Mesh-independent prediction of skin burns injury

This paper presents a robust finite element model (FEM) with multiple-layers of varying properties for investigation of burn effects on human skin during a burning process resulting from exposure of skin surface to a contact heat source and a hot moving fluid. Henriques' theory of skin burns is used in conjunction with two-dimensional Pennes bioheat transfer equation for determining the spatial and temporal extent of burn injury. The model developed is a two-dimensional axisymmetric model in cylindrical coordinates. The various tissue layers account for changing thermal properties with respect to skin anatomy. A finite element scheme that uses the backward Euler method is used to solve the problem. The injury processes of skin subsequent to the removal of the heat source (post-burn) will also be inspected. The mesh employed in this model consists of a high density of nodes and elements in which a thorough mesh convergence study was done. A comparison of the transient temperature field computed by this model against Diller's results using the FE technique with a comparatively coarse mesh of 125 elements and experimental data by Orgill et al. has been done in the present study. It concluded that improved accurate solutions have been performed using the robust model developed due to the achievement of a mesh-independent solution.     

足部有限元模型的构建与验证

背景：目前国内所建的足部模型大部分是采用自动划分网格的四面体有限元模型,虽然四面体网格自动剖分技术给三维实体的有限元网格自动剖分带来了极大的方便,但力学性能较差。 目的：基于CT图片构建六面体网格足部有限元模型。 方法：选取中国正常男性人体足部的CT数据,利用Mimics软件对足部几何模型进行重构,运用NURBS 曲面的节点插入算法,对足部几何模型进行了细化,构建了具有较高生物仿真度的人体足部有限元模型,利用Pam-crash软件对模型进行了碰撞仿真分析。 结果与结论：仿真结果与尸体实验结果基本一致,证明模型可信。实验基于CT图片构建的六面体网格足部有限元模型,添加了足底肌肉、肌腱、皮肤等结构,更真实的反映了足部解剖学结构特征,进而提高了有限元模型的质量,更能有效地研究足部损伤机制,从而为提高汽车安全性设计提供参考依据。     

Prediction of transient temperature fields and cumulative tissue destruction for radio frequency heating of a tumor

A therapeutic hyperthermia protocol using a radio frequency (rf) electrode placed adjacent to a bronchial wall tumor has been modeled using the finite element technique. Variable physical properties and variable blood perfusion have been assigned to the tumor and to the surrounding normal lung tissue. The Laplace equation was solved on a curvilinear grid for a single rf source electrode to determine the steady-state electric field, which in turn governs the energy deposition function. The heat generation in the tumor and in the lung tissue is then calculated from the energy deposition profile, and the bioheat equation is solved on the same finite element mesh to determine the transient temperature history. The temperatures are displayed as isothermal contours at designated times during the protocol and as temperature histories at selected points. In addition, an Arrhenius-type injury model has been implemented to predict thermally induced damage, from which equal total amounts of energy are deposited into the tissue using a constant power density for an appropriate time or using a cyclic heating pattern. The cyclic heating pattern consisted of a series of equal duration time periods during which the rf current source is alternately turned on and off (50% duty cycle). This study illustrates how a finite element model could be used to evaluate alternative protocols for heating a tumor of a specific geometry and to evaluate thermally induced damage to surrounding normal tissue.     

A second-order finite element algorithm for solving the three-dimensional EEG forward problem

A finite element algorithm has been developed to solve the electroencephalogram (EEG) forward problem. A new computationally efficient approach to calculate the stiffness matrix of second-order tetrahedral elements has been developed for second-order tetrahedral finite element models. The present algorithm has been evaluated by means of computer simulations, by comparing with analytic solutions in a multi-spheres concentric head model. The developed finite element method (FEM) algorithm has also been applied to address questions of interest in the EEG forward problem. The present simulation study indicates that the second-order FEM provides substantially enhanced numerical accuracy and computational efficiency, as compared with the first-order FEM for comparable numbers of tetrahedral elements. The anisotropic conductivity distribution of the head tissue can be taken into account in the present FEM algorithm. The effects of dipole eccentricity, size of finite elements and local mesh refinement on solution accuracy are also addressed in the present simulation study.     

