The Influence of Cavity Shape on the Stresses in Composite Dental Restorations: A Finite Element Study

Dental restoration adhering to the cavity exhibits fundamentally different load transfer mechanisms from non-adhering restorations. It is therefore questionable that traditional cavity designs are optimal from a purely mechanical point of view when working with composite materials. Drawing from general engineering experience, it can be hypothesised that smooth, well rounded designs with bevelled margins are superior. A finite element model is used in the present investigation to determine the stress field in four different cavity designs as it develops during the curing of the restoration. The results show that a significant reduction of the stress along the adhesive interface between the tooth and the restoration can be achieved through the use of a rounded cavity shape. They also show that the adoption of bevelled margins leads to a reduction of the stress concentration at this location. These results are confirmed by a set of experimental results published in the literature. It is concluded that adhering restorations will perform better from a mechanical point of view if an appropriate cavity shape is selected.     

A Voxel-based Formulation for Contact Finite Element Analysis

To date, voxel-based finite element models have not been feasible for contact problems, owing to the inherent stair-step boundary discontinuities. New preprocessing techniques are reported herein to mesh these boundaries smoothly, for purposes of contact stress analysis. Further, new techniques are reported to concentrate the mesh resolution automatically near the articular surface, thus reducing the problem size to levels compatible with executing nonlinear problems on contemporary engineering workstations. Close approximations to Hertzian analytical solutions were obtained for spherical and cylindrical geometries meshed in this manner, and an illustrative anatomical contact problem of the human hip joint is presented.     

A Finite Element Approach for Skeletal Muscle using a Distributed Moment Model of Contraction

Abstract

The present paper describes a geometrically and physically nonlinear continuum model to study the mechanical behaviour of passive and active skeletal muscle. The contraction is described with a Huxley type model. A Distributed Moments approach is used to convert the Huxley partial differential equation in a set of ordinary differential equations. An isoparametric brick element is developed to solve the field equations numerically. Special arrangements are made to deal with the combination of highly nonlinear effects and the nearly incompressible behaviour of the muscle. For this a Natural Penalty Method (NPM) and an Enhanced Stiffness Method (ESM) are tested. Finally an example of an analysis of a contracting tibialis anterior muscle of a rat is given. The DM-method proved to be an efficient tool in the numerical solution process. The ESM showed the best performance in describing the incompressible behaviour.     

Stochastic Finite Element Analysis of Biological Systems: Comparison of a Simple Intervertebral Disc Model with Experimental Results

Statistical methods allow the effects of uncertainty to be incorporated into finite element models. This has potential benefits for the analysis of biological systems where natural variability can give rise to substantial uncertainty in both material and geometrical properties. In this study, a simple model of the intervertebral disc under compression was created and analysed as both a deterministic and a stochastic system. Factorial analysis was used to determine the important parameters to be included in the stochastic analysis. The predictions from the model were compared to experimental results from 21 sheep discs. The size and shape of the distribution of the axial deformations predicted by the model was consistent with the experimental results given that the number of model solutions far exceeded the number of experimental results. Stochastic models could be valuable in determining the range and most likely value of stress in a tissue or implant.     

A Finite Element Analysis Methodology for Representing the Articular Cartilage Functional Structure

Recognising that the unique biomechanical properties of articular cartilage are a consequence of its structure, this paper describes a finite element methodology which explicitly represents this structure using a modified overlay element model. The validity of this novel concept was then tested by using it to predict the axial curling forces generated by cartilage matrices subjected to saline solutions of known molality and concentration in a novel experimental protocol. Our results show that the finite element modelling methodology accurately represents the intrinsic biomechanical state of the cartilage matrix and can be used to predict its transient load-carriage behaviour. We conclude that this ability to represent the intrinsic swollen condition of a given cartilage matrix offers a viable avenue for numerical analysis of degenerate articular cartilage and also those matrices affected by disease.     

Numerical Analysis of An Anastomotic Device

The explicit dynamic finite element method was utilized to investigate the deformation behaviour of a woven wire mesh tubular device that is used in a side-to-side anastomotic procedure for achieving gastrointestinal anastomosis. The numerical model was initially verified by comparison to experimental results that were obtained using a specialized testing mechanism. Once validated, the finite element model (FEM) was parameterized to ascertain the influence of several device parameters on its deformation behaviour. The importance of these parameters, as related to its optimal design for use in minimally invasive surgery (MIS), was subsequently ascertained and discussed.     

