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.     

Tissue Aspiration and Inverse Finite Element Characterisation of Soft Tissues

In this work we examined the determination of soft tissue parameters via tissue aspiration experiments and inverse finite element characterisation. An aspiration tube was put against the target tissue. The deformation of the tissue inside the tube caused by weak suction was tracked with a video based system. A strain energy function was employed to model the elastic behaviour of soft tissue and viscoelasticity was accounted for by means of a quasi-linear viscoelastic formulation. Friction between the aspiration tube and the aspirated tissue was included in the model. Based on the assumed material model, an optimal set of material parameters was found, in order to best fit the experimental data obtained from ex-vivo experiments on pig kidney cortex. The inverse method resulted in robust determination of the unknown material parameters.     

Simulation and study of the geometric parameters in the inguinal area and the genesis of inguinal hernias

We are interested in studying the genesis of a very common pathology: the human inguinal hernia. How the human inguinal hernia appears is not definitively clear, but it is accepted that it is caused by a combination of mechanical and biochemical alterations, and that muscular simulation plays an important role in this. This study proposes a model to explain how some physical parameters affect the ability to simulate the region dynamically and how these parameters are involved in generating inguinal hernias. We are particularly interested in understanding the mechanical alterations in the inguinal region because little is known about them or how they behave dynamically. Our model corroborates the most important theories regarding the generation of inguinal hernias and is an initial approach to numerically evaluating this affection.     

Characterisation and simulation of an active microvalve for glaucoma

Glaucoma drainage device (GDD) has the potential to eliminate hypotony but still suffers from poor flow control and fibrosis. The ideal shunt should change its hydraulic resistance to achieve the desired intraocular pressure (IOP). In this study, the characterisation of a preliminary design of a new GDD is presented. This is activated by means of a diaphragm, which is actuated by conducting polymers. The valve can be manufactured employing microelectromechanical system technology by soft lithography. The characterisation process is performed by numerical simulation using the finite element method, considering the coupling between the fluid and the structure (diaphragm) obtaining the hydraulic resistance for several positions of the diaphragm. To analyse the hydraulic system of the microvalve implanted in a human eye, an equivalent circuit model was used. The parameters of the equivalent circuit model were obtained from numerical simulation. The hydraulic resistance of the designed GDD varies in the range of 13.08–0.36 mmHg min/μl compared with 3.38–0.43 mmHg min/μl for the Ahmed valve. The maximum displacement of the diaphragm in the vertical direction is 18.9 μm, and the strain in the plane is 2%. The proposed preliminary design allows to control the IOP by varying the hydraulic resistance in a greater range than the existing passive valves, and the numerical simulation facilitates the characterisation and the improvement of the design before its construction, reducing time and costs.     

An analytical model for the ergometer rowing: inverse multibody dynamics analysis

A model for the ergometer rowing exercise is presented in this paper. From the quantitative observations of a particular trajectory (motion), the model is used to determine the moment of the forces produced by the muscles about each joint. These forces are evaluated according to the continuous system of equations of motion. An inverse dynamics analysis is performed in order to predict the joint torques developed by the muscles during the execution of the task. An elementary multibody mechanical system is used as an example to discuss the assumptions and procedures adopted.     

Preliminary simulation model toward the study of the effects caused by different mandibular advancement devices in OSAS treatment

Abstract

The paper aims to evaluate the effects caused by a Mandibular Advancement Device (MAD) for Obstructive Sleep Apnoea Syndrome (OSAS) treatment. This study is based on Finite Element Method (FEM) for evaluating the load distribution on temporomandibular joint, especially on the mandibular condyle and disc, and on periodontal ligaments. The stress values on condyle and periodontal ligaments lead authors to consider MAD a safe procedure even for a long period. The obtained results also show the relationship between MAD material and load distribution at the periodontal ligaments. The paper is a step toward future analyses for studying and comparing the effects of MAD features, such as material, shape and dimensions, in order to allow the clinician prescribing the most fitting device.     

