Anisotropic Permeability of Trabecular Bone and its Relationship to Fabric and Architecture: A Computational Study.

Trabecular bone is a porous, mineralized tissue found in vertebral bodies, the metaphyses and epiphyses of long bones, and in the irregular and flat shaped bones. The pore space is filled with bone marrow, a highly cellular fluid. Together, the bone and marrow behave as a poroelastic solid. In poroelasticity theory, the permeability is the primary material property that governs the momentum transfer between the solid and fluid constituents. In the linearized theory, the permeability of a material depends on the shape and connectivity of the pores. Developing a model of the relationship between trabecular microarchitecture and permeability could lead to improved simulations of trabecular bone mechanical response, which can be used to investigate bone adaptation, mechanobiological signaling, and progression of diseases such as osteoporosis. This study used finite element models of the trabecular pore space to calculate the complete anisotropic permeability tensor of 12 human and 18 porcine femoral trabecular bone samples. The sensitivity of the simulations to model assumptions and post-processing was analyzed to improve confidence in the result. The orthotropic permeability tensor depended on the fabric tensor, trabecular spacing, and structure model index through a power law relationship. Porosity and fabric alone also provided a reasonable prediction, which may be useful in cases where the image resolution is insufficient to obtain detailed measures of architecture.

Primary cilia expression in bone marrow in response to mechanical stimulation in explant bioreactor culture.

Bone marrow contains a multitude of mechanically sensitive cells that may participate in mechanotransduction. Primary cilia are sensory organelles expressed on mesenchymal stem cells (MSCs), osteoblasts, osteocytes, and other cell types that sense fluid flow in monolayer culture. In marrow, cilia could similarly facilitate the sensation of relative motion between adjacent cells or interstitial fluid. The goal of this study was to determine the response of cilia to mechanical stimulation of the marrow. Bioreactors were used to supply trabecular bone explants with low magnitude mechanical stimulation (LMMS) of 0.3 ×g at 30 Hz for 1 h/d, 5 d/week, inducing shear stresses in the marrow. Four groups were studied: unstimulated (UNSTIM), stimulated (LMMS), and with and without chloral hydrate (UNSTIM+CH and LMMS+CH, respectively), which was used to disrupt cilia. After 19 days of culture, immunohistochemistry for acetylated α-tubulin revealed that more cells expressed cilia in culture compared to in vivo controls. Stimulation decreased the number of cells expressing cilia in untreated explants, but not in CH-treated explants. MSCs represented a greater fraction of marrow cells in the untreated explants than CH-treated explants. MSCs harvested from the stimulated groups were more proliferative than in the unstimulated explants, but this effect was absent from CH treated explants. In contrast to the marrow, neither LMMS nor CH treatment affected bone formation as measured by mineralising surface. Computational models indicated that LMMS does not induce bone strain, and the reported effects were thus attributed to shear stress in the marrow. From a clinical perspective, genetic or pharmaceutical alterations of cilia expression may affect marrow health and function.

An Experimental and Computational Investigation of Bone Formation in Mechanically Loaded Trabecular Bone Explants.

Understanding how bone marrow multipotent stromal cells (MSCs) contribute to new bone formation and remodeling in vivo is of principal importance for informing the development of effective bone tissue engineering strategies in vitro. However, the precise in situ stimuli that MSCs experience have not been fully established. The shear stress generated within the bone marrow of physiologically loaded samples has never been determined, but could be playing an important role in the generation of sufficient stimulus for MSCs to undergo osteogenic differentiation. In this study fluid structure interaction (FSI) computational models were used in conjunction with a bioreactor which physiologically compresses explanted trabecular bone samples to determine whether MSCs can be directly stimulated by mechanical cues within the bone marrow. Experimentally loaded samples were found to have greater osteogenic activity, as verified by bone histomorphometry, compared to control static samples. FSI models demonstrated a linear relationship between increasing shear stress and decreasing bone volume. The FSI models demonstrated that bone strain, not marrow shear stress, was likely the overall driving mechanical signal for new bone formation during compression. However, the shear stress generated in the models is within the range of values which has been shown previously to generate an osteogenic response in MSCs.

