Periosteal and endosteal control of bone remodeling under torsional loading.

The shape changes that occur in the mid-diaphysis of a long bone due to adaptive remodeling induced by increasing or decreasing the axial and/or torsional loading of the bone are investigated using a simple model. In this model the mid-diaphysis of a long bone is represented as a hollow thick-walled right-circular cylinder, and different optimal strategies for bone remodeling are considered. It is shown that if such a thick-walled right-circular cylinder capable of surface remodeling is subjected to an axial compressive load and a twisting torque, then the remodeling patterns depend on whether the periosteal surface or the endosteal surface controls the limits of the remodeling process. It is shown that the effect of increasing the torque is always opposite to the effect of increasing the compressive load. Thus, similar remodeling patterns are obtained by increasing one type of loading and decreasing the other. Aside from the restriction of idealized cylindrical geometry, the only assumptions made are that the bone tissue is linearly elastic and that there exists a finite range of remodeling equilibrium stresses. Only those loading situations which maintain the bone in remodeling equilibrium are considered in this work. It follows that the results presented are independent of the specific type of rule governing the temporal evolution of the bone shape, since any such rule applies only in situations where there is active remodeling and, hence, no remodeling equilibrium.     

Regional distribution of axial strain and circumferential residual strain in the layered rabbit oesophagus

The oesophagus is subjected to large axial strains in vivo and the zero-stress state is not a closed cylinder but an open circular cylindrical sector. The closed cylinder with no external loads applied is called the no-load state and residual strain is the difference in strain between the no-load state and zero-stress state. To understand oesophageal physiology and pathophysiology, it is necessary to know the distribution of axial strain, the zero-stress state, the stress-strain relations of oesophageal tissue, and the changes of these states and relationships due to biological remodeling of the tissue under stress. This study is addressed to such biomechanical properties in normal rabbits. The oesophagi were marked on the surface in vivo, photographed, excised (in vitro state), photographed again, and sectioned into rings (no-load state) in an organ bath containing calcium-free Kreb's solution with dextran and EGTA added. The rings were cut radially to obtain the zero-stress state for the non-separated wall and further dissected to separate the muscle and submucosa layers. Equilibrium was awaited for 30min in each state and the specimens were photographed in no-load and the zero-stress states. The oesophageal length, circumferences, layer thicknesses and areas, and openings angle were measured from the digitised images. The oesophagus shortened axially by 35% after excision. The in vivo axial strain showed a significant variation with the highest values in the mid-oesophagus (p<0.001). Luminal area, circumferences, and wall and layer thicknesses and areas varied in axial direction (in all tests p<0.05). The residual strain was compressive at the mucosal surface and tensile at the serosal surface. The dissection studies demonstrated shear forces between the two layers in the non-separated wall in the no-load and zero-stress states. In conclusion, our data show significant axial variation in passive morphometric and biomechanical properties of the oesophagus. The oesophagus is a layered composite structure with nonlinear and anisotropic mechanical behaviour.     

Experimental and finite element analysis of the rat ulnar loading model-correlations between strain and bone formation following fatigue loading

The rat forelimb compression model has been used widely to study bone response to mechanical loading. We used strain gages to assess load sharing between the ulna and radius in the forelimb of adult Fisher rats. We used histology and peripheral quantitative computed tomography (pQCT) to quantify ulnar bone formation 12 days after in vivo fatigue loading. Lastly, we developed a finite element model of the ulna to predict the pattern of surface strains during compression. Our findings indicate that at the mid-shaft the ulna carries 65% of the applied compressive force on the forelimb. We observed large variations in fatigue-induced bone formation over the circumference and length of the ulna. Bone formation was greatest 1-2 mm distal to the mid-shaft. At the mid-shaft, we observed woven bone formation that was greatest medially. Finite element analysis indicated a strain pattern consistent with a compression-bending loading mode, with the greatest strains occurring in compression on the medial surface and lesser tensile strains occurring laterally. A peak strain of -5190 microepsilon (for 13.3N forelimb compression) occurred 1-2 mm distal to the mid-shaft. The pattern of bone formation in the longitudinal direction was highly correlated to the predicted peak compressive axial strains at seven cross-sections (r2 = 0.89, p = 0.014). The in-plane pattern of bone formation was poorly correlated to the predicted magnitude of axial strain at 51 periosteal locations (r2 = 0.21, p < 0.001), because the least bone formation was observed where tensile strains were highest. These findings indicate that the magnitude of bone formation after fatigue loading is greatest in regions of high compressive strain.     

