Estimation of the poroelastic parameters of cortical bone

Computer model of non-Newtonian canalicular fluid flow in lacunar-canalicular system of bone tissue

Brittle bone diseases are a global healthcare problem for orthopaedic clinicians, that reduces bone strength and promotes bone fracture risk. In vivo studies reported that loading-induced fluid flow through the lacunar-canalicular channel (LCS) of bone tissue inhibit such bone loss and encourages osteogenesis i.e. new bone formation. Canalicular fluid flow converts mechanical signals into biological signals and regulates bone reconstruction by releasing signalling molecules responsible for mechanotransduction. In-silico model mostly considers canalicular fluid is Newtonian, however, physiological canalicular fluid may be non-Newtonian in nature as it contains nutrients and supplements. Accordingly, this study attempts to develop a two-dimensional in-silico model to compute loading-induced non-Newtonian canalicular fluid flow in a complex LCS of bone tissue. Moreover, canalicular fluid is considered as a Jeffery fluid, that can easily be reduced to Newtonian fluid as a special case. The results show that physiological loading modulates the canalicular fluid flow, wall shear stress (WSS) and streamline in bone LCS. Fluid velocity and WSS increases with increase in non-dimensional frequency and non-Newtonian parameter (Jeffery fluid parameters) and reduce with change in permeability. The outcomes of this study may provide new insights in the role of mechanical loading-induced non-Newtonian canalicular fluid flow dynamics in bone LCS. The key findings of this study can be used to improve the understanding of osteocyte mechanobiology involved inside the bone tissue.

Computation of physiological loading induced interstitial fluid motion in muscle standardized femur: Healthy vs. osteoporotic bone

BACKGROUND AND OBJECTIVES

Physiological loading-induced mechanical environments regulate bone modeling and remodeling. Thus, loading-induced normal strain is typically considered a stimulus to osteogenesis. However, several studies noticed new bone formation near the sites of minimal normal strain, e.g., the neutral axis of bending in long bones, which raises a question on how bone mass is maintained near these sites. Secondary mechanical components such as shear strain and interstitial fluid flow also stimulate bone cells and regulate bone mass. However, the osteogenic potential of these components is not well established. Accordingly, the present study estimates the distribution of physiological muscle loading-induced mechanical environments such as normal strain, shear strain, pore pressure, and interstitial fluid flow in long bones.

METHODS

A poroelastic finite element muscle standardized femur (MuscleSF) model is developed to compute the distribution of the mechanical environment as a function of bone porosities associated with osteoporotic and disuse bone loss.

RESULTS

The results indicate the presence of higher shear strain and interstitial fluid motion near the minimal strain sites, i.e., the neutral axis of bending of femoral cross-sections. This suggests that secondary stimuli may maintain the bone mass at these locations. Pore pressure and interstitial fluid motion reduce with the increased porosity associated with bone disorders, possibly resulting in diminished skeletal mechano-sensitivity to exogenous loading.

CONCLUSIONS

These outcomes present a better understanding of mechanical environment-mediated regulation of site-specific bone mass, which can be beneficial in developing prophylactic exercise to prevent bone loss in osteoporosis and muscle disuse.

Prediction of osteoporotic degradation of tibia human bone at trabecular scale

A theoretical numerical model is proposed to predict patient dependent osteoporotic bone degradation. The model parameters are identified through a particle swarm optimization algorithm and based on individual patient high resolution peripherical quantitative computer tomography (HRpQCT) scan data. The degradation model is based on cellular activity initiated by the elastic strain energy developed in the bone microstructure through patient's body weight. The macro (organ scale) and meso (trabecular scale) scale analyses are carried out and predicted bone volume fraction and microstructure evolution are compared with in-vivo experimental bone degradation for four elderly women over a period of 10 years. A significant correlation (r > 0.9) is observed between the model predictions and in-vivo experiments in all cases with an average deviation error of 1.46%. The model can easily be extended to other patients and provide good predictions for different population categories such as ethnicity, gender, age, etc.

A lumped model for long bone behavior based on poroelastic deformation and Darcy flow

The present paper provides a simplified model for compact bone behavior by accounting for bone fluid flow coupled to the elasticity of the porous structure. The lumped model considers the bone material as a layered poroelastic structure and predicts normal pressure versus displacement, i.e, a stress-strain curve. There is a parametric dependency on porosity and permeability but, in addition, on pressure history. Specifically, the pressure impulse (the integral of pressure versus time) plays a key role. This factor is alluded to in several past studies, but not highlighted in a simplified fashion. Based on a global flow balance, bone displacement depends on the fluid flow in a channel according to the classical Darcy model of 1856, and on the rate of change of fluid within the porous solid according to the 1941 classical model of Biot. The present results agree with those of Perrin et al. which, in turn, agree with results of a detailed numerical simulation.

Using Finite Element Modeling in Bone Mechanoadaptation

PURPOSE OF THE REVIEW

Bone adapts structure and material properties in response to its mechanical environment, a process called mechanoadpatation. For the past 50 years, finite element modeling has been used to investigate the relationships between bone geometry, material properties, and mechanical loading conditions. This review examines how we use finite element modeling in the context of bone mechanoadpatation.

RECENT FINDINGS

Finite element models estimate complex mechanical stimuli at the tissue and cellular levels, help explain experimental results, and inform the design of loading protocols and prosthetics. FE modeling is a powerful tool to study bone adaptation as it complements experimental approaches. Before using FE models, researchers should determine whether simulation results will provide complementary information to experimental or clinical observations and should establish the level of complexity required. As imaging technics and computational capacity continue increasing, we expect FE models to help in designing treatments of bone pathologies that take advantage of mechanoadaptation of bone.

Computational modeling for osteogenic potential assessment of physical exercises based on loading-induced mechanobiological environments in cortical bone remodeling

Osteoporosis and disuse can cause bone loss which reduces the weight-bearing strength of long bones. Physical exercise or mechanical loading prevents bone loss as it promotes bone modeling through osteogenesis, i.e., new bone formation. Several studies have observed distinct bone remodeling responses to physical exercises; nevertheless, the underlying mechanism behind such responses is not well established. Loading-induced pore-pressure and fluid motion act as mechanobiological stimuli to bone cells namely osteocytes which further initiate osteoactivities. The shape of loading waveforms also affects the poromechanical environment of bone. Accordingly, the present study hypothesizes that loading waveforms associated with physiological exercises may expose the bone to different mechanobiological stimuli resulting in distinct bone remodeling. A poromechanical finite element model is developed to compute pore-pressure and interstitial fluid velocity in femoral cortical bone tissue (healthy and osteoporotic) subjected to loading waveforms of three physiological exercises namely walking, running, and jumping. The model also computes the mechanobiological stimulus as a function of fluid velocity. The outcomes indicate that pore-pressure and fluid velocity decrease significantly in osteoporotic bone tissue in comparison with healthy tissue. Jumping and running both improve pore-pressure and fluid velocity in healthy and osteoporotic tissues, whereas running significantly enhances mechanobiological stimulus in both the tissues which indicates a possible explanation for distinct bone remodeling to different physical exercises. The present work also suggests that running may be recommended as a potential biomechanical therapeutic to prevent bone loss. Overall, the present work contributes to the area of orthopedic research to develop effective designs of prophylactic exercises to improve bone health.

