Poroelastic properties of bovine vertebral trabecular bone

Adaptable test bench for ASTM-compliant permeability measurement of porous scaffolds for tissue engineering

Intrinsic permeability describes the ability of a porous medium to be penetrated by a fluid. Considering porous scaffolds for tissue engineering (TE) applications, this macroscopic variable can strongly influence the transport of oxygen and nutrients, the cell seeding process, and the transmission of fluid forces to the cells, playing a crucial role in determining scaffold efficacy. Thus, accurately measuring the permeability of porous scaffolds could represent an essential step in their optimization process. In literature, several methods have been proposed to characterize scaffold permeability. Most of the currently adopted approaches to assess permeability limit their applicability to specific scaffold structures, hampering protocols standardization, and ultimately leading to incomparable results among different laboratories. The content of novelty of this study is in the proposal of an adaptable test bench and in defining a specific testing protocol, compliant with the ASTM International F2952-22 guidelines, for reliable and repeatable measurements of the intrinsic permeability of TE porous scaffolds. The developed permeability test bench (PTB) exploits the pump-based method, and it is composed of a modular permeability chamber integrated within a closed-loop hydraulic circuit, which includes a peristaltic pump and pressure sensors, recirculating demineralized water. A specific testing protocol was defined for characterizing the pressure drop associated with the scaffold under test, while minimizing the effects of uncertainty sources. To assess the operational capabilities and performance of the proposed test bench, permeability measurements were conducted on PLA scaffolds with regular (PS) and random (RS) micro-architecture and on commercial bovine bone matrix-derived scaffolds (CS) for bone TE. To validate the proposed approach, the scaffolds were as well characterized using an alternative test bench (ATB) based on acoustic measurements, implementing a blind randomized testing procedure. The consistency of the permeability values measured using both the test benches demonstrated the reliability of the proposed approach. A further validation of the PTB's measurement reliability was provided by the agreement between the measured permeability values of the PS scaffolds and the theory-based predicted permeability value. Once validated the proposed PTB, the performed measurements allowed the investigation of the scaffolds' transport properties. Samples with the same structure (guaranteed by the fused-deposition modeling technique) were characterized by similar permeability values, and CS and RS scaffolds showed permeability values in agreement with the values reported in the literature for bovine trabecular bone. In conclusion, the developed PTB and the proposed testing protocol allow the characterization of the intrinsic permeability of porous scaffolds of different types and dimensions under controlled flow regimes, representing a powerful tool in view of providing a reliable and repeatable framework for characterizing and optimizing scaffolds for TE applications.

A Novel Fiber-Reinforced Poroviscoelastic Bovine Intervertebral Disc Finite Element Model for Organ Culture Experiment Simulations

Intervertebral disc (IVD) degeneration and methods for repair and regeneration have commonly been studied in organ cultures with animal IVDs under compressive loading. With the recent establishment of a novel multi-axial organ culture system, accurate predictions of the global and local mechanical response of the IVD are needed for control system development and to aid in experiment planning. This study aimed to establish a finite element model of bovine IVD capable of predicting IVD behavior at physiological and detrimental load levels. A finite element model was created based on the dimensions and shape of a typical bovine IVD used in the organ culture. The nucleus pulposus (NP) was modeled as a neo-Hookean poroelastic material and the annulus fibrosus (AF) as a fiber-reinforced poroviscoelastic material. The AF consisted of 10 lamella layers and the material properties were distributed in the radial direction. The model outcome was compared to a bovine IVD in a compressive stress-relaxation experiment. A parametric study was conducted to investigate the effect of different material parameters on the overall IVD response. The model was able to capture the equilibrium response and the relaxation response at physiological and higher strain levels. Permeability and elastic stiffness of the AF fiber network affected the overall response most prominently. The established model can be used to evaluate the response of the bovine IVD at strain levels typical for organ culture experiments, to define relevant boundaries for such studies, and to aid in the development and use of new multi-axial organ culture systems.

