the permeability computed for linear flow. Estimates of penetration are achieved by running the model in a quasi-steady state fashion with pressure applied over a fixed time increment. Close agreement is shown between model predictions of penetration depth and experimental results available in the literature.     

A micromechanically-based, three-dimensional interface finite element for the modelling of the periodontal ligament

Some ideas are presented for the implementation of an interface finite element capable to model in 3-dimensions several mechanical features of the periodontal ligament. Such an element is based on a simple 2-cable micromechanical model, able to reproduce the periodontal ligament stiffness and strength under any loading condition, including the pure torsion of a tooth. A single cable represents a sufficiently populated sample of collagen fibres, each with an initially crimped geometry; a single collagen fibre can provide a mechanical response, in tension, only when it is completely uncoiled. The macroscopic interface behaviour is obtained by statistical integrations over the uncoiled length of each collagen fibre, up to the fibre failure. Such a model can reproduce the periodontal ligament anisotropy due to the variable fibre orientation along the tooth root, its different behaviour in tension/compression/shear, its different behaviour for extrusive/intrusive loading, and so forth. Some numerical examples illustrate the potentialities of this interface element, quite simple in essence but rather complete from an engineering viewpoint.     

Comparative study of viscoelastic arterial wall models in nonlinear one-dimensional finite element simulations of blood flow

It is well known that blood vessels exhibit viscoelastic properties, which are modeled in the literature with different mathematical forms and experimental bases. The wide range of existing viscoelastic wall models may produce significantly different blood flow, pressure, and vessel deformation solutions in cardiovascular simulations. In this paper, we present a novel comparative study of two different viscoelastic wall models in nonlinear one-dimensional (1D) simulations of blood flow. The viscoelastic models are from papers by Holenstein et al. in 1980 (model V1) and Valdez-Jasso et al. in 2009 (model V2). The static elastic or zero-frequency responses of both models are chosen to be identical. The nonlinear 1D blood flow equations incorporating wall viscoelasticity are solved using a space-time finite element method and the implementation is verified with the Method of Manufactured Solutions. Simulation results using models V1, V2 and the common static elastic model are compared in three application examples: (i) wave propagation study in an idealized vessel with reflection-free outflow boundary condition; (ii) carotid artery model with nonperiodic boundary conditions; and (iii) subject-specific abdominal aorta model under rest and simulated lower limb exercise conditions. In the wave propagation study the damping and wave speed were largest for model V2 and lowest for the elastic model. In the carotid and abdominal aorta studies the most significant differences between wall models were observed in the hysteresis (pressure-area) loops, which were larger for V2 than V1, indicating that V2 is a more dissipative model. The cross-sectional area oscillations over the cardiac cycle were smaller for the viscoelastic models compared to the elastic model. In the abdominal aorta study, differences between constitutive models were more pronounced under exercise conditions than at rest. Inlet pressure pulse for model V1 was larger than the pulse for V2 and the elastic model in the exercise case. In this paper, we have successfully implemented and verified two viscoelastic wall models in a nonlinear 1D finite element blood flow solver and analyzed differences between these models in various idealized and physiological simulations, including exercise. The computational model of blood flow presented here can be utilized in further studies of the cardiovascular system incorporating viscoelastic wall properties.     

A fluid--structure interaction finite element analysis of pulsatile blood flow through a compliant stenotic artery.

A new model is used to analyze the fully coupled problem of pulsatile blood flow through a compliant, axisymmetric stenotic artery using the finite element method. The model uses large displacement and large strain theory for the solid, and the full Navier-Stokes equations for the fluid. The effect of increasing area reduction on fluid dynamic and structural stresses is presented. Results show that pressure drop, peak wall shear stress, and maximum principal stress in the lesion all increase dramatically as the area reduction in the stenosis is increased from 51 to 89 percent. Further reductions in stenosis cross-sectional area, however, produce relatively little additional change in these parameters due to a concomitant reduction in flow rate caused by the losses in the constriction. Inner wall hoop stretch amplitude just distal to the stenosis also increases with increasing stenosis severity, as downstream pressures are reduced to a physiological minimum. The contraction of the artery distal to the stenosis generates a significant compressive stress on the downstream shoulder of the lesion. Dynamic narrowing of the stenosis is also seen, further augmenting area constriction at times of peak flow. Pressure drop results are found to compare well to an experimentally based theoretical curve, despite the assumption of laminar flow.     