On computational predictions of fluid flow and its effects on bone healing in dental implant treatments: an investigation of spatiotemporal fluid flow in cyclic loading

Fluid flow in (porous) bone plays an important role in its maintenance, adaptation, and healing after an injury. Experimental and computational studies apply mechanical loading on bone to predict fluid flow development and/or to find its material properties. In most cases, mechanical loading is applied as a linear function in time. Multiple loading functions-with identical peak load and loading frequency-were used to investigate load-induced fluid flow and predict bone healing surrounding a dental implant. Implementing an instantaneous healing stimulus led to major differences in healing predictions for slightly different loading functions. Load-induced fluid flow was found to be displacement-rate dependent with complex spatial-temporal variations and not necessarily symmetrical during loading and unloading phases. Haversine loading resulted in more numerical stability compared to ramped/triangular loading, providing the opportunity for further investigation of the effects of various physiological masticatory loadings. It was concluded that using the average healing stimulus during cyclic loading gives the most robust bone healing predictions.

Study on ultrasonic wave propagation in equine leg bone for screening bucked shin

For simple, safe, portable, and inexpensive evaluation suitable for leg bone diseases of racehorses in the field, an ultrasonic measurement technique was applied to evaluate wave velocities. A digital model of the third metacarpal bone with the bucked shin was fabricated using high-resolution peripheral quantitative computerized tomography data of a racehorse. This model was anisotropic and heterogeneous, and was constructed using the measured ultrasonic wave velocities in the bone. With this model, ultrasonic wave propagation along the bone axis was simulated using the elastic finite-difference time-domain method. We found two main waves with different propagation velocities. The fast-waves showed a wave velocity close to the longitudinal wave in the axial direction. However, the apparent velocities changed dramatically owing to bone surface irregularities (changes of the shape) in the area of bucked shin. The slow-waves showed a wave velocity close to the shear wave, which was unaffected by the bone surface irregularities. The simple comparison of different wave behaviors may be a suitable parameter for the initial in vivo screening of bucked shin in the legs of racehorses, which can be performed in the field.

Interactive effects of various loading parameters on the fluid dynamics within the lacunar-canalicular system for a single osteocyte

The osteocyte lacunar-canalicular system (LCS) serves as a mechanotransductive core where external loading applied to the skeleton is transduced into mechanical signals (e.g., fluid shear) that can be sensed by mechanosensors (osteocytes). The fluid velocity and shear stress within the LCS are affected by various loading parameters. However, the interactive effect of distinct loading parameters on the velocity and shear stress in the LCS remains unclear. To address this issue, we developed a multiscale modeling approach, combining a poroelastic finite element (FE) model with a single osteocytic LCS unit model to calculate the flow velocity and shear stress within the LCS. Next, a sensitivity analysis was performed to investigate individual and interactive effects of strain magnitude, strain rate, number of cycles, and intervening short rests between loading cycles on the velocity and shear stress around the osteocyte. Lastly, we developed a relatively simple regression model to predict those outcomes. Our results demonstrated that the strain magnitude or rate alone were the main factors affecting the velocity and shear stress; however, the combination of these two was not directly additive, and addition of a short rest between cycles could enhance the combination of these two related factors. These results show highly interactive effects of distinct loading parameters on fluid velocity and shear stress in the LCS. Specifically, our results suggest that an enhanced fluid dynamics environment in the LCS can be achieved with a brief number of load cycles combined with short rest insertion and high strain magnitude and rate.

3D bioprinting of osteon-mimetic scaffolds with hierarchical microchannels for vascularized bone tissue regeneration

The integration of three-dimensional (3D) bioprinted scaffold's structure and function for critical-size bone defect repair is of immense significance. Inspired by the basic component of innate cortical bone tissue--osteons, many studies focus on biomimetic strategy. However, the complexity of hierarchical microchannels in the osteon, the requirement of mechanical strength of bone, and the biological function of angiogenesis and osteogenesis remain challenges in the fabrication of osteon-mimetic scaffolds. Therefore, we successfully built mimetic scaffolds with vertically central medullary canals, peripheral Haversian canals, and transverse Volkmann canals structures simultaneously by 3D bioprinting technology using polycaprolactone and bioink loading with bone marrow mesenchymal stem cells (BMSCs) and bone morphogenetic protein-4 (BMP-4). Subsequently, endothelial progenitor cells (EPCs) were seeded into the canals to enhance angiogenesis. The porosity and compressive properties of bioprinted scaffolds could be well controlled by altering the structure and canal numbers of the scaffolds. The osteon-mimetic scaffolds showed satisfactory biocompatibility and promotion of angiogenesis and osteogenesis in vitro and prompted the new blood vessels and new bone formation in vivo. In summary, this study proposes a biomimetic strategy for fabricating structured and functionalized 3D bioprinted scaffolds for vascularized bone tissue regeneration.

Finite Element Models of Osteocytes and Their Load-Induced Activation

PURPOSE OF REVIEW

Osteocytes are the conductors of bone adaptation and remodelling. Buried inside the calcified matrix, they sense mechanical cues and signal osteoclasts in case of low activity, and osteoblasts when stresses are high. How do osteocytes detect mechanical stress? What physical signal do they perceive? Finite element analysis is a useful tool to address these questions as it allows calculating stresses, strains and fluid flow where they cannot be measured. The purpose of this review is to evaluate the capabilities and challenges of finite element models of bone, in particular the osteocytes and load-induced activation mechanisms.

RECENT FINDINGS

High-resolution imaging and increased computational power allow ever more detailed modelling of osteocytes, either in isolation or embedded within the mineralised matrix. Over the years, homogeneous models of bone and osteocytes got replaced by heterogeneous and microstructural models, including, e.g. the lacuno-canalicular network and the cytoskeleton. The lacuno-canalicular network induces strain amplifications and the osteocyte protrusions seem to be stimulated much more than the cell body, both by strain and fluid flow. More realistic cell geometries, like minute constrictions of the canaliculi, increase this effect. Microstructural osteocyte models describe the transduction of external stimuli to the nucleus. Supracellular multiscale models (e.g. of a tunnelling osteon) allow to study differential loading of osteocytes and to distinguish between strain and fluid flow as the pivotal stimulatory cue. In the future, the finite element models may be enhanced by including chemical transport and intercellular communication between osteocytes, osteoclasts and osteoblasts.