Symmetry breaking and effects of nutrient walkway in time-dependent bone remodeling incorporating poroelasticity

Bone is an extraordinary biological material that continuously adapts its hierarchical microstructure to respond to static and dynamic loads for offering optimal mechanical features, in terms of stiffness and toughness, across different scales, from the sub-microscopic constituents within osteons—where the cyclic activity of osteoblasts, osteoclasts, and osteocytes redesigns shape and percentage of mineral crystals and collagen fibers—up to the macroscopic level, with growth and remodeling processes that modify the architecture of both compact and porous bone districts. Despite the intrinsic complexity of the bone mechanobiology, involving coupling phenomena of micro-damage, nutrients supply driven by fluid flowing throughout hierarchical networks, and cells turnover, successful models and numerical algorithms have been presented in the literature to predict, at the macroscale, how bone remodels under mechanical stimuli, a fundamental issue in many medical applications such as optimization of femur prostheses and diagnosis of the risk fracture. Within this framework, one of the most classical strategies employed in the studies is the so-called Stanford’s law, which allows uploading the effect of the time-dependent load-induced stress stimulus into a biomechanical model to guess the bone structure evolution. In the present work, we generalize this approach by introducing the bone poroelasticity, thus incorporating in the model the role of the fluid content that, by driving nutrients and contributing to the removal of wastes of bone tissue cells, synergistically interacts with the classical stress fields to change homeostasis states, local saturation conditions, and reorients the bone density rate, in this way affecting growth and remodeling. Through two paradigmatic example applications, i.e. a cylindrical slice with internal prescribed displacements idealizing a tract of femoral diaphysis pushed out by the pressure exerted by a femur prosthesis and a bone element in a form of a bent beam, it is highlighted that the present model is capable to catch more realistically both the transition between spongy and cortical regions and the expected non-symmetrical evolution of bone tissue density in the medium–long term, unpredictable with the standard approach. A real study case of a femur is also considered at the end in order to show the effectiveness of the proposed remodeling algorithm.

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.

Study of the variations of fall induced hip fracture risk between right and left femurs using CT-based FEA

Background

Hip fracture of elderly people—suffering from osteoporosis—is a severe public health concern, which can be reduced by providing a prior assessment of hip fracture risk. Image-based finite element analysis (FEA) has been considered an effective computational tool to assess the hip fracture risk. Considering the femoral neck region is the weakest, fracture risk indicators (FRI) are evaluated for both single-legged stance and sideways fall configurations and are compared between left and right femurs of each subject. Quantitative Computed Tomography (QCT) scan datasets of thirty anonymous patients’ left and right femora have been considered for the FE models, which have been simulated with an equal magnitude of load applied to the aforementioned configurations. The requirement of bilateral hip assessment in predicting the fracture risk has been explored in this study.

Results

Comparing the sideways fall and single-legged stance, the FRI varies by 64 to 74% at the superior aspects and by 14 to 19% at the inferior surfaces of both the femora. The results of this in vivo analysis clearly substantiate that the fracture is expected to initiate at the superior surface of femoral neck region if a patient falls from his/her standing height. The distributions of FRI between the femurs vary considerably, and the variability is significant at the superior aspects. The p value (= 0.02) obtained from paired sample t-Test yields p value ≤ 0.05, which shows the evidence of variability of the FRI distribution between left and right femurs. Moreover, the comparison of FRIs between the left and right femur of men and women shows that women are more susceptible to hip fracture than men.

Conclusions

The results and statistical variation clearly signify a need for bilateral hip scanning in predicting hip fracture risk, which is clinically conducted, at present, based on one hip chosen randomly and may lead to inaccurate fracture prediction. This study, although preliminary, may play a crucial role in assessing the hip fractures of the geriatric population and thereby, reducing the cost of treatment by taking predictive measure.

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.

