Anisotropic adaptive finite element method for modelling blood flow

In this study, we present an adaptive anisotropic finite element method (FEM) and demonstrate how computational efficiency can be increased when applying the method to the simulation of blood flow in the cardiovascular system. We use the SUPG formulation for the transient 3D incompressible Navier–Stokes equations which are discretised by linear finite elements for both the pressure and the velocity field.

Given the pulsatile nature of the flow in blood vessels we have pursued adaptivity based on the average flow over a cardiac cycle. Error indicators are derived to define an anisotropic mesh metric field. Mesh modification algorithms are used to anisotropically adapt the mesh according to the desired size field. We demonstrate the efficiency of the method by first applying it to pulsatile flow in a straight cylindrical vessel and then to a porcine aorta with a stenosis bypassed by a graft. We demonstrate that the use of an anisotropic adaptive FEM can result in an order of magnitude reduction in computing time with no loss of accuracy compared to analyses obtained with uniform meshes.     

Automated three-dimensional finite element modelling of bone: a new method

Three-dimensional finite element stress analysis of bone is a key to understanding bone remodelling, assessing fracture risk, and designing prostheses; however, the cost and complexity of predicting the stress field in bone with accuracy has precluded the routine use of this method. A new, automated method of generating patient-specific three-dimensional finite element models of bone is presented — it uses digital computed tomographic (CT) scan data to derive the geometry of the bone and to estimate its inhomogeneous material properties. Cubic elements of a user-specified size are automatically defined and then individually assigned the CT scan-derived material properties. The method is demonstrated by predicting the stress, strain, and strain energy in a human proximal femur in vivo. Three-dimensional loading conditions corresponding to the stance phase of gait were taken from the literature and applied to the model. Maximum principal compressive stresses of 8–23 MPa were computed for the medial femoral neck. Automated generation of additional finite element models with larger numbers of elements was used to verify convergence in strain energy.     

An adaptive finite element model for steerable needles

Biomechanics and Modeling in Mechanobiology - Penetration of a flexible and steerable needle into a soft target material is a complex problem to be modelled, involving several mechanical...     

Mesh considerations for finite element blast modelling in biomechanics

Finite element (FE) modelling is a popular tool for studying human body response to blast exposure. However, blast modelling is a complex problem owing to more numerous fluid–structure interactions (FSIs) and the high–frequency loading that accompanies blast exposures. This study investigates FE mesh design for blast modelling using a sphere in a closed-ended shock tube meshed with varying element sizes using both tetrahedral and hexahedral elements. FSI was consistent for sphere-to-fluid element ratios between 0.25 and 4, and acceleration response was similar for both element types (R² = 0.997). Tetrahedral elements were found to become increasingly volatile following shock loading, causing higher pressures and stresses than predicted with the hexahedral elements. Deviatoric stress response was dependent on the sphere mesh size (p < 0.001), while the pressure response was dependent on the shock tube mesh size (p < 0.001). The results of this study highlight the necessity for mesh sensitivity analysis in blast models.     

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.     

Measuring morphological parameters of the pelvic floor for finite element modelling purposes

The goal of this study was to obtain a complete data set needed for studying the complex biomechanical behaviour of the pelvic floor muscles using a computer model based on the finite element (FE) theory. The model should be able to predict the effect of surgical interventions and give insight into the function of pelvic floor muscles. Because there was a lack of any information concerning morphological parameters of the pelvic floor muscle structures, we performed an experimental measurement to uncover those morphological parameters. Geometric parameters as well as muscle parameters of the pelvic floor muscles were measured on an embalmed female cadaver. A three-dimensional (3D) geometric data set of the pelvic floor including muscle fibre directions was obtained using a palpator device. A 3D surface model based on the experimental data, needed for mathematical modelling of the pelvic floor, was created. For all parts of the diaphragma pelvis, the optimal muscle fibre length was determined by laser diffraction measurements of the sarcomere length. In addition, other muscle parameters such as physiological cross-sectional area and total muscle fibre length were determined. Apart from these measurements we obtained a data set of the pelvic floor structures based on nuclear magnetic resonance imaging (MRI) on the same cadaver specimen. The purpose of this experiment was to discover the relationship between the MRI morphology and geometrical parameters obtained from the previous measurements. The produced data set is not only important for biomechanical modelling of the pelvic floor muscles, but it also describes the geometry of muscle fibres and is useful for functional analysis of the pelvic floor in general. By the use of many reference landmarks all these morphologic data concerning fibre directions and optimal fibre length can be morphed to the geometrical data based on segmentation from MRI scans.These data can be directly used as an input for building a mathematical model based on FE theory.     

