Propagation of errors from skull kinematic measurements to finite element tissue responses

Real-time quantification of head impacts using wearable sensors is an appealing approach to assess concussion risk. Traditionally, sensors were evaluated for accurately measuring peak resultant skull accelerations and velocities. With growing interest in utilizing model-estimated tissue responses for injury prediction, it is important to evaluate sensor accuracy in estimating tissue response as well. Here, we quantify how sensor kinematic measurement errors can propagate into tissue response errors. Using previous instrumented mouthguard validation datasets, we found that skull kinematic measurement errors in both magnitude and direction lead to errors in tissue response magnitude and distribution. For molar design instrumented mouthguards susceptible to mandible disturbances, 150–400% error in skull kinematic measurements resulted in 100% error in regional peak tissue response. With an improved incisor design mitigating mandible disturbances, errors in skull kinematics were reduced to <50%, and several tissue response errors were reduced to <10%. Applying 30\(^{\circ }\) rotations to reference kinematic signals to emulate sensor transformation errors yielded below 10% error in regional peak tissue response; however, up to 20% error was observed in peak tissue response for individual finite elements. These findings demonstrate that kinematic resultant errors result in regional peak tissue response errors, while kinematic directionality errors result in tissue response distribution errors. This highlights the need to account for both kinematic magnitude and direction errors and accurately determine transformations between sensors and the skull.     

Muscle-driven finite element simulation of human foot movements

This paper describes a finite element scheme for realistic muscle-driven simulation of human foot movements. The scheme is used to simulate human ankle plantar flexion. A three-dimensional anatomically detailed finite element model of human foot and lower leg is developed and the idea of generating natural foot movement based entirely on the contraction of the plantar flexor muscles is used. The bones, ligaments, articular cartilage, muscles, tendons, as well as the rest soft tissues of human foot and lower leg are included in the model. A realistic three-dimensional continuum constitutive model that describes the biomechanical behaviour of muscles and tendons is used. Both the active and passive properties of muscle tissue are accounted for. The materials for bones and ligaments are considered as homogeneous, isotropic and linearly elastic, whereas the articular cartilage and the rest soft tissues (mainly fat) are defined as hyperelastic materials. The model is used to estimate muscle tissue deformations as well as stresses and strains that develop in the lower leg muscles during plantar flexion of the ankle. Stresses and strains that develop in Achilles tendon during such a movement are also investigated.     

Incorporation of spinal flexibility measurements into finite element analysis

This technical note demonstrates two methods of incorporating the experimental stiffness of spinal motion segments into a finite element analysis of the spine. The first method is to incorporate the experimental data directly as a stiffness matrix. The second method approximates the experimental data as a beam element.     

A finite element model for protein transport in vivo

Background  

Biological mass transport processes determine the behavior and function of cells, regulate interactions between synthetic agents and recipient targets, and are key elements in the design and use of biosensors. Accurately predicting the outcomes of such processes is crucial to both enhancing our understanding of how these systems function, enabling the design of effective strategies to control their function, and verifying that engineered solutions perform according to plan.     

Stability analysis and finite element simulation of bone remodeling model

Bone remodeling is widely viewed as a dynamic process--maintaining bone structure through a balance between the opposed activities of osteoblast and osteoclast cells--in which the stability problem is often pointed out. By an analytical approach, we present a bone remodeling model applied to n unit-elements in order to analyze the stationary states and the condition of their stability. In addition, this theory has been simulated in a computer model using the Finite Element Method (FEM) to show a relationship between the bone remodeling process and the stability analysis.     

Biphasic finite element modeling of hydrated soft tissue contact using an augmented Lagrangian method

A study of biphasic soft tissues contact is fundamental to understanding the biomechanical behavior of human diarthrodial joints. To date, biphasic-biphasic contact has been developed for idealized geometries and not been accessible for more general geometries. In this paper a finite element formulation is developed for contact of biphasic tissues. The augmented Lagrangian method is used to enforce the continuity of contact traction and fluid pressure across the contact interface, and the resulting method is implemented in the commercial software COMSOL Multiphysics. The accuracy of the implementation is verified using 2D axisymmetric problems, including indentation with a flat-ended indenter, indentation with spherical-ended indenter, and contact of glenohumeral cartilage layers. The biphasic finite element contact formulation and its implementation are shown to be robust and able to handle physiologically relevant problems.     