The effect of stress concentration on bone remodeling: theoretical predictions

Theoretical predictions of internal bone remodeling around an elliptical hole are studied. The internal remodeling theory due to Cowin and Hegedus is employed. The bone is modeled as an initially homogeneous adaptive elastic plate with an elliptical hole under a superposed steady compressive load. It is shown that there will exist a final inhomogeneous remodeling distribution around the hole that will disappear away from the hole. The remodeling is such that the compressive stress concentration causes the bone structure to evolve to one of greater density and stiffer elastic coefficients. The speed of remodeling around the hole and its variation with respect to distance is investigated and discussed. It is shown that the rate of bone reinforcement in the area of compressive stress concentration is much higher than the rate of bone resorption in the area of existing tensile stress. Special cases of a circular hole and vertical and horizontal slots are studied and discussed.     

A musculoskeletal model of the equine forelimb for determining surface stresses and strains in the humerus--part I. Mathematical modeling

Knowledge of the forces that act upon the equine humerus while the horse is standing and the resulting strains experienced by the bone is useful for the prevention and treatment of fractures and for assessing the proximolateral aspect of the bone as a site for obtaining autogenous bone graft material. The first objective was to develop a mathematical model to predict the loads on the proximal half of the humerus created by the surrounding musculature and ground reaction forces while the horse is standing. The second objective was to calculate surface bone stresses and strains at three cross sections on the humerus corresponding to the donor site for bone grafts, a site predisposed to stress fracture, and the middle of the diaphysis. A three-dimensional mathematical model employing optimization techniques and asymmetrical beam analysis was used to calculate shoulder muscle forces and surface strains on the proximal and mid-diaphyseal aspects of the humerus. The active shoulder muscles, which included the supraspinatus, infraspinatus, subscapularis, and short head of the deltoid, produced small forces while the horse is standing; all of which were limited to 4.3% of their corresponding maximum voluntary contraction. As a result, the strains calculated at the proximal cross sections of the humerus were small, with maximum compressive strains of -104microepsilon at the cranial aspect of the bone graft donor cross section. The middle of the diaphysis experienced larger strain magnitudes with compressive strains at the lateral and the caudal aspects and tensile strains at the medial and cranial aspects (-377microepsilon and 258microepsilon maximum values, respectively) while the horse is standing. Small strains at the donor bone graft site do not rule out using this location to harvest bone graft tissue, although strains while rising to a standing position during recovery from anesthesia are unknown. At the site common to stress fractures, small strains imply that the stresses seen by this region while the horse is standing, although applied for long periods of time, are not a cause of fracture in this location. Knowing the specific regions of the middle of the diaphysis of the humerus that experience tensile and compressive strains is valuable in determining optimum placement of internal fixation devices for the treatment of complete fractures.     

Comparative effects of alendronate and alfacalcidol on cancellous and cortical bone mass and bone mechanical properties in ovariectomized rats.