On the effects of different strategies in modelling balloon-expandable stenting by means of finite element method

In recent years, computational structural analyses have emerged as important tools to investigate the mechanical response of stent placement into arterial walls. Although most coronary stents are expanded by inflating a polymeric balloon, realistic computational balloon models have been introduced only recently. In the present study, the finite element method is applied to simulate three different approaches to evaluate stent-free expansion and stent expansion inside an artery. Three different stent expansion modelling techniques were analysed by: (i) imposing a uniform pressure on the stent internal surface, (ii) a rigid cylindrical surface expanded with displacement control and (iii) modelling a polymeric deformable balloon. The computational results showed differences in the free and confined-stent expansions due to different expansion techniques. The modelling technique of the balloon seems essential to estimate the level of injury caused on arterial walls during stent expansion.     

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.     

Prediction of stenting related adverse events through patient-specific finite element modelling

Right ventricular outflow tract (RVOT) calcific obstruction is frequent after homograft conduit implantation to treat congenital heart disease. Stenting and percutaneous pulmonary valve implantation (PPVI) can relieve the obstruction and prolong the conduit lifespan, but require accurate pre-procedural evaluation to minimize the risk of coronary artery (CA) compression, stent fracture, conduit injury or arterial distortion.Herein, we test patient-specific finite element (FE) modeling as a tool to assess stenting feasibility and investigate clinically relevant risks associated to the percutaneous intervention.Three patients undergoing attempted PPVI due to calcific RVOT conduit failure were enrolled; the calcific RVOT, the aortic root and the proximal CA were segmented on CT scans for each patient. We numerically reproduced RVOT balloon angioplasty to test procedure feasibility and the subsequent RVOT pre-stenting expanding the stent through a balloon-in-balloon delivery system.Our FE framework predicted the occurrence of CA compression in the patient excluded from the real procedure. In the two patients undergoing RVOT stenting, numerical results were consistent with intraprocedural in-vivo fluoroscopic evidences. Furthermore, it quantified the stresses on the stent and on the relevant native structures, highlighting their marked dependence on the extent, shape and location of the calcific deposits. Stent deployment induced displacement and mechanical loading of the calcific deposits, also impacting on the adjacent anatomical structures.This novel workflow has the potential to tackle the analysis of complex RVOT clinical scenarios, pinpointing the procedure impact on the dysfunctional anatomy and elucidating potential periprocedural complications.     

Harmonizing finite element modelling for non-invasive strength estimation by high-resolution peripheral quantitative computed tomography

The finite element (FE) method based on high-resolution peripheral quantitative computed tomography (HR-pQCT) use a variety of tissue constitutive properties and boundary conditions at different laboratories making comparison of mechanical properties difficult. Furthermore, the advent of a second-generation HR-pQCT poses challenges due to improved resolution and a larger region of interest (ROI). This study addresses the need to harmonize results across FE models. The aims are to establish the relationship between FE results as a function of boundary conditions and a range of tissue properties for the first-generation HR-pQCT system, and to determine appropriate model parameters for the second-generation HR-pQCT system. We implemented common boundary conditions and tissue properties on a large cohort (N = 1371), and showed the relationships were highly linear (R² > 0.99) for yield strength and reaction force between FE models. Cadaver radii measured on both generation HR-pQCT with matched ROIs were used to back-calculate a tissue modulus that accounts for the increased resolution (61 µm versus 82 µm), resulting in a modulus of 8748 MPa for second-generation HR-pQCT to produce bone yield strength and reaction force equivalent to using 6829 MPa for first-generation HR-pQCT. Finally, in vivo scans (N = 61) conducted on both generations demonstrated that the larger ROI in the second-generation system results in stronger bone outcome measures, suggesting it is not advisable to convert FE results across HR-pQCT generations without matching ROIs. Together, these findings harmonize FE results by providing a means to compare findings with different boundary conditions and tissue properties, and across scanner generations.     

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.