Analysis of synaptic transmission in the neuromuscular junction using a continuum finite element model.

There is a steadily growing body of experimental data describing the diffusion of acetylcholine in the neuromuscular junction and the subsequent miniature endplate currents produced at the postsynaptic membrane. To gain further insights into the structural features governing synaptic transmission, we have performed calculations using a simplified finite element model of the neuromuscular junction. The diffusing acetylcholine molecules are modeled as a continuum, whose spatial and temporal distribution is governed by the force-free diffusion equation. The finite element method was adopted because of its flexibility in modeling irregular geometries and complex boundary conditions. The resulting simulations are shown to be in accord with experiment and other simulations.     

Tissue-fluid interface analysis using biphasic finite element method

Numerical studies on fluid-structure interaction have primarily relied on decoupling the solid and fluid sub-domains with the interactions treated as external boundary conditions on the individual sub-domains. The finite element applications for the fluid-structure interactions can be divided into iterative algorithms and sequential algorithms. In this paper, a new computational methodology for the analysis of tissue-fluid interaction problems is presented. The whole computational domain is treated as a single biphasic continuum, and the same space and time discretisation is carried out for the sub-domains using a penalty-based finite element model. This procedure does not require the explicit modelling of additional boundary conditions or interface elements. The developed biphasic interface finite element model is used in analysing blood flow through normal and stenotic arteries. The increase in fluid flow velocity when passing through a stenosed artery and the drop in pressure at the region are captured using this method.     

Distributed parameters deterministic model for treatment of brain tumors using Galerkin finite element method

In this paper, we present a distributed parameters deterministic model for treatment of brain tumors using Galerkin finite element method. The dynamic model comprises system of three coupled reaction-diffusion models, involving the tumor cells, the normal tissues and the drug concentration. An optimal control problem is formulated with the goal of minimizing the tumor cell density and reducing the side effects of the drug. A distributed parameters method based on the application of variational calculus is used on an integral-Hamiltonian, which is then used to obtain an optimal coupled system of forward state equations and backward co-state equations. The Galerkin finite element method is used to realistically represent the brain structure as well as to facilitate computation. Finally a three-dimensional test case is considered and partitioned into a set of spherical finite elements, using tri-linear basis functions, except for the elements affected by singularities of polar and azimuthal angles, as well as the origin.     

A new method to investigate in vivo knee behavior using a finite element model of the lower limb

Several finite element models have been developed for estimating the mechanical response of joint internal structures, where direct or indirect in vivo measurement is difficult or impossible. The quality of the predictions made by those models is largely dependent on the quality of the experimental data (e.g. load/displacement) used to drive them. Also numerical problems have been described in the literature when using implicit finite element techniques to simulate problems that involve contacts and large displacements. In this study, a unique strategy was developed combining high accuracy in vivo three-dimensional kinematics and a lower limb finite element model based on explicit finite element techniques. The method presents an analytical technique applied to a dynamic loading condition (impact during hopping on one leg). The validation of the lower limb model focused on the response of the whole model and the knee joint in particular to the imposed 3D femoral in vivo kinematics and ground reaction forces. The approach outlined in this study introduces a generic tool for the study of in vivo knee joint behavior.     

Study on multicellular systems using a phase field model

A model of multicellular systems with several types of cells is developed from the phase field model. The model is presented as a set of partial differential equations of the field variables, each of which expresses the shape of one cell. The dynamics of each cell is based on the criteria for minimizing the surface area and retaining a certain volume. The effects of cell adhesion and excluded volume are also taken into account. The proposed model can be used to find the position of the membrane and/or the cortex of each cell without the need to adopt extra variables. This model is suitable for numerical simulations of a system having a large number of cells. The two-dimensional results of cell division, cell adhesion, rearrangement of a cell cluster, chemotaxis, and cell sorting as well as the three-dimensional results of cell clusters on the substrate are presented.     

