Coupled Biomechanical Response of the Cornea Assessed by Non-Contact Tonometry. A Simulation Study

The mechanical response of the cornea subjected to a non-contact air-jet tonometry diagnostic test represents an interplay between its geometry, the corneal material behavior and the loading. The objective is to study this interplay to better understand and interpret the results obtained with a non-contact tonometry test. A patient-specific finite element model of a healthy eye, accounting for the load free configuration, was used. The corneal tissue was modeled as an anisotropic hyperelastic material with two preferential directions. Three different sets of parameters within the human experimental range obtained from inflation tests were considered. The influence of the IOP was studied by considering four pressure levels (10–28 mmHg) whereas the influence of corneal thickness was studied by inducing a uniform variation (300–600 microns). A Computer Fluid Dynamics (CFD) air-jet simulation determined pressure loading exerted on the anterior corneal surface. The maximum apex displacement showed a linear variation with IOP for all materials examined. On the contrary, the maximum apex displacement followed a cubic relation with corneal thickness. In addition, a significant sensitivity of the apical displacement to the corneal stiffness was also obtained. Explanation to this behavior was found in the fact that the cornea experiences bending when subjected to an air-puff loading, causing the anterior surface to work in compression whereas the posterior surface works in tension. Hence, collagen fibers located at the anterior surface do not contribute to load bearing. Non-contact tonometry devices give useful information that could be misleading since the corneal deformation is the result of the interaction between the mechanical properties, IOP, and geometry. Therefore, a non-contact tonometry test is not sufficient to evaluate their individual contribution and a complete in-vivo characterization would require more than one test to independently determine the membrane and bending corneal behavior.     

Force platform for rats measures fore and hind forces concurrently

Animal models are commonly used to test the efficacy of impact loading regimens on bone strength. We designed an inexpensive force platform to concurrently measure the separate peak vertical impact forces produced by the fore and hindfeet of immature F-344 rats when dropped onto the platform. The force platform consisted of three load cells placed in a triangular pattern under a flat plate. Rats were dropped from heights of 30, 45 and 60 cm onto the platform so that they landed on all four feet concurrently. The peak vertical impact forces produced by the feet of the rats were measured using a sampling frequency of 100 kHz. The location of each foot at landing relative to the load cells, and the force received by each load cell were combined in a series of static equations to solve for the vertical impact forces produced by the fore and hindfeet. The forces produced by feet when rats stood on the single platform were similarly determined. The forces exerted separately by the fore and hindfeet of young rats when landing on the plate as a ratio to standing forces were then calculated. Rats when standing bore more weight on their hindfeet but landed with more weight on their forefeet, which provides rationale for the greater response to landing forces of bones in the forelimbs than those in the hindlimbs. This system provided a useful method to simultaneously measure peak vertical impact forces in fore and hindfeet in rats.     

Mechanical analysis of a rodent segmental bone defect model: The effects of internal fixation and implant stiffness on load transfer

Segmental bone defect animal models are often used for evaluating the bone regeneration performance of bone substituting biomaterials. Since bone regeneration is dependent on mechanical loading, it is important to determine mechanical load transfer after stabilization of the defect and to study the effects of biomaterial stiffness on the transmitted load. In this study, we assess the mechanical load transmitted over a 6 mm femur defect that is stabilized with an internal PEEK fixation plate. Subsequently, three types of selective laser melted porous titanium implants with different stiffness values were used to graft the defect (five specimens per group). In one additional group, the defect was left empty. Micro strain gauges were used to measure strain values at four different locations of the fixation plate during external loading on the femoral head. The load sharing between the fixation plate and titanium implant was highly variable with standard deviations of measured strain values between 31 and 93% of the mean values. As a consequence, no significant differences were measured between the forces transmitted through the titanium implants with different elastic moduli. Only some non-significant trends were observed in the mean strain values that, consistent with the results of a previous finite element study, implied the force transmitted through the implant increases with the implant stiffness. The applied internal fixation method does not standardize mechanical loading over the defect to enable detecting small differences in bone regeneration performances of bone substituting biomaterials. In conclusion, the fixation method requires further optimization to reduce the effects of the operative procedure and make the mechanical loading more consistent and improve the overall sensitivity of this rat femur defect model.     

