Simulation of fracture healing incorporating mechanoregulation of tissue differentiation and dispersal/proliferation of cells

Modelling the course of healing of a long bone subjected to loading has been the subject of several investigations. These have succeeded in predicting the differentiation of tissues in the callus in response to a static mechanical load and the diffusion of biological factors. In this paper an approach is presented which includes both mechanoregulation of tissue differentiation and the diffusion and proliferation of cell populations (mesenchymal stem cells, fibroblasts, chondrocytes, and osteoblasts). This is achieved in a three-dimensional poroelastic finite element model which, being poroelastic, can model the effect of the frequency of dynamic loading. Given the number of parameters involved in the simulation, a parameter variation study is reported, and final parameters are selected based on comparison with an in vivo experiment. The model predicts that asymmetric loading creates an asymmetric distribution of tissues in the callus, but only for high bending moments. Furthermore the frequency of loading is predicted to have an effect. In conclusion, a numerical algorithm is presented incorporating both mechanoregulation and evolution of cell populations, and it proves capable of predicting realistic difference in bone healing in a 3D fracture callus.     

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.     

The mechanical behaviour of brain tissue: large strain response and constitutive modelling

The non-linear mechanical behaviour of porcine brain tissue in large shear deformations is determined. An improved method for rotational shear experiments is used, producing an approximately homogeneous strain field and leading to an enhanced accuracy. Results from oscillatory shear experiments with a strain amplitude of 0.01 and frequencies ranging from 0.04 to 16 Hz are given. The immediate loss of structural integrity, due to large deformations, influencing the mechanical behaviour of brain tissue, at the time scale of loading, is investigated. No significant immediate mechanical damage is observed for these shear deformations up to strains of 0.45. Moreover, the material behaviour during complex loading histories (loading-unloading) is investigated. Stress relaxation experiments for strains up to 0.2 and constant strain rate experiments for shear rates from 0.01 to 1 s(-1) and strains up to 0.15 are presented. A new differential viscoelastic model is used to describe the mechanical response of brain tissue. The model is formulated in terms of a large strain viscoelastic framework and considers non-linear viscous deformations in combination with non-linear elastic behaviour. This constitutive model is readily applicable in three-dimensional head models in order to predict the mechanical response of the intra-cranial contents due to an impact.     

On the use of a patient-specific rapid-prototyped model to simulate the response of the human head to impact and comparison with analytical and finite element models

Every year, thousands of fatalities result from head injuries, the majority of which are sustained in automotive accidents. In this paper, an experimental study of the response of the human head to impact is presented. A rapid prototyped model of a human head was generated based on high-resolution magnetic resonance imaging (MRI) scan data. The physical model was subjected to low velocity impacts using a metallic pendulum and a sensitivity study was performed to explore the influence of various parameters, including mass and velocity of the impactor, on the response. The experimental response characteristics are compared with predictions from an analytical model as well as with numerical predictions from finite element (FE) models generated from the same MRI data set. The results from the experimental tests closely match those predicted by both the analytical and the FE models and thus provide us with substantive corroboration of all three approaches. The remarkable agreement obtained between the measured response characteristics of rapid-prototyped skulls and numerical (FE) models obtained from in vivo MRI data clearly demonstrates the potential use of rapid-prototyping to generate experimental models for head impact studies, and, more generally, for the study of the response of complex bio-structures to loading. In addition, the quantitative and qualitative accuracy of the predictions from the analytical model is clearly demonstrated by the FE and experimental corroboration. In particular, the analytical prediction that, as impact mass drops the impact duration becomes increasingly short, appears to be substantiated, which has important implications for the onset of high pressure and shear strain gradients in the brain with potentially deleterious effects.     

Response of a human head/neck/upper-torso replica to dynamic loading--II. Analytical/numerical model

A three-dimensional lumped-parameter model of the human head/neck/upper-torso was developed to predict its motion for any specified initial conditions and that could also be used to compare with the results of other investigators. This model consists of ten rigid bodies representing the head, cervical vertebrae C1-C7, T1 and T2 combined with the rest of the torso. These rigid bodies were connected by intervertebral joints described by a stiffness matrix relating the force (moment) and translation (rotation). Fifteen pairs of muscles were incorporated in the model, represented by three-point linear elements with nonlinear constitutive relationships obtained from cadaver test results. The calculated response compared favorably with human volunteer data for both flexion and lateral whiplash. However, tests on an inanimate replica of a human indicated greater flexibility than predicted by the corresponding numerical model. The difference is believed to be due to insufficient mass of the muscles incorporated in the structure.     