Study of stress variations in single-stance and sideways fall using image-based finite element analysis

Image-based finite element analysis (FEA) has been considered an effective computational tool to predict hip fracture risk. The patient specific FEA gives an insight into the inclusive effect of three-dimensional (3D) complex bone geometry, and the distribution of inhomogeneous isotropic material properties in conjunction with loading conditions. The neck region of a femur is primarily the weakest in which fracture is likely to happen, when someone falls. A sideways fall results in the development of greater tensile and compressive stresses, respectively, in the inferior and superior aspects of the femoral neck, whereas the state of stress is reversed in usual gait or stance configuration. Herein, the variations of stresses have been investigated at the femoral neck region considering both single-stance and sideways fall. Finite element models of ten human femora have been generated using Quantitative Computed Tomography (QCT) scan datasets and have been simulated with an equal magnitude of load applied to the aforementioned configurations. Fracture risk indicator, defined as the ratio of the maximum compressive or tensile stress computed at the superior and inferior surfaces to the corresponding yield stress, has been used in this work to measure the variations of fracture risk between single-stance and sideways fall. The average variations of the fracture risk indicators between the fall and stance are at least 24.3% and 8% at the superior and inferior surfaces, respectively. The differences may interpret why sideways fall is more dangerous for the elderly people, causing hip fracture.

The application of digital volume correlation (DVC) to study the microstructural behaviour of trabecular bone during compression

Digital Volume Correlation (DVC) has been emerged recently as an innovative approach to full volume (i.e. internal) displacement and strain field measurement in materials and structures, particularly in conjunction with high resolution X-ray computed tomography (CT). As a relatively novel technique certain aspects of precision, accuracy and the breadth of application are yet to be fully established. This study has applied DVC to volume images of porcine trabecular bone assessing the effect of noise and sub-volume size on strain measurement. Strain resolutions ranging between 70 and 800με were obtained for the optimum sub-volume size of 64 voxels with a 50% overlap for metrological studies conducted. These values allowed the mechanical behaviour of porcine trabecular bone during compression to be investigated. During compression a crushed layer formed adjacent to the boundary plate which increased in thickness as the specimen was further deformed. The structure of the crushed layer was altered to such an extent that it confounded the correlation method. While investigating this factor, it was found that for reliable strain calculations a correlation coefficient of 0.90 or above was required between the sub-volumes in the reference and the deformed volumes. Good agreements between the results and published bone strain failures were obtained. Using the full field strain measurements, Poisson's ratio was identified for each compression step using a dedicated inverse method called the virtual fields method (VFM). It was found that for a given region outside of the crushed zone the Poisson ratio decreased from 0.32 to 0.21 between the first and the final compression steps, which was hypothesised to be due to the bone geometry and its resulting deformation behaviour. This study demonstrates that volumetric strain measurement can be obtained successfully using DVC, making it a useful tool for quantitatively investigating the micro-mechanical behaviour of macroscale bone specimens.

IN VITROACOUSTIC WAVE PROPAGATION IN HUMAN AND BOVINE CANCELLOUS BONE AS PREDICTED BY BIOT'S THEORY

Recent in vitro studies have provided evidence of the propagation of two different longitudinal wave modes at ultrasonic frequencies in cancellous bone. The genesis of these two plane waves in fluid-saturated porous media is predicted by the poroelastic approach to wave propagation originally developed by Biot. However, wave velocity is usually analyzed as a function of bone mass density only; therefore, the influence of the cancellous bone microstructure over the wave velocity is not taken into account. In the present study, a descriptor of the microstructure is considered in Biot's theory. This model is used to evaluate the large experimental variability of both fast and slow wave velocities measured on randomly oriented human and bovine cancellous bone samples. The role of the anisotropic solid structure and fluid in the behavior of fast and slow wave velocities is examined. Experimental and theoretically predicted velocities are found in close agreement when analyzed as a function of both porosity and structural index. This model has the potential to be used to determine an acoustically derived structural index in cancellous bone.