Thermal effects of radiation from cellular telephones

A finite element thermal model of the head has been developed to calculate temperature rises generated in the brain by radiation from cellular telephones and similar electromagnetic devices. A 1 mm resolution MRI dataset was segmented semiautomatically, assigning each volume element to one of ten tissue types. A finite element mesh was then generated using a fully automatic tetrahedral mesh generator developed at NRPB. There are two sources of heat in the model: firstly the natural metabolic heat production; and secondly the power absorbed from the electromagnetic field. The SAR was derived from a finite difference time domain model of the head, coupled to a model 'mobile phone', namely a quarter-wavelength antenna mounted on a metal box. The steady-state temperature distribution was calculated using the standard Pennes 'bioheat equation'. In the normal cerebral cortex the high blood perfusion rate serves to provide an efficient cooling mechanism. In the case of equipment generally available to the public, the maximum temperature rise found in the brain was about 0.1 degrees C. These results will help in the further development of criteria for exposure guidelines, and the technique developed may be used to assess temperature rises associated with SARs for different types of RF exposure.     

基于有限元法的人类头部损伤生物力学的模拟分析

根据正常头部螺旋CT扫描影像，通过对CT扫描影像的图像处理，利用计算机辅助工程技术，采用单元网格划分和三维重构技术，开发、建立了三维的人类头部有限元计算模型。应用本模型模拟颅脑在直接碰撞中的生物力学问题。计算模型比较真实地反映了头颅实际碰撞实验中的物理反应，比较忠实地再现了某些实验的结果，如头部撞击合力和脑压力/强等。同时，脑压力，强的分布再次证实了经典的撞击压-对撞压产生理论。本研究的计算模型可为进一步的头部损伤生物力学研究提供一种新的工具。     

Geometric modeling of the human torso using cubic hermite elements

We discuss the advantages and problems associated with fitting geometric data of the human torso obtained from magnetic resonance imaging, with high-order (bicubic Hermite) surface elements. These elements preserve derivative (C ¹) continuity across element boundaries and permit smooth anatomically accurate surfaces to be obtained with relatively few elements. These elements are fitted to the data with a new nonlinear fitting procedure that minimizes the error in the fit while maintainingC ¹ continuity with nonlinear constraints. Nonlinear Sobelov smoothing is also incorporated into this fitting scheme. The structures fitted along with their corresponding root meansquared error, number of elements used, and number of degrees of freedom (df) per variable are: epicardium (0.91 mm, 40 elements, 142 df), left lung (1.66 mm, 80 elements, 309 df), right lung (1.69 mm, 80 elements, 309 df), skeletal muscle surface (1.67 mm, 264 elements, 1,010 df), fat layer (1.79 mm, 264 elements, 1,010 df), and the skin layer (1.43 mm, 264 elements, 1,010 df). The fitted surfaces are assembled into a combined finite element/boundary element model of the torso in which the exterior surfaces of the heart and lungs are modeled with two-dimensional boundary elements and the layers of the skeletal muscle, fat, and skin are modeled with finite elements. The skeletal muscle and fat layers are modeled with bicubic Hermite linear elements and are obtained by joining the adjacent surface elements for each layer. Applications for the torso model include the forward and inverse problems of electrocardiography, defibrillation studies, radiation dosage studies, and heat transfer studies.     

Finite element solution of steady state temperature distribution in the human torso

A finite element model of the steady state temperature distribution in the human torso is developed. The torso is approximated by a circular cylinder of core surrounded by a layer of muscle and insulating layers of fat and skin. The model is simplified by neglecting longitudinal heat flow. The region occupied by a circular cross-section of the torso is discretized into a mesh of triangles and the boundary of the torso, that is, the skin surface, is consequently approximated by a polygon. The elliptic partial differential equation governing the steady state temperature distribution, together with the associated boundary conditions, are expressed in equivalent variational form. Linear basis functions are used and the resulting integral is minimized over the region bounded by the approximating polygon. Results for two numerical experiments are determined by solving systems of linear equations.     

Generation of an Anatomically Based Geometric Coronary Model

A discrete anatomically accurate finite element model of the largest six generations of the coronary arterial network is developed. Using a previously developed anatomically accurate model of ventricular geometry the boundaries of the coronary mesh are defined from measured epicardial coronaries. Network topology is then generated stochastically from published anatomical data. Spatial information is added to this topological data using an avoidance algorithm accounting for global network geometry and optimal local branch angle properties. The generated vessel lengths, radii and connectivity are consistent with the published studies and a relativity even spatial distribution of vessels within the ventricular mesh is achieved. The local finite element coordinates of the coronary nodes within the ventricular mesh are calculated such that the coronary geometry can be recalculated within a deformed ventricular mesh. © 2000 Biomedical Engineering Society. PAC00: 8710+e, 8718Bb, 0270Dh     

