Improving the local solution accuracy of large-scale digital image-based finite element analyses

Digital image-based finite element modeling (DIBFEM) has become a widely utilized approach for efficiently meshing complex biological structures such as trabecular bone. While DIBFEM can provide accurate predictions of apparent mechanical properties, its application to simulate local phenomena such as tissue failure or adaptation has been limited by high local solution errors at digital model boundaries. Furthermore, refinement of digital meshes does not necessarily reduce local maximum errors. The purpose of this study was to evaluate the potential to reduce local mean and maximum solution errors in digital meshes using a post-processing filtration method. The effectiveness of a three-dimensional, boundary-specific filtering algorithm was found to be mesh size dependent. Mean absolute and maximum errors were reduced for meshes with more than five elements through the diameter of a cantilever beam considered representative of a single trabecula. Furthermore, mesh refinement consistently decreased errors for filtered solutions but not necessarily for non-filtered solutions. Models with more than five elements through the beam diameter yielded absolute mean errors of less than 15% for both Von Mises stress and maximum principal strain. When applied to a high-resolution model of trabecular bone microstructure, boundary filtering produced a more continuous solution distribution and reduced the predicted maximum stress by 30%. Boundary-specific filtering provides a simple means of improving local solution accuracy while retaining the model generation and numerical storage efficiency of the DIBFEM technique.     

2D calculation method based on composite beam theory for the determination of local homogenised stiffnesses of long bones

A calculation method using the finite element technique is presented. Its main objective was to determine strains, stresses and more particularly stiffnesses in any cross section of a tibia, thus enabling the localisation of tibial torsion in vivo. Each tibial cross section was considered to be a non-uniform cross section of a composite beam with arbitrary orientation of fibres. The determination of stresses, strains and stiffnesses within a composite beam cross section has been defined by solving a variational problem. The validation of this method was performed on a tibial diaphysis of which each cross section was assumed to be the cross section of a composite beam made of orthotropic materials with orthotropic axes of any orientation with respect to the principal axis of the bone. The comparison of the results, from our model and that of a three-dimensional one, was performed on each nodal value (strains, stresses) of the meshed cross section as it was impossible to obtain local stiffnesses by experimentation. The good agreement between the results has validated our finite element program. Actually, this method has enabled to treat directly 2D geometric reconstructions from CT scan images with a good accuracy to determine locally the homogenised mechanical characteristics of human tibia in vivo, and particularly to quantify torsional tibial abnormalities of children without approximation of the shape of the cross section and by calculating the real moment of inertia J. The importance of the fibre orientation with regards to the stiffness values has been emphasised. This 2D method has also allowed to reduce CPU time of the 3D modelling and calculation.     

Theoretical Study on the Dynamic Behavior of a Plate-Like Micro-Cantilever with Multiple Particles Attached

In this study, the dynamic characteristics of a plate-like micro-cantilever beam attached with multiple concentrated masses are studied. The vibration modes of the cantilever plate are represented by combinations of beam functions. Using classical mechanics (the effect of size is not considered) and the corrected Cosserat’s theorem (the effect of size is considered), we employ the Lagrange equations to establish a dynamic model of the plate-like micro-cantilever beam attached with multiple concentrated masses. The accuracy of the model proposed in this paper is verified by comparing with the results of published literature. Then, the natural frequencies of the cantilever plates are calculated with self-compiled algorithms, and the results of the plates with 1–5 masses are displayed. The results are in high accordance with the exact solution, and all errors are within 0.5%. The analysis shows that the proposed model and analysis method converges quickly and is highly efficient. In addition, the effects of characteristic lengths, Poisson''s ratios and plate thickness on the micro-cantilever plate’s resonant frequency for the first five modes are analyzed.     