An MRI-compatible foot-loading device for assessment of internal tissue deformation

It is well known that mechanical forces acting within the soft tissues of the foot can contribute to the formation of neuropathic ulcers in people with diabetes. Presently, only surface measurements of plantar pressure are used clinically to estimate risk status due to mechanical loading. It is currently not known how surface measurements relate to the three-dimensional (3-D) internal stress/strain state of the foot. This article describes the development of a foot-loading device that allows for the direct observation of the internal deformation of foot tissues under known forces. Ground reaction forces and plantar pressure distributions during normal walking were measured in ten healthy young adults. One instant in the gait cycle, when pressure under the metatarsal heads reached a peak, was extracted for simulation in an MR imager. T1-weighted 3-D gradient echo MRI sets were collected as the simulated walking ground reaction force was incrementally applied to the foot by the novel foot-loading device. The sub-metatarsal head soft-tissue thickness decreased rapidly at first and then reached a plateau. Peak plantar pressure measurements collected within the loading device (161+/-75kPa) were lower in magnitude and less focal than pressures measured during walking (492+/-91kPa). This finding implies that although the device successfully applied full peak walking ground reaction forces to the foot, they were not distributed in the same manner as during walking. Although not representative of gait, the data collected from this in vivo mechanical test are suitable for determination of foot tissue material properties or, when combined with finite element modeling, to examine the relationship between surface loading and internal stress.     

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.     

Topological remodeling of cultured endothelial cells by characterized cyclic strains

Evaluation of mechanical environment on cellular function is a major field of study in cellular engineering. Endothelial cells lining the entire vascular lumen are subjected to pulsatile blood pressure and flow. Mechanical stresses caused by such forces determine function of arteries and their remodeling. Critical values of mechanical stresses contribute to endothelial damage, plaque formation and atherosclerosis. A device to impose cyclic strain on cultured cells inside an incubator was designed and manufactured operating with different load amplitudes, frequencies, numbers of cycles and ratios of extension to relaxation. Endothelial cells cultured on collagen coated silicon scaffolds were subjected to cyclic loading. Effects of mechanical loading on cell morphology were quantified using image processing methods. Results showed change in cell orientation from a randomly oriented before the test up to 80 degrees alignment from load axis after loading. Endothelial cells were elongated with shape index reductions up to 47% after cyclic stretch. By increase of strain amplitude, loading frequency and number of cycles, significant decrease in shape index and significant increase in orientation angle were observed. Change of load waveform similar to arterial pulse pressure waveform resulted in alteration of cell alignment with 9.7% decrease in shape index, and 10.8% increase in orientation angle. Results of cyclic loading tests in a disturbed environment with elevated PH showed lack of remodeling. It was concluded that tensile loading of endothelial cells influences cell morphology and alignment, a mechanism for structural regulation, functional adaptation and remodeling. Disturbed environment results in endothelial dysfunction and injury.     

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.     

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.     

Effect of load position on muscle forces,internal loads and stability of the human spine in upright postures

A novel kinematics-based approach coupled with a non-linear finite element model was used to investigate the effect of changes in the load position and posture on muscle activity, internal loads and stability margin of the human spine in upright standing postures. In addition to 397 N gravity, external loads of 195 and 380 N were considered at different lever arms and heights. Muscle forces, internal loads and stability margin substantially increased as loads displaced anteriorly away from the body. Under same load magnitude and location, adopting a kyphotic posture as compared with a lordotic one increased muscle forces, internal loads and stability margin. An increase in the height of a load held at a fixed lever arm substantially diminished system stability thus requiring additional muscle activations to maintain the same margin of stability. Results suggest the importance of the load position and lumbar posture in spinal biomechanics during various manual material handling operations.     

Effect of load position on muscle forces, internal loads and stability of the human spine in upright postures

A novel kinematics-based approach coupled with a non-linear finite element model was used to investigate the effect of changes in the load position and posture on muscle activity, internal loads and stability margin of the human spine in upright standing postures. In addition to 397 N gravity, external loads of 195 and 380 N were considered at different lever arms and heights. Muscle forces, internal loads and stability margin substantially increased as loads displaced anteriorly away from the body. Under same load magnitude and location, adopting a kyphotic posture as compared with a lordotic one increased muscle forces, internal loads and stability margin. An increase in the height of a load held at a fixed lever arm substantially diminished system stability thus requiring additional muscle activations to maintain the same margin of stability. Results suggest the importance of the load position and lumbar posture in spinal biomechanics during various manual material handling operations.     