The purpose of the present study was to compare the effects of alendronate and alfacalcidol on cancellous and cortical bone mass and bone mechanical properties in ovariectomized rats. Twenty-six female Sprague-Dawley rats, 7 months of age, were randomized by the stratified weight method into four groups: the sham-operated control (Sham) group and the three ovariectomy (OVX) groups, namely, OVX + vehicle, OVX + alendronate (2.5 mg/kg, p.o., daily), and OVX + alfacalcidol (0.5 mug/kg, p.o., daily). At the end of the 8-week experimental period, bone histomorphometric analyses of cancellous bone at the proximal tibial metaphysis and cortical bone at the tibial diaphysis were performed, and the mechanical properties of the femoral distal metaphysis and femoral diaphysis were evaluated. OVX decreased cancellous bone volume per total tissue volume (BV/TV), and the maximum load of the femoral distal metaphysis, as a result of increases in serum osteocalcin (OC) levels, and also the number of osteoclasts (N.Oc), osteoclast surface (OcS) and bone formation rate (BFR) per bone surface (BS), and BFR/BV, without any effect on cortical area (Ct Ar), or maximum load of the femoral diaphysis. Alendronate prevented this decrease in cancellous BV/TV by suppressing increases in N.Oc/BS, OcS/BS, BFR/BS, and BFR/BV, without any apparent effect on Ct Ar, or maximum load of the femoral distal metaphysis and femoral diaphysis. On the other hand, alfacalcidol increased cancellous BV/TV, Ct Ar, and the maximum load of the femoral distal metaphysis and femoral diaphysis, by mildly decreasing trabecular BFR/BV, maintaining trabecular mineral apposition rate and osteoblast surface per BS, increasing periosteal and endocortical BFR/BS, and preventing an increase in endocortical eroded surface per BS. The present study clearly showed the differential skeletal effects of alendronate and alfacalcidol in ovariectomized rats. Alendronate prevented OVX-induced cancellous bone loss by suppressing bone turnover, while alfacalcidol improved cancellous and cortical bone mass and bone strength by suppressing bone resorption and maintaining or even increasing bone formation.     

Perivascular tethering modulates the geometry and biomechanics of cerebral arterioles

Recent studies have renewed interest in the effects of perivascular tethering on vascular mechanics, particularly growth and remodeling. We quantified effects of axial and circumferential tethering on rabbit pial arterioles from the ventral occipital lobe of the brain. The homeostatic axial pre-stretch, which is influenced by perivascular tethering, was measured in situ to be 1.24±0.04. Using a cannulated microvessel preparation, wall mechanics were then quantified in vitro for isolated arterioles at low (1.10) or normal (1.24) values of axial stretch and for tethered arterioles having perivascular support. Axial stretch did not significantly affect changes in circumferential stretch or stress upon pressurization, but circumferential tethering caused arteriolar geometry to change from a circular cross-section at normal pressure to an elliptical one at pressures above and below normal. Calculations suggested that the observed levels of ellipticity could cause a modest decrease in volumetric blood flow, but also a pronounced variation in shear stress around the circumference of the arteriole. An elliptical cross-section could thus increase vascular resistance or promote luminal remodeling at pressures different from normal. This characterization of effects of perivascular tethering on pial arterioles should prove useful in future studies of roles of perturbed cerebral blood flow on the propensity of the cerebral microcirculation to remodel.     

Normal contact of elastic spheres with two elastic layers as a model of joint articulation.

An analytical model of two elastic spheres with two elastic layers in normal, frictionless contact is developed which simulates contact of articulating joints, and allows for the calculation of stresses and displacements in the layered region of contact. Using various layer/layer/substrate combinations, the effects of variations in layer and substrate properties are determined in relation to the occurrence of tensile and shear stresses as the source of crack initiation in joint cartilage and bone. Vertical cracking at the cartilage surface and horizontal splitting at the tidemark have been observed in joints with primary osteoarthritis. Deep vertical cracks in the calcified cartilage and underlying bone have been observed in blunt trauma experiments. The current model shows that cartilage stresses for a particular system are a function of the ratio of contact radius to total layer thickness (a/h). Surface tension, which is observed for a/h small, is alleviated as a/h is increased due to increased load, softening and/or thinning of the cartilage layer. Decreases in a/h due to cartilage stiffening lead to increased global compressive stresses and increased incidence of surface tension, consistent with impact-induced surface cracks. Cartilage stresses are not significantly affected by variations in stiffness of the underlying material. Tensile radial strains in the cartilage layer approach one-third of the normal compressive strains, and increase significantly with cartilage softening. For cases where the middle layer stiffness exceeds that of the underlying substrate, tensile stresses occur at the base of the middle layer, consistent with impact induced cracks in the zone of calcified cartilage and subchondral bone. The presence of the superficial tangential zone appears to have little effect on underlying cartilage stresses.     