Anisotropic constitutive equations and experimental tensile behavior of brain tissue

The present study deals with the experimental analysis and mechanical modeling of tensile behavior of brain soft tissue. A transversely isotropic hyperelastic model recently proposed by Meaney (2003) is adopted and mathematically studied under uniaxial loading conditions. Material parameter estimates are obtained through tensile tests on porcine brain materials accounting for regional and directional differences. Attention is focused on the short-term response. An extrapolation of tensile test data to the compression range is performed theoretically, to study the effect of the heterogeneity in the tensile/compressive response on the material parameters. Experimental and numerical results highlight the sensitivity of the adopted model to the test direction.     

A finite element model technique to determine the mechanical response of a lumbar spine segment under complex loads

This study presents a CT-based finite element model of the lumbar spine taking into account all function-related boundary conditions, such as anisotropy of mechanical properties, ligaments, contact elements, mesh size, etc. Through advanced mesh generation and employment of compound elements, the developed model is capable of assessing the mechanical response of the examined spine segment for complex loading conditions, thus providing valuable insight on stress development within the model and allowing the prediction of critical loading scenarios. The model was validated through a comparison of the calculated force-induced inclination/deformation and a correlation of these data to experimental values. The mechanical response of the examined functional spine segment was evaluated, and the effect of the loading scenario determined for both vertebral bodies as well as the connecting intervertebral disc.     

An In Vivo Experimental Validation of a Computational Model of Human Foot

Reliable computational foot models offer an alternative means to enhance knowledge on the biomechanics of human foot.Model validation is one of the most critical aspects of the entire foot modeling and analysis process.This paper presents an invivo experiment combining motion capture system and plantar pressure measure platform to validate a three-dimensional finiteelement model of human foot.The Magnetic Resonance Imaging(MRI)slices for the foot modeling and the experimental datafor validation were both collected from the same volunteer subject.The validated components included the comparison of staticmodel predictions of plantar force,plantar pressure and foot surface deformation during six loading conditions,to equivalentmeasured data.During the whole experiment,foot surface deformation,plantar force and plantar pressure were recorded simultaneouslyduring six different loaded standing conditions.The predictions of the current FE model were in good agreementwith these experimental results.     

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.     

A computational model of blast loading on the human eye

Ocular injuries from blast have increased in recent wars, but the injury mechanism associated with the primary blast wave is unknown. We employ a three-dimensional fluid–structure interaction computational model to understand the stresses and deformations incurred by the globe due to blast overpressure. Our numerical results demonstrate that the blast wave reflections off the facial features around the eye increase the pressure loading on and around the eye. The blast wave produces asymmetric loading on the eye, which causes globe distortion. The deformation response of the globe under blast loading was evaluated, and regions of high stresses and strains inside the globe were identified. Our numerical results show that the blast loading results in globe distortion and large deviatoric stresses in the sclera. These large deviatoric stresses may be indicator for the risk of interfacial failure between the tissues of the sclera and the orbit.     

On the effects of cyclic transversal forces on osseointegrated dental implants: experimental and finite element shakedown analyses

This paper is concerned with the mechanical strength of fixed osseointegrated dental implants subjected to cyclic external loads, applied mainly in a direction orthogonal to their axis. Such a loading condition, seen as a basic design action for the implant, has been given little attention so far. Experimental results and numerical simulations, performed on two- and three-dimensional Finite Element models, are discussed. The shakedown theory is used to show that a common implant design (threaded fixture-abutment-connection screw) is susceptible of low-cycle fatigue failure under loading conditions well within the working range, even if the same design is able to withstand loading of the same type, but applied monotonically, much in excess of the working values. The shakedown analyses give an indication of several possible failure modalities: the low-cycle fatigue either of the implant or of the connection screw, or the loosening of the connection screw itself. Experimental and numerical results are in good qualitative agreement, and both suggest that the issue of transversal cyclic loading on fixed dental implants should be carefully reconsidered in the design phase.     

Mechanical property determination of bone through nano- and micro-indentation testing and finite element simulation

Measurement of the mechanical properties of bone is important for estimating the stresses and strains exerted at the cellular level due to loading experienced on a macro-scale. Nano- and micro-mechanical properties of bone are also of interest to the pharmaceutical industry when drug therapies have intentional or non-intentional effects on bone mineral content and strength. The interactions that can occur between nano- and micro-indentation creep test condition parameters were considered in this study, and average hardness and elastic modulus were obtained as a function of indentation testing conditions (maximum load, load/unload rate, load-holding time, and indenter shape). The results suggest that bone reveals different mechanical properties when loading increases from the nano- to the micro-scale range (microN to N), which were measured using low- and high-load indentation testing systems. A four-parameter visco-elastic/plastic constitutive model was then applied to simulate the indentation load vs. depth response over both load ranges. Good agreement between the experimental data and finite element model was obtained when simulating the visco-elastic/plastic response of bone. The results highlight the complexity of bone as a biological tissue and the need to understand the impact of testing conditions on the measured results.     

