大腿残肢步态过程的非线性有限元分析

目的利用三维有限元分析方法研究大腿截肢患者在行走过程中3个不同时相下残肢的生物力学特性,为建立完整的大腿接受腔测量、设计与评估系统提供研究基础。方法首先根据CT图像三维重建大腿截肢患者的骨骼、肌肉软组织和接受腔的三维几何模型;定义软组织为超弹性和线弹性材料属性,并相应建立两个有限元仿真模型;定义残端与接受腔之间的接触关系,约束残肢近端,对模型的远端施加膝关节载荷,模拟步态周期中足跟着地时期、站立相中期、脚尖离地3个时相下大腿残肢-接受腔系统所受载荷;计算分析接触界面上的应力,并对比分析超弹性和线弹性软组织力学特性对接触界面力学行为特性的影响。结果无论线弹性还是超弹性模型,3个时相下大腿残肢-接受腔界面的最大接触压力均在残肢末端达到最大值。超弹性模型3个时相下接触压力峰值分别为55.80、47.63和50.44 kPa;而线弹性模型接触压力的最大值都增加2倍以上,其值分别为149.86、118.55和139.68 kPa。同时通过分析接触面间的径向剪切应力和轴向剪切应力发现,3个时相下接触界面间的应力在残肢末端较集中,在足跟着地到脚尖离地过程中,有部分力通过接受腔后侧缘传递转向接受腔前缘传递。结论不同时相下残肢与接受腔接触界面的压力和剪切应力分布情况不同,在设计接受腔时需要充分考虑其受力特点。     

Comparison of computational analysis with clinical measurement of stresses on below-knee residual limb in a prosthetic socket

Interface pressures and shear stresses between a below-knee residual limb and prosthetic socket predicted using finite element analyses were compared with experimental measurements. A three-dimensional nonlinear finite element model, based on actual residual geometry and incorporating PTB socket rectification and interfacial friction/slip conditions, was developed to predict the stress distribution. A system for measuring pressures and bi-axial shear stresses was used to measure the stresses in the PTB socket of a trans-tibial amputee. The FE-predicted results indicated that the peak pressure of 226 kPa occurred at the patellar tendon area and the peak shear stress of 50 kPa at the anterolateral tibia area. Quantitatively, FE-predicted pressures were 11%, on average, lower than those measured by triaxial transducers placed at all the measurement sites. Because friction/slip conditions between the residual limb and socket liner were taken into consideration by using interface elements in the FE model, the directions and magnitudes of shear stresses match well between the FE prediction and clinical measurements. The results suggest that the nonlinear mechanical properties of soft tissues and dynamic effects during gait should be addressed in future work.     

Finite element analysis for the evaluation of the structural behaviour,of a prosthesis for trans-tibial amputees

The finite element analysis (FEA) has been identified as a useful tool for the stress and strain behaviour determination in lower limb prosthetics. The residual limb and prosthetic socket interface was the main subject of interest in previous studies. This paper focuses on the finite element analysis for the evaluation of structural behaviour of the Sure-flex? prosthetic foot and other load-bearing components. A prosthetic socket was not included in the FEA. An approach for the finite element modelling including foot analysis, reverse engineering and material property testing was used. The foot analysis incorporated ground reaction forces measurement, motion analysis and strain gauge analysis. For the material model determination, non-destructive laboratory testing and its FE simulation was used. A new, realistic way of load application is presented along with a detailed investigation of stress distribution in the load-bearing components of the prosthesis. A novel approach for numerical and experimental agreement determination was introduced. This showed differences in the strain on the pylon between the experimental and the numerical model within 30% for the anteroposterior bending and up to 25% for the compression. The highest von Mises stresses were found on the foot–pylon connecting component at toe off. Peak stress of 216 MPa occurred on the posterior adjusting screw and maximum stress of 156 MPa was found at the neck of the male pyramid.     

