Implementation of controlling strategy in a biomechanical lower limb model with active muscles for coupling multibody dynamics and finite element analysis

Computational biomechanics for human body modeling has generally been categorized into two separated domains: finite element analysis and multibody dynamics. Combining the advantages of both domains is necessary when tissue stress and physical body motion are both of interest. However, the method for this topic is still in exploration. The aim of this study is to implement unique controlling strategies in finite element model for simultaneously simulating musculoskeletal body dynamics and in vivo stress inside human tissues. A finite element lower limb model with 3D active muscles was selected for the implementation of controlling strategies, which was further validated against in-vivo human motion experiments. A unique feedback control strategy that couples together a basic Proportion-Integration-Differentiation (PID) controller and generic active signals from Computed Muscle Control (CMC) method of the musculoskeletal model or normalized EMG singles was proposed and applied in the present model. The results show that the new proposed controlling strategy show a good correlation with experimental test data of the normal gait considering joint kinematics, while stress distribution of local lower limb tissue can be also detected in real-time with lower limb motion. In summary, the present work is the first step for the application of active controlling strategy in the finite element model for concurrent simulation of both body dynamics and tissue stress. In the future, the present method can be further developed to apply it in various fields for human biomechanical analysis to monitor local stress and strain distribution by simultaneously simulating human locomotion.     

An Analysis and Comparison of Convergence and Uniqueness of Time-Independent Bone Adaptation Models

Several stimuli are proposed in the bone remodeling theory. It is not clear, if a unique solution exists and if the result is convergent using a certain stimulus. In this study, the strain stimulus, strain energy stimulus and the von Mises stress stimulus for bone remodeling are compared and applied to a square plate model using the finite element method. In the plane stress state, the remodeling equilibrium equations are transformed into functions of only the principal strains and the graphs of these functions are drawn in a diagram using the principal strains as the variables of two coordinate axes. The equation of the sum of principal strain squared equal to a constant is a circle in the diagram. The remodeling equilibrium equation of the strain stimulus is a quadrangle fitting into the circle, the remodeling equilibrium equation of the strain energy stimulus is an ellipse and the remodeling equilibrium equation of the von Mises stress stimulus is also an ellipse close to the principal strains circle when we take the same constants in the above equations. Using the finite element method, two models are performed with the uniform initial elastic properties and with the semi-random initial distribution of the elastic properties. The principal strains as the final finite element results converge within 2% of the objective constant for all the different stimuli. The obtained Young's moduli of two models as the adaptation object are different but in equilibrium, i.e. the equilibrium solution of adaptation model is not unique. The principal strains can not be used to examine the uniqueness of solution, since two different solutions can have the same results of principal strains. Using a certain stimulus, certain initial properties and a certain iterative equation, the solution is unique in equilibrium. The results using the model in this study show also that the same results can be obtained using any of the three stimuli when a proper constant in each remodeling equilibrium equation is chosen.     

A nonlinear viscoelastic finite element model of polyethylene

A nonlinear viscoelastic finite element model of ultra-high molecular weight polyethylene (UHMWPE) was developed in this study. Eight cylindrical specimens were machined from ram extruded UHMWPE bar stock (GUR 1020) and tested under constant compression at 7% strain for 100 sec. The stress strain data during the initial ramp up to 7% strain was utilized to model the "instantaneous" stress-strain response using a Mooney-Rivlin material model. The viscoelastic behavior was modeled using the time-dependent relaxation in stress seen after the initial maximum stress was achieved using a stored energy formulation. A cylindrical model of similar dimensions was created using a finite element analysis software program. The cylinder was made up of hexahedral elements, which were given the material properties utilizing the "instantaneous" stress-strain curve and the energy-relaxation curve obtained from the experimental data. The cylinder was compressed between two flat rigid bodies that simulated the fixtures of the testing machine. Experimental stress-relaxation, creep and dynamic testing data were then used to validate the model. The mean error for predicted versus experimental data for stress relaxation at different strain levels was 4.2%. The mean error for the creep test was 7% and for dynamic test was 5.4%. Finally, dynamic loading in a hip arthroplasty was modeled and validated experimentally with an error of 8%. This study establishes a working finite element material model of UHMWPE that can be utilized to simulate a variety of postoperative arthroplasty conditions.     