Divalent metal cations stimulate skeleton interoception for new bone formation in mouse injury models

Bone formation induced by divalent metal cations has been widely reported; however, the underlying mechanism is unclear. Here we report that these cations stimulate skeleton interoception by promoting prostaglandin E2 secretion from macrophages. This immune response is accompanied by the sprouting and arborization of calcitonin gene-related polypeptide-α⁺ nerve fibers, which sense the inflammatory cue with PGE₂ receptor 4 and convey the interoceptive signals to the central nervous system. Activating skeleton interoception downregulates sympathetic tone for new bone formation. Moreover, either macrophage depletion or knockout of cyclooxygenase-2 in the macrophage abolishes divalent cation-induced skeleton interoception. Furthermore, sensory denervation or knockout of EP4 in the sensory nerves eliminates the osteogenic effects of divalent cations. Thus, our study reveals that divalent cations promote bone formation through the skeleton interoceptive circuit, a finding which could prompt the development of novel biomaterials to elicit the therapeutic power of these divalent cations.

Mechanisms underlying bone formation induced by divalent metal cations remain largely unknown. Here the authors show that these cations can activate the skeleton interoceptive circuit through the immune-neural axis to initiate new bone formation.

Computational framework for analyzing flow-induced strain on osteocyte as modulated by microenvironment

Osteocytes buried in bone matrix are major mechanosensory cells that regulate bone remodeling in response to interstitial fluid flow in a lacuno-canalicular porosity. To gain an understanding of the mechanism of osteocyte mechanosensing, it is important to be able to evaluate the local strain on the osteocyte process membrane induced by the interstitial fluid flow. The microenvironment of the osteocytes, including the pericellular matrix (PCM) and canalicular ultrastructure, is a key modulator of the flow-induced strain on the osteocyte process membrane because it produces heterogeneous flow patterns in the pericellular space. To investigate the effect of changes in the microenvironment of osteocytes on the flow-induced strain, we developed a novel computational framework for analyzing the fluid-structure interaction. Computer simulations based on the proposed framework enabled evaluation of the spatial distribution of flow-induced strain on the osteocyte process membrane according to changes in the PCM density and canalicular curvature. The simulation results reveal that a decrease in PCM density and an increase in canalicular curvature, each of which is associated with aging and bone disease, have the notable effect of enhancing local flow-induced strain on the osteocyte process membrane. We believe that the proposed computational framework is a promising framework for investigating cell-specific mechanical stimuli and that it has the potential to accelerate the mechanobiological study of osteocytes by providing a deeper understanding of their mechanical environment in living bone tissue.

Simulation study on the effects of cancellous bone structure in the skull on ultrasonic wave propagation

The transcranial Doppler method (TCD) enables the measurement of cerebral blood flow velocity and detection of emboli by applying an ultrasound probe to the temporal bone window, or the orbital or greater occipital foramina. TCD is widely used for evaluation of cerebral vasospasm after subarachnoid hemorrhage, early detection of patients with arterial stenosis, and the assessment of brain death. However, measurements often become difficult in older women. Among various factors contributing to this problem, we focused on the effect of the diploe in the skull bone on the penetration of ultrasound into the brain. In particular, the effect of the cancellous bone structure in the diploe was investigated. Using a 2D digital bone model, wave propagation through the skull bone was investigated using the finite-difference time-domain (FDTD) method. We fabricated digital bone models with similar structure but different BV/TV (bone volume/total volume) values in the diploe. At a BV/TV of approximately 50–60% (similar to that of older women), the minimum ultrasound amplitude was observed as a result of scattering and multiple reflections in the cancellous diploe. These results suggest that structural changes such as osteoporosis may be one factor hampering TCD measurements.

Physiological Loading-Induced Interstitial Fluid Dynamics in Osteon of Osteogenesis Imperfecta Bone

Osteogenesis imperfecta (OI), also known as "brittle bone disease," is a genetic bone disorder. OI bones experience frequent fractures. Surgical procedures are usually followed by clinicians in the management of OI. It has been observed physical activity is equally beneficial in reducing OI bone fractures in both children and adults as mechanical stimulation improves bone mass and strength. Loading-induced mechanical strain and interstitial fluid flow stimulate bone remodeling activities. Several studies have characterized strain environment in OI bones, whereas very few studies attempted to characterize the interstitial fluid flow. OI significantly affects bone micro-architecture. Thus, this study anticipates that canalicular fluid flow reduces in OI bone in comparison to the healthy bone in response to physiological loading due to altered poromechanical properties. This work attempts to understand the canalicular fluid distribution in single osteon models of OI and healthy bone. A poromechanical model of osteon is developed to compute pore-pressure and interstitial fluid flow as a function of gait loading pattern reported for OI and healthy subjects. Fluid distribution patterns are compared at different time-points of the stance phase of the gait cycle. It is observed that fluid flow significantly reduces in OI bone. Additionally, flow is more static than dynamic in OI osteon in comparison to healthy subjects. This work attempts to identify the plausible explanation behind the diminished mechanotransduction capability of OI bone. This work may further be extended for designing better biomechanical therapies to enhance the fluid flow in order to improve osteogenic activities in OI bone.

Closing the osteon: Do osteocytes sense strain rate rather than fluid flow?

Osteons are cylindrical structures of bone created by matrix resorbing osteoclasts, followed by osteoblasts that deposit new bone. Osteons align with the principal loading direction and it is thought that the osteoclasts are directed by osteocytes, the mechanosensitive cells that reside inside the bone matrix. These osteocytes are presumably controlled by interstitial fluid flow, induced by the physiological loading of bones. Here I consider the stimulation of osteocytes while the osteon is closed by osteoblasts. In a conceptual finite element model, bone is considered a poro-elastic material and subjected to locomotion-induced loading conditions. It appears that the magnitude of flow is constant along the closing cone, while shear strain rate in the bone matrix diminishes linearly with the deposition of bone. This suggests that shear strain rate, rather than fluid flow, is the physical cue that controls osteocytes and bone deposition in newly formed osteons.