Fabric dependence of wave propagation in anisotropic porous media

Current diagnosis of bone loss and osteoporosis is based on the measurement of the bone mineral density (BMD) or the apparent mass density. Unfortunately, in most clinical ultrasound densitometers: 1) measurements are often performed in a single anatomical direction, 2) only the first wave arriving to the ultrasound probe is characterized, and 3) the analysis of bone status is based on empirical relationships between measurable quantities such as speed of sound (SOS) and broadband ultrasound attenuation (BUA) and the density of the porous medium. However, the existence of a second wave in cancellous bone has been reported, which is an unequivocal signature of poroelastic media, as predicted by Biot's poroelastic wave propagation theory. In this paper, the governing equations for wave motion in the linear theory of anisotropic poroelastic materials are developed and extended to include the dependence of the constitutive relations upon fabric-a quantitative stereological measure of the degree of structural anisotropy in the pore architecture of a porous medium. This fabric-dependent anisotropic poroelastic approach is a theoretical framework to describe the microarchitectural-dependent relationship between measurable wave properties and the elastic constants of trabecular bone, and thus represents an alternative for bone quality assessment beyond BMD alone.

Refinement of elastic, poroelastic, and osmotic tissue properties of intervertebral disks to analyze behavior in compression

Intervertebral disks support compressive forces because of their elastic stiffness as well as the fluid pressures resulting from poroelasticity and the osmotic (swelling) effects. Analytical methods can quantify the relative contributions, but only if correct material properties are used. To identify appropriate tissue properties, an experimental study and finite element analytical simulation of poroelastic and osmotic behavior of intervertebral disks were combined to refine published values of disk and endplate properties to optimize model fit to experimental data. Experimentally, nine human intervertebral disks with adjacent hemi-vertebrae were immersed sequentially in saline baths having concentrations of 0.015, 0.15, and 1.5 M and the loss of compressive force at constant height (force relaxation) was recorded over several hours after equilibration to a 300-N compressive force. Amplitude and time constant terms in exponential force-time curve-fits for experimental and finite element analytical simulations were compared. These experiments and finite element analyses provided data dependent on poroelastic and osmotic properties of the disk tissues. The sensitivities of the model to alterations in tissue material properties were used to obtain refined values of five key material parameters. The relaxation of the force in the three bath concentrations was exponential in form, expressed as mean compressive force loss of 48.7, 55.0, and 140 N, respectively, with time constants of 1.73, 2.78, and 3.40 h. This behavior was analytically well represented by a model having poroelastic and osmotic tissue properties with published tissue properties adjusted by multiplying factors between 0.55 and 2.6. Force relaxation and time constants from the analytical simulations were most sensitive to values of fixed charge density and endplate porosity.

Limitation of finite element analysis of poroelastic behavior of biological tissues undergoing rapid loading

The finite element method is used in biomechanics to provide numerical solutions to simulations of structures having complex geometry and spatially differing material properties. Time-varying load deformation behaviors can result from solid viscoelasticity as well as viscous fluid flow through porous materials. Finite element poroelastic analysis of rapidly loaded slow-draining materials may be ill-conditioned, but this problem is not widely known in the biomechanics field. It appears as instabilities in the calculation of interstitial fluid pressures, especially near boundaries and between different materials. Accurate solutions can require impractical compromises between mesh size and time steps. This article investigates the constraints imposed by this problem on tissues representative of the intervertebral disc, subjected to moderate physiological rates of deformation. Two test cylindrical structures were found to require over 10(4) linear displacement-constant pressure elements to avoid serious oscillations in calculated fluid pressure. Fewer Taylor-Hood (quadratic displacement-linear pressure elements) were required, but with complementary increases in computational costs. The Vermeer-Verruijt criterion for 1D mesh size provided guidelines for 3D mesh sizes for given time steps. Pressure instabilities may impose limitations on the use of the finite element method for simulating fluid transport behaviors of biological soft tissues at moderately rapid physiological loading rates.

Would increased interstitial fluid flow through in situ mechanical stimulation enhance bone remodeling?