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.     

Can sulci protect the brain from traumatic injury?

The influence of sulci in dynamic finite element simulations of the human head has been investigated. First, a detailed 3D FE model was constructed based on an MRI scan of a human head. A second model with a smoothed brain surface was created based on the same MRI scan as the first FE model. These models were validated against experimental data to confirm their human-like dynamic responses during impact. The validated FE models were subjected to several acceleration impulses and the maximum principle strain and strain rate in the brain were analyzed. The results suggested that the inclusion of sulci should be considered for future FE head models as it alters the strain and strain distribution in an FE model.     

Dynamic finite element implementation of nonlinear,anisotropic hyperelastic biological membranes

We present a novel method for the implementation of hyperelastic finite strain, non-linear strain-energy functions for biological membranes in an explicit finite element environment. The technique is implemented in LS-DYNA but may also be implemented in any suitable non-linear explicit code. The constitutive equations are implemented on the foundation of a co-rotational uniformly reduced Hughes-Liu shell. This shell is based on an updated-Lagrangian formulation suitable for relating Cauchy stress to the rate-of-deformation, i.e. hypo-elasticity. To accommodate finite deformation hyper-elastic formulations, a co-rotational deformation gradient is assembled over time, resulting in a formulation suitable for pseudo-hyperelastic constitutive equations that are standard assumptions in biomechanics. Our method was validated by comparison with (1) an analytic solution to a spherically-symmetric dynamic membrane inflation problem, incorporating a Mooney-Rivlin hyperelastic equation and (2) with previously published finite element solutions to a non-linear transversely isotropic inflation problem. Finally, we implemented a transversely isotropic strain-energy function for mitral valve tissue. The method is simple and accurate and is believed to be generally useful for anyone who wishes to model biologic membranes with an experimentally driven strain-energy function.     

Parametric convergence sensitivity and validation of a finite element model of the human lumbar spine

The primary objective of this study was to generate a finite element model of the human lumbar spine (L1-L5), verify mesh convergence for each tissue constituent and perform an extensive validation using both kinematic/kinetic and stress/strain data. Mesh refinement was accomplished via convergence of strain energy density (SED) predictions for each spinal tissue. The converged model was validated based on range of motion, intradiscal pressure, facet force transmission, anterolateral cortical bone strain and anterior longitudinal ligament deformation predictions. Changes in mesh resolution had the biggest impact on SED predictions under axial rotation loading. Nonlinearity of the moment-rotation curves was accurately simulated and the model predictions on the aforementioned parameters were in good agreement with experimental data. The validated and converged model will be utilised to study the effects of degeneration on the lumbar spine biomechanics, as well as to investigate the mechanical underpinning of the contemporary treatment strategies.     

Parametric convergence sensitivity and validation of a finite element model of the human lumbar spine

The primary objective of this study was to generate a finite element model of the human lumbar spine (L1–L5), verify mesh convergence for each tissue constituent and perform an extensive validation using both kinematic/kinetic and stress/strain data. Mesh refinement was accomplished via convergence of strain energy density (SED) predictions for each spinal tissue. The converged model was validated based on range of motion, intradiscal pressure, facet force transmission, anterolateral cortical bone strain and anterior longitudinal ligament deformation predictions. Changes in mesh resolution had the biggest impact on SED predictions under axial rotation loading. Nonlinearity of the moment-rotation curves was accurately simulated and the model predictions on the aforementioned parameters were in good agreement with experimental data. The validated and converged model will be utilised to study the effects of degeneration on the lumbar spine biomechanics, as well as to investigate the mechanical underpinning of the contemporary treatment strategies.     