Heterogeneous meshing and biomechanical modeling of human spine

We aim to develop a patient-specific biomechanical model of human spine for the purpose of surgical training and planning. In this paper, we describe the development of a finite-element model of the spine from the VHD Male Data. The finite-element spine model comprises volumetric elements suitable for deformation and other finite-element analysis using ABAQUS. The mesh generation solution accepts segmented radiological slices as input, and outputs three-dimensional (3D) volumetric finite element meshes that are ABAQUS compliant. The proposed mesh generation method first uses a grid plane to divide the contours of the anatomical boundaries and its inclusions into discrete meshes. A grid frame is then built to connect the grid planes between any two adjacent planes using a novel scheme. The meshes produced consist of brick elements in the interior of the contours and with tetrahedral and wedge elements at the boundaries. The nodal points are classified according to their materials and hence, elements can be assigned different properties. The resultant spine model comprises a detailed model of the 7 cervical vertebrae, 12 thoracic vertebrae, 5 lumbar vertebrae, and S1. Each of the vertebrae and intervertebral disc has between 1200 and 6000 elements, and approximately 1200 elements, respectively. The accuracy of the resultant VHD finite element spine model was good based on visual comparison of volume-rendered images of the original CT data, and has been used in a computational analysis involving needle insertion and static deformation. We also compared the mesh generated using our method against two automatically generated models; one consists of purely tetrahedral elements and the other hexahedral elements.     

非接触式灸疗温度场的估计

目的研究非接触性艾灸的温度场分布,为调控灸疗过程和提高灸疗效果提供依据。方法根据生物传热的相关理论,建立描述人体组织内部在非接触性艾灸时的温度场理论模型,并据此推导当艾灸强度确定时,影响该温度场分布的体内异常热源深度与施灸处皮肤温度的对应关系。结果在不同艾灸强度下,根据对应关系计算出的结果与有限元的分析结果进行比较,结果显示对体内异常热源深度的估测结果与有限元仿真分析结果十分接近。而组织内部温度场理论模型的正确性也得到了物理实验的验证。结论本文提出的根据人体皮肤表面温度和艾灸强度估计体内异常热源的深度信息,继而估计出组织内温度场的方法具有一定的适用性,将有助于临床灸疗的方案设计。     

Adaptive Macro Finite Elements for the Numerical Solution of Monodomain Equations in Cardiac Electrophysiology

Many problems in Biology and Engineering are governed by anisotropic reaction–diffusion equations with a very rapidly varying reaction term. This usually implies the use of very fine meshes and small time steps in order to accurately capture the propagating wave while avoiding the appearance of spurious oscillations in the wave front. This work develops a family of macro finite elements amenable for solving anisotropic reaction–diffusion equations with stiff reactive terms. The developed elements are incorporated on a semi-implicit algorithm based on operator splitting that includes adaptive time stepping for handling the stiff reactive term. A linear system is solved on each time step to update the transmembrane potential, whereas the remaining ordinary differential equations are solved uncoupled. The method allows solving the linear system on a coarser mesh thanks to the static condensation of the internal degrees of freedom (DOF) of the macroelements while maintaining the accuracy of the finer mesh. The method and algorithm have been implemented in parallel. The accuracy of the method has been tested on two- and three-dimensional examples demonstrating excellent behavior when compared to standard linear elements. The better performance and scalability of different macro finite elements against standard finite elements have been demonstrated in the simulation of a human heart and a heterogeneous two-dimensional problem with reentrant activity. Results have shown a reduction of up to four times in computational cost for the macro finite elements with respect to equivalent (same number of DOF) standard linear finite elements as well as good scalability properties.     