Scanning gel chromatography: determination of transport parameters from dynamic profiles measured at low solute concentration

Direct optical scanning of solute boundaries in large zone gel Chromatography experiments provides an accurate means of determining boundary profile shapes and rates of motion. A method has been developed for correcting such boundaries to a constant time frame, eliminating the distortion which arises from finite column scanning rate Centroids or the corrected profiles can be used to determine the partition cross section for the solute of interest The partition cross section and flow rate determine translational motion within the column. The axial dispersion coefficient, L, which characterizes rate of boundary spreading may also be calculated from the profiles. In order to explore these procedures a study of four noninteracting solutes was conducted. Partition cross sections determined from rates of motion of boundary centroids were found to be in good agreement with those determined by the equilibrium saturation method on the same column.In order to explore the lowest concentration limits of the technique and to illustrate the boundary characteristics for a selfassociating solute, a study of carboxyhemoglobin was conducted over a wide concentration range. From measurements at 220 nm the lowest concentration where useful data could be obtained was 2 micrograms per ml (0.12 πM heme) These results establish validity of the procedures used in analyzing the rates of boundary transport and in studying solute transport over a wide range of conditions.     

Computational method for muscle-path representation in musculoskeletal models

 This paper presents a new and efficient method to calculate the line-of-action of a muscle as it wraps over bones and other tissues on its way from origin to insertion. The muscle is assumed to be a one-dimensional, massless, taut string, and the surfaces of bones that the muscle may wrap around are approximated by cross-sectional boundaries obtained by slicing geometrical models of bones. Each cross-sectional boundary is approximated by a series of connected line segments. Thus, the muscle path to be calculated is piecewise linear with vertices being the contact points on the cross-sectional boundaries of the bones. Any level of geometric accuracy can be obtained by increasing the number of cross sections and the number of line segments in each cross section. The algorithm is computationally efficient even for large numbers of cross sections. Received: 9 July 2001 / Accepted in revised form: 11 March 2002     

Three-dimensional modeling of the cochlea by use of an arc fitting approach

Purpose: A cochlea modeling approach is presented allowing for a user defined degree of geometry simplification which automatically adjusts to the patient specific anatomy. Model generation can be performed in a straightforward manner due to error estimation prior to the actual generation, thus minimizing modeling time. Therefore, the presented technique is well suited for a wide range of applications including finite element analyses where geometrical simplifications are often inevitable. Methods: The method is presented for n=5 cochleae which were segmented using a custom software for increased accuracy. The linear basilar membrane cross sections are expanded to areas while the scalae contours are reconstructed by a predefined number of arc segments. Prior to model generation, geometrical errors are evaluated locally for each cross section as well as globally for the resulting models and their basal turn profiles. The final combination of all reconditioned features to a 3D volume is performed in Autodesk Inventor using the loft feature. Results: Due to the volume generation based on cubic splines, low errors could be achieved even for low numbers of arc segments and provided cross sections, both of which correspond to a strong degree of model simplification. Model generation could be performed in a time efficient manner. Conclusion: The proposed simplification method was proven to be well suited for the helical cochlea geometry. The generated output data can be imported into commercial software tools for various analyses representing a time efficient way to create cochlea models optimally suited for the desired task.     

Image-based axon model highlights heterogeneity in initiation of damage

Head injury simulations predict the occurrence of traumatic brain injury by placing a threshold on the calculated strains for axon tracts within the brain. However, a current roadblock to accurate injury prediction is the selection of an appropriate axon damage threshold. While several computational studies have used models of the axon cytoskeleton to investigate damage initiation, these models all employ an idealized, homogeneous axonal geometry. This homogeneous geometry with regularly spaced microtubules, evenly distributed throughout the model, overestimates axon strength because, in reality, the axon cytoskeleton is heterogeneous. In the heterogeneous cytoskeleton, the weakest cross section determines the initiation of failure, but these weak spots are not present in a homogeneous model. Addressing one source of heterogeneity in the axon cytoskeleton, we present a new semiautomated image analysis pipeline for using serial-section transmission electron micrographs to reconstruct the microtubule geometry of an axon. The image analysis procedure locates microtubules within the images, traces them throughout the image stack, and reconstructs the microtubule structure as a finite element mesh. We demonstrate the image analysis approach using a C. elegans touch receptor neuron due to the availability of high-quality serial-section transmission electron micrograph data sets. The results of the analysis highlight the heterogeneity of the microtubule structure in the spatial variation of both microtubule number and length. Simulations comparing this image-based geometry with homogeneous geometries show that structural heterogeneity in the image-based model creates significant spatial variation in deformation. The homogeneous geometries, on the other hand, deform more uniformly. Since no single homogeneous model can replicate the mechanical behavior of the image-based model, our results argue that heterogeneity in axon microtubule geometry should be considered in determining accurate axon failure thresholds.     