A Computational Model for Cortical Endosteal Surface Remodeling Induced by Mechanical Disuse

In mechanical disuse conditions associated with immobilization and microgravity in spaceflight, cortical endosteal surface moved outward with periosteal surface moving slightly or unchanged, resulting in reduction of cortical thickness. Reduced thickness of the shaft cortex of long bone can be considered as an independent predictor of fractures. Accordingly, it is important to study the remodeling process at cortical endosteal surface. This paper presents a computer simulation of cortical endosteal remodeling induced by mechanical disuse at the Basic Multicellular Units level with cortical thickness as controlling variables. The remodeling analysis was performed on a representative rectangular slice of the cross section of cortical bone volume. The pQCT data showing the relationship between the duration of paralysis and bone structure of spinal cord injured patients by Eser et al. (2004) were used as an example of mechanical disuse to validate the model. Cortical thickness, BMU activation frequency, mechanical load and principal compressive strain for tibia and femur cortical models were simulated. The effects of varying the mechanical load and maximum BMU activation frequency were also investigated. The cortical thicknesses of femur and tibia models were both consistent with the clinical data. Varying the decreasing coefficient in mechanical load equation had little effect on the steady state values of cortical thickness and BMU activation frequency. However, it had much effect on the time to reach steady state. The maximum BMU activation frequency had effects on both the steady state value and the time to reach steady state for cortical thickness and BMU activation frequency. The computational model for cortical endosteal surface remodeling developed in this paper can be further used to quantify and predict the effects of mechanical factors and biological factors on cortical thickness and help us to better understand the relationship between bone morphology and mechanical as well as biological environment.     

Accuracy of specimen-specific nonlinear finite element analysis for evaluation of radial diaphysis strength in cadaver material

The feasibility of a user-specific finite element model for predicting the in situ strength of the radius after implantation of bone plates for open fracture reduction was established. The effect of metal artifact in CT imaging was characterized. The results were verified against biomechanical test data. Fourteen cadaveric radii were divided into two groups: (1) intact radii for evaluating the accuracy of radial diaphysis strength predictions with finite element analysis and (2) radii with a locking plate affixed for evaluating metal artifact. All bones were imaged with CT. In the plated group, radii were first imaged with the plates affixed (for simulating digital plate removal). They were then subsequently imaged with the locking plates and screws removed (actual plate removal). Fracture strength of the radius diaphysis under axial compression was predicted with a three-dimensional, specimen-specific, nonlinear finite element analysis for both the intact and plated bones (bones with and without the plate captured in the scan). Specimens were then loaded to failure using a universal testing machine to verify the actual fracture load. In the intact group, the physical and predicted fracture loads were strongly correlated. For radii with plates affixed, the physical and predicted (simulated plate removal and actual plate removal) fracture loads were strongly correlated. This study demonstrates that our specimen-specific finite element analysis can accurately predict the strength of the radial diaphysis. The metal artifact from CT imaging was shown to produce an overestimate of strength.     