Osteoarthritis: New Strategies for Transport and Drug Delivery Across Length Scales

Osteoarthritis (OA) is the fourth leading cause of disability in adults. Yet, few viable pharmaceutical options exist for pain abatement and joint restoration, aside from joint replacement at late and irreversible stages of the disease. From the first onset of OA, as joint pain increases, individuals with arthritis increasingly reach for drug delivery solutions, from taking oral glycosaminoglycans (GAGs) bought over the counter from retail stores (e.g., Costco) to getting injections of viscous, GAG-containing synovial fluid supplement in the doctor's office. Little is known regarding the efficacy of delivery mode and/or treatment by such disease-modulating agents. This Review addresses the interplay of mechanics and biology on drug delivery to affected joints, which has profound implications for molecular transport in joint health and (patho)physiology. Multiscale systems biology approaches lend themselves to understand the relationship between the cell and joint health in OA and other joint (patho)physiologies. This Review first describes OA-related structural and functional changes in the context of the multilength scale anatomy of articular joints. It then summarizes and categorizes, by size and charge, published molecular transport studies, considering changes in permeability induced through inflammatory pathways. Finally, pharmacological interventions for OA are outlined in the context of molecular weights and modes of drug delivery. Taken together, the current state-of-the-art points to a need for new drug delivery strategies that harness systems-based interactions underpinning molecular transport and maintenance of joint structure and function at multiple length scales from molecular agents to cells, tissues, and tissue compartments which together make up articular joints. Cutting edge and cross-length and -time scale imaging represents a key discovery enabling technology in this process.

Anatomical variations in cortical bone surface permeability: Tibia versus femur

Cortical bone surfaces (periosteal and endosteal) exhibit differential (re)modelling response to mechanical loading. This poses a serious challenge in establishing an in silico model to predict site-specific new bone formation as a function of mechanical stimulus. In this regard, mechanical loading-induced fluid motion in lacunar-canalicular system (LCS) is assumed osteogenic. Micro-architectural properties, especially permeability regulate canalicular fluid motion within the bone. The knowledge of these properties is required to compute flow distribution. Along the same line, it is possible that cortical surfaces may experience differential fluid distribution due to anatomical variations in microarchitectural properties which may induce distinct new bone response at cortical surfaces. Nevertheless, these properties are not well reported for cortical surfaces in the literature. Accordingly, the present study aims to measure microarchitectural properties especially permeability at different anatomical locations (medial, lateral, anterior, and posterior) of periosteal and endosteal surfaces using nanoindentation. A standard poroelastic optimization technique was used to estimate permeability, shear modulus, and Poisson's ratio. The properties are also compared for two weight-bearing bones i.e. tibia and femur. Endosteal surface was found more permeable as compared to the periosteal surface. Tibial endosteal surface had shown greater permeability values at most of the anatomical locations as compared to femoral endosteal surface. The outcomes may be used to precisely predict site-specific osteogenesis in cortical bone as a function of canalicular flow distribution. This work may ultimately be beneficial in designing the loading parameters to stimulate desired new bone response for the prevention and the cure of bone loss.

Spherical depth-sensing nanoindentation of human anterior skull base bones: Establishment of a test protocol

The mechanical properties of anterior skull base (ASB) bones are not well understood due to their complex geometry and deep location. However, it is of particular interest for skull base surgeons to appraise the force range they can apply during procedures and know what kind of haptic feedback a simulation device should produce in order to be realistic for trainees. The aim of this study was to establish a measurement protocol to set the level of hydration state, temperature and curve analysis method for spherical depth sensing nanoindentation of ASB bones. A definitive screening design method was used to test the different possible combinations of these factors. Two samples of ASB bones from the heads of two human body donors (two specimens) were selected according to their microstructure as assessed by micro-CT (microtomography): low-porosity (16.87%, sphenoid bone) and high-porosity (79.85%, ethmoid bone). Depth measurement series of 36 nanoindentations (n = 288) were performed on specimen 1 according to the L8 Taguchi orthogonal array to study the effect of temperature (two levels: 20 or 37 °C), hydration state (dry or immerged in physiological saline sodium chloride), and loading curve analysis according to the Hertzian contact theory (fitting at the start or at the end). The mean values of reduced Young's (E*) modulus varied significantly depending on the hydration status and bone microstructure. In order to obtain the physiological properties of ASB bones, we thus propose performing immersion tests. To simplify the experimentation protocol, future experiments must include a room temperature level and a fit of the curve at the end of the load. A validation series was performed on the second specimen to assess the set of parameters. The E* in dry bone gave mean values of 994.68 MPa, versus 409.79 MPa in immerged bones (p < 0.00001). This is the first time a study has been carried out on ASB bones, defining the experimental parameters related to physiological conditions.

Mechanical performance and implications on bone healing of different screw configurations for plate fixation of diaphyseal tibia fractures: a computational study

Diaphyseal tibia fractures may require plate fixation for proper healing to occur. Currently, there is no consensus on the number of screws required for proper fixation or the optimal placement of the screws within the plate. Mechanical stability of the construct is a leading criterion for choosing plate and screws configuration. However, number and location of screws have implications on the mechanical environment at the fracture site and, consequently, on bone healing response: The interfragmentary motion attained with a specific plate and screw construct may elicit mechano-transduction signals influencing cell-type differentiation, which in turn affects how well the fracture heals. This study investigated how different screw configurations affect mechanical performance of a tibia plate fixation construct. Three configurations of an eight-hole plate were considered with the fracture in the center of the plate: eight screws-screws at first, fourth, fifth and eighth hole and screws at first, third, sixth and eighth hole. Constructs' stiffness was compared through biomechanical tests on bone surrogates. A finite element model of tibia diaphyseal fracture was used to conduct a stress analysis on the implanted hardware. Finally, the potential for bone regeneration of each screw configuration was assessed via the computational model through the evaluation of the magnitude of mechano-transduction signals at the bone callus. The results of this study indicate that having screws at fourth and fifth holes represents a preferable configuration since it provides mechanical properties similar to those attained by the stiffest construct (eight screws), and elicits an ideal bone regenerative response.

Signalling molecule transport analysis in lacunar-canalicular system

Mechanical loading-induced fluid flow in lacunar-canalicular space (LCS) of bone excites osteocyte cells to release signalling molecules which initiate osteo-activities. Theoretical models considered canaliculi as a uniform and symmetrical space/channel in bone. However, experimental studies reported that canalicular walls are irregular and curvy resulting in inhomogeneous fluid motion which may influence the molecular transport. Therefore, a new mathematical model of LCS with curvy canalicular walls is developed to characterize cantilever bending-induced canalicular flow behaviour in terms of pore-pressure, fluid velocity, and streamlines. The model also analyses the mobility of signalling molecules involved in bone mechanotransduction as a function of loading frequency and permeability of LCS. Inhomogeneous flow is observed at higher loading frequency which amplifies mechanotransduction; nevertheless, it also promotes trapping of signalling molecules. The effects of shape and size of signalling molecules on transport behaviour are also studied. Trivially, signalling molecules larger in size and weight move slower as compared to molecules small in size and weight which validates the findings of the present study. The outcomes will ultimately be useful in designing better biomechanical exercise in combination with pharmaceutical agents to improve the bone health.