Bone accommodates to changes in its functional environment ensuring that sufficient skeletal mass is appropriately positioned to withstand the mechanical loads that result from functional activities. Increasing physical activity will result in increased bone mass, while the removal of functional loading would result in bone loss. Bone is a composite material made up of a collagen-hydroxyapatite matrix and a complex network of lacunae-canaliculi channels occupied by osteocyte and osteoblast processes, immersed in interstitial fluid. There are strong indications that changes in interstitial fluid flow velocity or pressure are the means by which an external load signal is communicated to the cell. In vitro studies indicate that shear stress, induced by interstitial fluid flow, is a potent bone cell behavior regulator. One of the forms of altering interstitial fluid flow is through the mechanical deformation of skeletal tissue in response to applied loads. Other methods include increased intramedullary pressure, negative-pressure tissue regeneration, or external mechanical stimulation. Analysis of these methods poses the question of process effectiveness. The efficacy of each method theoretically will depend on the mechanical efficiency of transmitting an external load and converting it into changes in interstitial fluid flow. In this paper, we combine recent knowledge on the effect of the bone's interstitial fluid flow, different fluid patterns, the role of gap junctions, and the concept of mechanical effectiveness of different methods that influence interstitial fluid flow within bone, and we hypothesize that the efficiency of bone remodeling can be improved if a small mechanical percussion device could be placed directly in contact with the bone, thus inducing local interstitial fluid flow variations. Enhancement of bone repair and remodeling through controlled interstitial fluid flow possesses many clinical applications. Further investigations and in vivo experiments are required. Practical methods and clinical apparatuses need to be conceived and developed to validate and facilitate the clinical use of this technique.

Sensitivity of tissue differentiation and bone healing predictions to tissue properties

Computational models are employed as tools to investigate possible mechano-regulation pathways for tissue differentiation and bone healing. However, current models do not account for the uncertainty in input parameters, and often include assumptions about parameter values that are not yet established. The aim was to clarify the importance of the assumed tissue material properties in a computational model of tissue differentiation during bone healing. An established mechano-biological model was employed together with a statistical approach. The model included an adaptive 2D finite element model of a fractured long bone. Four outcome criteria were quantified: (1) ability to predict sequential healing events, (2) amount of bone formation at specific time points, (3) total time until healing, and (4) mechanical stability at specific time points. Statistical analysis based on fractional factorial designs first involved a screening experiment to identify the most significant tissue material properties. These seven properties were studied further with response surface methodology in a three-level Box-Behnken design. Generally, the sequential events were not significantly influenced by any properties, whereas rate-dependent outcome criteria and mechanical stability were significantly influenced by Young's modulus and permeability. Poisson's ratio and porosity had minor effects. The amount of bone formation at early, mid and late phases of healing, the time until complete healing and the mechanical stability were all mostly dependent on three material properties; permeability of granulation tissue, Young's modulus of cartilage and permeability of immature bone. The consistency between effects of the most influential parameters was high. To increase accuracy and predictive capacity of computational models of bone healing, the most influential tissue mechanical properties should be accurately quantified.

Fluid and Solute Transport in Bone: Flow-Induced Mechanotransduction

Much recent evidence suggests that bone cells sense their mechanical environment via interstitial fluid flow. In this review, we summarize theoretical and experimental approaches to quantify fluid and solute transport in bone, starting with the early investigations of fluid shear stress applied to bone cells. The pathways of bone interstitial fluid and solute movement are high-lighted based on recent theoretical models, as well as a new generation of tracer experiments that have clarified and refined the structure and function of the osteocyte pericellular matrix. Then we trace how the fluid-flow models for mechanotransduction have evolved as new ultrastructural features of the osteocyte lacunar-canalicular porosity have been identified and how more recent in vitro fluid-flow and cell-stretch experiments have helped elucidate at the molecular level the possible pathways for cellular excitation in bone.