A one-dimensional finite element method for simulation-based medical planning for cardiovascular disease

We have previously described a new approach to planning treatments for cardiovascular disease, Simulation-Based Medical Planning, whereby a physician utilizes computational tools to construct and evaluate a combined anatomic/physiologic model to predict the outcome of alternative treatment plans for an individual patient. Current systems for Simulation-Based Medical Planning utilize finite element methods to solve the time-dependent, three-dimensional equations governing blood flow and provide detailed data on blood flow distribution, pressure gradients and locations of flow recirculation, low wall shear stress and high particle residence. However, these methods are computationally expensive and often require hours of time on parallel computers. This level of computation is necessary for obtaining detailed information about blood flow, but likely is unnecessary for obtaining information about mean flow rates and pressure losses. We describe, herein, a space-time finite element method for solving the one-dimensional equations of blood flow. This method is applied to compute flow rate and pressure in a single segment model, a bifurcation, an idealized model of the abdominal aorta, in three alternate treatment plans for a case of aorto-iliac occlusive disease and in a vascular bypass graft. All of these solutions were obtained in less than 5 min of computation time on a personal computer.     

A new method for finite element simulation of orthodontic appliance-teeth-periodontium-alveolus system

This paper describes a new simulation method to analyze the initial behavior of the total system comprising orthodontic appliance, teeth, and their supporting structures. It is based on a finite element method which additionally takes account of a rotational degree of freedom. Beam and rod elements are used for finite element idealization of orthodontic appliance. Through spring elements it is connected with the teeth supported by the alveolar structures. The technique of 'initial strain' is introduced so as to analyze the effects of a gable bend and activation on the force system which is delivered by the orthodontic appliance. As compared with the photoelastic technique hitherto used, this method serves to investigate systematically and quantitatively the initial aspect of orthodontic tooth movement.     

A penetration-based finite element method for hyperelastic 3D biphasic tissues in contact. Part II: finite element simulations

The penetration method allows for the efficient finite element simulation of contact between soft hydrated biphasic tissues in diarthrodial joints. Efficiency of the method is achieved by separating the intrinsically nonlinear contact problem into a pair of linked biphasic finite element analyses, in which an approximate, spatially and temporally varying contact traction is applied to each of the contacting tissues. In Part I of this study, we extended the penetration method to contact involving nonlinear biphasic tissue layers, and demonstrated how to derive the approximate contact traction boundary conditions. The traction derivation involves time and space dependent natural boundary conditions, and requires special numerical treatment. This paper (Part II) describes how we obtain an efficient nonlinear finite element procedure to solve for the biphasic response of the individual contacting layers. In particular, alternate linearization of the nonlinear weak form, as well as both velocity-pressure, v-p, and displacement-pressure, u-p, mixed formulations are considered. We conclude that the u-p approach, with linearization of both the material law and the deformation gradients, performs best for the problem at hand. The nonlinear biphasic contact solution will be demonstrated for the motion of the glenohumeral joint of the human shoulder joint.     

Experiments and finite element modelling for the study of prolapse in the pelvic floor system

Pelvic prolapse affects one woman in three of all ages combined and is quite common for more than 60% of patients over 60 years of age. The treatment of this pathological problem is one of the biggest challenges to the gynaecologist today. The rate of surgical intervention failure is quite significant. The recurrence of prolapse could be related to inadequate surgical technique or the pathology or/and biomechanical deficiency of the soft tissues. The modelling and simulation of the behaviour of the pelvic cavity could be a major tool for specific evaluation of pelvic status. A first stage of this model is being developed and reported. The computer-aided design model of the organs of the pelvic floor is created using magnetic resonance image data and the ligament boundary conditions are defined. A multi-organ geometric model is thus created and studied.     

