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Measuring the nonlinear elastic properties of tissue-like phantoms.

A direct mechanical system simultaneously measuring external force and deformation of samples over a wide dynamic range is used to obtain force-displacement curves of tissue-like phantoms under plain strain deformation. These measurements, covering a wide deformation range, then are used to characterize the nonlinear elastic properties of the phantom materials. The model assumes incompressible media, in which several strain energy potentials are considered. Finite-element analysis is used to evaluate the performance of this material characterization procedure. The procedures developed allow calibration of nonlinear elastic phantoms for elasticity imaging experiments and finite-element simulations.

Adult↗

An analysis of the complete strain field within Flexercell membranes.

The purpose of the current investigation was to use finite element analysis to quantify the complete strain field for the membranes of the Flexercell apparatus, a device extensively used to study the effects of mechanical loading on cultured cells. Four vacuum pressure simulations were run for the membrane for both the uniaxial and biaxial loading post, yielding the distribution of longitudinal (Exx) and transverse (Eyy) strain for the uniaxial post, and the radial (Err) and the circumferential (Ethetatheta) strain for the biaxial post. The discrete values of each strain were evaluated at the center of the loading post as well as the region off of the post. Experimental measurements were made for both types of loading posts in order to validate our simulations. The biaxial post simulation was found to provide a central circular region of equal and constant Err and Ethetatheta in the membrane on the post. Likewise, the uniaxial post simulation provided a definitive region of constant Exx for a central rectangular region on the post. For the uniaxial simulation, the region on the post resulted in small compressive Eyy, while the region off the post resulted in tensile Eyy. The biaxial simulation resulted in large tensile Err and Ethetatheta on the post, while the region off the post resulted in large Err and smaller Ethetatheta. Our simulations were reasonably consistent with the experimental measurements made for both types of loading posts. We believe that the results of this study will allow scientists to more accurately describe the response of cells to known strains on all portions of the membrane, thus increasing the range of known strain regions for investigation in the Flexercell apparatus.

Biomechanical Phenomena↗

Development of an integrated CAD-FEA process for below-knee prosthetic sockets.

BACKGROUND: Computer-aided design and manufacturing has been successfully used in prosthetic applications since 1980s. It simplifies the socket rectification process and improves reproducibility but does not introduce any new principle into socket design. Integrating finite element analysis to CAD will provide a more objective assessment of socket fit and improve the chance of a successful first fitting. METHODS: Current study aims to establish a finite element model generation technique directly from geometrical information of commercial prosthetic CAD workstation. A program developed in-house automatically performs meshing of the stump geometry and assigns suitable material properties, load and boundary conditions to the model. The model was validated by comparing predicted pressure with experimentally measured values for one amputee subject. FINDINGS: The predicted pressure distribution has an root-mean-square error of 8.8 kPa compared to experimental values at 10%, 25% and 50% of the gait cycle. INTERPRETATION: Current method was able to develop a finite element model to predict interface pressure reasonably well and can be integrated with prosthetic CAD system to provide quantitative feedback to the prosthetist in an automated process.

Artificial Limbs↗

Assessing mechanical function of the zygomatic region in macaques: validation and sensitivity testing of finite element models.

Crucial to the interpretation of the results of any finite element analysis of a skeletal system is a test of the validity of the results and an assessment of the sensitivity of the model parameters. We have therefore developed finite element models of two crania of Macaca fascicularis and investigated their sensitivity to variations in bone material properties, the zygomatico-temporal suture and the loading regimen applied to the zygomatic arch. Maximum principal strains were validated against data derived from ex vivo strain gauge experiments using non-physiological loads applied to the macaque zygomatic arch. Elastic properties of the zygomatic arch bone and the zygomatico-temporal suture obtained by nanoindentation resulted in a high degree of congruence between experimental and simulated strains. The findings also indicated that the presence of a zygomatico-temporal suture in the model produced strains more similar to experimental values than a completely separated or fused arch. Strains were distinctly higher when the load was applied through the modelled superficial masseter compared with loading an array of nodes on the arch. This study demonstrates the importance of the accurate selection of the material properties involved in predicting strains in a finite element model. Furthermore, our findings strongly highlight the influence of the presence of craniofacial sutures on strains experienced in the face. This has implications when investigating craniofacial growth and masticatory function but should generally be taken into account in functional analyses of the craniofacial system of both extant and extinct species.