The importance of craniofacial sutures in biomechanical finite element models of the domestic pig

Craniofacial sutures are a ubiquitous feature of the vertebrate skull. Previous experimental work has shown that bone strain magnitudes and orientations often vary when moving from one bone to another, across a craniofacial suture. This has led to the hypothesis that craniofacial sutures act to modify the strain environment of the skull, possibly as a mode of dissipating high stresses generated during feeding or impact. This study tests the hypothesis that the introduction of craniofacial sutures into finite element (FE) models of a modern domestic pig skull would improve model accuracy compared to a model without sutures. This allowed the mechanical effects of sutures to be assessed in isolation from other confounding variables. These models were also validated against strain gauge data collected from the same specimen ex vivo. The experimental strain data showed notable strain differences between adjacent bones, but this effect was generally not observed in either model. It was found that the inclusion of sutures in finite element models affected strain magnitudes, ratios, orientations and contour patterns, yet contrary to expectations, this did not improve the fit of the model to the experimental data, but resulted in a model that was less accurate. It is demonstrated that the presence or absence of sutures alone is not responsible for the inaccuracies in model strain, and is suggested that variations in local bone material properties, which were not accounted for by the FE models, could instead be responsible for the pattern of results.     

Requirements for comparing the performance of finite element models of biological structures

The widespread availability of three-dimensional imaging and computational power has fostered a rapid increase in the number of biologists using finite element analysis (FEA) to investigate the mechanical function of living and extinct organisms. The inevitable rise of studies that compare finite element models brings to the fore two critical questions about how such comparative analyses can and should be conducted: (1) what metrics are appropriate for assessing the performance of biological structures using finite element modeling? and, (2) how can performance be compared such that the effects of size and shape are disentangled? With respect to performance, we argue that energy efficiency is a reasonable optimality criterion for biological structures and we show that the total strain energy (a measure of work expended deforming a structure) is a robust metric for comparing the mechanical efficiency of structures modeled with finite elements. Results of finite element analyses can be interpreted with confidence when model input parameters (muscle forces, detailed material properties) and/or output parameters (reaction forces, strains) are well-documented by studies of living animals. However, many researchers wish to compare species for which these input and validation data are difficult or impossible to acquire. In these cases, researchers can still compare the performance of structures that differ in shape if variation in size is controlled. We offer a theoretical framework and empirical data demonstrating that scaling finite element models to equal force: surface area ratios removes the effects of model size and provides a comparison of stress-strength performance based solely on shape. Further, models scaled to have equal applied force:volume ratios provide the basis for strain energy comparison. Thus, although finite element analyses of biological structures should be validated experimentally whenever possible, this study demonstrates that the relative performance of un-validated models can be compared so long as they are scaled properly.     

The impact of glenoid labrum thickness and modulus on labrum and glenohumeral capsule function

The glenoid labrum is an integral component of the glenohumeral capsule's insertion into the glenoid, and changes in labrum geometry and mechanical properties may lead to the development of glenohumeral joint pathology. The objective of this research was to determine the effect that changes in labrum thickness and modulus have on strains in the labrum and glenohumeral capsule during a simulated physical examination for anterior instability. A labrum was incorporated into a validated, subject-specific finite element model of the glenohumeral joint, and experimental kinematics were applied simulating application of an anterior load at 0 deg, 30 deg, and 60 deg of external rotation and 60 deg of glenohumeral abduction. The radial thickness of the labrum was varied to simulate thinning tissue, and the tensile modulus of the labrum was varied to simulate degenerating tissue. At 60 deg of external rotation, a thinning labrum increased the average and peak strains in the labrum, particularly in the labrum regions of the axillary pouch (increased 10.5% average strain) and anterior band (increased 7.5% average strain). These results suggest a cause-and-effect relationship between age-related decreases in labrum thickness and increases in labrum pathology. A degenerating labrum also increased the average and peak strains in the labrum, particularly in the labrum regions of the axillary pouch (increased 15.5% strain) and anterior band (increased 10.4% strain). This supports the concept that age-related labrum pathology may result from tissue degeneration. This work suggests that a shift in capsule reparative techniques may be needed in order to include the labrum, especially as activity levels in the aging population continue to increase. In the future validated, finite element models of the glenohumeral joint can be used to explore the efficacy of new repair techniques for glenoid labrum pathology.     

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.     