Mechanical stimulation of bone marrow in situ induces bone formation in trabecular explants.

Low magnitude high frequency (LMHF) loading has been shown to have an anabolic effect on trabecular bone in vivo. However, the precise mechanical signal imposed on the bone marrow cells by LMHF loading, which induces a cellular response, remains unclear. This study investigates the influence of LMHF loading, applied using a custom designed bioreactor, on bone adaptation in an explanted trabecular bone model, which isolated the bone and marrow. Bone adaptation was investigated by performing micro CT scans pre and post experimental LMHF loading, using image registration techniques. Computational fluids dynamic models were generated using the pre-experiment scans to characterise the mechanical stimuli imposed by the loading regime prior to adaptation. Results here demonstrate a significant increase in bone formation in the LMHF loaded group compared to static controls and media flow groups. The calculated shear stress in the marrow was between 0.575 and 0.7 Pa, which is within the range of stimuli known to induce osteogenesis by bone marrow mesenchymal stem cells in vitro. Interestingly, a correlation was found between the bone formation balance (bone formation/resorption), trabecular number, trabecular spacing, mineral resorption rate, bone resorption rate and mean shear stresses. The results of this study suggest that the magnitude of the shear stresses generated due to LMHF loading in the explanted bone cores has a contributory role in the formation of trabecular bone and improvement in bone architecture parameters.

Multiscale modeling of trabecular bone marrow: understanding the micromechanical environment of mesenchymal stem cells during osteoporosis.

Mechanical loading directs the differentiation of mesenchymal stem cells (MSCs) in vitro and it has been hypothesized that the mechanical environment plays a role in directing the cellular fate of MSCs in vivo. However, the complex multicellular composition of trabecular bone marrow means that the precise nature of mechanical stimulation that MSCs experience in their native environment is not fully understood. In this study, we developed a multiscale model that discretely represents the cellular constituents of trabecular bone marrow and applied this model to characterize mechanical stimulation of MCSs in vivo.We predicted that cell-level strains in certain locations of the trabecular marrow microenvironment were greater in magnitude (maximum e12»24,000 le) than levels that have been found to result in osteogenic differentiation of MSCs in vitro (>8000 le),which may indicate that the native mechanical environment of MSCs could direct cellular fate in vivo. The results also showed that cell­cell adhesions could play an important role in mediating mechanical stimulation within the MSC population in vivo. The model was applied to investigate how changes that occur during osteoporosis affected mechanical stimulation in the cellular microenvironment of trabecular bone marrow. Specifically,a reduced bone volume (BV) resulted in an overall increase in bone deformation, leading to greater cell-level mechanical stimulation in trabecular bone marrow (maximume12»48,000 le). An increased marrow adipocyte content resulted in slightly lower levels of stimulation within the adjacent cell population due to a shielding effect caused by the more compliant behavior of adipocytes (maximum e12»41,000 le). Despite this reduction, stimulation levels in trabecular bone marrow during osteoporosis remained much higher than those predicted to occur under healthy conditions. It was found that compensatory mechanobiological responses that occur during osteoporosis, such as increased trabecular stiffness and axial alignment of trabeculae, would be effective in returning MSC stimulation in trabecular marrow to normal levels. These results have provided novel insight into the mechanical stimulation of the trabecular marrow MSC population in both healthy and osteoporotic bone, and could inform the design three dimensional(3D) in vitro bioreactor strategies techniques, which seek to emulate physiological conditions.

Computational modelling of the mechanics of trabecular bone and marrow using fluid structure interaction techniques.