Principles of determination and verification of muscle forces in the human musculoskeletal system: Muscle forces to minimise bending stress

While there are a growing number of increasingly complex methodologies available to model geometry and material properties of bones, these models still cannot accurately describe physical behaviour of the skeletal system unless the boundary conditions, especially muscular loading, are correct. Available in vivo measurements of muscle forces are mostly highly invasive and offer no practical way to validate the outcome of any computational model that predicts muscle forces. However, muscle forces can be verified indirectly using the fundamental property of living tissue to functional adaptation and finite element (FE) analysis. Even though the mechanisms of the functional adaptation are not fully understood, its result is clearly seen in the shape and inner structure of bones. The FE method provides a precise tool for analysis of the stress/strain distribution in the bone under given loading conditions. The present work sets principles for the determination of the muscle forces on the basis of the widely accepted view that biological systems are optimized light-weight structures with minimised amount of unloaded/underloaded material and hence evenly distributed loading throughout the structure. Bending loading of bones is avoided/compensated in bones under physiological loading. Thus, bending minimisation provides the basis for the determination of the musculoskeletal system loading. As a result of our approach, the muscle forces for a human femur during normal gait and sitting down (peak hip joint force) are obtained such that the bone is loaded predominantly in compression and the stress distribution in proximal and diaphyseal femur corresponds to the material distribution in bone.     

The effects of misalignment during in vivo loading of bone: Techniques to detect the proximity of objects in three-dimensional models

Theories of mechanical adaptation of bone suggest that mechanical loading causes bone formation at discrete locations within bone microstructure experiencing the greatest mechanical stress/strain. Experimental testing of such theories requires in vivo loading experiments and high-resolution finite element models to determine the distribution of mechanical stresses. Finite element models of in vivo loading experiments typically assume idealized boundary conditions with applied load perfectly oriented on the bone, however small misalignments in load orientation during an in vivo experiment are unavoidable, and potentially confound the ability of finite element models to predict locations of bone formation at the scale of micrometers. Here we demonstrate two different three-dimensional spatial correlation methods to determine the effects of misalignment in load orientation on the locations of high mechanical stress/strain in the rodent tail loading model. We find that, in cancellous bone, the locations of tissue with high stress are maintained under reasonable misalignments in load orientation (p<0.01). In cortical bone, however, angular misalignments in the dorsal direction can alter the locations of high mechanical stress, but the locations of tissue with high stress are maintained under other misalignments (p<0.01). We conclude that, when using finite element models of the rodent tail loading model, small misalignments in loading orientation do not affect the predicted locations of high mechanical stress within cancellous bone.     

Intracellular stress tomography reveals stress focusing and structural anisotropy in cytoskeleton of living cells

We describe a novel synchronous detection approach to map the transmission of mechanical stresses within the cytoplasm of an adherent cell. Using fluorescent protein-labeled mitochondria or cytoskeletal components as fiducial markers, we measured displacements and computed stresses in the cytoskeleton of a living cell plated on extracellular matrix molecules that arise in response to a small, external localized oscillatory load applied to transmembrane receptors on the apical cell surface. Induced synchronous displacements, stresses, and phase lags were found to be concentrated at sites quite remote from the localized load and were modulated by the preexisting tensile stress (prestress) in the cytoskeleton. Stresses applied at the apical surface also resulted in displacements of focal adhesion sites at the cell base. Cytoskeletal anisotropy was revealed by differential phase lags in X vs. Y directions. Displacements and stresses in the cytoskeleton of a cell plated on poly-L-lysine decayed quickly and were not concentrated at remote sites. These data indicate that mechanical forces are transferred across discrete cytoskeletal elements over long distances through the cytoplasm in the living adherent cell. mechanical forces; deformation; focal adhesion; microfilament     

Apparatus to obtain rotational flexibility of the human knee under moment loads in vivo