Characterization of craniofacial sutures using the finite element method

Characterizing the biomechanical behavior of sutures in the human craniofacial skeleton (CFS) is essential to understand the global impact of these articulations on load transmission, but is challenging due to the complexity of their interdigitated morphology, the multidirectional loading they are exposed to and the lack of well-defined suture material properties. This study aimed to quantify the impact of morphological features, direction of loading and suture material properties on the mechanical behavior of sutures and surrounding bone in the CFS. Thirty-six idealized finite element (FE) models were developed. One additional specimen-specific FE model was developed based on the morphology obtained from a µCT scan to represent the morphological complexity inherent in CFS sutures. Outcome variables of strain energy (SE) and von Mises stress (σ_vm) were evaluated to characterize the sutures’ biomechanical behavior. Loading direction was found to impact the relationship between SE and interdigitation index and yielded varied patterns of σ_vm in both the suture and surrounding bone. Adding bone connectivity reduced suture strain energy and altered the σ_vm distribution. Incorporating transversely isotropic material properties was found to reduce SE, but had little impact on stress patterns. High-resolution µCT scanning of the suture revealed a complex morphology with areas of high and low interdigitations. The specimen specific suture model results were reflective of SE absorption and σ_vm distribution patterns consistent with the simplified FE results. Suture mechanical behavior is impacted by morphologic factors (interdigitation and connectivity), which may be optimized for regional loading within the CFS.     

Mechanics of cranial sutures using the finite element method

To investigate how cranial suture morphology and the arrangement of sutural collagen fibres respond to compressive and tensile loads, an idealised bone–suture–bone complex was analysed using a two-dimensional finite element model. Three suture morphologies were simulated with an increasing interdigitation index (I.I.): butt-ended, moderate interdigitated, and complex interdigitated. The collagen matrix within all sutures was modelled as an isotropic material, and as an orthotropic material in the interdigitated sutures with fibre alignment as reported in studies of miniature pigs. Static uniform compressive or tensile loading was applied to the complex. In interdigitated sutures with isotropic material properties, the orientation of the maximum (tensile) principal stresses within the suture matched the collagen fibre orientation observed in compressed and tensed sutures of miniature pigs. This suggests that randomly arranged sutural collagen fibres could optimise to an orientation most appropriate to withstand the predominant type of loading. A compression-resistant fibre arrangement imparted the highest suture strain energy relative to the isotropic and tension-resistant arrangements, indicating that this configuration maximises energy storage. A comparison across the different suture morphologies indicated that bone strain energy generally decreased with a decrease in I.I., irrespective of the sutural fibre arrangement. However, high bone stress at the interdigitation apices shifted to the limbs of the suture with an increase in I.I. These combined findings highlight the importance of suture morphology and anisotropy as properties having a significant influence on sutural mechanics.     

A finite element model of myocardial infarction using a composite material approach

Computational models are effective tools to study cardiac mechanics under normal and pathological conditions. They can be used to gain insight into the physiology of the heart under these conditions while they are adaptable to computer assisted patient-specific clinical diagnosis and therapeutic procedures. Realistic cardiac mechanics models incorporate tissue active/passive response in conjunction with hyperelasticity and anisotropy. Conventional formulation of such models leads to mathematically-complex problems usually solved by custom-developed non-linear finite element (FE) codes. With a few exceptions, such codes are not available to the research community. This article describes a computational cardiac mechanics model developed such that it can be implemented using off-the-shelf FE solvers while tissue pathologies can be introduced in the model in a straight-forward manner. The model takes into account myocardial hyperelasticity, anisotropy, and active contraction forces. It follows a composite tissue modeling approach where the cardiac tissue is decomposed into two major parts: background and myofibers. The latter is modelled as rebars under initial stresses mimicking the contraction forces. The model was applied in silico to study the mechanics of infarcted left ventricle (LV) of a canine. End-systolic strain components, ejection fraction, and stress distribution attained using this LV model were compared quantitatively and qualitatively to corresponding data obtained from measurements as well as to other corresponding LV mechanics models. This comparison showed very good agreement.     