Real-Time Patient-Specific Finite Element Analysis of Internal Stresses in the Soft Tissues of a Residual Limb: A New Tool for Prosthetic Fitting

Fitting of a prosthetic socket is a critical stage in the process of rehabilitation of a trans-tibial amputation (TTA) patient, since a misfit may cause pressure ulcers or a deep tissue injury (DTI: necrosis of the muscle flap under intact skin) in the residual limb. To date, prosthetic fitting typically depends on the subjective skills of the prosthetist, and is not supported by biomedical instrumentation that allows evaluation of the quality of fitting. Specifically, no technology is presently available to provide real-time continuous information on the internal distribution of mechanical stresses in the residual limb during fitting of the prosthesis, or while using it and this severely limits patient evaluations. In this study, a simplified yet clinically oriented patient-specific finite element (FE) model of the residual limb was developed for real-time stress analysis. For this purpose we employed a custom-made FE code that continuously calculates internal stresses in the residual limb, based on boundary conditions acquired in real-time from force sensors, located at the limb-prosthesis interface. Validation of the modeling system was accomplished by means of a synthetic phantom of the residual limb, which allowed simultaneous measurements of interface pressures and internal stresses. Human studies were conducted subsequently in five TTA patients. The dimensions of bones and soft tissues were obtained from X-rays of the residual limb of each patient. An indentation test was performed in order to obtain the effective elastic modulus of the soft tissues of the residual limb. Seven force sensors were placed between the residual limb and the prosthetic liner, and subjects walked on a treadmill during analysis. Generally, stresses under the shinbones were ∼threefold higher than stresses at the soft tissues behind the bones. Usage of a thigh corset decreased the stresses in the residual limb during gait by approximately 80%. Also, the stresses calculated during the trial of a subject who complained about pain and discomfort were the highest, confirming that his socket was not adequately fitted. We conclude that real-time patient-specific FE analysis of internal stresses in deep soft tissues of the residual limb in TTA patients is feasible. This method is promising for improving the fitting of prostheses in the clinical setting and for protecting the residual limb from pressure ulcers and DTI.     

Triaxial force transducer for investigating stresses at the stump/socket interface

Although normal pressures at the stump socket interface of the lowerlimb amputee have been investigated, little is known about the shear stresses that also occur. Studies suggest that the combination of both shear and normal stresses significantly exacerbates discomfort and vascular and tissue damage. A means of simultaneously measuring normal and shear stresses will aid in the investigation and improvement of prosthetic fit. A miniature triaxial force transducer (4·9×16 mm diameter) has been developed which can be recessed into the socket wall. The principle of operation, construction, performance and limitations of the device are described. Preliminary measurements of the interface stress variations over the gait cycle in a supra-condylar PTB socket are presented. These show clear differences in the stress patterns present when two different prosthetic feet are used.     

A computational model for stress reduction at the skin-implant interface of osseointegrated prostheses

Osseointegrated implants (OI)s for transfemoral prosthetic attachment offer amputees an alternative to the traditional socket attachment. Potential benefits include a natural transfer of loads directly to the skeleton via the percutaneous abutment, relief of pain and discomfort of residual limb soft tissues by eliminating sockets, increased sensory feedback, and improved function. Despite the benefits, the skin-implant interface remains a critical limitation, as it is highly prone to bacterial infection. One approach to improve clinical outcomes is to minimize stress concentrations at the skin-implant interface due to shear loading, reducing soft tissue breakdown and subsequent risk of infection. We hypothesized that broadening the bone base at the distal end of the femur would provide added surface area for skin adhesion and reduce stresses at the skin-implant interface. We tested this hypothesis using finite element models of an OI in a residual limb. Results showed a dramatic decrease in stress reduction, with up to ~90% decrease in stresses at the skin-implant interface as cortical bone thickness increased from 2 to 8 mm. The findings in this study suggests that surgical techniques could stabilize the skin-implant interface, thus enhancing a skin-to-bone seal around the percutaneous device and minimizing infection.     