Multiscale methodology for bone remodelling simulation using coupled finite element and neural network computation

The aim of this paper is to develop a multiscale hierarchical hybrid model based on finite element analysis and neural network computation to link mesoscopic scale (trabecular network level) and macroscopic (whole bone level) to simulate the process of bone remodelling. As whole bone simulation, including the 3D reconstruction of trabecular level bone, is time consuming, finite element calculation is only performed at the macroscopic level, whilst trained neural networks are employed as numerical substitutes for the finite element code needed for the mesoscale prediction. The bone mechanical properties are updated at the macroscopic scale depending on the morphological and mechanical adaptation at the mesoscopic scale computed by the trained neural network. The digital image-based modelling technique using μ-CT and voxel finite element analysis is used to capture volume elements representativeof 2 mm³ at the mesoscale level of the femoral head. The input data for the artificial neural network are a set of bone material parameters, boundary conditions and the applied stress. The output data are the updated bone properties and some trabecular bone factors. The current approach is the first model, to our knowledge, that incorporates both finite element analysis and neural network computation to rapidly simulate multilevel bone adaptation.     

Assessment of factors influencing finite element vertebral model predictions

This study aimed to establish model construction and configuration procedures for future vertebral finite element analysis by studying convergence, sensitivity, and accuracy behaviors of semiautomatically generated models and comparing the results with manually generated models. During a previous study, six porcine vertebral bodies were imaged using a microcomputed tomography scanner and tested in axial compression to establish their stiffness and failure strength. Finite element models were built using a manual meshing method. In this study, the experimental agreement of those models was compared with that of semiautomatically generated models of the same six vertebrae. Both manually and semiautomatically generated models were assigned gray-scale-based, element-specific material properties. The convergence of the semiautomatically generated models was analyzed for the complete models along with material property and architecture control cases. A sensitivity study was also undertaken to test the reaction of the models to changes in material property values, architecture, and boundary conditions. In control cases, the element-specific material properties reduce the convergence of the models in comparison to homogeneous models. However, the full vertebral models showed strong convergence characteristics. The sensitivity study revealed a significant reaction to changes in architecture, boundary conditions, and load position, while the sensitivity to changes in material property values was proportional. The semiautomatically generated models produced stiffness and strength predictions of similar accuracy to the manually generated models with much shorter image segmentation and meshing times. Semiautomatic methods can provide a more rapid alternative to manual mesh generation techniques and produce vertebral models of similar accuracy. The representation of the boundary conditions, load position, and surrounding environment is crucial to the accurate prediction of the vertebral response. At present, an element size of 2x2x2 mm(3) appears sufficient since the error at this size is dominated by factors, such as the load position, which will not be improved by increasing the mesh resolution. Higher resolution meshes may be appropriate in the future as models are made more sophisticated and computational processing time is reduced.     

A fluid-immersed multi-body contact finite element formulation for median nerve stress in the carpal tunnel

Carpal tunnel syndrome (CTS) is among the most important of the family of musculoskeletal disorders caused by chronic peripheral nerve compression. Despite the large body of research in many disciplinary areas aimed at reducing CTS incidence and/or severity, means for objective characterization of the biomechanical insult directly responsible for the disorder have received little attention. In this research, anatomical image-based human carpal tunnel finite element (FE) models were constructed to enable study of median nerve mechanical insult. The formulation included large-deformation multi-body contact between the nerve, the nine digital flexor tendons, and the carpal tunnel boundary. These contact engagements were addressed simultaneously with nerve and tendon fluid-structural interaction (FSI) with the synovial fluid within the carpal tunnel. The effects of pertinent physical parameters on median nerve stress were explored. The results suggest that median nerve stresses due to direct structural contact are typically far higher than those from fluid pressure.     