Tissue-fluid interface analysis using biphasic finite element method

Numerical studies on fluid-structure interaction have primarily relied on decoupling the solid and fluid sub-domains with the interactions treated as external boundary conditions on the individual sub-domains. The finite element applications for the fluid-structure interactions can be divided into iterative algorithms and sequential algorithms. In this paper, a new computational methodology for the analysis of tissue-fluid interaction problems is presented. The whole computational domain is treated as a single biphasic continuum, and the same space and time discretisation is carried out for the sub-domains using a penalty-based finite element model. This procedure does not require the explicit modelling of additional boundary conditions or interface elements. The developed biphasic interface finite element model is used in analysing blood flow through normal and stenotic arteries. The increase in fluid flow velocity when passing through a stenosed artery and the drop in pressure at the region are captured using this method.     

Modeling analytical ultracentrifugation experiments with an adaptive space-time finite element solution for multicomponent reacting systems

We describe an extension of the adaptive space-time finite element method (ASTFEM) used in the solution of the Lamm equation to the case of multicomponent reacting systems. We use an operator splitting technique to decouple the sedimentation-diffusion process from the reaction process. The former is solved with an ASTFEM approach based on the Petrov-Galerkin method and on adaptive moving grids, and the latter is solved with the implicit midpoint Euler's method. Our solution can effectively eliminate the sedimentation errors for each component or species involved in the reaction, and it is free from oscillation near the cell bottom. It offers second-order accuracy, and guarantees conservation of mass without any additional postprocessing, and it permits modeling of multicomponent, equilibrating systems where the reaction rate can be kinetically controlled between an instantaneous reaction and a noninteracting mixture. The proposed ASTFEM solution provides improved efficiency and accuracy compared to classical approaches, especially when medium-sized and large molecules are modeled.     

Cement flow during impaction allografting: a finite element analysis

Cement intrusion into cancellous or impacted bone is not well understood. We adopted an engineering mechanics approach to predict the effect of surgical variables on the cement intrusion into impacted cancellous bone, used for the revision of failed total hip replacement with the impaction allografting technique. Specifically, a three-dimensional finite element model was used to determine the effects of cement viscosity, the magnitude and duration of pressurization, and the distribution of the porosity along the femur on cement intrusion. The overall averaged mean intrusion depth difference between the finite element model prediction and the cadaveric measurements was 1.1mm. The depth of penetration increased with higher pressurization pressure, duration of pressurization, and earlier stem insertion (lower viscosity), but maintained a similar profile. The distribution of the porosity along the femur determined the intrusion profile. Cement viscosity, the applied pressure or the duration of the pressurization can be adjusted to limit the cement volume injected into the medullary canal and therefore prevent the cement from reaching the endosteal surface.     

A finite element method for mechanical response of hair cell ciliary bundles

This paper describes the development of a methodology for performing a mechanical analysis of hair cell ciliary bundles. The cilia were modeled as shear deformable beams, and interconnections were modeled as two-force members. These models were incorporated into software, which performs a finite element analysis of a user-defined bundle. The algorithm incorporates aspects of the bundle such as geometric realignment and buckling of compressed side links. A sample bundle is introduced and results of modeling it are presented.     

A fully implicit finite element method for bidomain models of cardiac electrophysiology

This work introduces a novel, unconditionally stable and fully coupled finite element method for the bidomain system of equations of cardiac electrophysiology. The transmembrane potential Φ(i)-Φ(e) and the extracellular potential Φ(e) are treated as independent variables. To this end, the respective reaction-diffusion equations are recast into weak forms via a conventional isoparametric Galerkin approach. The resultant nonlinear set of residual equations is consistently linearised. The method results in a symmetric set of equations, which reduces the computational time significantly compared to the conventional solution algorithms. The proposed method is inherently modular and can be combined with phenomenological or ionic models across the cell membrane. The efficiency of the method and the comparison of its computational cost with respect to the simplified monodomain models are demonstrated through representative numerical examples.