Studies of biaxial mechanical properties and nonlinear finite element modeling of skin

The objective of this research is to conduct mechanical property studies of skin from two individual but potentially connected aspects. One is to determine the mechanical properties of the skin experimentally by biaxial tests, and the other is to use the finite element method to model the skin properties. Dynamic biaxial tests were performed on 16 pieces of abdominal skin specimen from rats. Typical biaxial stress-strain responses show that skin possesses anisotropy, nonlinearity and hysteresis. To describe the stress-strain relationship in forms of strain energy function, the material constants of each specimen were obtained and the results show a high correlation between theory and experiments. Based on the experimental results, a finite element model of skin was built to model the skin's special properties including anisotropy and nonlinearity. This model was based on Arruda and Boyce's eight-chain model and Bischoff et al.'s finite element model of skin. The simulation results show that the isotropic, nonlinear eight-chain model could predict the skin's anisotropic and nonlinear responses to biaxial loading by the presence of an anisotropic prestress state.     

Smooth muscle contraction: mechanochemical formulation for homogeneous finite strains

Chemical kinetics of smooth muscle contraction affect mechanical properties of organs that function under finite strains. In an effort to gain further insight into organ physiology, we formulate a mechanochemical finite strain model by considering the interaction between mechanical and biochemical components of cell function during activation. We propose a new constitutive framework and use a mechanochemical device that consists of two parallel elements: (i) spring for the cell stiffness; (ii) contractile element for the sarcomere. We use a multiplicative decomposition of cell elongation into filament contraction and cross-bridge deformation, and suggest that the free energy be a function of stretches, four variables (free unphosphorylated myosin, phosphorylated cross-bridges, phosphorylated and dephosphorylated cross-bridges attached to actin), chemical state variable driven by Ca2+-concentration, and temperature. The derived constitutive laws are thermodynamically consistent. Assuming isothermal conditions, we specialize the mechanical phase such that we recover the linear model of Yang et al. [2003a. The myogenic response in isolated rat cerebrovascular arteries: smooth muscle cell. Med. Eng. Phys. 25, 691-709]. The chemical phase is also specialized so that the linearized chemical evolution law leads to the four-state model of Hai and Murphy [1988. Cross-bridge phosphorylation and regulation of latch state in smooth muscle. Am. J. Physiol. 254, C99-C106]. One numerical example shows typical mechanochemical effects and the efficiency of the proposed approach. We discuss related parameter identification, and illustrate the dependence of muscle contraction (Ca2+-concentration) on active stress and related stretch. Mechanochemical models of this kind serve the mathematical basis for analyzing coupled processes such as the dependency of tissue properties on the chemical kinetics of smooth muscle.     

Search for critical loading condition of the spine--a meta analysis of a nonlinear viscoelastic finite element model

The relative vulnerability of spinal motion segments to different loading combinations remains unknown. The meta-analysis described here using the results of a validated L2-L3 nonlinear viscoelastic finite element model was designed to investigate the critical loading and its effect on the internal mechanics of the human lumbar spine. A Box-Behnken experimental design was used to design the magnitude of seven independent variables associated with loads, rotations and velocity of motion. Subsequently, an optimization method was used to find the primary and secondary variables that influence spine mechanical output related to facet forces, disc pressure, ligament forces, annulus matrix compressive/shear stresses and anulus fibers strain. The mechanical responses with respect to the two most-relevant variables were then regressed linearly using the response surface quadratic model. Axial force and sagittal rotation were identified as the most-relevant variables for mechanical responses. The procedure developed can be used to find the critical loading for finite element models with multi input variables. The derived meta-models can be used to predict the risk associated with various loading parameters and in setting safer load limits.     

A dynamic finite element analysis of impulsive loading of the extension-splinted rabbit knee

A dynamic nonlinear finite element model was developed to study juxtarticular stresses in the splinted rabbit knee, an established laboratory model for creating osteoarthrosis due to impulsive loading. Plane strain finite element results were validated by comparison with corresponding experimental data. Parametric effects studied included the input tibial displacement speed, the local bone density distribution, and the modulus of cartilage and subchondral bone. While the computed resultant contact force magnitude was sensitive to a number of model parameters, the stress patterns, when normalized to a given resultant force magnitude, were not. Despite comparable force peaks, the finite element results showed approximately six-fold higher effective strain rate levels for a severely impulsive loading protocol known to induce rapid osteoarthrosis, versus those for a mildly impulsive loading protocol not usually associated with cartilage damage. A propensity for elevated shear in the deep cartilage layer near the contact periphery, observed in nearly all computed stress distributions, is consistent with previous experimental findings of fissuring at that level in the impulsively loaded rabbit knee.     