Using computational simulation to aid in the prediction of socket fit: a preliminary study

This study illustrates the use of computational analysis to predict prosthetic socket fit. A simple indentation test is performed by applying force to the residual limb of a trans-tibial amputee through an indenter until the subject perceives the onset of pain. Computational finite element (FE) analysis is then applied to evaluate the magnitude of pressure underlying the indenter that initiates pain (pain threshold pressure), and the pressure at the prosthetic socket-residual limb interface. The assessment of socket fit is examined by studying whether or not the socket-limb interface pressure exceeds the pain threshold pressure of the limb. Based on the computer-aided assessment, a new prosthetic socket is then fabricated and fitted to the amputee subject. Successful socket fit is achieved at the end of this process. The approach of using computational analysis to aid in assessing socket fit allows a more efficient evaluation and re-design of the socket even before the actual fabrication and fitting of the prosthetic socket. However, more thorough investigations are required before this approach can be widely used. A subsequent part of this paper discusses the limitations and suggests future research directions in this area.     

Effects of liner stiffness for trans-tibial prosthesis: a finite element contact model

The socket liner plays a crucial role in redistribution of the interface stresses between the stump and the socket, so that the peak interface stress could be reduced. However, how the peak stress is affected by various liner stiffnesses is still unknown, especially when the phenomenon of the stump slide within the socket is considered. This study employed nonlinear contact finite element analyses to study the biomechanical reaction of the stump sliding with particular attention to the liner stiffness effects of the trans-tibial prosthesis. To validate the finite element outcomes, experimental measurements of the interface stresses and sliding distance were further executed. The results showed that the biomechanical response of the stump sliding are highly nonlinear. With a less stiff liner, the slide distance of the stump would increase with a larger contact area. However, this increase in the contact area would not ensure a reduction in the peak interface stress and this is due to the combined effects of the non-uniform shape of the socket and the various sliding distances generated by the different liner stiffnesses.     

一体化小腿假肢的三维有限元应力分析

建立一体化小腿假肢和残肢的三维模型，应用有限元分析方法，计算此模型在模拟Mid—Stance步态时相的载荷作用下各节点的应力，从而得到此模型内外表面的应力分布，为一体化假肢设计的CAD＼CAM系统提供理论依据。计算结果表明，接受腔的应力值较小，假腿的应力值较大，高应力区出现在假腿下端及接受腔与假腿的交界区域。     

足部三维有限元建模方法及其生物力学应用

目的探讨建立足部三维有限元模型的方法,应用模型模拟分析研究鞋垫设计参数,不同软组织刚度和受力情况下对足部的生物力学影响。方法建立基于解剖结构,包括软组织,韧带和腱膜,考虑材料的非线性和关节接触的足部三维有限元模型。有限元模型的可靠性利用模拟足踝关节在不同病理、手术和鞋垫矫治情况下的生物力学反应来验证。结果有限元分析结果表明,定制型鞋垫的形状比鞋垫材料的刚度对减少足底最大压力有更重要影响。软组织刚度的增加引起足底接触面积的减小,从而会导致足底跖骨区最大压力增加。部分和完全松解足底腱膜都会降低足弓高度,并增加足底韧带的张力和增加中足和跖骨的应力。体重增加和跟腱拉力增加都将成倍足底筋膜的拉力。结论所建足部有限元模型能预测足底压力分布和足内部骨骼软组织应力、应变情况,可以成为设计鞋垫和研究足部各种临床状况提供有力的分析工具。     

Fibre reinforced composite dental bridge. Part II: Numerical investigation

Motivated by the clinical success and limitations on experimental investigation of the fibre-reinforced composite dental bridge, this paper aims at providing a numerical investigation into the bridge structure. The finite element (FE) model adopted here is constructed from computer tomography images of a physical bridge specimen. The stress and strain distributions in the bridge structure especially in the bonding interfaces are analyzed in detail. The peak stresses and their variations with the different bridge designs are evaluated. Due to the lower bond strengths of adhesives and the high stress concentration in the pontic-abutment interface, the likelihood of failure in the interface is predicted by finite element analysis. The validity of the numerical results is established by a good agreement between the FE prediction and the tests in the load-deflection responses, the structural stiffness as well as the failure location of the composite dental bridge.     