A musculoskeletal model of the equine forelimb for determining surface stresses and strains in the humerus-part II. Experimental testing and model validation

The first objective of this study was to experimentally determine surface bone strain magnitudes and directions at the donor site for bone grafts, the site predisposed to stress fracture, the medial and cranial aspects of the transverse cross section corresponding to the stress fracture site, and the middle of the diaphysis of the humerus of a simplified in vitro laboratory preparation. The second objective was to determine whether computing strains solely in the direction of the longitudinal axis of the humerus in the mathematical model was inherently limited by comparing the strains measured along the longitudinal axis of the bone to the principal strain magnitudes and directions. The final objective was to determine whether the mathematical model formulated in Part I [Pollock et al., 2008, ASME J. Biomech. Eng., 130, p. 041006] is valid for determining the bone surface strains at the various locations on the humerus where experimentally measured longitudinal strains are comparable to principal strains. Triple rosette strain gauges were applied at four locations circumferentially on each of two cross sections of interest using a simplified in vitro laboratory preparation. The muscles included the biceps brachii muscle in addition to loaded shoulder muscles that were predicted active by the mathematical model. Strains from the middle grid of each rosette, aligned along the longitudinal axis of the humerus, were compared with calculated principal strain magnitudes and directions. The results indicated that calculating strains solely in the direction of the longitudinal axis is appropriate at six of eight locations. At the cranial and medial aspects of the middle of the diaphysis, the average minimum principal strain was not comparable to the average experimental longitudinal strain. Further analysis at the remaining six locations indicated that the mathematical model formulated in Part I predicts strains within +/-2 standard deviations of experimental strains at four of these locations and predicts negligible strains at the remaining two locations, which is consistent with experimental strains. Experimentally determined longitudinal strains at the middle of the diaphysis of the humerus indicate that tensile strains occur at the cranial aspect and compressive strains occur at the caudal aspect while the horse is standing, which is useful for fracture fixation.     

Axial-shear interaction effects on microdamage in bovine tibial trabecular bone

Because many osteoporotic fractures occur during a fall, understanding the effect of off-axis loads on initiation and propagation of microdamage in trabecular bone should provide further insight into the biomechanics of age-related fractures. Fourteen on-axis cylindrical specimens were prepared from 12 bovine tibiae. Fluorescent stains were used to label the microdamage due to a sequence of compressive and torsional damaging loads. The mean decrease in Young's modulus was over four times greater than that in the shear modulus after the compressive overload, while there was no difference between the decrease in the axial and torsional stiffnesses after the torsional overload. The total microcrack density due to compression was uniform across the radius of the cylindrical specimens, while the mean density of microcracks due to torsional overloading increased from the axis of the cylindrical specimen to the circumference. The high density of microcracks near the axis of the specimen following torsional overloading was unexpected because of the low strains. Nearly 40% of the microcracks due to torsion propagated from pre-existing microcracks caused by axial compression, indicating that existing microcracks may extend at relatively low strain if the loading mode changes. The propagating microcracks were, on average, longer than the initiating microcracks due to either compressive or torsional loading. Damage due to axial compression appears to increase the susceptibility of trabecular bone to damage propagation during subsequent torsional loads, but it has little effect on the elastic properties in shear.     

Uniform stress state in bone structure with residual stress.

Residual stress and strain in living tissues have been investigated from the viewpoint of mechanical optimality maintained by adaptive remodeling. In this study, the residual stresses in the cortical-cancellous bone complex of bovine coccygeal vertebrae were examined. Biaxial strain gages were bonded onto the cortical surface, so that the gage axes were aligned in the cephalocaudal and circumferential directions. Strains induced by removal of the end-plate and the cancellous bone were recorded sequentially. The results revealed the existence of compressive residual stress in the cortical bone and tensile residual stress in the cancellous bone in both the cephalocaudal and the circumferential direction. The observed strains were examined on the basis of the uniform stress hypothesis using a three-bar model for the cephalocaudal direction and a three-layered cylinder model for the circumferential direction. In this model study, the magnitude of effective stresses, which is defined as the macroscopic stress divided by the area fraction of bone material, was found not to differ significantly between cephalocaudal and circumferential directions, although they were evaluated using independent models. These results demonstrate that the uniform stress state of the cortical-cancellous bone structure is consistent with results obtained in the cutting experiment when the existence of residual stress is taken into account.     