Study on the biomechanical responses of the loaded bone in macroscale and mesoscale by multiscale poroelastic FE analysis

BACKGROUND

Bone is a hierarchically structured composite material, and different hierarchical levels exhibit diverse material properties and functions. The stress and strain distribution and fluid flow in bone play an important role in the realization of mechanotransduction and bone remodeling.

METHODS

To investigate the mechanotransduction and fluid behaviors in loaded bone, a multiscale method was developed. Based on poroelastic theory, we established the theoretical and FE model of a segment bone to provide basis for researching more complex bone model. The COMSOL Multiphysics software was used to establish different scales of bone models, and the properties of mechanical and fluid behaviors in each scale were investigated.

RESULTS

FE results correlated very well with analytical in macroscopic scale, and the results for the mesoscopic models were about less than 2% different compared to that in the macro-mesoscale models, verifying the correctness of the modeling. In macro-mesoscale, results demonstrated that variations in fluid pressure (FP), fluid velocity (FV), von Mises stress (VMS), and maximum principal strain (MPS) in the position of endosteum, periosteum, osteon, and interstitial bone and these variations can be considerable (up to 10, 8, 4 and 3.5 times difference in maximum FP, FV, VMS, and MPS between the highest and the lowest regions, respectively). With the changing of Young's modulus (E) in each osteon lamella, the strain and stress concentration occurred in different positions and given rise to microscale spatial variations in the fluid pressure field. The heterogeneous distribution of lacunar-canalicular permeability (klcp) in each osteon lamella had various influence on the FP and FV, but had little effect on VMS and MPS.

CONCLUSION

Based on the idealized model presented in this article, the presence of endosteum and periosteum has an important influence on the fluid flow in bone. With the hypothetical parameter values in osteon lamellae, the bone material parameters have effect on the propagation of stress and fluid flow in bone. The model can also incorporate alternative material parameters obtained from different individuals. The suggested method is expected to provide dependable biological information for better understanding the bone mechanotransduction and signal transduction.

Computed tomography porosity and spherical indentation for determining cortical bone millimetre-scale mechanical properties

The cortex of the femoral neck is a key structural element of the human body, yet there is not a reliable metric for predicting the mechanical properties of the bone in this critical region. This study explored the use of a range of non-destructive metrics to measure femoral neck cortical bone stiffness at the millimetre length scale. A range of testing methods and imaging techniques were assessed for their ability to measure or predict the mechanical properties of cortical bone samples obtained from the femoral neck of hip replacement patients. Techniques that can potentially be applied in vivo to measure bone stiffness, including computed tomography (CT), bulk wave ultrasound (BWUS) and indentation, were compared against in vitro techniques, including compression testing, density measurements and resonant ultrasound spectroscopy. Porosity, as measured by micro-CT, correlated with femoral neck cortical bone's elastic modulus and ultimate compressive strength at the millimetre length scale. Large-tip spherical indentation also correlated with bone mechanical properties at this length scale but to a lesser extent. As the elastic mechanical properties of cortical bone correlated with porosity, we would recommend further development of technologies that can safely measure cortical porosity in vivo.

A surrogate mechanostatistical microstructural model to inform whole hip cortical bone remodelling

Multiscale models of bone remodelling which incorporate clinically important features at a wide range of spatial scales are computationally intractable. In addition, there is a large gap in existing bone remodelling literature which deals with Haversian-level cortical bone remodelling behaviour and its effect on whole organ bone strength. In this study, we present an integration between continuum mechanics and surrogate modelling as an efficient circumvention to the problem of intractability, linked with an intricate 3D cortical bone remodelling algorithm which captures realistic microanatomical features at the Haversian level. The surrogate model predicted clear differentiation in long-term bone strength changes in clinically significant cases with extremely high computational efficiency.

Mechanical behavior of metastatic femurs through patient-specific computational models accounting for bone-metastasis interaction

This paper proposes a computational model based on a finite-element formulation for describing the mechanical behavior of femurs affected by metastatic lesions. A novel geometric/constitutive description is introduced by modelling healthy bone and metastases via a linearly poroelastic constitutive approach. A Gaussian-shaped graded transition of material properties between healthy and metastatic tissues is prescribed, in order to account for the bone-metastasis interaction. Loading-induced failure processes are simulated by implementing a progressive damage procedure, formulated via a quasi-static displacement-driven incremental approach, and considering both a stress- and a strain-based failure criterion. By addressing a real clinical case, left and right patient-specific femur models are geometrically reconstructed via an ad-hoc imaging procedure and embedding multiple distributions of metastatic lesions along femurs. Significant differences in fracture loads, fracture mechanisms, and damage patterns, are highlighted by comparing the proposed constitutive description with a purely elastic formulation, where the metastasis is treated as a pseudo-healthy tissue or as a void region. Proposed constitutive description allows to capture stress/strain localization mechanisms within the metastatic tissue, revealing the model capability in describing possible strain-induced mechano-biological stimuli driving onset and evolution of the lesion. The proposed approach opens towards the definition of effective computational strategies for supporting clinical decision and treatments regarding metastatic femurs, contributing also to overcome some limitations of actual standards and procedures.

Numerical modeling of bone as a multiscale poroelastic material by the homogenization technique

Bone is a complex material showing a hierarchical and porous structure but also a natural ability to remodel thanks to cells sensitive to fluid flows. Based on these characteristics, a multiscale numerical model has been developed in order to represent the bone response under mechanical solicitation. It relies on the homogenization technique, simulating bone as a homogeneous structure having a porous microstructure saturated with bone fluid. The numerical modeling of the loading of a finite volume of bone enables the determination of an equivalent poroelastic stiffness. Focusing on two extreme fluid boundary conditions, the study of the corresponding structural response provides an overview of the fluid contribution to the poroelastic behavior, impacting the stiffness of the considered material. This parameter is either reduced (when the fluid can flow out of the structure) or increased (when the fluid is kept inside the structure) and quantified through this model. The presented poroelastic numerical model is here developed in the perspective of providing a bio-reliable model of bones, to determine the critical parameters that might impact bone remodeling.

Heterogeneous modeling based prosthesis design with porosity and material variation

The work proposes the development of heterogeneous bio-implants with the aim to minimize stress shielding effect and enhance bone ingrowth. Stress shielding in the implant can be minimized by reducing the overall stiffness of the implant, which is achieved here by varying the material based on stress distribution across the prosthesis. To increase overall stability of the implant by simultaneous enhancing osseointegration and reducing stress shielding, the work proposes the design of heterogeneous prosthesis with graded porosity and material having radial, axial and mixed (simultaneous radial and axial) variations. Static analysis for material variation models and consolidation analysis for graded porosity and material variation models are performed. After comparisons of results among different models, radial variation model was observed to deliver the results.