An extended biphasic model for charged hydrated tissues with application to the intervertebral disc

Finite element models for hydrated soft biological tissue are numerous but often exhibit certain essential deficiencies concerning the reproduction of relevant mechanical and electro-chemical responses. As a matter of fact, singlephasic models can never predict the interstitial fluid flow or related effects like osmosis. Quite a few models have more than one constituent, but are often restricted to the small-strain domain, are not capable of capturing the intrinsic viscoelasticity of the solid skeleton, or do not account for a collagen fibre reinforcement. It is the goal of this contribution to overcome these drawbacks and to present a thermodynamically consistent model, which is formulated in a very general way in order to reproduce the behaviour of almost any charged hydrated tissue. Herein, the Theory of Porous Media (TPM) is applied in combination with polyconvex Ogden-type material laws describing the anisotropic and intrinsically viscoelastic behaviour of the solid matrix on the basis of a generalised Maxwell model. Moreover, other features like the deformation-dependent permeability, the possibility to include inhomogeneities like varying fibre alignment and behaviour, or osmotic effects based on the simplifying assumption of Lanir are also included. Finally, the human intervertebral disc is chosen as a representative for complex soft biological tissue behaviour. In this regard, two numerical examples will be presented with focus on the viscoelastic and osmotic capacity of the model.

Use of high-resolution MRI for investigation of fluid flow and global permeability in a material with interconnected porosity

We present a multi-scale experimental approach designed to improve the investigation of both localized and global fluid flow in biomaterials with randomly interconnected porosity. Coralline hydroxyapatite (ProOsteon 500 from Interpore-Cross), having a relatively well-defined porosity, was used as an in vitro model of typical bone architecture. Axial fluid velocity profiles within the pores of a cylindrical hydroxyapatite sample were characterized using high-resolution MRI in conjunction with the measurement of global flow and associated permeability based on the Darcy-type relationship. Assuming Newtonian fluid behaviour, image analysis permitted computation of local porosity, intra-pore fluid shear, and visualization of flow heterogeneity within the sample. These results may benefit applications in biomaterials for the evaluation of factors influencing bony incorporation in porous scaffolds and on porous implant and bone surfaces. Normal and diseased biological tissues are also clinical relevant applications.

Rate dependence of hydraulic resistance in human lumbar vertebral bodies

STUDY DESIGN

Twenty-one intact human lumbar vertebral bodies (L3 and L4) were used to determine the changes in measured intraosseous pressure for 2 volumetric flow rates and to calculate hydraulic resistance in both cases.

OBJECTIVE

To evaluate changes in hydraulic resistance in intact vertebral bodies under different rates of flow.

SUMMARY OF BACKGROUND DATA

Hydraulic resistance has been implicated in the creation of high-speed vertebral injuries, such as burst fracture, but no previous study has measured hydraulic resistance under high-speed loading conditions. Previous work in whole bone preparations showed that hydraulic resistance was constant under low-speed conditions. The authors hypothesized that: (1) measured pressure would increase with increasing input flow rates, and (2) hydraulic resistance would remain constant at increased input flow rates.

METHODS

Using 2 input velocity conditions (10 mm/s and 2500 mm/s), resultant pressures were measured and hydraulic resistance calculated. Trabecular architecture was determined using micro-computerized tomography after testing.

RESULTS

Measured pressure increased with increasing input flow rates. However, average hydraulic resistance decreased significantly when comparing low-speed (3.40 +/- 1.58kPa*s/mL) and high-speed (0.16 +/- 0.08kPa*s/mL) groups.

CONCLUSIONS

Current hydraulic resistance results contradict previous findings. The observed decrease in hydraulic resistance suggests that, during high-speed injury events, marrow flow may damage the trabeculae and thereby weaken the vertebra.

Estimation of bone permeability using accurate microstructural measurements

While interstitial fluid flow is necessary for the viability of osteocytes, it is also believed to play a role in bone's mechanosensory system by shearing bone cell membranes or causing cytoskeleton deformation and thus activating biochemical responses that lead to the process of bone adaptation. However, the fluid flow properties that regulate bone's adaptive response are poorly understood. In this paper, we present an analytical approach to determine the degree of anisotropy of the permeability of the lacunar-canalicular porosity in bone. First, we estimate the total number of canaliculi emanating from each osteocyte lacuna based on published measurements from parallel-fibered shaft bones of several species (chick, rabbit, bovine, horse, dog, and human). Next, we determine the local three-dimensional permeability of the lacunar-canalicular porosity for these species using recent microstructural measurements and adapting a previously developed model. Results demonstrated that the number of canaliculi per osteocyte lacuna ranged from 41 for human to 115 for horse. Permeability coefficients were found to be different in three local principal directions, indicating local orthotropic symmetry of bone permeability in parallel-fibered cortical bone for all species examined. For the range of parameters investigated, the local lacunar-canalicular permeability varied more than three orders of magnitude, with the osteocyte lacunar shape and size along with the 3-D canalicular distribution determining the degree of anisotropy of the local permeability. This two-step theoretical approach to determine the degree of anisotropy of the permeability of the lacunar-canalicular porosity will be useful for accurate quantification of interstitial fluid movement in bone.