A comparison of bone strain measurements at anatomically relevant sites using surface gauges versus strain gauged bone staples

Instrumented bone staples were first introduced as an alternative to surface-mounted strain gauges for use in human in vivo bone strain measurements because their fixation to bone is secure and requires not only minimally invasive surgery. Bench-top bone bending models have shown that the output from strain gauged bone staples compares favorably to that of traditional mounted gauges. However their within- and across-subject performance at sites typically instrumented in vivo has never been examined. This study used seven human cadaver lower extremities with an age range of 23-81 years old and a dynamic gait simulator to examine and compare axial strains in the mid tibial diaphysis and on the dorsal surface of the second metatarsal as measured simultaneously with strain gauged bone staples and with traditional surface-mounted gauges. Rosette configurations were used at the tibial site for deriving principal compression and tension, and shear strains. Axial outputs from the two gauge types demonstrated strong linear relationships for the tibia (r(2)=0.78-0.94) and the second metatarsal (r(2)=0.96-0.99), but coefficients (slopes) for the relationship were variable (range 7-20), across subjects and across sites. The apparent low reliability of strain gauged staples may be explained by the fact that both strain gauged staples and surface strain gauges are inexact to some degree, do not measure strains from exactly the same areas and strain gauged staples reflect surface strains as well as deformations within the cortex. There were no relationships for the principal tibia compression, tension or shear strain measurements derived from the two rosette gauge types, reflecting the very different anatomical areas measured by each of the constructs in this study. Strain gauged bone staples may be most useful in comparing relative axial intra-subject differences between activities, but inter-subject variability may require larger sample sizes to detect differences between populations.     

Different skeletal regional response to continuous brain infusion of leptin in the rat

This study was designed to evaluate whether or not continuous intracerebroventricular infusion of leptin (1.5 microg/rat/24 h, for 28 days) produced different regional response on the skeleton of growing rats. Leptin reduce the accretion of total femoral bone mineral content (BMC) and density (BMD). This effect was related to a reduction of metaphyseal femur as no changes were detected in the diaphysis. Despite the reduced accretion in the volumetric of both femur and tibia compared to controls, leptin had no significant effects on the lumbar vertebrae. Urine deoxypyrydinoline and serum osteocalcin remained more elevated in the leptin-treated group as compared to controls. The results demonstrate that long-term central infusion of leptin activates bone remodeling with a negative balance. Leptin induces distinct responses in the different structure of bone and in the axial and appendicular skeleton.     

Characterization of dynamic three-dimensional strain fields in the canine radius

This note describes a method to approximate the 3-D mechanical environment of a long bone during a normal daily activity. Our specific goal was to characterize the temporal and spatial strain distributions in the mid-shaft region of the canine radius during gait. Direct measurement of strains along the entire surface of in vivo bone is not feasible, so we employed a combination of experimental measurements and numerical interpolation techniques to approximate the time-varying longitudinal strain distribution. Using standard in vivo strain gauging techniques, we measured dynamic strains at nine locations (three locations on each of three cross sections, data pooled from two experimental animals) on the canine radius during trotting gait. These in vivo strain measurements were then used to approximate the time course of the strain field for the entire radius mid-shaft region using a 3-D numerical interpolation scheme using finite element basis functions. Despite limitations in the present implementation of the method, the results show that there are considerable time-dependent variations in the strain distribution occurring at different transverse sections along the length of the diaphysis with substantial anteroposterior bending and rotation of neutral axis locations during the gait cycle.     