Correction of distortion of histologic sections of arteries

Histologic sections of arteries can be used to generate three-dimensional (3D) geometric models and identify structural constituents. However, geometric distortions are introduced by fixation, embedding and sectioning; distortions which can, for example, lead to errors in stresses predicted by finite element models. We developed a method to measure and correct for distortions caused by acrylic processing and applied it to intact, healthy porcine coronary arteries. Micro-computed tomography was used to image arteries in the fresh and embedded states. Tissue blocks were sectioned, stained and imaged using a light microscope. Each section contained four registration marks used to determine strains introduced by sectioning and staining. Using these three image sets, 3D geometric models were generated and distortions were measured. Fixation, processing, and embedding resulted in shrinkage of 6.4+/-2.3% axially and 35.4+/-5.0% in mean cross-sectional area (n=5). Shrinkage in a cross section was well characterized by a uniform, equibiaxial strain. Sectioning and staining resulted in additional compressive strains in the sectioning direction of 0.067+/-0.011 and, in the direction perpendicular to sectioning, of 0.023+/-0.005 (n=5). These strains are assumed uniform and form the basis for correcting section geometry. Reconstructions using corrections for sectioning and shrinkage-related distortions had errors of 1.6+/-0.5% (n=5) and 4.0+/-1.7% (n=5), respectively.     

Simulation of the human airways using virtual topology tools and meshing optimization

A method is proposed to improve the quality of the three-dimensional airway geometric models using a commercial software, checking the number of elements, meshing time, and aspect ratio and skewness parameters. The use of real and virtual topologies combined with patch-conforming and patch-independent meshing algorithms results in four different models being the best solution the combination of virtual topology and patch-independent algorithm, due to an excellent aspect ratio and skewness of the elements, and minimum meshing time. The result is a reduction in the computational time required for both meshing and simulation due to a smaller number of cells. The use of virtual topologies combined with patch-independent meshing algorithms could be extended in bioengineering because the geometries handling is similar to this case. The method is applied to a healthy person using their computed tomography images. The resulting numerical models are able to simulate correctly a forced spirometry.     

Large deformation analysis of orthodontic appliances

The deformations of orthodontic appliances used for space closure are large so that any mathematical analysis will require a nonlinear approach. Existing incremental finite element and finite difference numerical methods suffer from excessive computational effort when analyzing these problems. An accurate segmental technique is proposed to handle these difficulties in an extremely efficient fashion. The segmental technique starts by assuming that an orthodontic appliance is composed of a number of smaller segments, the ends of which undergo small relative rotation. With an appropriate choice of local coordinate system the equilibrium equations for each segment are linearized and solved in a straightforward manner. The segments are then assembled using geometric and force compatibility relations similar to the transfer matrix method. Consequently, the original nonlinear boundary value problem is solved as a sequence of linear initial value problems which converge to the required boundary conditions. As only one segment need be considered at a time, the computations can be performed accurately and efficiently on a PC type computer. Although an iterative solution is used to match the boundary conditions, the time required to solve a given problem ranges from a few seconds to a couple of minutes depending on the initial geometric complexity. The accuracy of the segmental technique is verified by comparison with an exact solution for an initially curved cantilever beam with an end load. In addition, comparisons are made with existing experimental and numerical results as well as with a new set of experimental data. In all cases the segmental technique is in excellent agreement with the results of these other studies.     

Validation of an efficient method of assigning material properties in finite element analysis of pelvic bone

Bone in the pelvis is a composite material with a complex anatomical structure that is difficult to model computationally. Rather than assigning material properties to increasingly smaller elements to capture detail in three-dimensional finite element (FE) models, properties can be assigned to Gauss points within larger elements. As part of a validation process, we compared experimental and analytical results from a composite beam under four-point load to FE models with material properties assigned to refined elements and Gauss points within larger elements. Both FE models accurately predicted deformation and the analytical predictions of internal shear stress.     