Finite Element Analysis as a Tool for Parametric Prosthetic Foot Design and Evaluation. Technique Development in the Solid Ankle Cushioned Heel (SACH) Foot

In this study, we developed an approach for prosthetic foot design incorporating motion analysis, mechanical testing and computer analysis. Using computer modeling and finite element analysis, a three-dimensional (3D), numerical foot model of the solid ankle cushioned heel (SACH) foot was constructed and analyzed based upon loading conditions obtained from the gait analysis of an amputee and validated experimentally using mechanical testing. The model was then used to address effects of viscoelastic heel performance numerically. This is just one example of the type of parametric analysis and design enabled by this approach. More importantly, by incorporating the unique gait characteristics of the amputee, these parametric analyses may lead to prosthetic feet more appropriately representing a particular user's needs, comfort and activity level.     

A Finite Element Model of the L5-S1 Functional Spinal Unit: Development and Comparison with Biomechanical Tests In Vitro

The main objective of this work is to develop a three-dimensional finite element model of the L5-S1 segment that is able to simulate its passive mobility measured in vitro . Due to their limited role in segment mobility, an isotropic linear elastic constitutive law was used for cartilage, cancellous and cortical bone. The intervertebral disk ground substance was modeled with a non-linear hyperelastic polynomial law. Fibers of the disk, as well as ligaments, were modeled with piecewise linear springs. Flexion-extension, axial rotation, and lateral bending torques were applied to the model. A comparison with the experimental results obtained on the same segment for these three major motions was conducted. The compliance of the segment subjected to pure torques was found to be similar between numerical and experimental results for all major motions. Coupled motions and translations were also similar, even in their amplitude. For lateral bending, the normal coupled motions originate from the geometry of the disk and not from the facet geometry.     

有限元分析法在腰椎生物力学研究中的应用及新进展

有限元分析法是指对复杂形态物体的应力及应变进行分析,具有力学性能测试全面、客观、可重复性的特点。目前,有限元分析法已被广泛应用于脊柱畸形、腰椎损伤以及假体植入等人体复杂结构生物力学的研究中。本文主要介绍有限元分析法在腰椎的椎体、间盘、韧带及肌肉组织中的应用,结合其概念、原理、建模方法等,总结该方法在新型内固定物力学特性研究中的优势,探讨其对不同植骨内固定术式选择的临床意义。     

A Comparative Analysis of Different Treatments for Distal Femur Fractures using the Finite Element Method

The main objective of this work is the evaluation, by means of the finite element method (FEM) of the mechanical stability and long-term microstructural modifications in bone induced to three different kinds of fractures of the distal femur by three types of implants: the Condyle Plate, the less invasive stabilization system plate (LISS) and the distal femur nail (DFN). The displacement and the stress distributions both in bone and implants and the internal bone remodelling process after fracture and fixation are obtained and analysed by computational simulation. The main conclusions of this work are that distal femoral fractures can be treated correctly with the Condyle Plate, the LISS plate and the DFN. The stresses both in LISS and DFN implant are high especially around the screws. When respect to remodelling, the LISS produces an important resorption in the fractured region, while the other two implants do not strongly modify bone tissue microstructure.     

不同材料充填修复下颌第一前磨牙楔状缺损的应力分析

目的研究三种材料对两种角度下颌第一前磨牙楔状缺损的修复效果。方法在下颌第一前磨牙颊颈部深度为1mm,夹角分别为30°、90°的楔状缺损有限元模型上用银汞合金、复合树脂和玻璃离子粘固粉三种材料进行缺损修复,以未修复的楔模型为对照,加载100N轴向力后,利用三维有限元方法进行牙颈部应力分析。结果三种材料修复均改善了缺损牙体的应力集中。银汞合金修复体较其他两种材料承受了更大的应力,使缺损局部牙体应力集中状况得以更多缓解,在角度增加时作用更明显。复合树脂最有效降低牙体内部区域的应力集中。结论楔状缺损充填修复可缓解缺损区牙体硬组织的应力集中,复合树脂相对理想。     