Material properties of the ovine mitral valve anterior leaflet in vivo from inverse finite element analysis

We measured leaflet displacements and used inverse finite-element analysis to define, for the first time, the material properties of mitral valve (MV) leaflets in vivo. Sixteen miniature radiopaque markers were sewn to the MV annulus, 16 to the anterior MV leaflet, and 1 on each papillary muscle tip in 17 sheep. Four-dimensional coordinates were obtained from biplane videofluoroscopic marker images (60 frames/s) during three complete cardiac cycles. A finite-element model of the anterior MV leaflet was developed using marker coordinates at the end of isovolumic relaxation (IVR; when the pressure difference across the valve is approximately 0), as the minimum stress reference state. Leaflet displacements were simulated during IVR using measured left ventricular and atrial pressures. The leaflet shear modulus (G(circ-rad)) and elastic moduli in both the commisure-commisure (E(circ)) and radial (E(rad)) directions were obtained using the method of feasible directions to minimize the difference between simulated and measured displacements. Group mean (+/-SD) values (17 animals, 3 heartbeats each, i.e., 51 cardiac cycles) were as follows: G(circ-rad) = 121 +/- 22 N/mm2, E(circ) = 43 +/- 18 N/mm2, and E(rad) = 11 +/- 3 N/mm2 (E(circ) > E(rad), P < 0.01). These values, much greater than those previously reported from in vitro studies, may result from activated neurally controlled contractile tissue within the leaflet that is inactive in excised tissues. This could have important implications, not only to our understanding of mitral valve physiology in the beating heart but for providing additional information to aid the development of more durable tissue-engineered bioprosthetic valves.     

Nonlinear finite element analysis of anular lesions in the L4/5 intervertebral disc

Degenerate intervertebral discs exhibit both material and structural changes. Structural defects (lesions) develop in the anulus fibrosus with age. While degeneration has been simulated in numerous previous studies, the effects of structural lesions on disc mechanics are not well known. In this study, a finite element model (FEM) of the L4/5 intervertebral disc was developed in order to study the effects of anular lesions and loss of hydrostatic pressure in the nucleus pulposus on the disc mechanics. Models were developed to simulate both healthy and degenerate discs. Degeneration was simulated with either rim, radial or circumferential anular lesions and by equating nucleus pressure to zero. The anulus fibrosus ground substance was represented as a nonlinear incompressible material using a second-order polynomial, hyperelastic strain energy equation. Hyperelastic material parameters were derived from experimentation on sheep discs. Endplates were assumed to be rigid, and annulus lamellae were assumed to be vertical in the unloaded state. Loading conditions corresponding to physiological ranges of rotational motion were applied to the models and peak rotation moments compared between models. Loss of nucleus pulposus pressure had a much greater effect on the disc mechanics than the presence of anular lesions. This indicated that the development of anular lesions alone (prior to degeneration of the nucleus) has minimal effect on disc mechanics, but that disc stiffness is significantly reduced by the loss of hydrostatic pressure in the nucleus. With the degeneration of the nucleus, the outer innervated anulus or surrounding osteo-ligamentous anatomy may therefore experience increased strains.     

Testing dental implants with an in vivo finite element model]

The finite element method (FEM) makes it possible to simulate biomechanical situations on a computer. In the present study the so-called voxel method [9, 14, 17, 18, 19] was used for the construction of the mandible model. For this, the relationship between the biological tissue (e.g. bone) and the corresponding attenuation coefficient of CT data (Hounsfield units = HU) were utilized. The CT data were obtained from an edentulous patient provided with a prosthesis borne on two titanium implants. In a parallel study, the bite forces of the same individual were measured. These were recorded digitally in three dimensions (cranio-caudal, anterior-posterior and left-right) The forces determined by a special program were then transferred to the FEM model implants. We were able to show that a bar joining the implants had a far greater effect on maximum equivalent stress than was expected from the measuring data alone. The highest stress at maximum occlusive force was lowered by 704% on using the connecting bar. On chewing, a stress reduction of 59.9% was observed. The reduction in stress achieved by the bar could, we believe, prolong the life of the implant.     

Remedy for fictive negative pressures in biphasic finite element models of the intervertebral disc during unloading

Previous biphasic finite element studies investigated the temporal response of a spinal segment under rather simplified loading conditions with no attention to unloading and recovery phases. Employment of existing constitutive relations in porous media yields rather large suction-type pore pressures in the disc as the load suddenly disappears. Such negative pressures are absent in vivo and are hence fictive. The aim of this study was to search for remedies to avoid the computation of negative pressures upon unloading. Partial saturation for the disc or a rest load (RL) higher than 400 N totally eliminated the negative pressures. Decreasing the voids ratio (VR) also led to a reduced negative pressure. When defining a partial saturated disc or using a lower VR in combination with a boundary pressure of 0.25 MPa and a RL of 350 N, no negative pressure was calculated. It appears that the constraint of full saturation and a high mobile fluid fraction of the disc tissues along with inadequate tissue properties are the likely causes of negative pressures during unloading.     