Animals↗

Conduction analysis of cement interface temperature in total knee arthroplasty.

We applied an axisymmetric model of the tibia to a finite element method and analyzed the heat conduction from bone cement in total knee arthroplasty using numerical simulation with the finite element analysis software, ABACUS. We hypothesized the thermal necrotic map of bone. Moreover, we suggested a method for preventing thermal necrosis of bone using this simulation. We adopted an initial temperature of 32?C and a cement layer of 3mm to our simulation and analyzed heat conduction. The maximum temperature into the cement layer was 65?C and 56?C at the bone-cement interface 200 sec after the start of heat generation. Bone necrosis was observed approximately 2mm from the bone-cement interface. To thin the cement layer, the maximum temperature and bone necrotic area reduced. At a cement layer of less than 1mm no bone necrotic area was observed. To lower the initial temperature of the bone surface, the maximum temperature and bone necrotic area was also reduced. At an initial temperature of less than 28?C we did not find any bone necrosis. Even if we hypothesized pouring cold water around the prosthesis, the maximum temperature did not reduce at any time, neither did the necrotic area reduce. We should make the cement layer as thin as possible and cool the bone before cementing to prevent thermal bone necrosis.

Arthroplasty, Replacement, Knee↗

Experimental and finite element study of a human mandible.

Knowledge of the complex biomechanical behaviour of the human mandible is of great importance in various clinical situations. Various approaches can be used to evaluate the physical behaviour of bony specimens. In the course of this study, we investigated mandibular deformation under mechanical loads in an experimental setting and compared them with results derived from finite element analysis (FEA). A special apparatus was developed to apply various forces under defined conditions on an explanted human mandible in vitro. Strains on the surface of the mandible were measured with strain gauges and subsequently a voxel based finite element mesh was generated. Strain patterns of the mandible were calculated in the FE analysis and matched with the experimental data. Comparing the numerical with the experimental data, we found a good correlation between in vitro measurements and mathematical modelling (correlation coefficient = 0.992). Then the FE model was used to evaluate mandibular biomechanics relative to aspects of load transfer, stress distribution and displacements. It is concluded that the applied procedure of generating the FE model is a valid and accurate, non-invasive method to predict different parameters of the complex biomechanical behaviour of human mandibles.

Biomechanical Phenomena↗

Analysis of three-dimensional software EIT (electrical impedance tomography) phantoms by the finite element method.

In electrical impedance tomography, two-dimensional (2D) finite element solutions are used in the imaging algorithms. It is assumed that a major part of the current flowing through the object is restricted to the measurement plane (i.e. the plane determined by the electrodes which are used for measuring voltage differences) and the current flowing elsewhere is negligible. However, there is usually a three-dimensional (3D) variation of the conductivity distribution and if there are regions of high contrast close to the measurement plane, the measured voltage values may be considerably affected. In this work a 3D finite element analysis is utilised to demonstrate the previously mentioned effects. Examples are given to show the measured voltage differences for conductivity distributions which are identical on the measurement plane but different elsewhere.

Algorithms↗

Measurement of cancellous bone strain during mechanical tests using a new extensometer device.

A device for measuring mid-substance strain in bone during uniaxial compression was developed with special attention to subsequent FE modelling. It is based on dual instrumented cantilever arms that measure the difference in tip-to-tip deflection. The so-called extensometer device was compared to two standard methods of measuring strain based on platen measurements. The extensometer device output was highly linear with tip deflection (r(2)>0.99), and contact of the devices with the specimen was optimized by using an axial distribution of three devices fixed in a free-floating jig. Deflection of the extensometer arms was accurate to 4.8 microm, and precision was between 2-5 microm. Tests included measuring rubber test specimens and cylindrical cancellous bone cores extracted from canine femoral condyles. A trend of decreasing apparent modulus with decreasing strain rate was evident with the extensometer technique. Correlation between the extensometer method and the other two methods was r(2)=0.55. The measure of mid-substance strain avoids non-linearities in the compression tests caused by early failure at the specimen ends, and the uniaxial testing conditions result in boundary conditions that are well suited for subsequent finite element analysis.

Animals↗

The influence of specimen attachment and dimension on microtensile strength.