Search for critical loading condition of the spine–A meta analysis of a nonlinear viscoelastic finite element model

The relative vulnerability of spinal motion segments to different loading combinations remains unknown. The meta-analysis described here using the results of a validated L2–L3 nonlinear viscoelastic finite element model was designed to investigate the critical loading and its effect on the internal mechanics of the human lumbar spine. A Box-Behnken experimental design was used to design the magnitude of seven independent variables associated with loads, rotations and velocity of motion. Subsequently, an optimization method was used to find the primary and secondary variables that influence spine mechanical output related to facet forces, disc pressure, ligament forces, annulus matrix compressive/shear stresses and anulus fibers strain. The mechanical responses with respect to the two most-relevant variables were then regressed linearly using the response surface quadratic model. Axial force and sagittal rotation were identified as the most-relevant variables for mechanical responses. The procedure developed can be used to find the critical loading for finite element models with multi input variables. The derived meta-models can be used to predict the risk associated with various loading parameters and in setting safer load limits.     

Optimizing cardiac material parameters with a genetic algorithm

Determining the unknown material parameters of intact ventricular myocardium can be challenging due to highly nonlinear material behavior. Previous studies combining a gradient-search optimization procedure with finite element analysis (FEA) were limited to two-dimensional (2D) models or simplified three-dimensional (3D) geometries. Here we present a novel scheme to estimate unknown material parameters for ventricular myocardium by combining a genetic algorithm (GA) with nonlinear finite element analysis. This approach systematically explores the domain of the material parameters. The objective function to minimize was the error between simulated strain data and finite element model strains. The proposed scheme was validated for a 2D problem using a realistic material law for ventricular myocardium. Optimized material parameters were generally within 0.5% of the true values. To demonstrate the robustness of the new scheme, unknown material parameters were also determined for a realistic 3D heart model with an exponential hyperelastic material law. When using strains from two material points, the algorithm converged to parameters within 5% of the true values. We conclude that the proposed scheme is robust when estimating myocardial material parameters in 2D and 3D models.     

Vacuum-assisted closure: microdeformations of wounds and cell proliferation

The mechanism of action of the Vacuum Assisted Closure Therapy (VAC; KCI, San Antonio, Texas), a recent novel innovation in the care of wounds, remains unknown. In vitro studies have revealed that cells allowed to stretch tend to divide and proliferate in the presence of soluble mitogens, whereas retracted cells remain quiescent. The authors hypothesize that application of micromechanical forces to wounds in vivo can promote wound healing through this cell shape-dependent, mechanical control mechanism. The authors created a computer model (finite element) of a wound and simulated VAC application. Finite element modeling is commonly used to engineer complex systems by breaking them down into simple discrete elements. In this model, the authors altered the pressure, pore diameter, and pore volume fraction to study the effects of vacuum-induced material deformations. The authors compared the morphology of deformation of this wound model with histologic sections of wounds treated with the VAC. The finite element model showed that most elements stretched by VAC application experienced deformations of 5 to 20 percent strain, which are similar to in vitro strain levels shown to promote cellular proliferation. Importantly, the deformation predicted by the model also was similar in morphology to the surface undulations observed in histologic cross-sections of the wounds. The authors hypothesize that this tissue deformation stretches individual cells, thereby promoting proliferation in the wound microenvironment. The application of micromechanical forces may be a useful method with which to stimulate wound healing through promotion of cell division, angiogenesis, and local elaboration of growth factors. Finite element modeling of the VAC device is consistent with this mechanism of action.     

Finite Element Modeling of a Beetle Wing

Numerical simulation is a very important method for understanding the behaviors of insect flight. In this study, a method of building a finite element model is proposed on the basis of a real beetle wing, which is 50 mm long in the spanwise direction and 20 mm long in the chordwise direction. We scanned a real beetle wing using a scanner to get the 2D image. The scanned 2D image was used to produce CAD data of the outer lines of the membranes and veins. Then the lines were used to build the finite element model. The model was divided into 48 regions so that the variation in the thickness of the membranes and veins could be taken into account. The effect of the cross section of the veins on the exactness of the finite element model was investigated. The finite element model was used to simulate the bending test of a real beetle wing, and the analysis results are in agreement with the experimental results.