A mathematical model of tissue-engineered cartilage development under cyclic compressive loading

In this work a coupled model of solute transport and uptake, cell proliferation, extracellular matrix synthesis and remodeling of mechanical properties accounting for the impact of mechanical loading is presented as an advancement of a previously validated coupled model for free-swelling tissue-engineered cartilage cultures. Tissue-engineering constructs were modeled as biphasic with a linear elastic solid, and relevant intrinsic mechanical stimuli in the constructs were determined by numerical simulation for use as inputs of the coupled model. The mechanical dependent formulations were derived from a calibration and parametrization dataset and validated by comparison of normalized ratios of cell counts, total glycosaminoglycans and collagen after 24-h continuous cyclic unconfined compression from another dataset. The model successfully fit the calibration dataset and predicted the results from the validation dataset with good agreement, with average relative errors up to 3.1 and 4.3 %, respectively. Temporal and spatial patterns determined for other model outputs were consistent with reported studies. The results suggest that the model describes the interaction between the simultaneous factors involved in in vitro tissue-engineered cartilage culture under dynamic loading. This approach could also be attractive for optimization of culture protocols, namely through the application to longer culture times and other types of mechanical stimuli.     

Nucleotomy reduces the effects of cyclic compressive loading with unloaded recovery on human intervertebral discs

The first objective of this study was to determine the effects of physiological cyclic loading followed by unloaded recovery on the mechanical response of human intervertebral discs. The second objective was to examine how nucleotomy alters the disc?s mechanical response to cyclic loading. To complete these objectives, 15 human L5-S1 discs were tested while intact and subsequent to nucleotomy. The testing consisted of 10,000 cycles of physiological compressive loads followed by unloaded hydrated recovery. Cyclic loading increased compression modulus (3%) and strain (33%), decreased neutral zone modulus (52%), and increased neutral zone strain (31%). Degeneration was not correlated with the effect of cyclic loading in intact discs, but was correlated with cyclic loading effects after nucleotomy, with more degenerate samples experiencing greater increases in both compressive and neutral zone strain following cyclic loading. Partial removal of the nucleus pulposus decreased the compression and neutral zone modulus while increasing strain. These changes correspond to hypermobility, which will alter overall spinal mechanics and may impact low back pain via altered motion throughout the spinal column. Nucleotomy also reduced the effects of cyclic loading on mechanical properties, likely due to altered fluid flow, which may impact cellular mechanotransduction and transport of disc nutrients and waste. Degeneration was not correlated with the acute changes of nucleotomy. Results of this study provide an ideal protocol and control data for evaluating the effectiveness of a mechanically-based disc degeneration treatment, such as a nucleus replacement.     

The micromechanical environment of intervertebral disc cells: effect of matrix anisotropy and cell geometry predicted by a linear model

Cells of the intervertebral disc exhibit spatial variations in phenotype and morphology that may be related to differences in their local mechanical environments. In this study, the stresses, strains, and dilatations in and around cells of the intervertebral disc were studied with an analytical model of the cell as a mechanical inclusion embedded in a transversely isotropic matrix. In response to tensile loading of the matrix, the local mechanical environment of the cell differed among the anatomic regions of the disc and was strongly influenced by changes in both matrix anisotropy and parameters of cell geometry. The results of this study suggest that the local cellular mechanical environment may play a role in determining both cell morphology in situ and the inhomogeneous response to mechanical loading observed in cells of the disc.     

A centric/non-centric impact protocol and finite element model methodology for the evaluation of American football helmets to evaluate risk of concussion

American football reports high incidences of head injuries, in particular, concussion. Research has described concussion as primarily a rotation dominant injury affecting the diffuse areas of brain tissue. Current standards do not measure how helmets manage rotational acceleration or how acceleration loading curves influence brain deformation from an impact and thus are missing important information in terms of how concussions occur. The purpose of this study was to investigate a proposed three-dimensional impact protocol for use in evaluating football helmets. The dynamic responses resulting from centric and non-centric impact conditions were examined to ascertain the influence they have on brain deformations in different functional regions of the brain that are linked to concussive symptoms. A centric and non-centric protocol was used to impact an American football helmet; the resulting dynamic response data was used in conjunction with a three-dimensional finite element analysis of the human brain to calculate brain tissue deformation. The direction of impact created unique loading conditions, resulting in peaks in different regions of the brain associated with concussive symptoms. The linear and rotational accelerations were not predictive of the brain deformation metrics used in this study. In conclusion, the test protocol used in this study revealed that impact conditions influences the region of loading in functional regions of brain tissue that are associated with the symptoms of concussion. The protocol also demonstrated that using brain deformation metrics may be more appropriate when evaluating risk of concussion than using dynamic response data alone.     