Measuring bone stiffness using spherical indentation

Objectives

Bone material properties are a major determinant of bone health in older age, both in terms of fracture risk and implant fixation, in orthopaedics and dentistry. Bone is an anisotropic and hierarchical material so its measured material properties depend upon the scale of metric used. The scale used should reflect the clinical problem, whether it is fracture risk, a whole bone problem, or implant stability, at the millimetre-scale. Indentation, an engineering technique involving pressing a hard-tipped material into another material with a known force, may be able to assess bone stiffness at the millimetre-scale (the apparent elastic modulus). We aimed to investigate whether spherical-tip indentation could reliably measure the apparent elastic modulus of human cortical bone.

Materials and methods

Cortical bone samples were retrieved from the femoral necks of nineteen patients undergoing total hip replacement surgery (10 females, 9 males, mean age: 69 years). The samples underwent indentation using a 1.5 mm diameter, ruby, spherical indenter tip, with sixty indentations per patient sample, across six locations on the bone surfaces, with ten repeated indentations at each of the six locations. The samples then underwent mechanical compression testing. The repeatability of indentation measurements of elastic modulus was assessed using the co-efficient of repeatability and the correlation between the bone elastic modulus measured by indentation and compression testing was analysed by least-squares regression.

Results

In total, 1140 indentations in total were performed. Indentation was found to be repeatable for indentations performed at the same locations on the bone samples with a mean co-efficient of repeatability of 0.4 GigaPascals (GPa), confidence interval (C.I): 0.33–0.42 GPa. There was variation in the indentation modulus results between different locations on the bone samples (mean co-efficient of repeatability: 3.1 GPa, C.I: 2.2–3.90 GPa). No clear correlation was observed between indentation and compression values of bone elastic modulus (r = 0.33, p = 0.17). The mean apparent elastic modulus obtained by spherical indentation was 9.9 GPa, the standard deviation for each indent cycle was 0.11 GPa, and the standard deviation between locations on the same sample was 1.01 GPa. The mean compression apparent elastic modulus was 4.42 GPa, standard deviation 1.02 GPa.

Discussion

Spherical-tip indentation was found to be a repeatable test for measuring the elastic modulus of human cortical bone, demonstrated by a low co-efficient of repeatability in this study. It could not, however, reliably predict cortical bone elastic modulus determined by platens compression testing in this study. This may be due to indentation only probing mechanical properties at the micro-scale while platens compression testing assesses millimetre length-scale properties. Improvements to the testing technique, including the use of a larger diameter spherical indenter tip, may improve the measurement of bone stiffness at the millimetre scale and should be investigated further.

Engineering vascularized and innervated bone biomaterials for improved skeletal tissue regeneration

Blood vessels and nerve fibers are distributed throughout the entirety of skeletal tissue, and play important roles during bone development and fracture healing by supplying oxygen, nutrients, and cells. However, despite the successful development of bone mimetic materials that can replace damaged bone from a structural point of view, most of the available bone biomaterials often do not induce sufficient formation of blood vessels and nerves. In part, this is due to the difficulty of integrating and regulating multiple tissue types within artificial materials, which causes a gap between native skeletal tissue. Therefore, understanding the anatomy and underlying interaction mechanisms of blood vessels and nerve fibers in skeletal tissue is important to develop biomaterials that can recapitulate its complex microenvironment. In this perspective, we highlight the structure and osteogenic functions of the vascular and nervous system in bone, in a coupled manner. In addition, we discuss important design criteria for engineering vascularized, innervated, and neurovascularized bone implant materials, as well as recent advances in the development of such biomaterials. We expect that bone implant materials with neurovascularized networks can more accurately mimic native skeletal tissue and improve the regeneration of bone tissue.

Computational Investigation on the Biomechanical Responses of the Osteocytes to the Compressive Stimulus: A Poroelastic Model

Osteocytes, the major type of bone cells embedded in the bone matrix and surrounded by the lacunar and canalicular system, can serve as biomechanosensors and biomechanotranducers of the bone. Theoretical analytical methods have been employed to investigate the biomechanical responses of osteocytes in vivo; the poroelastic properties have not been taken into consideration in the three-dimensional (3D) finite element model. In this study, a 3D poroelastic idealized finite element model was developed and was used to predict biomechanical behaviours (maximal principal strain, pore pressure, and fluid velocity) of the osteocyte-lacunar-canalicular system under 150-, 1000-, 3000-, and 5000-microstrain compressive loads, respectively, representing disuse, physiological, overuse, and pathological overload loading stimuli. The highest local strain, pore pressure, and fluid velocity were found to be highest at the proximal region of cell processes. These data suggest that the strain, pore pressure, and fluid velocity of the osteocyte-lacunar-canalicular system increase with the global loading and that the poroelastic material property affects the biomechanical responses to the compressive stimulus. This new model can be used to predict the mechanobiological behaviours of osteocytes under the four different compressive loadings and may provide an insight into the mechanisms of mechanosensation and mechanotransduction of the bone.

A numerical investigation and experimental verification of size effects in loaded bovine cortical bone

In this paper, we present 2- and 3-dimensional finite element-based numerical models of loaded bovine cortical bone that explicitly incorporate the dominant microstructural feature: the vascular channel or Haversian canal system. The finite element models along with the representation of the microstructure within them are relatively simple: 2-dimensional models, consisting of a structured mesh of linear elastic planar elements punctuated by a periodic distribution of circular voids, are used to represent beam samples of cortical bone in which the channels are orientated perpendicular to the sample major axis, while 3-dimensional models, using a corresponding mesh of equivalent solid elements, represent those samples in which the canals are aligned with the axis. However, these models are exploited in an entirely novel approach involving the representation of material samples of different sizes and surface morphology. The numerical results obtained for the virtual material samples when loaded in bending indicate that they exhibit size effects not forecast by either classical (Cauchy) or more generalized elasticity theories. However, these effects are qualitatively consistent with those that we observed in a series of carefully conducted experiments involving the flexural testing of bone samples of different sizes. Encouraged by this qualitative agreement, we have identified appropriate model parameters, primarily void volume fraction but also void separation and matrix modulus by matching the computed size effects to those we observed experimentally. Interestingly, the parameter choices that provide the most suitable match of these effects broadly concur with those we actually observed in cortical bone.