Bone marrow found within the porous structure of trabecular bone provides a specialized environment for numerous cell types, including mesenchymal stem cells (MSCs). Studies have sought to characterize the mechanical environment imposed on MSCs, however, a particular challenge is that marrow displays the characteristics of a fluid, while surrounded by bone that is subject to deformation, and previous experimental and computational studies have been unable to fully capture the resulting complex mechanical environment. The objective of this study was to develop a fluid structure interaction (FSI) model of trabecular bone and marrow to predict the mechanical environment of MSCs in vivo and to examine how this environment changes during osteoporosis. An idealized repeating unit was used to compare FSI techniques to a computational fluid dynamics only approach. These techniques were used to determine the effect of lower bone mass and different marrow viscosities, representative of osteoporosis, on the shear stress generated within bone marrow. Results report that shear stresses generated within bone marrow under physiological loading conditions are within the range known to stimulate a mechanobiological response in MSCs in vitro. Additionally, lower bone mass leads to an increase in the shear stress generated within the marrow, while a decrease in bone marrow viscosity reduces this generated shear stress.

Osteogenic differentiation of mesenchymal stem cells is regulated by osteocyte and osteoblast cells in a simplified bone niche.

Mesenchymal stem cells (MSCs) within their native environment of the stem cell niche in bone receive biochemical stimuli from surrounding cells. These stimuli likely influence how MSCs differentiate to become bone precursors. The ability of MSCs to undergo osteogenic differentiation is well established in vitro;however, the role of the natural cues from bone's regulatory cells, osteocytes and osteoblasts in regulating the osteogenic differentiation of MSCs in vivo are unclear. In this study we delineate the role of biochemical signalling from osteocytes and osteoblasts, using conditioned media and co-culture experiments, to understand how they direct osteogenic differentiation of MSCs. Furthermore, the synergistic relationship between osteocytes and osteoblasts is examined by transwell co-culturing of MSCs with both simultaneously. Osteogenic differentiation of MSCs was quantified by monitoring alkaline phosphatase (ALP) activity, calcium deposition and cell number. Intracellular ALP was found to peak earlier and there was greater calcium deposition when MSCs were co-cultured with osteocytes rather than osteoblasts, suggesting that osteocytes are more influential than osteoblasts in stimulating osteogenesis in MSCs. Osteoblasts initially stimulated an increase in the number of MSCs, but ultimately regulated MSC differentiation down the same pathway. Our novel co-culture system confirmed a synergistic relationship between osteocytes and osteoblasts in producing biochemical signals to stimulate the osteogenic differentiation of MSCs. This study provides important insights into the mechanisms at work within the native stem cell niche to stimulate osteogenic differentiation and outlines a possible role for the use of co-culture or conditioned media methodologies for tissue engineering applications.

High strain rate testing of bovine trabecular bone.

In spinal vertebral burst fractures, the dynamic properties of the trabecular centrum, which is the central region of porous bone inside the vertebra, can play an important role in determining the failure mode. If the failure occurs in the posterior portion of the vertebral body, spinal canal occlusion can occur and ejected trabecular bone can impact the spinal cord resulting in serious injury. About 15% of all spinal cord injuries are caused by such burst fractures. Unfortunately, due to the uniqueness of burst fracture injuries, postinjury investigation cannot always accurately assess the degree of damage caused by these fractures. This research makes an effort to begin understanding the governing effects in this important bone fracture event. Measurements of the dynamic deformation response of bovine trabecular bone with the marrow intact and marrow removed using a modified split-Hopkinson pressure bar apparatus are reported and compared with quasistatic deformation response results. Because trabecular bone is more compliant and lower in strength than cortical bone, typical Hopkinson pressure bar experimental techniques used for high strain rate testing of harder materials cannot be applied. Instead, a quartz-crystal-embedded, split-Hopkinson pressure bar developed for testing compliant, low strength materials is used. Care is taken into account for the orthotropic properties in the bone by testing only along the principle material axes, determined through microcomputed tomography. In addition, shaping of the stress wave pulse is used to ensure a constant strain rate and homogeneous specimen deformation. Results indicate that the strength of trabecular bone increases by a factor of approximately 2-3 when the strain rate increases from 10(-3) s(-1) to 500 s(-1) and that the bone fractures beyond a critical strain.

Biomechanics of trabecular bone.