数字照片在树干解析上的应用

介绍了一种利用摄影测量技术开展树干解析的新方法.通过求算横截面积,换算成理论直径及年轮宽度.此法可以提高测量精度,特别是在树干横截面不规则的情况下,可以提高准确度.选择一个基本圆满的圆盘,直接测量直径和由面积换算比较年轮宽度,二者差异平均为10%,最大达32%.由于图像上直接测量的是面积,树皮的横截面可以更加准确获得,而传统的方法无法克服这个缺点.数字照片还是储存年轮信息的理想形式,便于保存和复查.本法使用的是普通的数码照片,方便适用,是开展森林精密测量简单易行手段.     

Boundaries of transcriptionally silent chromatin in Saccharomyces cerevisiae

In the budding yeast Saccharomyces cerevisiae, heterochromatic gene silencing has been found within HMR and HML silent mating type loci, the telomeres, and the rRNA-encoding DNA. There may be boundary elements that regulate the spread of silencing to protect genes adjacent to silenced domains from this epigenetic repressive effect. Many assays show that specific DNA regulatory elements separate a euchromatic locus from a neighboring heterochromatic domain and thereby function as a boundary. Alternatively, DNA-independent mechanisms such as competition between acetylated and deacetylated histones are also reported to contribute to gene insulation. However, the mechanism by which boundaries are formed is not clear. Here, the characteristics and functions of boundaries at silenced domains in S. cerevisiae are discussed.     

Nuclear fragmentation of clinical silicon beam

Heavy ions used for biomedical studies fragment when they pass through matter. It is known that different fragments cause different types of biological damage. In this paper, results pertaining to different kinds of secondary fragments produced by a 28Si beam at 463 MeV/nucleon in its interaction with nuclear emulsion are presented. It is observed that the production frequencies of secondary fragments are independent of the target. Partial production cross sections and fluences of the secondary fragments are also discussed. The partial production cross sections for different fragments at three lower energy ranges are practically the same within their statistical errors except for the cross section for Li fragments, which is larger by almost a factor of 1.5 at the lowest energy investigated. The dose contributions of the primary Si beam and its components at different points of the Bragg curve are presented for two different energy regions.     

Boundary swapping in the Drosophila Bithorax complex

Although the boundary elements of the Drosophila Bithorax complex (BX-C) have properties similar to chromatin insulators, genetic substitution experiments have demonstrated that these elements do more than simply insulate adjacent cis-regulatory domains. Many BX-C boundaries lie between enhancers and their target promoter, and must modulate their activity to allow distal enhancers to communicate with their target promoter. Given this complex function, it is surprising that the numerous BX-C boundaries share little sequence identity. To determine the extent of the similarity between these elements, we tested whether different BX-C boundary elements can functionally substitute for one another. Using gene conversion, we exchanged the Fab-7 and Fab-8 boundaries within the BX-C. Although the Fab-8 boundary can only partially substitute for the Fab-7 boundary, we find that the Fab-7 boundary can almost completely replace the Fab-8 boundary. Our results suggest that although boundary elements are not completely interchangeable, there is a commonality to the mechanism by which boundaries function. This commonality allows different DNA-binding proteins to create functional boundaries.     

SnapDRAGON: a method to delineate protein structural domains from sequence data

We describe a method to identify protein domain boundaries from sequence information alone based on the assumption that hydrophobic residues cluster together in space. SnapDRAGON is a suite of programs developed to predict domain boundaries based on the consistency observed in a set of alternative ab initio three-dimensional (3D) models generated for a given protein multiple sequence alignment. This is achieved by running a distance geometry-based folding technique in conjunction with a 3D-domain assignment algorithm. The overall accuracy of our method in predicting the number of domains for a non-redundant data set of 414 multiple alignments, representing 185 single and 231 multiple-domain proteins, is 72.4 %. Using domain linker regions observed in the tertiary structures associated with each query alignment as the standard of truth, inter-domain boundary positions are delineated with an accuracy of 63.9 % for proteins comprising continuous domains only, and 35.4 % for proteins with discontinuous domains. Overall, domain boundaries are delineated with an accuracy of 51.8 %. The prediction accuracy values are independent of the pair-wise sequence similarities within each of the alignments. These results demonstrate the capability of our method to delineate domains in protein sequences associated with a wide variety of structural domain organisation.