Apparent Young's modulus of human radius using inverse finite-element method

The ability to assess the elastic and failure properties of cortical bone at the radial diaphysis has a clinical importance. A new generation of quantitative ultrasound (QUS) devices and peripheral quantitative computed tomography (p-QCT) has been developed to assess non-invasively bone material and structural properties at the distal radius. This anatomical site is characterized by a thin cortical thickness that complicates traditional mechanical testing methods on specimens. Until now, mechanical properties of cortical bone at distal radius (e.g., elastic modulus, yield stress and strain) remain rarely studied probably due to experimental difficulties. The present study introduces an inverse finite-element method strategy to measure the elastic modulus and yield properties of human cortical specimens of the radial diaphysis. Twenty millimeter-thick portions of diaphysis were cut from 40 human radii (ages 45-90) for biomechanical test. Subsequently the same portion was modeled in order to obtain a specimen-specific three dimensional finite-element model (3D-FEM). Longitudinal elastic constants at the apparent level and stress characterizations were performed by coupling mechanical parameters with isotropic linear-elastic simulations. The results indicated that the mean apparent Young's modulus for radial cortical bone was 16 GPa (SD 1.8) and the yield stress was 153 MPa (SD 33). Breaking load was 12,946 N (SD 3644), cortical thickness 2.9 mm (SD 0.6), structural effective strain at the yield (epsilon(y)=0.0097) and failure (epsilon(u)=0.0154) load were also calculated. The 3D-FEM strategy described here may help to investigate bone mechanical properties when some difficulties arise from machining mechanical sample.     

Trabecular surface remodeling simulation for cancellous bone using microstructural voxel finite element models

A computational simulation method for three-dimensional trabecular surface remodeling was proposed, using voxel finite element models of cancellous bone, and was applied to the experimental data. In the simulation, the trabecular microstructure was modeled based on digital images, and its morphological changes due to surface movement at the trabecular level were directly expressed by removing/adding the voxel elements from/to the trabecular surface. A remodeling simulation at the single trabecular level under uniaxial compressive loading demonstrated smooth morphological changes even though the trabeculae were modeled with discrete voxel elements. Moreover, the trabecular axis rotated toward the loading direction with increasing stiffness, simulating functional adaptation to the applied load. In the remodeling simulation at the trabecular structural level, a cancellous bone cube was modeled using a digital image obtained by microcomputed tomography (microCT), and was uniaxially compressed. As a result, the apparent stiffness against the applied load increased by remodeling, in which the trabeculae reoriented to the loading direction. In addition, changes in the structural indices of the trabecular architecture coincided qualitatively with previously published experimental observations. Through these studies, it was demonstrated that the newly proposed voxel simulation technique enables us to simulate the trabecular surface remodeling and to compare the results obtained using this technique with the in vivo experimental data in the investigation of the adaptive bone remodeling phenomenon.     

Parametric finite element analysis of vertebral bodies affected by tumors

The vertebral column is the most frequent site of metastatic involvement of the skeleton. Due to the proximity to the spinal cord, from 5% to 10% of all cancer patients develop neurologic manifestations. As a consequence, fracture risk prediction has significant clinical importance. In this study, we model the metastatically involved vertebra so as to parametrically investigate the effects of tumor size, material properties and compressive loading rate on vertebral strength. A two-dimensional axisymmetric finite element model of a spinal motion segment consisting of the first lumbar vertebral body (no posterior elements) and adjacent intervertebral disc was developed to allow the inclusion of a centrally located tumor in the vertebral body. After evaluating elastic, mixed, and poroelastic formulations, we concluded that the poroelastic representation was most suitable for modeling the metastatically involved vertebra's response to compressive load. Maximum principal strains were used to localize regions of potential vertebral trabecular bone failure. Radial and axial vertebral body displacements were used as relative indicators of spinal canal encroachment and endplate failure. Increased tumor size and loading rate, and reduced trabecular bone density all elevated axial and radial displacements and maximum tensile strains. The results of this parametric study suggest that vertebral tumor size and bone density contribute significantly to a patients risk for vertebral fracture and should be incorporated in clinical assessment paradigms.