On the Effects of Cyclic Transversal Forces on Osseointegrated Dental Implants: Experimental and Finite Element Shakedown Analyses

This paper is concerned with the mechanical strength of fixed osseointegrated dental implants subjected to cyclic external loads, applied mainly in a direction orthogonal to their axis. Such a loading condition, seen as a basic design action for the implant, has been given little attention so far. Experimental results and numerical simulations, performed on two- and three-dimensional Finite Element models, are discussed. The shakedown theory is used to show that a common implant design (threaded fixture-abutment-connection screw) is susceptible of low-cycle fatigue failure under loading conditions well within the working range, even if the same design is able to withstand loading of the same type, but applied monotonically, much in excess of the working values. The shakedown analyses give an indication of several possible failure modalities: the low-cycle fatigue either of the implant or of the connection screw, or the loosening of the connection screw itself. Experimental and numerical results are in good qualitative agreement, and both suggest that the issue of transversal cyclic loading on fixed dental implants should be carefully reconsidered in the design phase.     

Site specific bone adaptation response to mechanical loading

Over 25 million Americans suffer from osteoporosis. Bone size and strength depends both upon the level of adaptation due to physical activity (applied load), and genetics. We hypothesized that bone adaptation to loads differs among mice breeds and bone sites. Forty-five adult female mice from three inbred strains (C57BL/6 [B6], C3H/HeJ [C3], and DBA/2J [D2]) were loaded at the right tibia and ulna in vivo with non-invasive loading devices. Each loading session consisted of 99 cycles at a force range that induced approximately 2000 microstrain (microepsilon) at the mid-shaft of the tibia (2.5 to 3.5 N force) and ulna (1.5 to 2 N force). The right and left ulnae and tibiae were collected and processed using protocols for histological undecalcified cortical bone slides. Standard histomorphometry techniques were used to quantify new bone formation. The histomorphometric variables include percentage mineralizing surface (%MS), mineral apposition rate (MAR), and bone formation rate (BFR). Net loading response [right-left limb] was compared between different breeds at tibial and ulnar sites using two-way ANOVA with repeated measures (p<0.05). Significant site differences in bone adaptation response were present within each breed (p<0.005). In all the three breeds, the tibiae showed greater percentage MS, MAR and BFR than the ulna at similar in vivo load or mechanical stimulus (strain). These data suggest that the bone formation due to loading is greater in the tibiae than the ulnae. Although, no significant breed-related differences were found in response to loading, the data show greater trends in tibial bone response in B6 mice as compared to D2 and C3 mice. Our data indicate that there are site-specific skeletal differences in bone adaptation response to similar mechanical stimulus.     

Tonic finite element model of the lower limb

It is widely admitted that muscle bracing influences the result of an impact, facilitating fractures by enhancing load transmission and reducing energy dissipation. However, human numerical models used to identify injury mechanisms involved in car crashes hardly take into account this particular mechanical behavior of muscles. In this context, in this work we aim to develop a numerical model, including muscle architecture and bracing capability, focusing on lower limbs. The three-dimensional (3-D) geometry of the musculoskeletal system was extracted from MRI images, where muscular heads were separated into individual entities. Muscle mechanical behavior is based on a phenomenological approach, and depends on a reduced number of input parameters, i.e., the muscle optimal length and its corresponding maximal force. In terms of geometry, muscles are modeled with 3-D viscoelastic solids, guided in the direction of fibers with a set of contractile springs. Validation was first achieved on an isolated bundle and then by comparing emergency braking forces resulting from both numerical simulations and experimental tests on volunteers. Frontal impact simulation showed that the inclusion of muscle bracing in modeling dynamic impact situations can alter bone stresses to potentially injury-inducing levels.     

The effects of external bending moments on lumbar muscle force distribution

A detailed biomechanical model of the low-back musculature that predicts muscle-force distribution in response to external loading is presented. The paper shows that the class of loading tasks that involve an erect posture and an arbitrary load placed on the upper limbs can be described as a loading plane whose axes are the flexion and lateral bending moments. Under these conditions, the individual muscle forces are described as a three-dimensional surface defined by the loading plane and termed the muscle activity surface (MAS). The MAS and the loading plane intersect along the switching curve which separates the load combinations that activate the muscle from those that do not. The paper suggests the existence of a recruitment order of low back muscles in response to external loads and presents a comprehensive framework for examining earlier studies that used EMG measurements to validate physiological and mechanical predictions.