Prediction of shape and internal structure of the proximal femur using a modified level set method for structural topology optimisation

A computational framework was developed to simulate the bone remodelling process as a structural topology optimisation problem. The mathematical formulation of the Level Set technique was extended and then implemented into a coronal plane model of the proximal femur to simulate the remodelling of internal structure and external geometry of bone into the optimal state. Results indicated that the proposed approach could reasonably mimic the major geometrical and material features of the natural bone. Simulation of the internal bone remodelling on the typical gross shape of the proximal femur, resulted in a density distribution pattern with good consistency with that of the natural bone. When both external and internal bone remodelling were simulated simultaneously, the initial rectangular design domain with a regularly distributed mass reduced gradually to an optimal state with external shape and internal structure similar to those of the natural proximal femur.     

Optimization of the Emerson–Trinder enzymatic reaction by response surface methodology

The Emerson–Trinder reaction has been optimized in this work using an initial rate spectrophotometric method and response surface methodology (RSM). In this investigation, the variation range of critical variables along with the fixed parameters were selected based on a preliminary ‘one at a time’ (OVAT) procedure for the subsequent RSM chemometric analysis as follows: pH (6–10), buffer concentration (50–250?mM), 4-aminoantipyrine (4-AAP) concentration (1–5?mM), temperature (25–45°C). The optimum values of fixed parameters were: 4-fluorophenol (4-FP, 30?mM), horseradish peroxidase (HRP) enzyme activity (0.12?U?mL^?1), and the fixed concentration of the H₂O₂ in the chemometric experiments was 11.4 µM. The non-linear nature of the experimental response of the reaction system was explained by a second-order polynomial equation, which revealed the impact of the experimental factors, their interactions and also their optimum values. The results of the reported RSM analysis proved to be quite appropriate for the design and optimization of this reaction, as illustrated by the relatively high value of the determination coefficient (R²=96.7%) for the fitting of quadratic model, along with the satisfactory results generated by the analysis of variance (ANOVA). All the evaluated analytical characteristics of this method: typical reaction progress curves, resulting linear calibration curve, within-day precisions at low and at high levels, and the upper and lower detection limits were, also, reported. In addition, to check the quality of the optimization and validity of the model, the assay of H₂O₂, in pooled serum matrix and in cosmetic samples, was performed.     

Numerical Models for the Simulation of Flexible Artificial Heart Valves: Part I - Computational Methods

Abstract

A numerical model of the coupled motion of a flexing surface in a high Reynolds number flow is presented for the simulation of flexible polyurethane heart valves in the aortic position. This is achieved by matching a Lagrangian dynamic leaflet model with a panel method based flow solver. The two models are coupled via the time-dependent pressure field using the unsteady Bernoulli equation.

Incorporation of sub-cycling in the dynamic model equations and fast pre conditioning techniques in the panel method solver yields efficient convergence and near real-time simulations of valve motion. The generality of dynamic model allows different material properties and/or geometries to be studied easily and interactively. This interactivity is realized by embedding the models within a design environment created using the software IRIS Explorer ^TM.

Two flow domains are developed, an infinite domain and an internal domain using conformal mapping theory. In addition bending stress on the valve is computed using a simple stress model based on spline and circle equation techniques.     

Detailed finite element modelling of deep needle insertions into a soft tissue phantom using a cohesive approach

Detailed finite element modelling of needle insertions into soft tissue phantoms encounters difficulties of large deformations, high friction, contact loading and material failure. This paper demonstrates the use of cohesive elements in high-resolution finite element models to overcome some of the issues associated with these factors. Experiments are presented enabling extraction of the strain energy release rate during crack formation. Using data from these experiments, cohesive elements are calibrated and then implemented in models for validation of the needle insertion process. Successful modelling enables direct comparison of finite element and experimental force–displacement plots and energy distributions. Regions of crack creation, relaxation, cutting and full penetration are identified. By closing the loop between experiments and detailed finite element modelling, a methodology is established which will enable design modifications of a soft tissue probe that steers through complex mechanical interactions with the surrounding material.