Mechanical response of a simple finite element model of the intervertebral disc under complex loading

A simple axisymmetric finite element model of a human spine segment containing two adjacent vertebrae and the intervening intervertebral disc was constructed. The bodies and disc were modeled by three substructures; one to represent each of the vertebral bodies, the annulus fibrosus, and the nucleus pulposus. A semi-analytic technique was used to maintain the computational economies of a two-dimensional analysis when non- axisymmetric loads were imposed on the model. The response of the model to compression, shear, torsion and bending loads applied to the superior vertebral body was examined to determine the effects of disc geometry and material properties on response. Comparisons of model responses with experimentally measured responses were made to estimate material property values for which model behaviors are in agreement with measured behaviors.     

Dynamic finite element knee simulation for evaluation of knee replacement mechanics

In vitro pre-clinical testing of total knee replacement (TKR) devices is a necessary step in the evaluation of new implant designs. Whole joint knee simulators, like the Kansas knee simulator (KKS), provide a controlled and repeatable loading environment for comparative evaluation of component designs or surgical alignment under dynamic conditions. Experimental testing, however, is time and cost prohibitive for design-phase evaluation of tens or hundreds of design variations. Experimentally-verified computational models provide an efficient platform for analysis of multiple components, sizes, and alignment conditions. The purpose of the current study was to develop and verify a computational model of a dynamic, whole joint knee simulator. Experimental internal-external and valgus-varus laxity tests, followed by dynamic deep knee bend and gait simulations in the KKS were performed on three cadaveric specimens. Specimen-specific finite element (FE) models of posterior-stabilized TKR were created from magnetic resonance images and CAD geometry. The laxity data was used to optimize mechanical properties of tibiofemoral soft-tissue structures on a specimen-specific basis. Each specimen was subsequently analyzed in a computational model of the experimental KKS, simulating both dynamic activities. The computational model represented all joints and actuators in the experimental setup, including a proportional-integral-derivative (PID) controller to drive quadriceps actuation. The computational model was verified against six degree-of-freedom patellofemoral (PF) and tibiofemoral (TF) kinematics and actuator loading during both deep knee bend and gait activities, with good agreement in trends and magnitudes between model predictions and experimental kinematics; differences were less than 1.8 mm and 2.2° for PF and TF translations and rotations. The whole joint FE simulator described in this study can be applied to investigate a wide range of clinical and research questions.     

A new method for finite element simulation of orthodontic appliance-teeth-periodontium-alveolus system

This paper describes a new simulation method to analyze the initial behavior of the total system comprising orthodontic appliance, teeth, and their supporting structures. It is based on a finite element method which additionally takes account of a rotational degree of freedom. Beam and rod elements are used for finite element idealization of orthodontic appliance. Through spring elements it is connected with the teeth supported by the alveolar structures. The technique of 'initial strain' is introduced so as to analyze the effects of a gable bend and activation on the force system which is delivered by the orthodontic appliance. As compared with the photoelastic technique hitherto used, this method serves to investigate systematically and quantitatively the initial aspect of orthodontic tooth movement.     

A finite element beam-model for efficient simulation of large-scale porous structures

This paper presents a new method for the generation of a beam finite element (FE) model from a three-dimensional (3D) data set acquired by micro-computed tomography (micro-CT). This method differs from classical modeling of trabecular bone because it models a specific sample only and differs from conventional solid hexahedron element-based FE approaches in its computational efficiency. The stress-strain curve, characterizing global mechanical properties of a porous structure, could be well predicted (R(2)=0.92). Furthermore, validation of the method was achieved by comparing local displacements of element nodes with the displacements directly measured by time-lapsed imaging methods of failure, and these measures were in good agreement. The presented model is a first step in modeling specific samples for efficient strength analysis by FE modeling. We believe that with upcoming high-resolution in-vivo imaging methods, this approach could lead to a novel and accurate tool in the risk assessment for osteoporotic fractures.     

A microstructural finite element simulation of mechanically induced bone formation.