Microstructural changes associated with osteoporosis negatively affect loading-induced fluid flow around osteocytes in cortical bone

Loading-induced interstitial fluid flow in the microporosities of bone is critical for osteocyte mechanotransduction and for the maintenance of tissue health, enhancing convective transport in the lacunar-canalicular system. In recent studies, our group has reported alterations of bone's vascular porosity and lacunar-canalicular system microarchitecture in a rat model of postmenopausal osteoporosis. In this work, poroelastic finite element analysis was used to investigate whether these microstructural changes can affect interstitial fluid flow around osteocytes. Animal-specific finite element models were developed combining micro-CT reconstructions of bone microstructure and measures of the poroelastic material properties. These models were used to quantify and compare loading-induced fluid flow in the lacunar-canalicular system of ovariectomized and sham-operated rats. A parametric analysis was also used to quantify the influence of the lacunar-canalicular permeability and vascular porosity on the fluid velocity magnitude. Results show that mechanically-induced interstitial fluid velocity can be significantly reduced in the lacunar-canalicular system of ovariectomized rats. Interestingly, the vascular porosity is shown to have a major influence on interstitial fluid flow, while the lacunar-canalicular permeability influence is limited when larger than 10^-20m². Altogether our results suggest that microstructural changes associated with the osteoporotic condition can negatively affect interstitial fluid flow around osteocytes in the lacunar-canalicular system of cortical bone. This fluid flow reduction could impair mechanosensation of the osteocytic network, possibly playing a role in the initiation and progression of age-related bone loss and postmenopausal osteoporosis.

Porotic paradox: distribution of cortical bone pore sizes at nano- and micro-levels in healthy vs. fragile human bone

Bone is a remarkable biological nanocomposite material showing peculiar hierarchical organization from smaller (nano, micro) to larger (macro) length scales. Increased material porosity is considered as the main feature of fragile bone at larger length-scales. However, there is a shortage of quantitative information on bone porosity at smaller length-scales, as well as on the distribution of pore sizes in healthy vs. fragile bone. Therefore, here we investigated how healthy and fragile bones differ in pore volume and pore size distribution patterns, considering a wide range of mostly neglected pore sizes from nano to micron-length scales (7.5 to 15000 nm). Cortical bone specimens from four young healthy women (age: 35 ± 6 years) and five women with bone fracture (age: 82 ± 5 years) were analyzed by mercury porosimetry. Our findings showed that, surprisingly, fragile bone demonstrated lower pore volume at the measured scales. Furtnermore, pore size distribution showed differential patterns between healthy and fragile bones, where healthy bone showed especially high proportion of pores between 200 and 15000 nm. Therefore, although fragile bones are known for increased porosity at macroscopic level and level of tens or hundreds of microns as firmly established in the literature, our study with a unique assessment range of nano-to micron-sized pores reveal that osteoporosis does not imply increased porosity at all length scales. Our thorough assessment of bone porosity reveals a specific distribution of porosities at smaller length-scales and contributes to proper understanding of bone structure which is important for designing new biomimetic bone substitute materials.

Micromotion-induced peri-prosthetic fluid flow around a cementless femoral stem

Micromotion-induced interstitial fluid flow at the bone-implant interface has been proposed to play an important role in aseptic loosening of cementless implants. High fluid velocities are thought to promote aseptic loosening through activation of osteoclasts, shear stress induced control of mesenchymal stem cells differentiation, or transport of molecules. In this study, our objectives were to characterize and quantify micromotion-induced fluid flow around a cementless femoral stem using finite element modeling. With a 2D model of the bone-implant interface and full-factorial design, we first evaluated the relative influence of material properties, and bone-implant micromotion and gap on fluid velocity. Transverse sections around a femoral stem were built from computed tomography images, while boundary conditions were obtained from experimental measurements on the same femur. In a second step, a 3D model was built from the same data-set to estimate the shear stress experienced by cells hosted in the peri-implant tissues. The full-factorial design analysis showed that local micromotion had the most influence on peak fluid velocity at the interface. Remarkable variations in fluid velocity were observed in the macrostructures at the surface of the implant in the 2D transverse sections of the stem. The 3D model predicted peak fluid velocities extending up to 2.2 mm/s in the granulation tissue and to 3.9 mm/s in the trabecular bone. Peak shear stresses on the cells hosted in these tissues ranged from 0.1 to 12.5 Pa. These results offer insight into mechanical stimuli encountered at the bone-implant interface.

Estimation of anisotropic permeability in trabecular bone based on microCT imaging and pore-scale fluid dynamics simulations

In this paper, a comprehensive framework is proposed to estimate the anisotropic permeability matrix in trabecular bone specimens based on micro-computed tomography (microCT) imaging combined with pore-scale fluid dynamics simulations. Two essential steps in the proposed methodology are the selection of (i) a representative volume element (RVE) for calculation of trabecular bone permeability and (ii) a converged mesh for accurate calculation of pore fluid flow properties. Accurate estimates of trabecular bone porosities are obtained using a microCT image resolution of approximately 10 μm. We show that a trabecular bone RVE in the order of 2 × 2 × 2 mm³ is most suitable. Mesh convergence studies show that accurate fluid flow properties are obtained for a mesh size above 125,000 elements. Volume averaging of the pore-scale fluid flow properties allows calculation of the apparent permeability matrix of trabecular bone specimens. For the four specimens chosen, our numerical results show that the so obtained permeability coefficients are in excellent agreement with previously reported experimental data for both human and bovine trabecular bone samples. We also identified that bone samples taken from long bones generally exhibit a larger permeability in the longitudinal direction. The fact that all coefficients of the permeability matrix were different from zero indicates that bone samples are generally not harvested in the principal flow directions. The full permeability matrix was diagonalized by calculating the eigenvalues, while the eigenvectors showed how strongly the bone sample's orientations deviated from the principal flow directions. Porosity values of the four bone specimens range from 0.83 to 0.86, with a low standard deviation of ± 0.016, principal permeability values range from 0.22 to 1.45 ⋅ 10 ^-8 m², with a high standard deviation of ± 0.33. Also, the anisotropic ratio ranged from 0.27 to 0.83, with high standard deviation. These results indicate that while the four specimens are quite similar in terms of average porosity, large variability exists with respect to permeability and specimen anisotropy. The utilized computational approach compares well with semi-analytical models based on homogenization theory. This methodology can be applied in bone tissue engineering applications for generating accurate pore morphologies of bone replacement materials and to consistently select similar bone specimens in bone bioreactor studies.