The higher microtensile bond strength values found for specimens with a smaller cross-sectional area are often explained by the lower occurrence of internal defects and surface flaws. We hypothesized that this aberrant behavior is mainly caused by the lateral way of attachment of the specimens to the testing device, which makes the strength dependent on the thickness. This study showed that composite bars of 1x1x10, 1x2x10, and 1x3x10mm attached at their 1-mm-wide side (situation A) fractured at loads of the same magnitude, as a result of which the microtensile strength ( micro TS), calculated as F/A (force at fracture/cross-sectional area), significantly increased for specimens with decreasing thickness. Attachment at the 1-, 2-, or 3-mm-wide side (situation B) resulted in equal micro TS values (P > 0.05). Finite element analysis showed different stress patterns for situation A, but comparable patterns for situation B. Both situations showed the same maximum stress at fracture.

Analysis of Variance↗

Gait cycle finite element comparison of rotating-platform total knee designs.

Functional load transmission and kinematic performance were compared for standard versus posterior-stabilized versions of a rotating-platform total knee implant, over a standardized loading cycle, using three-dimensional contact finite element analysis. These two design variants differ primarily in terms of the latter's polyethylene insert having a cam that engages with the femoral component during appreciable flexion, thereby inducing femoral component rollback. The finite element model, previously validated experimentally, afforded direct comparisons of anterior lift-off of the insert from the tibial tray, of bearing mobility (insert rotation about the pivot post), of femoral rollback, and of metal-on-polyethylene contact stresses at the bearing and backside surfaces of the insert. Both design variants generally performed comparably, exhibiting an internal and external rotation range of approximately 5 degrees, approximately 1.5 mm peak lift-off at the anterior aspect of the insert, and approximately 15 mm of posterior rollback, the respective maxima for both designs occurring at approximately the same instants in the gait cycle. However, the posterior-stabilized design had slightly more rollback, and slightly less anterior lift-off and rotation, than did the standard rotating-platform design. Peak polyethylene stresses occurred on the backside of the insert near the posterior edge of the medial compartment, the magnitude being approximately 18% higher for the posterior-stabilized design (21 MPa) than for the standard design.

Finite Element Analysis↗

Invariant formulation for dispersed transverse isotropy in aortic heart valves: an efficient means for modeling fiber splay.

Most soft tissues possess an oriented architecture of collagen fiber bundles, conferring both anisotropy and nonlinearity to their elastic behavior. Transverse isotropy has often been assumed for a subset of these tissues that have a single macroscopically-identifiable preferred fiber direction. Micro-structural studies, however, suggest that, in some tissues, collagen fibers are approximately normally distributed about a mean preferred fiber direction. Structural constitutive equations that account for this dispersion of fibers have been shown to capture the mechanical complexity of these tissues quite well. Such descriptions, however, are computationally cumbersome for two-dimensional (2D) fiber distributions, let alone for fully three-dimensional (3D) fiber populations. In this paper, we develop a new constitutive law for such tissues, based on a novel invariant theory for dispersed transverse isotropy. The invariant theory is derived from a novel closed-form 'splay invariant' that can easily handle 3D fiber populations, and that only requires a single parameter in the 2D case. The model fits biaxial data for aortic valve tissue as accurately as the standard structural model. Modification of the fiber stress-strain law requires no reformulation of the constitutive tangent matrix, making the model flexible for different types of soft tissues. Most importantly, the model is computationally expedient in a finite-element analysis, demonstrated by modeling a bioprosthetic heart valve.

Anisotropy↗

Three dimensional stereolithography models of cancellous bone structures from muCT data: testing and validation of finite element results.

Stereolithography (STL) models of complex cancellous bone structures have been produced from three-dimensional micro-computed tomography data sets of human cancellous bone histological samples from four skeletal sites. The STL models have been mechanically tested and the derived stiffness compared with that predicted by finite element analysis. The results show a strong correlation (R2 = 0.941) between the predicted and calculated stiffnesses of the structures and show promise for the use of STL as an additional technique to complement the use of finite element models, for the assessment of the mechanical properties of complex cancellous bone structures.

Biomimetics↗

An analysis of craniofacial form in cleft palate patients.