Active muscle response using feedback control of a finite element human arm model

Mathematical human body models (HBMs) are important research tools that are used to study the human response in car crash situations. Development of automotive safety systems requires the implementation of active muscle response in HBM, as novel safety systems also interact with vehicle occupants in the pre-crash phase. In this study, active muscle response was implemented using feedback control of a nonlinear muscle model in the right upper extremity of a finite element (FE) HBM. Hill-type line muscle elements were added, and the active and passive properties were assessed. Volunteer tests with low impact loading resulting in elbow flexion motions were performed. Simulations of posture maintenance in a gravity field and the volunteer tests were successfully conducted. It was concluded that feedback control of a nonlinear musculoskeletal model can be used to obtain posture maintenance and human-like reflexive responses in an FE HBM.     

Failure analysis of a new post-and-core restoration system using the finite element method

Human teeth with substantial coronal defects are subject to reconstruction by means of post-and-core restorations. Typically, such a restoration comprises a slightly cylindrical post onto which an abutment of varying shape, depending on the designated restoration, is attached. As clinical results are not satisfactory to date, a new post-and-core design which makes use of positive locking (rather than relying on chemical bonding agents for retention in the residual root) was proposed. Using proprietary burs, an inversely conical hole is machined into the root, into which the prefabricated post-and-core restoration is inserted. This part can be spread at the bottom to match the cavity's undercut form, resulting in a positive lock which can only be separated by destruction of root, restoration or both. Another key feature of this system is a ring/groove geometry which is able to absorb the wedging forces created by said spreading and the stress of loading of the restoration which arises from mascatory forces. To assess the properties, especially in terms of the stress imposed on the remaining tooth at highest possible loading, both finite element simulations and in vitro failure tests were performed and the findings compared. The results suggest that the parameters of the finite element simulations are in good agreement with reality. As calculated and measured force levels immediately before failure of the restoration are high, the introduced new geometry has significant advantages over the classical restoration.     

Validating a voxel-based finite element model of a human mandible using digital speckle pattern interferometry

Finite element analysis is a powerful tool for predicting the mechanical behaviour of complex biological structures like bones, but to be confident in the results of an analysis, the model should be validated against experimental data. In such validation experiments, the strains in the loaded bones are usually measured with strain gauges glued to the bone surface, but the use of strain gauges on bone can be difficult and provides only very limited data regarding surface strain distributions. This study applies the full-field strain measurement technique of digital speckle pattern interferometry to measure strains in a loaded human mandible and compares the results with the predictions of voxel-based finite element models of the same specimen. It is found that this novel strain measurement technique yields consistent, reliable measurements. Further, strains predicted by the finite element analysis correspond well with the experimental data. These results not only confirm the usefulness of this technique for future validation studies in the field of bone mechanics, but also show that the modelling approach used in this study is able to predict the experimental results very accurately.     

Calculation of protein form birefringence using the finite element method.

An approach based on the finite element method (FEM) is employed to calculate the optical properties of macromolecules, specifically form birefringence. Macromolecules are treated as arbitrarily shaped particles suspended in a solvent of refraction index n1. The form birefringence of the solution is calculated as the difference in its refractive index when all the particles of refractive index n2 are either parallel to or normal to the direction of the polarization of light. Since the particles of interest are small compared to the wavelength of light, a quasi-static approximation for the refractive index is used, i.e., that it is equal to the square root of the dielectric constant of the suspension. The average dielectric constant of the mixture is calculated using the finite element method. This approach has been tested for ellipsoidal particles and a good agreement with theoretical results has been obtained. Also, numerical results for the motor domains of ncd and kinesin, small arbitrarily shaped proteins with known x-ray structures, show reasonable agreement with the experimental data obtained from transient electric birefringence experiments.     