Influence of mesh density,cortical thickness and material properties on human rib fracture prediction

The purpose of this paper was to investigate the sensitivity of the structural responses and bone fractures of the ribs to mesh density, cortical thickness, and material properties so as to provide guidelines for the development of finite element (FE) thorax models used in impact biomechanics. Subject-specific FE models of the second, fourth, sixth and tenth ribs were developed to reproduce dynamic failure experiments. Sensitivity studies were then conducted to quantify the effects of variations in mesh density, cortical thickness, and material parameters on the model-predicted reaction force–displacement relationship, cortical strains, and bone fracture locations for all four ribs. Overall, it was demonstrated that rib FE models consisting of 2000–3000 trabecular hexahedral elements (weighted element length 2–3 mm) and associated quadrilateral cortical shell elements with variable thickness more closely predicted the rib structural responses and bone fracture force–failure displacement relationships observed in the experiments (except the fracture locations), compared to models with constant cortical thickness. Further increases in mesh density increased computational cost but did not markedly improve model predictions. A ±30% change in the major material parameters of cortical bone lead to a ?16.7 to 33.3% change in fracture displacement and ?22.5 to +19.1% change in the fracture force. The results in this study suggest that human rib structural responses can be modeled in an accurate and computationally efficient way using (a) a coarse mesh of 2000–3000 solid elements, (b) cortical shells elements with variable thickness distribution and (c) a rate-dependent elastic–plastic material model.     

Advanced modeling strategy for the analysis of heart valve leaflet tissue mechanics using high-order finite element method

Modeling soft tissue using the finite element method is one of the most challenging areas in the field of biomechanical engineering. To date, many models have been developed to describe heart valve leaflet tissue mechanics, which are accurate to some extent. Nevertheless, there is no comprehensive method to modeling soft tissue mechanics, This is because (1) the degree of anisotropy in the heart valve leaflet changes layer by layer due to a variety of collagen fiber densities and orientations that cannot be taken into account in the model and also (2) a constitutive material model fully describing the mechanical properties of the leaflet structure is not available in the literature. In this framework, we develop a new high-order element using p-type finite element formulation to create anisotropic material properties similar to those of the heart valve leaflet tissue in only one single element. This element also takes the nonlinearity of the leaflet tissue into consideration using a bilinear material model. This new element is composed a two-dimensional finite element in the principal directions of leaflet tissue and a p-type finite element in the direction of thickness. The proposed element is easy to implement, much more efficient than standard elements available in commercial finite element packages. This study is one step towards the modeling of soft tissue mechanics using a meshless finite element approach to be applied in real-time haptic feedback of soft-tissue models in virtual reality simulation.     

Measurement of skin dose variations produced by a silicon-based protective dressing in radiotherapy

Variations in skin dose caused by a silicon-based burn dressing used in radiotherapy during treatment have been investigated. Measurement of these variations in skin dose has been achieved using thermoluminescent dosimeters (TLDs) and Gafchromic film. For a 6 MV x-ray beam results have shown that an approximately 0.4 mm thick silicon mesh dressing increases the average surface dose by approximately 12.5% to 14% of the maximum and average dose at 1 mm depth and by 4% to 6% of the maximum for field sizes ranging from 5 cm x 5 cm up to 40 cm x 40 cm at 100 cm source to surface distance (SSD). The radiation effective thickness of the silicon dressing was calculated to be 0.5 mm +/- 0.05 mm water equivalent. TLDs of various thicknesses provide point-dose assessment and Gafchromic film can provide a detailed two-dimensional dose map with a high spatial resolution. Results have shown that a large variation in skin dose is delivered under the dressing depending on the amount of material directly above it as defined by the silicon mesh outline.     

儿童肱骨三维有限元建模及验证

背景：有限元数值模拟力学实验方法是对人体进行生物力学结构研究的有效手段。 目的：建立正常6岁健康儿童肱骨的三维有限元模型。 方法：使用某6岁儿童志愿者的人体CT数据,导入到Mimics 10.01软件中,应用阈值分割的方法进行肱骨三维重建。运用Geomagic Studio 12.0对模型表面进行表面优化处理及曲面片的划分,然后使用TrueGrid软件进行网格划分,最后对其进行材料属性赋值,完成有限元模型的构建。施加边界条件及约束,模拟肱骨的三点弯曲试验,输出模拟结果。 结果与结论：建立完成的肱骨有限元模型包括3 024个节点,8节点六面体单元1 875个,实验分别加载0.01 m/s和3 m/s的动态载荷,肱骨中部均发生断裂,载荷-位移曲线与尸体试验结果近似。模拟结果显示,儿童肱骨的有限元模型仿真结果与尸体试验结果较为接近,有限元仿真法可以很好的模拟人体骨骼的物理特性。     