Lateral cephalometric form was compared between age-sex matched cleft palate and normocephalic (control) samples aged 6-12 years. Analogous arrays of 3 cephalometric datum points were subjected to finite element analysis, a rigorous geometric technique. The results showed that normocephalic craniofacial size changes were greater than those of the cleft palate sample, although the degree of contrast varied depending upon the particular finite element included in the analysis. More complex lateral cephalometric shape changes were denoted by this technique, however, again depending upon the specific finite element included in the analysis. These data therefore suggested that the differences in craniofacial size and shape changes between normocephalic and cleft palate patients were far more complex than traditionally envisaged.

Cephalometry↗

Stress analysis of a partially slotted intramedullary nail.

A finite element analysis of the Arbeitsgemeinschaft für Osteosynthesefragen/Association for the Study of Internal Fixation (AO/ASIF) intramedullary femoral nail was performed to study the failure of the nail from circumferential cracking near the slot tip. These failures are evidently the result of a stress-concentrating effect owing to the partially slotted nail design. Several finite element models were created of the proximal one-fourth of the nail. One model of the nail incorporated the cloverleaf profile as it is presently manufactured, and one had a circular cross section. An additional three models were created with alternative slot-tip geometries: a narrowed slot, a tapered slot, and a widened slot. Antero-posterior (AP) and medio-lateral (ML) bending loads and torsion loads were applied in two fundamentally different loading modes: (1) loads that were applied on both sides of the slot tip (spanned); and (2) loads that were self-equilibrating distal to the slot tip (non-spanned). For the load cases studied, for all models, the stresses predicted from the finite element models were locally highest at the junction between the open and closed cross sections. Alternative slot-tip shapes had a marked effect on the predicted stresses, in one case reducing maximum stress by 40%. However, no alternative slot tip shape was uniformly superior for all load cases. Therefore, until the in vivo loading modes are known more precisely, an alternative slot-tip shape cannot be proposed.

Biomechanical Phenomena↗

Analysis of the crimping method of producing toric surfaces in contact lens blanks using finite element and experimental methods.

One of the most common methods of producing a toric surface in a contact lens blank is crimping. This method has the advantages of being simple and cheap, but the toric surface dimensions obtained, especially at higher cylinders, can be less accurate. The relationships between the crimping parameters used to produce the toric surface and the dimensions of the toric surface obtained are not well known. If these relationships are known, improved toric surface dimensions may be obtained. In this paper, finite element analysis and experimental results obtained for these relationships are presented and discussed.

Journal Article↗

From structure to process, from organ to cell: recent developments of FE-analysis in orthopaedic biomechanics.

The introduction of finite element analysis (FEA) into orthopaedic biomechanics allowed continuum structural analysis of bone and bone-implant composites of complicated shapes (Huiskes and Chao, J. Biomechanics, Vol. 16, 1983, pp. 385-409). However, besides having complicated shapes, musculoskeletal tissues are hierarchical composites with multiple structural levels that adapt to their mechanical environment. Mechanical adaptation influences the success of many orthopaedic treatments, especially total joint replacements. Recent advances in FEA applications have begun to address questions concerning the optimality of bone structure, the processes of bone remodeling, the mechanics of soft hydrated tissues, and the mechanics of tissues down to the microstructural and cell levels. Advances in each of these areas, which have brought FEA from a continuum stress analysis tool to a tool which plays an ever-increasing role in the scientific understanding of tissue structure, adaptation, and the optimal design of orthopaedic implants, are reviewed.

Adaptation, Physiological↗

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.

Adult↗

Prediction of volumetric strain in the human temporomandibular joint cartilage during jaw movement.

Human temporomandibular joint loading causes pressurization and flow of interstitial fluid in its cartilaginous structures. This largely determines its load-bearing and maintenance capacity. It was hypothesized that during cyclical jaw movements normal pressure distribution dynamics would enable fluid to reach all necessary cartilage regions. This was tested qualitatively by analysis of local volumetric strain dynamics during jaw open-close movements predicted by a dynamic model of the human masticatory system. Finite-element analysis was performed in separate regions of the articular cartilage layers and articular disc. Heterogeneous patterns of dilatation and compression were predicted. Compression was found to be more dominant during jaw closing than opening. The pressure gradient in the superior layer of the articular disc was more mediolaterally orientated than in its inferior layer. The findings suggest that, where necessary, regionally the cartilage can imbibe fluid to protect the subchondral bone from impact loads effectively. In the disc itself presumably all areas receive regular refreshment of interstitial fluid.

Cartilage, Articular↗