Trabecular bone is a complex material with substantial heterogeneity. Its elastic and strength properties vary widely across anatomic sites, and with aging and disease. Although these properties depend very much on density, the role of architecture and tissue material properties remain uncertain. It is interesting that the strains at which the bone fails are almost independent of density. Current work addresses the underlying structure-function relations for such behavior, as well as more complex mechanical behavior, such as multiaxial loading, time-dependent failure, and damage accumulation. A unique tool for studying such behavior is the microstructural class of finite element models, particularly the "high-resolution" models. It is expected that with continued progress in this field, substantial insight will be gained into such important problems as osteoporosis, bone fracture, bone remodeling, and design/analysis of bone-implant systems. This article reviews the state of the art in trabecular bone biomechanics, focusing on the mechanical aspects, and attempts to identify important areas of current and future research.

Sensitivity of damage predictions to tissue level yield properties and apparent loading conditions.

High-resolution finite element models of trabecular bone failure could be used to augment current techniques for measuring damage in trabecular bone. However, the sensitivity of such models to the assumed tissue yield properties and apparent loading conditions is unknown. The goal of this study was to assess the sensitivity of the amount and mode (tension vs. compression) of tissue level yielding in trabecular bone to these factors. Linear elastic, high-resolution finite element models of nine bovine tibial trabecular bone specimens were used to calculate the fraction of the total tissue volume that exceeded each criterion for apparent level loading to the reported elastic limit in both on-axis and transverse compression and tension, and in shear. Four candidate yield criteria were studied, based on values suggested in the literature. Both the amount and the failure mode of yielded tissue were sensitive to the magnitudes of the tissue yield strains, the degree of tension-compression asymmetry of the yield criterion, and the applied apparent loads. The amount of yielded tissue was most sensitive to the orientation of the applied apparent loading, with the most tissue yielding for loading along the principal trabecular orientation and the least for loading perpendicular to it, regardless of the assumed tissue level yield criterion. Small changes in the magnitudes and the degree of asymmetry of the tissue yield criterion resulted in much larger changes in the amount of yielded tissue in the model. The results indicate that damage predictions based on high-resolution finite element models are highly sensitive to the assumed tissue yield properties. As such, good estimates of these values are needed before high-resolution finite element models can be applied to the study of trabecular bone damage. Regardless of the assumed tissue yield properties, the amount and type of damage that occurs in trabecular bone depends on the relative orientations of the applied apparent loads to the trabecular architecture, and this parameter should be controlled for both experimental and computational damage studies.

High-resolution finite element models with tissue strength asymmetry accurately predict failure of trabecular bone.

The ability to predict trabecular failure using microstructure-based computational models would greatly facilitate study of trabecular structure-function relations, multiaxial strength, and tissue remodeling. We hypothesized that high-resolution finite element models of trabecular bone that include cortical-like strength asymmetry at the tissue level, could predict apparent level failure of trabecular bone for multiple loading modes. A bilinear constitutive model with asymmetric tissue yield strains in tension and compression was applied to simulate failure in high-resolution finite element models of seven bovine tibial specimens. Tissue modulus was reduced by 95% when tissue principal strains exceeded the tissue yield strains. Linear models were first calibrated for effective tissue modulus against specimen-specific experimental measures of apparent modulus, producing effective tissue moduli of (mean+/-S.D.) 18.7+/-3.4GPa. Next, a parameter study was performed on a single specimen to estimate the tissue level tensile and compressive yield strains. These values, 0.60% strain in tension and 1.01% strain in compression, were then used in non-linear analyses of all seven specimens to predict failure for apparent tensile, compressive, and shear loading. When compared to apparent yield properties previously measured for the same type of bone, the model predictions of both the stresses and strains at failure were not statistically different for any loading case (p>0.15). Use of symmetric tissue strengths could not match the experimental data. These findings establish that, once effective tissue modulus is calibrated and uniform but asymmetric tissue failure strains are used, the resulting models can capture the apparent strength behavior to an outstanding level of accuracy. As such, these computational models have reached a level of fidelity that qualifies them as surrogates for destructive mechanical testing of real specimens.