内骨架一体化小腿假肢的生物力学研究

一体化假肢是以聚合物为材料从接受腔到假腿一体成型的新型下肢假肢，它比传统型假肢更经济、美观、轻便，具有较大的应用前景。目前的相关研究主要集中在设计与制作及少量的临床研究方面。由于一体化假肢与传统型假肢在结构上的差异，有必要对其进行应力分析。本研究的目的是开展内骨架一体化假肢的生物力学研究，本研究基于内骨架一体化小腿假肢的真实几何构型，建立三维有限元模型，计算该模型在模拟Heel OH步态时相的载荷作用下的应力分布；在保持该模型的几何形状不变的情况下，建立了三个不同壁面厚度的一体化小腿假肢的有限元模型，分析壁面厚度对一体化小腿假肢应力分布的影响；通过分别赋予模型四种不同高分子聚合物的材料力学特性值，分析不同材料的一体化假肢的应力分布特点；分别对模型施加与正常步态的五个典型时相对应的载荷，分析一体化小腿假肢在各步态时相的应力分布特点。本研究结果对一体化假肢设计有指导价值。     

Finite element modeling of the contact interface between trans-tibial residual limb and prosthetic socket

Finite element method has been identified as a useful tool to understand the load transfer mechanics between a residual limb and its prosthetic socket. This paper proposed a new practical approach in modeling the contact interface with consideration of the friction/slip conditions and pre-stresses applied on the limb within a rectified socket. The residual limb and socket were modeled as two separate structures and their interactions were simulated using automated contact methods. Some regions of the limb penetrated into the socket because of socket modification. In the first step of the simulation, the penetrated limb surface was moved onto the inner surface of the socket and the pre-stresses were predicted. In the subsequent loading step, pre-stresses were kept and loadings were applied at the knee joint to simulate the loading during the stance phase of gait. Comparisons were made between the model using the proposed approach and the model having an assumption that the shape of the limb and the socket were the same which ignored pre-stress. It was found that peak normal and shear stresses over the regions where socket undercuts were made reduced and the stress values over other regions raised in the model having the simplifying assumption.     

小腿假肢接受腔的三维有限元分析

通过建立三维非线性有限元模型来分析小腿假肢接受腔与残肢之间的载荷分布。此模型基于残肢,骨头,软套和接受腔的三维几何形状,考虑界面摩擦滑动条件和软组织的大变形等非线性因素。模型可以预测不同外载下残肢和接受腔之间的压力,剪切力和相对滑动情况。并分析了不同的接受腔形状对载荷分布的影响。     

Automatic segmentation of magnetic resonance images of the trans-femoral residual limb

An automatic algorithm for the extraction of the skin and bone boundaries from axial magnetic resonance images of the residual limb of trans-femoral amputees is presented. The method makes use of K-means clustering and mathematical morphology. Statistical analysis of the results indicates that the computer-generated boundaries compare favourably to those drawn by human observers. The boundaries may be used in biomechanical modelling of the interaction between the residual limb and the prosthetic socket. The limb/socket interface determines the quality of prosthetic fit, therefore knowledge of this interface is important for the improvement of socket design in order to achieve patient comfort and mobility.     

Automatic segmentation of magnetic resonance images of the trans-femoral residual limb

An automatic algorithm for the extraction of the skin and bone boundaries from axial magnetic resonance images of the residual limb of trans-femoral amputees is presented. The method makes use of K-means clustering and mathematical morphology. Statistical analysis of the results indicates that the computer-generated boundaries compare favourably to those drawn by human observers. The boundaries may be used in biomechanical modelling of the interaction between the residual limb and the prosthetic socket. The limb/socket interface determines the quality of prosthetic fit, therefore knowledge of this interface is important for the improvement of socket design in order to achieve patient comfort and mobility.     