Arthropod touch reception: stimulus transformation and finite element model of spider tactile hairs

Striving towards an in depth understanding of stimulus transformation in arthropod tactile hairs, we studied the mechanical events associated with tactile stimulation. A finite element model was developed taking a tarsal tactile hair of the spider Cupiennius salei as an example. Considering hair diameter, wall thickness, and curvature, the hair is subdivided into six regions each with its specific mechanical properties. When the hair is touched from above with a flat surface oriented parallel to the tarsus the point of stimulus contact moves towards the hair base with increasing load and hair deflection. Thereby the effective lever arm is reduced protecting the hair against breaking near its base. At the same time the mechanical working range of the hair increases implying higher mechanical sensitivity for small deflections (about 5x10(-5) N/degrees) than for large deflections (about 1x10(-4) N/degrees). The major stresses within the hair shaft are axial stresses due to bending. The position of stress maxima moves along the shaft with the movement of the stimulus contact point. Remarkably, the amplitude of this maximum (about 1x10(5) N/m2) hardly changes with increasing loading force due to the way the hair shaft is deflected by the stimulus.     

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.     

Development of a three-dimensional finite element model of a human tibia using experimental modal analysis.

The modal analysis of a human tibia consisted of characterizing its dynamic behavior by determining natural frequency, damping ratio and mode shapes. Two methods were used to perform the modal analysis: (1) a finite element method (structural model); (2) an experimental modal analysis (modal model). The experimental modal model was used to optimize the structural model. After optimization, differences in results between the two models were found to be due only to mechanical properties and mass distribution. The influences of boundary conditions and geometric properties (such as inertia and length) were eliminated by the finite element model itself. The percent relative error between the two methods was approximately 3%, corresponding to the standard deviation of the measured frequencies. For the frequency range considered, the mode shapes were bending modes in two different vibration planes (latero-medial and sagittal), with a slight torsion effect due to the twisted geometry of the tibia.     

Experimental validation of a finite element model of the proximal femur using digital image correlation and a composite bone model

Computational biomechanical models are useful tools for supporting orthopedic implant design and surgical decision making, but because they are a simplification of the clinical scenario they must be carefully validated to ensure that they are still representative. The goal of this study was to assess the validity of the generation process of a structural finite element model of the proximal femur employing the digital image correlation (DIC) strain measurement technique. A finite element analysis model of the proximal femur subjected to gait loading was generated from a CT scan of an analog composite femur, and its predicted mechanical behavior was compared with an experimental model. Whereas previous studies have employed strain gauging to obtain discreet point data for validation, in this study DIC was used for full field quantified comparison of the predicted and experimentally measured strains. The strain predicted by the computational model was in good agreement with experimental measurements, with R(2) correlation values from 0.83 to 0.92 between the simulation and the tests. The sensitivity and repeatability of the strain measurements were comparable to or better than values reported in the literature for other DIC tests on tissue specimens. The experimental-model correlation was in the same range as values obtained from strain gauging, but the DIC technique produced more detailed, full field data and is potentially easier to use. As such, the findings supported the validity of the model generation process, giving greater confidence in the model's predictions, and digital image correlation was demonstrated as a useful tool for the validation of biomechanical models.     

Simulating the wrinkling and aging of skin with a multi-layer finite element model

One of the outward signs of the aging process of human skin is the increased appearance of wrinkles on its surface. Clinical studies show that the increased frequency of wrinkles with age may be attributed to changes in the composition of the various layers of skin, leading to a change in mechanical properties. A parameter study was performed on a previously proposed multi-layer finite element model of skin. A region of skin was subject to an in-plane compression, resulting in wrinkling. A number of physical properties of the skin model were changed and the effects these changes had on the size of the subsequent wrinkles were measured. Reducing the moisture content of the stratum corneum by 11% produces wrinkles 25–85% larger. Increasing the dermal collagen fibre density by 67%, results in wrinkles, which are 25–50% larger. A reduction and change in the pre-stress distribution in the skin model, which represents the natural tension and relaxed skin tension lines in real skin, also influences the wrinkle height in a similar manner to real aging skin. Typically, there can be up to a 100% increase in the height of wrinkles as skin ages. This model would be of benefit in the development of cosmetic moisturisers and plastic-surgery techniques to reduce the appearance of aging.