Analysis of parametric estimation of head tissue conductivities using Electrical Impedance Tomography

We study the theoretical performance of using Electrical Impedance Tomography (EIT) to measure the conductivity of the main tissues of the head. The governing equations are solved using the Finite Element Method for realistically shaped head models with isotropic and anisotropic electrical conductivities. We focus on the Electroencephalography (EEG) signal frequency range since EEG source localization is the assumed application. We obtain the Cramér-Rao Lower Bound (CRLB) to find the minimum conductivity estimation error expected with EIT measurements. The more convenient electrode pairs selected for current injection from a typical EEG array are determined from the CRLB. Moreover, using simulated data, the Maximum Likelihood Estimator of the conductivity parameters is shown to be close to the CRLB for a relatively low number of measurements. The results support the idea of using EIT as a low-cost and practical tool for individually measure the conductivity of the head tissues, and to use them when solving the EEG source localization. Even when the conductivity of the soft tissues of the head is available from Diffusion Tensor Imaging, EIT can complement the electrical model with the estimation of the skull and scalp conductivities.     

股骨骨折术后1 年随访骨愈合模型的有限元分析

目的：对股骨骨折髓内钉术后1 年骨愈合模型快速建模,通过有限元分析研究对比术前术后模型,通过术前判定内固定取出后骨折断端是否断裂。方法：运用Mimics、Geomagic Studio、Abaqus等软件采用快速个体化建模方法对股骨骨折髓内钉术后1年内固定取出术前后的多层螺旋CT 数据进行快速建立模型,术前模型模拟剥除钢板后进行有限元分析,施加人体单腿站立时的静力载荷和约束,并将分析结果与术后模型进行对比,观察米塞斯应力分布情况、最大值及其所处部位。结果：按照材料属性进行区别显示米赛斯应力的最大值及最小值,在不同应力载荷下,手术前后各类型材料的米赛斯应力最大值及最小值部位相同,各类型材料中,最大值均没有位于骨折断端,不同方法的最大应力值部位相近,均在股骨中远端1/4 交界处,手术前后应力分布基本相同。结论：采用个体化建模方法可以对骨折内固定取出前的骨愈合模型进行运算分析,快速预判术后是否导致骨折断端断裂。     

Adaptive Finite Element Analysis of the Anisotropic Biphasic Theory of Tissue-Equivalent Mechanics

Abstract

The nonlinear partial differential equations of the anisotropic biphasic theory of tissue-equivalent mechanics are solved with axial symmetry by an adaptive finite element system. The adaptive procedure operates within a method-of-lines framework using finite elements in space and backward difference software in time. Spatial meshes are automatically refined, coarsened, and relocated in response to error indications and material deformation. Problems with arbitrarily complex two-dimensional regions may be addressed. With meshes graded in high-error regions, the adaptive solutions have fewer degrees of freedom than solutions with comparable accuracy obtained on fixed quasi-uniform meshes. The adaptive software is used to address problems involving an isometric cell traction assay, where a cylindrical tissue equivalent is adhered at its end to fixed circular platens; a prototypical bioartificial artery; and a novel configuration that is intended as an initial step in a study to determine bioartificial arteries having optimal collagen and cell concentrations.     

股骨骨折术后1年随访骨愈合模型的有限元分析

目的：对股骨骨折髓内钉术后1年骨愈合模型快速建模,通过有限元分析研究对比术前术后模型,通过术前判定内固定取出后骨折断端是否断裂。方法：运用Mimics、Geomagic Studio、Abaqus等软件采用快速个体化建模方法对股骨骨折髓内钉术后1年内固定取出术前后的多层螺旋CT数据进行快速建立模型,术前模型模拟剥除钢板后进行有限元分析,施加人体单腿站立时的静力载荷和约束,并将分析结果与术后模型进行对比,观察米塞斯应力分布情况、最大值及其所处部位。结果：按照材料属性进行区别显示米赛斯应力的最大值及最小值,在不同应力载荷下,手术前后各类型材料的米赛斯应力最大值及最小值部位相同,各类型材料中,最大值均没有位于骨折断端,不同方法的最大应力值部位相近,均在股骨中远端1/4交界处,手术前后应力分布基本相同。结论：采用个体化建模方法可以对骨折内固定取出前的骨愈合模型进行运算分析,快速预判术后是否导致骨折断端断裂。     