A finite element method to simulate the formation of an interconnected trabectular bone microstructure oriented with respect to applied in vivo mechanical forces is introduced and quantitatively compared to experimental data from a hydraulic bone chamber implant model. Randomly located 45 microm mineralized nodules were used as the initial condition for the model simulations to represent an early stage of intramembranous bone formation. Boundary conditions were applied consistent with the mechanical environment provided by the in vivo bone chamber model. A two-dimensional repair simulation algorithim that incorporated strain energy density (SED), SED gradient, principal strain, or principal strain gradient as the local objective criterion was utilized to simulate the formation of an oriented trabecular bone microstructure. The simulation solutions were convergent, unique, and relatively insensitive to the assumed initial distribution of mineralized nodules. Model predictions of trabecular bone morphology and anisotropy were quantitatively compared to experimental results. All simulations produced structures that qualitatively resembled oriented trabecular bone. However only simulations utilizing a gradient objective criterion yielded results quantitatively similar to in vivo observations. This simulation approach coupled with an experimental model that delivers controlled in vivo mechanical stimuli can be utilized to study the relationship between physical factors and microstructural adaptation during bone repair.     

3D finite element simulation of the opening movement of the mandible in healthy and pathologic situations

One of the essential causes of disk disorders is the pathologic change in the ligamentous attachments of the disk-condyle complex. In this paper, the response of the soft components of a human temporomandibular joint during mouth opening in healthy and two pathologic situations was studied. A three-dimensional finite element model of this joint comprising the bone components, the articular disk, and the temporomandibular ligaments was developed from a set of medical images. A fiber reinforced porohyperelastic model was used to simulate the behavior of the articular disk, taking into account the orientation of the fibers in each zone of this cartilage component. The condylar movements during jaw opening were introduced as the loading condition in the analysis. In the healthy joint, it was obtained that the highest stresses were located at the lateral part of the intermediate zone of the disk. In this case, the collateral ligaments were subject to high loads, since they are responsible of the attachment of the disk to the condyle during the movement of the mandible. Additionally, two pathologic situations were simulated: damage of the retrodiscal tissue and disruption of the lateral discal ligament. In both cases, the highest stresses moved to the posterior part of the disk since it was displaced in the anterior-medial direction. In conclusion, in the healthy joint, the highest stresses were located in the lateral zone of the disk where perforations are found most often in the clinical experience. On the other hand, the results obtained in the damaged joints suggested that the disruption of the disk attachments may cause an anterior displacement of the disk and instability of the joint.     

Trabecular bone fracture healing simulation with finite element analysis and fuzzy logic

Trabecular bone fractures heal through intramembraneous ossification. This process differs from diaphyseal fracture healing in that the trabecular marrow provides a rich vascular supply to the healing bone, there is very little callus formation, woven bone forms directly without a cartilage intermediary, and the woven bone is remodelled to form trabecular bone. Previous studies have used numerical methods to simulate diaphyseal fracture healing or bone remodelling, however not trabecular fracture healing, which involves both tissue differentiation and trabecular formation. The objective of this study was to determine if intramembraneous bone formation and remodelling during trabecular bone fracture healing could be simulated using the same mechanobiological principles as those proposed for diaphyseal fracture healing. Using finite element analysis and the fuzzy logic for diaphyseal healing, the model simulated formation of woven bone in the fracture gap and subsequent remodelling of the bone to form trabecular bone. We also demonstrated that the trabecular structure is dependent on the applied loading conditions. A single model that can simulate bone healing and remodelling may prove to be a useful tool in predicting musculoskeletal tissue differentiation in different vascular and mechanical environments.     

The micromechanical environment of intervertebral disc cells determined by a finite deformation,anisotropic, and biphasic finite element model

Cellular response to mechanical loading varies between the anatomic zones of the intervertebral disc. This difference may be related to differences in the structure and mechanics of both cells and extracellular matrix, which are expected to cause differences in the physical stimuli (such as pressure, stress, and strain) in the cellular micromechanical environment. In this study, a finite element model was developed that was capable of describing the cell micromechanical environment in the intervertebral disc. The model was capable of describing a number of important mechanical phenomena: flow-dependent viscoelasticity using the biphasic theory for soft tissues; finite deformation effects using a hyperelastic constitutive law for the solid phase; and material anisotropy by including a fiber-reinforced continuum law in the hyperelastic strain energy function. To construct accurate finite element meshes, the in situ geometry of IVD cells were measured experimentally using laser scanning confocal microscopy and three-dimensional reconstruction techniques. The model predicted that the cellular micromechanical environment varies dramatically between the anatomic zones, with larger cellular strains predicted in the anisotropic anulus fibrosus and transition zone compared to the isotropic nucleus pulposus. These results suggest that deformation related stimuli may dominate for anulus fibrosus and transition zone cells, while hydrostatic pressurization may dominate in the nucleus pulposus. Furthermore, the model predicted that micromechanical environment is strongly influenced by cell geometry, suggesting that the geometry of IVD cells in situ may be an adaptation to reduce cellular strains during tissue loading.