颈椎椎体次全切除，钛网植骨钢板固定三维有限元模型的建立

目的 探讨利用螺旋 CT建立颈椎椎体次全切除减压植骨固定的三维有限元模型的高度数字化方法,为研究颈椎减压手术的生物力学实验提供标准模型。方法 对健康成年男性志愿者进行CT 扫描,获得C4～C7节段的断层图片,将数据保存为Dicom格式,导入Mimics 9.1 软件进行三维几何模型重建,形成三维图像,利用Freeform 软件进行模型修改和表面划分,以IGES格式转入有限元软件Ansys 9.0完成颈椎骨性模型的建立。利用有限元软件Ansys 9.0,在颈椎骨性模型的基础上,补建终板、补充建立终板、 椎间盘、 髓核、 前纵韧带、 后纵韧带、 黄韧带、 棘间韧带、 棘上韧带等结构。然后模拟颈椎椎体次全切除,将C5椎体、前纵韧带、上下椎间盘切除,将建立的钛网、钢板实体模型添加到减压区。采用合适的材料性质和实体单元类型对模型进行有限元网格划分。结果 颈椎脊柱三维模型有限元网格划分结果：利用三维重建软件Mimics 和有限元软件Ansys 9.0 , 成功进行椎体次全切除减压钛网植骨钢板固定三维模型有限元网格划分。整个模型共有138995个节点和94039个单元,建成后的三维有限元模型与实体组织具有良好的几何相似性。结论 建立的椎体次全切除植骨固定手术三维有限元模型接近真实的生物力学标本,可以进行临床和实验研究。     

Statistical modelling of the whole human femur incorporating geometric and material properties

When analysing the performance of orthopaedic implants the vast majority of computational studies use either a single or limited number of bone models. The results are then extrapolated to the population as a whole, overlooking the inherent and large interpatient variability in bone quality and geometry. This paper describes the creation of a three dimensional, statistical, finite element analysis (FEA) ready model of the femur using principal component analysis. To achieve this a registration scheme based on elastic surface matching and a mesh morphing algorithm has been developed. This method is fully automated enabling registration and generation of high resolution models. The variation in both geometry and material properties was extracted from 46 computer tomography scans and captured by the statistical model. Analysis of mesh quality showed this was maintained throughout the model generation and sampling process. Reconstruction of the training femurs showed 35 eigenmodes were required for accurate reproduction. A set of unique, anatomically realistic femur models were generated using the statistical model, with a variation comparable to that seen in the population. This study illustrates a methodology with the potential to generate femur models incorporating material properties for large scale multi-femur finite element studies.     

Development of a Parametric Clavicle Finite Element Model Using Principal Component Analysis and Mesh Morphing Algorithm

The susceptibility of the clavicle to injury underscores its role as an important loading path during both frontal impact and side impact crashes, since clavicle is loaded directly by shoulder belt in frontal impact and through shoulder in lateral impact crashes. This study aims to developing a parametric clavicle finite element model capable of simulating impact responses with different parameters. A statistical clavicle geometry model was developed based on computed tomography(CT) scans from 89 subjects using principal component analysis(PCA) and multivariate regression analysis. Using this statistical clavicle geometry model and mesh morphing method developed in this study, a series of detailed 3D clavicle geometries were predicted by age, gender, and length of the bone, all of which showed strong effects on clavicle geometry. After assigning material properties and validation process, this parametric model developed in this study can be used to investigate the effects of age, gender and length at the same time.     

Mapping Melanoma Lymphoscintigraphy Data onto a 3D Anatomically Based Model

This study describes three-dimensional (3D) visualization of two-dimensional (2D) melanoma lymphatic mapping data, to provide a framework for analysis of melanoma spread patterns and a platform for recording new lymphoscintigraphy (LS) data more accurately in 3D. Specifically, the Sydney Melanoma Unit’s LS database of over 5000 patients’ primary cutaneous melanoma sites and sentinel lymph nodes have been mapped from 2D images onto a 3D anatomically based model. Anatomically accurate model geometries were created using the Visible Human dataset, giving a bicubic finite element skin mesh and discrete sentinel lymph node model. The full dataset of 2D melanoma site coordinates, excluding the head and neck, has been transformed onto this 3D skin mesh via free-form deformation and projection techniques. Sentinel lymph nodes were mapped onto the generic lymph node model for each patient. Preliminary spatial analysis indicates that a patient with a primary melanoma on the torso around the waist (on the standardized 3D model this region is 180 mm above and 130 mm below the umbilicus) with lymphatic drainage to the left axilla or left groin, will have a 17.7% probability of dual drainage to both node fields, with 95% confidence limits between 14.5 and 21.0%.