Simulation study of axial ultrasonic wave propagation in heterogeneous bovine cortical bone

The effect of the heterogeneity of the long cortical bone is an important factor when applying the axial transmission technique. In this study, the axial longitudinal wave velocity distributions in specimens from the mid-shaft of a bovine femur were measured, in the MHz range. Bilinear interpolation and the piecewise cubic Hermite interpolating polynomial method were used to construct three-dimensional (3D) axial velocity models with a resolution of 40 μm. By assuming the uniaxial anisotropy of the bone and using the results of previous experimental studies [Yamato, Matsukawa, Yanagitani, Yamazaki, Mizukawa, and Nagano (2008b). Calcified Tissue Int. 82, 162-169; Nakatsuji, Yamamoto, Suga, Yanagitani, Matsukawa, Yamazaki, and Matsuyama (2011). Jpn. J. Appl. Phys. 50, 07HF18], the distributions of all elastic moduli were estimated to obtain a 3D heterogeneous bone model and a uniform model. In the heterogeneous model, moduli at the surface were smaller than those inside the model. The elastic finite-difference time-domain method was used to simulate axial ultrasonic wave propagation in these models. In the heterogeneous model, the wavefront of the first arriving signal (FAS) was dependent on the heterogeneity, and the FAS velocity depended on the measured position. These phenomena were not observed in the uniform model.

Contribution of fluid in bone extravascular matrix to strain-rate dependent stiffening of bone tissue - A poroelastic study

Osteoporotic fractures represent an increasing cost to society, and its diagnosis methods based on bone density still lack accuracy in identifying risk of fracture. This is why a better understanding of mechanical behavior of bone tissue is of importance, especially when it comes to relating experimental observations to realistic physiological fall loading conditions. This study aims at exploring the stiffening effect of pore fluid in bone extravascular matrix subject to high strain rate loading that is more realistic to simulate a physiological fall. A computational approach is used, where bone tissue microstructure extracted from micro-CT images is modeled using finite elements. The solid phase of bone tissue is modeled as a poroelastic material, a porous matrix filled with fluid. When the extravascular matrix experiences certain volumetric deformation, the fluid in pores presents load carrying capacity, which consequently varies the apparent stiffness of bone tissue. It is shown that effects of fluid stiffening in bone can be significant, depending on the chosen material properties, the amount of volumetric strain in tissue and the loading rate with respect to hydraulic conductivity and drainage conditions. It is also shown that such stiffening effect is influenced by bone microstructure, and is more significant in cortical bone than in trabecular bone.

Poromicromechanics reveals that physiological bone strains induce osteocyte-stimulating lacunar pressure

Mechanical loads which are macroscopically acting onto bony organs, are known to influence the activities of biological cells located in the pore spaces of bone, in particular so the signaling and production processes mediated by osteocytes. The exact mechanisms by which osteocytes are actually able to “feel” the mechanical loading and changes thereof, has been the subject of numerous studies, and, while several hypotheses have been brought forth over time, this topic has remained a matter of debate. Relaxation times reported in a recent experimental study of Gardinier et al. (Bone 46(4):1075–1081, 2010) strongly suggest that the lacunar pores are likely to experience, during typical physiological load cycles, not only fluid transport, but also undrained conditions. The latter entail the buildup of lacunar pore pressures, which we here quantify by means of a thorough multiscale modeling approach. In particular, the proposed model is based on classical poroelasticity theory, and able to account for multiple pore spaces. First, the model reveals distinct nonlinear dependencies of the resulting lacunar (and vascular) pore pressures on the underlying bone composition, highlighting the importance of a rigorous multiscale approach for appropriate computation of the aforementioned pore pressures. Then, the derived equations are evaluated for macroscopic (uniaxial as well as hydrostatic) mechanical loading of physiological magnitude. The resulting model-predicted pore pressures agree very well with the pressures that have been revealed, by means of in vitro studies, to be of adequate magnitude for modulating the responses of biological cells, including osteocytes. This underlines that osteocytes may respond to many types of loading stimuli at the same time, in particular so to fluid flow and hydrostatic pressure.

Bone ingrowth around porous-coated acetabular implant: a three-dimensional finite element study using mechanoregulatory algorithm

Fixation of uncemented implant is influenced by peri-prosthetic bone ingrowth, which is dependent on the mechanical environment of the implant-bone structure. The objective of the study is to gain an insight into the tissue differentiation around an acetabular component. A mapping framework has been developed to simulate appropriate mechanical environment in the three-dimensional microscale model, implement the mechanoregulatory tissue differentiation algorithm and subsequently assess spatial distribution of bone ingrowth around an acetabular component, quantitatively. The FE model of implanted pelvis subjected to eight static load cases during a normal walking cycle was first solved. Thereafter, a mapping algorithm has been employed to include the variations in implant-bone relative displacement and host bone material properties from the macroscale FE model of implanted pelvis to the microscale FE model of the beaded implant-bone interface. The evolutionary tissue differentiation was observed in each of the 13 microscale models corresponding to 13 acetabular regions. The total implant-bone relative displacements, averaged over each region of the acetabulum, were found to vary between 10 and 60 μm. Both the linear elastic and biphasic poroelastic models predicted similar mechanoregulatory peri-prosthetic tissue differentiation. Considerable variations in bone ingrowth (13-88%), interdigitation depth (0.2-0.82 mm) and average tissue Young's modulus (970-3430 MPa) were predicted around the acetabular cup. A progressive increase in the average Young's modulus, interdigitation depth and decrease in average radial strains of newly formed tissue layer were also observed. This scheme can be extended to investigate tissue differentiation for different surface texture designs on the implants.

Poroelastic analysis of interstitial fluid flow in a single lamellar trabecula subjected to cyclic loading

Trabecula, an anatomical unit of the cancellous bone, is a porous material that consists of a lamellar bone matrix and interstitial fluid in a lacuno-canalicular porosity. The flow of interstitial fluid caused by deformation of the bone matrix is believed to initiate a mechanical response in osteocytes for bone remodeling. In order to clarify the effect of the lamellar structure of the bone matrix--i.e., variations in material properties--on the fluid flow stimuli to osteocytes embedded in trabeculae, we investigated the mechanical behavior of an individual trabecula subjected to cyclic loading based on poroelasticity. We focused on variations in the trabecular permeability and developed an analytical solution containing both transient and steady-state responses for interstitial fluid pressure in a single trabecular model represented by a multilayered two-dimensional poroelastic slab. Based on the obtained solution, we calculated the pressure and seepage velocity of the interstitial fluid in lacuno-canalicular porosity, within the single trabecula, under various permeability distributions. Poroelastic analysis showed that a heterogeneous distribution of permeability produces remarkable variations in the fluid pressure and seepage velocity in the cross section of the individual trabecula, and suggests that fluid flow stimuli to osteocytes are mostly governed by the value of permeability in the neighborhood of the trabecular surfaces if there is no difference in the average permeability in a single trabecula.