The quasi-static response of compliant prosthetic sockets for transtibial amputees using finite element methods

The finite element method (FEM) is a very powerful tool for analyzing the behavior of structures, especially when the geometry and mechanics are too complex to be modeled with analytical methods. This study focuses on the analysis of patellar tendon bearing prosthetic sockets with integrated compliant features designed to relieve contact pressure between the residual limb and socket. We developed a FEM model composed of a socket, liner and residual limb and analyzed it under quasi-static loading conditions derived from experimentally measured ground reaction forces. The geometry of the residual limb, liner and socket were acquired from computed tomography (CT) data of a transtibial amputee. Three different compliant designs were analyzed using FEM to assess the structural integrity of the sockets and their ability to relieve local pressure at the fibula head during normal walking. The compliant features consisted of thin-wall sections and two variations of spiral slots integrated within the socket wall. One version of the spiral slots produced the largest pressure relief, with an average reduction in local interface pressure during single-leg stance (20-80% of the stance phase) from 172 to 66.4 kPa or 65.8% compared to a baseline socket with no compliant features. These results suggest that the integration of local compliant features is an effective method to reduce local contact pressure and improve the functional performance of prosthetic sockets.     

壁面厚度对一体化小腿假肢应力分布的影响

一体化假肢是以聚合物为材料从接受腔到假腿一体成型的新型下肢假肢 ,它比传统型假肢更经济、美观、轻便 ,具有较大的应用前景。如同传统假肢 ,应力分析对于一体化假肢的构型设计和优化具有重要的意义。由于假肢中的应力大小及分布与其所用材料的力学特性密切相关。本文的工作是基于一实验用内骨架一体化小腿假肢的真实几何构型 ,考虑残端软组织和骨 ,建立一体化小腿假肢的三维有限元模型 ;在保持假肢的几何形状不变的前提下 ,建立三个不同壁面厚度的一体化小腿假肢的三维模型 ,应用有限元分析方法 ,计算这些模型在模拟 Heel Off步态时相的载荷作用下的应力分布 ,分析壁面厚度对一体化小腿假肢应力分布的影响 ,为一体化小腿假肢壁面厚度的设计标准提供参考。结果表明 ,可以通过适当增加壁面厚度来减小一体化假肢的应力及软组织表面的压力。     

惯性载荷对截肢患者残肢/接受腔界面应力的影响研究

接受腔/残肢界面压力分布特征是假肢优化设计的基础,传统的有限元模型只限于静态分析,不符合实际情况。本文以小腿截肢患者为研究对象,建立了三维非线性有限元模型,给出了一个步态周期内残肢界面压力的变化规律,并对惯性载荷的影响进行了定量比较。结果表明:界面压力主要分布在髌韧带、胫骨内外侧和窝区,一个平地正常速度行走的步态周期内,站立相压力变化呈双峰蝶形,惯性载荷引起的平均压力幅值变化为8.4%;而在摆动相压力幅值变化高达20.1%,并且变化规律相反。行走过程中惯性载荷的影响不能忽略。     

Dynamic finite element simulation of dental prostheses during chewing using muscle equivalent force and trajectory approaches

The long-term application of dental prostheses inside the bone has a narrow relation to its biomechanical performance. Chewing is the most complicated function of a dental implant as it implements different forces to the implant at various directions. Therefore, a suitable holistic modelling of the jaw bone, implant, food, muscles, and their forces would be deemed significant to figure out the durability as well as functionality of a dental implant while chewing. So far, two approaches have been proposed to employ the muscle forces into the Finite Element (FE) models, i.e. Muscle Equivalent Force (MEF) and trajectory. This study aimed at propounding a new three-dimensional dynamic FE model based on two muscle forces modelling approaches in order to investigate the stresses and deformations in the dental prosthesis as well as maxillary bone during the time of chewing a cornflakes bio. The results revealed that both contact and the maximum von Mises stress in the implant and bones for trajectory approach considerably exceed those of the MEF. The maximum stresses, moreover, are located around the neck of implant which should be both clinically and structurally strong enough to functionally maintain the bone-implant interface. In addition, a higher displacement due to compressive load is observed for the implant head in trajectory approach. The results suggest the benefits provided by trajectory approach since MEF approach would significantly underestimate the stresses and deformations in both the dental prosthesis and bones.