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.     

Left ventricular wall stress compendium

Left ventricular (LV) wall stress has intrigued scientists and cardiologists since the time of Lame and Laplace in 1800s. The left ventricle is an intriguing organ structure, whose intrinsic design enables it to fill and contract. The development of wall stress is intriguing to cardiologists and biomedical engineers. The role of left ventricle wall stress in cardiac perfusion and pumping as well as in cardiac pathophysiology is a relatively unexplored phenomenon. But even for us to assess this role, we first need accurate determination of in vivo wall stress. However, at this point, 150 years after Lame estimated left ventricle wall stress using the elasticity theory, we are still in the exploratory stage of (i) developing left ventricle models that properly represent left ventricle anatomy and physiology and (ii) obtaining data on left ventricle dynamics. In this paper, we are responding to the need for a comprehensive survey of left ventricle wall stress models, their mechanics, stress computation and results. We have provided herein a compendium of major type of wall stress models: thin-wall models based on the Laplace law, thick-wall shell models, elasticity theory model, thick-wall large deformation models and finite element models. We have compared the mean stress values of these models as well as the variation of stress across the wall. All of the thin-wall and thick-wall shell models are based on idealised ellipsoidal and spherical geometries. However, the elasticity model's shape can vary through the cycle, to simulate the more ellipsoidal shape of the left ventricle in the systolic phase. The finite element models have more representative geometries, but are generally based on animal data, which limits their medical relevance. This paper can enable readers to obtain a comprehensive perspective of left ventricle wall stress models, of how to employ them to determine wall stresses, and be cognizant of the assumptions involved in the use of specific models.     

An object-oriented modelling framework for the arterial wall

An object-oriented modelling framework for the arterial wall is presented. The novelty of the framework is the possibility to generate customisable artery models, taking advantage of imaging technology. In our knowledge, this is the first object-oriented modelling framework for the arterial wall. Existing models do not allow close structural mapping with arterial microstructure as in the object-oriented framework. In the implemented model, passive behaviour of the arterial wall was considered and the tunica adventitia was the objective system. As verification, a model of an arterial segment was generated. In order to simulate its deformation, a matrix structural mechanics simulator was implemented. Two simulations were conducted, one for an axial loading test and other for a pressure–volume test. Each simulation began with a sensitivity analysis in order to determinate the best parameter combination and to compare the results with analogue controls. In both cases, the simulated results closely reproduced qualitatively and quantitatively the analogue control plots.     

Pulsatile non-Newtonian haemodynamics in a 3D bifurcating abdominal aortic aneurysm model

Numerical prediction of non-Newtonian blood flow in a 3D abdominal aortic aneurysm bifurcating model is carried out. The non-Newtonian Carreau model is used to characterise the shear thinning behaviour of the human blood. A physical inlet velocity waveform incorporating a radial velocity distribution reasonably representative of a practical case configuration is employed. Case studies subject to both equal and unequal outlet pressures at iliac bifurcations are presented to display convincingly the downstream pressure influences on the flow behaviour within the aneurysm. Simulations indicate that the non-Newtonian aspects of the blood cannot at all be neglected or given a cursory treatment. The wall shear stress (WSS) is found to change significantly at both the proximal and distal ends of the aneurysm. At the peak systole, the WSS is peak around the bifurcation point, whereas the WSS becomes zero in the bifurcation point. Differential downstream pressure fields display significant effects regarding the flow evolution in the iliac arteries, whereas little or no effects are observed directly on the flow details in the aneurysm.     

Effect of membrane stiffness and cytoskeletal element density on mechanical stimuli within cells: an analysis of the consequences of ageing in cells

A finite element model of a single cell was created and used to compute the biophysical stimuli generated within a cell under mechanical loading. Major cellular components were incorporated in the model: the membrane, cytoplasm, nucleus, microtubules, actin filaments, intermediate filaments, nuclear lamina and chromatin. The model used multiple sets of tensegrity structures. Viscoelastic properties were assigned to the continuum components. To corroborate the model, a simulation of atomic force microscopy indentation was performed and results showed a force/indentation simulation with the range of experimental results. A parametric analysis of both increasing membrane stiffness (thereby modelling membrane peroxidation with age) and decreasing density of cytoskeletal elements (thereby modelling reduced actin density with age) was performed. Comparing normal and aged cells under indentation predicts that aged cells have a lower membrane area subjected to high strain as compared with young cells, but the difference, surprisingly, is very small and may not be measurable experimentally. Ageing is predicted to have a more significant effect on strain deep in the nucleus. These results show that computation of biophysical stimuli within cells are achievable with single-cell computational models; correspondence between computed and measured force/displacement behaviours provides a high-level validation of the model. Regarding the effect of ageing, the models suggest only small, although possibly physiologically significant, differences in internal biophysical stimuli between normal and aged cells.     

Constitutive expression of cell wall invertase genes increases grain yield and starch content in maize

Grain size, number and starch content are important determinants of grain yield and quality. One of the most important biological processes that determine these components is the carbon partitioning during the early grain filling, which requires the function of cell wall invertase. Here, we showed the constitutive expression of cell wall invertase–encoding gene from Arabidopsis, rice (Oryza sativa) or maize (Zea mays), driven by the cauliflower mosaic virus (CaMV) 35S promoter, all increased cell wall invertase activities in different tissues and organs, including leaves and developing seeds, and substantially improved grain yield up to 145.3% in transgenic maize plants as compared to the wild‐type plants, an effect that was reproduced in our 2‐year field trials at different locations. The dramatically increased grain yield is due to the enlarged ears with both enhanced grain size and grain number. Constitutive expression of the invertase‐encoding gene also increased total starch content up to 20% in the transgenic kernels. Our results suggest that cell wall invertase gene can be genetically engineered to improve both grain yield and grain quality in crop plants.     

Brachypodium distachyon as a model plant toward improved biofuel crops: Search for secreted proteins involved in biogenesis and disassembly of cell wall polymers

Polysaccharides make up about 75% of plant cell walls and can be broken down to produce sugar substrates (saccharification) from which a whole range of products can be obtained, including bioethanol. Cell walls also contain 5–10% of proteins, which could be used to tailor them for agroindustrial uses. Here we present cell wall proteomics data of Brachypodium distachyon, a model plant for temperate grasses. Leaves and culms were analyzed during active growth and at mature stage. Altogether, 559 proteins were identified by LC‐MS/MS and bioinformatics, among which 314 have predicted signal peptides. Sixty‐three proteins were shared by two organs at two developmental stages where they could play housekeeping functions. Differences were observed between organs and stages of development, especially at the level of glycoside hydrolases and oxidoreductases. Differences were also found between the known cell wall proteomes of B. distachyon, Oryza sativa, and the Arabidopsis thaliana dicot. Three glycoside hydrolases could be immunolocalized in cell walls using polyclonal antibodies against proteotypic peptides. Organ‐specific expression consistent with proteomics results could be observed as well as cell‐specific localization. Moreover, the high number of proteins of unknown function in B. distachyon cell wall proteomes opens new fields of research for monocot cell walls.