The relevance of the moment arm of shoulder muscles with respect to axial rotation of the glenohumeral joint in four positions.

OBJECTIVE: This study was undertaken to determine the efficiency of the shoulder girdle muscles during axial humeral rotation based on measurements of the moment arms. DESIGN: The instantaneous muscle moment arms of 10 shoulder muscles, including the three portions of the deltoid, the rotator cuff muscles, teres major, and the thoracohumeral muscle group, were measured during four specified glenohumeral rotations. BACKGROUND: Axial humeral rotation is a commonly performed movement during activities of daily living and is a targeted motion of shoulder rehabilitation, particularly in those protocols emphasizing rotator cuff strengthening. An understanding of the function of the movers and stabilizers of the shoulder requires such basic information of muscle moment arms. METHODS: The instantaneous moment arm values of the muscles were derived from the slope of the plot of tendon excursion versus glenohumeral joint rotation angle. Motion studied included axial rotation with the humerus elevated 90 degrees in the coronal, scapular, and sagittal planes, as well as in the neutral position with the arm at the side. RESULTS: Based on the findings, with the humerus in both neutral and elevated positions, the infraspinatus is potentially the most powerful external rotator, followed by teres minor and posterior deltoid. Subscapularis and possibly pectoralis major are the most effective internal rotators in this position. CONCLUSIONS: The moment arm in providing axial humeral rotation of 10 shoulder muscles in four planes were obtained. In general, the teres minor and infraspinatus had the largest moment arms in external rotation, and the subscapularis had the largest moment arm in internal rotation. The muscle function for axial humeral rotation was found to be modified by the plane of arm elevation. RELEVANCE: The data could be used for developing exercise programs in physical therapy.

Kinematics of the proximal interphalangeal joint of the finger after surface replacement.

Nine fresh-frozen normal human cadaveric long fingers were used to compare the kinematics of the proximal interphalangeal joint (PIP) before and after a resurfacing metal-polyethylene prosthetic replacement (Avanta prosthesis, San Diego, CA) using the magnetic Isotrak system (Polhemus Navigational Systems, Colchester, VT). The kinematics of the PIP joint after replacement were similar to that of the normal joint. The maximum angular displacement was 5 degrees for lateral deviation and 9 degrees for rotation during the passive flexion and extension motion. The center of rotation after implant insertion was nearly identical to the center of rotation of the normal joint. This anatomically designed PIP prosthesis has potential to restore normal motion to the finger PIP joint while resisting physiologic out-of-plane forces such as pinch and grasp.

Biomechanical analysis of the trapeziometacarpal joint after surface replacement arthroplasty.

A biomechanical analysis of the trapeziometacarpal joint was performed in 7 fresh-frozen normal human cadaveric hands to compare the kinematics of the trapeziometacarpal joint before and after surface total joint replacement. Using a 3-space magnetic Isotrak system (Polhemus, Colchester, VT), which provides a 3-dimensional analysis of motion of joints as well as translation, we found that kinematics and stability of the trapeziometacarpal joint could be duplicated by joint surface replacement arthroplasty provided that normal ligament tensions were present.

The effects of wrist distraction on carpal kinematics.

Changes in carpal kinematics under wrist distraction were studied in fresh cadaveric specimens. A magnetic tracking device measured kinematic motions of the scaphoid, lunate, and third metacarpal relative to the fixed radius in 3 planes of passive motion (coronal, sagittal, and "dart throwers") under progressive distraction loads. The change in percent contribution of the radiocarpal and midcarpal joints was calculated. Radiocarpal motion during extension was decreased as increasing traction was applied, but it increased with flexion. Motion of the scaphoid relative to the lunate was smaller in the oblique plane, resulting in less radiocarpal motion than in the sagittal plane. In the coronal plane, traction had little effect on radial deviation, but ulnar angulation of the scaphoid was greater with ulnar deviation of the wrist. These results suggest that different degrees of tension exist in the palmar and dorsal ligaments with the wrist under traction and during different planes of wrist motion. If wrist motion is desired during fixed traction, such as used clinically with external fixation, the dart-throwers motion (wrist extension with radial deviation and wrist flexion with ulnar deviation) appears to have the least impact on radiocarpal motion. If greater radiocarpal motion is desired, however, such as during postoperative mobilization, flexion-extension and radioulnar deviation will create more radiocarpal motion than the dart-thrower's motion.