The contributions of this paper are twofold. One is the design and performance evaluation of new equipment to determine the rotational flexibility of the human knee in vivo. Since determining knee flexibility requires the application of external loads and the measurement of knee rotations, the new equipment consists of a load application stand and a triaxial goniometer. The triaxial goniometer noninvasively mounts to the leg and directly measures the relative three degrees-of-freedom rotations of the knee sequentially and independently. The goniometer incorporates several unique design features which enhance measurement accuracy. The load stand applies pure varus/valgus and external/internal axial moments either individually or in combination through the use of motors controlled by the test subject. Unique to this design are features which enable the application of moments to the knee which minimise shear forces. Other unique design features permit the stand to control hip and knee flexion angles, muscle contraction, and axial loading. To assess the accuracy with which rotations are measured during experiments, three tests were conducted with the equipment. One test evaluated the inherent accuracy of the goniometer, a second test assessed the potential for goniometer slippage during loading, and a third explored the effect of goniometer mounting on the repeatability of results. A special verification apparatus facilitated evaluation of goniometer inherent accuracy. A second contribution of the paper is an investigation of the effect of foot constraints (i.e. boundary conditions) on flexibility results. To make this investigation, three subjects were tested with the knee at 15 degrees of flexion. Results revealed large differences in flexibility between constraining the foot in both external/internal and varus/valgus rotations and permitting the foot to rotate freely in the direction not being loaded. Further, constraint moments as high as 23 Nm were also recorded. These results emphasise that in order to obtain accurate flexibility results for isolated loads, the foot must be unconstrained by the loading apparatus.     

Postoperative analysis of the mechanical interaction between stent and host tissue in patients after transcatheter aortic valve implantation

The analysis is based on a finite element procedure to extract the contact forces between an implanted Nitinol stent and the surrounding host tissue using postoperative CT images. The methodology was applied for patients (N=46) which have undergone a TAVI procedure with the Medtronic CoreValve Revalving System (MCRS) to obtain corresponding deformation and force maps. The postoperative CT data were recorded for each patient in both systolic and diastolic phase of the heart cycle. Scalar parameters were defined, which map deformed geometry and contact force field to mechanically relevant quantities: radial dilatation, radial shape distortion, non-convex points, mean force, a force deviation measure and a pressure equivalent. The latter demonstrates that in the area of the aortic root, the added circumferential loading is of the same order as the baseline average blood pressure, thus leading to a doubling of the local mechanical load. Generally the force distribution along the stent is non-homogeneous. A comparison of systolic and diastolic data revealed slightly higher contact forces during the diastole, indicating that the stent has to carry more load in this phase. The geometrical and mechanical parameters were compared for two types of clinical complication: para-valvular leakage (PVL) and permanent pacemaker requirement (PPM). It was found that an increase in mean force can be associated with both complications; significantly for PVL and as a trend for PPM.     

Computational neurotrauma—design, simulation, and analysis of controlled cortical impact model

The controlled cortical impact (CCI) model is widely used in many laboratories to study traumatic brain injury (TBI). Although external impact parameters during CCI tests could be clearly defined, little is known about the internal tissue-level mechanical responses of the rat brain. Furthermore, the external impact parameters tend to vary considerably among different labs making the comparison of research findings difficult if not impossible. In this study, a design of computer experiments was performed with typical external impact parameters commonly found in the literature. An anatomically detailed finite element (FE) rat brain model was used to simulate the CCI experiments to correlate external mechanical parameters (impact depth, impact velocity, impactor shape, impactor size, and craniotomy pattern) with rat brain internal responses, as predicted by the FE model. Systematic analysis of the results revealed that impact depth was the leading factor affecting the predicted brain internal responses. Interestingly, impactor shape ranked as the second most important factor, surpassing impactor diameter and velocity which were commonly reported in the literature as indicators of injury severity along with impact depth. The differences in whole brain response due to a unilateral or a bilateral craniotomy were small, but those of regional intracranial tissue stretches were large. The interaction effects of any two external parameters were not significant. This study demonstrates the potential of using numerical FE modeling to engineer better experimental TBI models in the future.     

Consideration of multiple load cases is critical in modelling orthotropic bone adaptation in the femur

Functional adaptation of the femur has been investigated in several studies by embedding bone remodelling algorithms in finite element (FE) models, with simplifications often made to the representation of bone’s material symmetry and mechanical environment. An orthotropic strain-driven adaptation algorithm is proposed in order to predict the femur’s volumetric material property distribution and directionality of its internal structures within a continuum. The algorithm was applied to a FE model of the femur, with muscles, ligaments and joints included explicitly. Multiple load cases representing distinct frames of two activities of daily living (walking and stair climbing) were considered. It is hypothesised that low shear moduli occur in areas of bone that are simply loaded and high shear moduli in areas subjected to complex loading conditions. In addition, it is investigated whether material properties of different femoral regions are stimulated by different activities. The loading and boundary conditions were considered to provide a physiological mechanical environment. The resulting volumetric material property distribution and directionalities agreed with ex vivo imaging data for the whole femur. Regions where non-orthogonal trabecular crossing has been documented coincided with higher values of predicted shear moduli. The topological influence of the different activities modelled was analysed. The influence of stair climbing on the properties of the femoral neck region is highlighted. It is recommended that multiple load cases should be considered when modelling bone adaptation. The orthotropic model of the complete femur is released with this study.     