人工半骨盆假体置换联合腰椎椎弓根螺钉固定术后生物力学的有限元分析

目的:建立人工半骨盆假体置换与联合腰椎椎弓根螺钉固定后的三维有限元模型,评价腰骶段生物力学改变后半骨盆假体力学结构的特点。方法:采用CT薄层扫描采集原始数据,分别建立正常骨盆、半骨盆假体置换术后以及半骨盆假体置换联合腰椎椎弓根螺钉固定术后骨盆的三维有限元模型,分别在第4腰椎上终板平面施以500 N的垂直纵向载荷,分析不同骨盆模型的应力分布特点。结果:与正常骨盆有限元模型相比,半骨盆假体置换术后健侧骨盆应力分布以骶髂关节、髋臼窝及耻骨为主,置换侧半骨盆假体以耻骨连接棒、髋臼杯及髂骨座为主,最大应力出现在耻骨连接棒,应力峰值为65.62 MPa。联合腰椎椎弓根螺钉固定后健侧应力相对减小,置换侧髂骨固定座与骶骨固定处应力相对减小,应力分布以腰椎椎弓根钉棒、耻骨连接棒及髋臼杯为主,最大应力出现在椎弓根螺钉,应力峰值为107 MPa。结论:半骨盆假体置换联合腰椎椎弓根螺钉固定后钉棒分担了半骨盆置换后健侧骨盆及置换侧髂骨固定座与骶骨固定处附近的部分应力,缓解应力集中现象,降低术后骨盆破坏风险,一定程度上增加了半骨盆置换后骨盆的稳定性。     

基于有限元的第5 掌骨颈骨折钢板螺钉内固定的生物力学分析

目的：应用有限元方法建立三种不同的治疗第5 掌骨颈骨折的钢板螺钉内固定模型,比较三种模型的生物力学稳定性,为 第5 掌骨颈骨折的临床早期功能康复提供参考。方法：选取一名健康青年志愿者,将CT 扫描数据导入三维有限元软件建立第5 掌骨颈骨折模型,并选取三种钢板螺钉内固定方法进行骨折固定。对三种模型施加外力荷载并进行生物力学有限元分析,对比骨 折断端的最大位移和钢板螺钉的应力分布情况。结果：方法一、二、三的第5 掌骨骨折端的最大位移分别为0.189775 mm、 0.181428 mm、0.224299 mm,以方法二的骨折端位移最小;内固定材料的最大应力分别为1.20 KPa、1.00 KPa、1.39 KPa,以方法二 的钢板螺钉应力最小。结论：采用近端三颗螺钉远端两颗螺钉的直型钢板内固定方法治疗第五掌骨颈骨折的生物力学稳定性更 好,术后早期功能锻炼的安全性更高,是治疗第5 掌骨颈骨折的理想内固定方法。     

Dega骨盆截骨术后最佳中心边缘角的三维有限元分析

目的:应用三维有限元技术评估发育性髋关节脱位(developmental dysplasia of the hip,DDH)患儿在Dega骨盆截骨术后不同中心边缘角(center-edge angle,CEA)状态下髋臼的应力分布,为术前的手术规划提供有参考价值的生物力学结果。方法:使用已建立的DDH患者髋关节三维有限元模型,以术后CEA27°为中间值,每3°为一个变量,在Mimics誖10.0软件的模拟手术模块分别构建7组髋臼截骨术后的模型。在单腿站立和双腿站立状态下测量不同CEA状态下髋臼的应力分布。结果:单腿站立情况下,CEA为24°、27°、30°和33°的术后模型患侧髋臼的峰值应力接近正常侧。双腿站立情况下,CEA为24°时双侧髋臼的峰值应力最为接近。结论:对于该患者而言,在7组术后CEA中,24°时患侧髋臼的峰值应力与健侧最为接近,可以认为是最佳的术后CEA。有限元技术能够为Dega手术的术前规划提供个性化的指导方案。