Convergence behavior of high-resolution finite element models of trabecular bone.

The convergence behavior of finite element models depends on the size of elements used, the element polynomial order, and on the complexity of the applied loads. For high-resolution models of trabecular bone, changes in architecture and density may also be important. The goal of this study was to investigate the influence of these factors on the convergence behavior of high-resolution models of trabecular bone. Two human vertebral and two bovine tibial trabecular bone specimens were modeled at four resolutions ranging from 20 to 80 microns and subjected to both compressive and shear loading. Results indicated that convergence behavior depended on both loading mode (axial versus shear) and volume fraction of the specimen. Compared to the 20 microns resolution, the differences in apparent Young's modulus at 40 microns resolution were less than 5 percent for all specimens, and for apparent shear modulus were less than 7 percent. By contrast, differences at 80 microns resolution in apparent modulus were up to 41 percent, depending on the specimen tested and loading mode. Overall, differences in apparent properties were always less than 10 percent when the ratio of mean trabecular thickness to element size was greater than four. Use of higher order elements did not improve the results. Tissue level parameters such as maximum principal strain did not converge. Tissue level strains converged when considered relative to a threshold value, but only if the strains were evaluated at Gauss points rather than element centroids. These findings indicate that good convergence can be obtained with this modeling technique, although element size should be chosen based on factors such as loading mode, mean trabecular thickness, and the particular output parameter of interest.

Mechanical advantage of the thumb muscles.

The purpose of this study was to measure the moment arms of four extrinsic muscles (flexor pollicis longus, extensor pollicis longus, extensor pollicis brevis, and abductor pollicis longus) and four intrinsic muscles (flexor pollicis brevis, abductor pollicis brevis, adductor pollicis, and opponents pollicis) of the thumb at the interphalangeal, the metacarpophalangeal, and the carpometacarpal joints in the same cadaver specimens and to examine the specific role of each muscle. Measurements were made on seven fresh frozen cadaver hands. The moment arms were measured during flexion/extension of the interphalangeal joint, flexion/extension and adduction/abduction of the metacarpophalangeal joint, and flexion/extension and adduction/abduction of the carpometacarpal joint. Moment arms were computed using the slope of the tendon excursion joint angle relationship. The specific function of each muscle was determined by multiplying the measured moment arms by the maximum force that each muscle can generate. It was found that the flexor pollicis longus was a pure flexor while flexor pollicis brevis was an adductor as well as a flexor, the extensor pollicis longus was an extensor and an adductor, extensor pollicis brevis was an extensor and a mild abductor, the abductor pollicis longus was an extensor as well as an abductor, the abductor pollicis brevis was mainly an abductor, the adductor pollicis was a major flexor as well as an adductor, and the opponents pollicis was a flexor and an abductor.

Comparison of two methods for computing abduction moment arms of the rotator cuff.

Biomechanical models of the shoulder mechanism require estimates of muscle moment arm magnitude. Some shoulder models have estimated muscle moment arms by assuming an idealized minimum distance path from the origin to insertion that passes around the bony geometry. Alternatively, the principle of virtual work can be used to estimate moment arms from tendon excursion and joint-angle data. The purpose of this study was to determine if these two methods give different estimates of abduction moment arms for the supraspinatus, infraspinatus, and subscapularis muscles. Muscle moment arms were estimated for these muscles on ten fresh frozen cadaver specimens. The results showed a significant difference between the two estimation methods. Average differences were 3.1 mm (10.6%), 3.9 mm (43.9%), and 7.2 mm (70.3%) for the supraspinatus, subscapularis, and infraspinatus muscles, respectively. These results suggest that shoulder models based on the origin-insertion method may give higher rotator cuff muscle force estimates than methods using the slope of the tendon excursion vs joint angle relationship.