Numerical simulation of load-induced bone structural remodelling using stress-limit criterion

A simple and efficient numerical method for predicting the remodelling of adaptive materials and structures under applied loading was presented and implemented within a finite element framework. The model uses the trajectorial architecture theory of optimisation to predict the remodelling of material microstructure and structural organisation under mechanical loading. We used the proposed model to calculate the density distribution of proximal femur in the frontal plane. The loading considered was the hip joint contact forces and muscular forces at the attachment sites of the muscles to the bone. These forces were estimated from a separate finite element calculation using a heterogeneous three-dimensional model of the proximal femur. The density distributions obtained by this procedure has a qualitative similarity with in vivo observations. Solutions displayed the characteristic high-density channels that are evident in the Dual X-ray Absorptiometry scan. There is also evidence of the intramedullary canal, as well as low-density regions in the femoral neck. Several parametric studies were carried out to highlight the advantages of the proposed method, which includes fast convergence and low-computational cost. The potential applications of the proposed method in predicting bone structural remodelling in cancer are also briefly discussed.     

Analysis of the mechanical behavior of chondrocytes in unconfined compression tests for cyclic loading

Experimental evidence indicates that the biosynthetic activity of chondrocytes is associated with the mechanical environment. For example, excessive, repetitive loading has been found to induce cell death, morphological and cellular damage, as seen in degenerative joint disease, while cyclic, physiological-like loading has been found to trigger a partial recovery of morphological and ultrastructural aspects in osteoarthritic human articular chondrocytes. Mechanical stimuli are believed to influence the biosynthetic activity via the deformation of cells. However, the in situ deformation of chondrocytes for cyclic loading conditions has not been investigated experimentally or theoretically. The purpose of the present study was to simulate the mechanical response of chondrocytes to cyclic loading in unconfined compression tests using a finite element model. The material properties of chondrocytes and extracellular matrix were considered to be biphasic. The time-histories of the shape and volume variations of chondrocytes at three locations (i.e., surface, center, and bottom) within the cartilage were predicted for static and cyclic loading conditions at two frequencies (0.02 and 0.1 Hz) and two amplitudes (0.1 and 0.2 MPa). Our results show that cells at different depths within the cartilage deform differently during cyclic loading, and that the depth dependence of cell deformation is influenced by the amplitude of the cyclic loading. Cell deformations under cyclic loading of 0.02 Hz were found to be similar to those at 0.1 Hz. We conclude from the simulation results that, in homogeneous cartilage layers, cell deformations are location-dependent, and further are affected by load magnitude. In physiological conditions, the mechanical environment of cells are even more complex due to the anisotropy, depth-dependent inhomogeneity, and tension-compression non-linearity of the cartilage matrix. Therefore, it is feasible to speculate that biosynthetic responses of chondrocytes to cyclic loading depend on cell location and load magnitude.     

MRI-based experimentations of fingertip flat compression: Geometrical measurements and finite element inverse simulations to investigate material property parameters

Modeling human-object interactions is a necessary step in the ergonomic assessment of products. Fingertip finite element models can help investigating these interactions, if they are built based on realistic geometrical data and material properties. The aim of this study was to investigate the fingertip geometry and its mechanical response under compression, and to identify the parameters of a hyperelastic material property associated to the fingertip soft tissues.Fingertip compression tests in an MRI device were performed on 5 subjects at either 2 or 4 N and at 15° or 50°. The MRI images allowed to document both the internal and external fingertip dimensions and to build 5 subject-specific finite element models. Simulations reproducing the fingertip compression tests were run to obtain the material property parameters of the soft tissues.Results indicated that two ellipses in the sagittal and longitudinal plane could describe the external fingertip geometry. The internal geometries indicated an averaged maximal thickness of soft tissues of 6.4 ± 0.8 mm and a 4 ± 1 mm height for the phalanx bone. The averaged deflections under loading went from 1.8 ± 0.3 mm at 2 N, 50° to 3.1 ± 0.2 mm at 4 N, 15°. Finally, the following set of parameters for a second order hyperelastic law to model the fingertip soft tissues was proposed: C₀₁ = 0.59 ± 0.09 kPa and C₂₀ = 2.65 ± 0.88 kPa.These data should facilitate further efforts on fingertip finite element modeling.