A comparison of structural and mechanical properties in cancellous bone from the femoral head and acetabulum

Mechanical interlock obtained by penetration of bone cement into cancellous bone is critical to the success of cemented total hip replacement (THR). Although acetabular component loosening is an important mode of THR failure, the properties of acetabular cancellous bone relevant to cement penetration are not well characterized. Bone biopsies (9mm diameter, 10mm long) were taken from the articular surfaces of the acetabulum and femoral head during total hip replacement. After mechanical and chemical defatting the two groups of bone specimens were characterized using flow measurement, mechanical testing and finally serial sectioning and three-dimensional computer reconstruction. The mean permeabilities of the acetabular group (1.064 × 10−10 m2) and femoral group (1.155x 10−10m2) were calculated from the flow measurements, which used saline solution and a static pressure of 9.8 kPa. The mean Young's modulus, measured non-destructively, was 47.4 MPa for the femoral group and 116.4MPa for the acetabular group. Three-dimensional computer reconstruction of the specimens showed no significant differences in connectivity and porosity between the groups. Results obtained using femoral head cancellous bone to investigate bone cement penetration and fixation are directly relevant to fixation in the acetabulum.

Hydraulic resistance and permeability in human lumbar vertebral bodies

Hydraulic resistance (HR) was measured for ten intact human lumbar vertebrae to further understand the mechanisms of fluid flow through porous bone. Oil was forced through the vertebral bodies under various volumetric flow rates and the resultant pressure was measured The pressure-flow relationship for each specimen was linear. Therefore, HR was constant with a mean of 2.22 +/- 1.45 kPa*sec/ml. The mean permeability of the intact vertebral bodies was 4.90x10(-10) +/- 4.45x10(-10) m2. These results indicate that this methodology is valid for whole bone samples and enables the exploration of the effects of HR on the creation of high-speed fractures.

Linear poroelastic cancellous bone anisotropy: trabecular solid elastic and fluid transport properties

The mechanical performance of cancellous bone is characterized using experiments which apply linear poroelasticity theory. It is hypothesized that the anisotropic organization of the solid and pore volumes of cancellous bone can be physically characterized separately (no deformable boundary interactive effects) within the same bone sample. Due to its spongy construction, the in vivo mechanical function of cancellous or trabecular bone is dependent upon fluid and solid materials which may interact in a hydraulic, convective fashion during functional loading. This project provides insight into the organization of the tissue, ie., the trabecular connectivity, by defining the separate nature of this biphasic performance. Previous fluid flow experiments [Kohles et al., 2001, Journal of Biomechanics, 34(11), pp. 1197-1202] describe the pore space via orthotropic permeability. Ultrasonic wave propagation through the trabecular network is used to describe the solid component via orthotropic elastic moduli and material stiffness coefficients. The linear poroelastic nature of the tissue is further described by relating transport (fluid flow) and elasticity (trabecular load transmission) during regression analysis. In addition, an empirical relationship between permeability and porosity is applied to the collected data. Mean parameters in the superior-inferior (SI) orientation of cubic samples (n=20) harvested from a single bovine distal femur were the largest (p<0.05) in comparison to medial-lateral (ML) and anterior-posterior (AP) orientations: Apparent elastic modulus (2,139 MPa), permeability (4.65x10(-10) m2), and material stiffness coefficient (13.6 GPa). A negative correlation between permeability as a predictor of structural elastic modulus supported a parametric relationship in the ML (R2=0.4793), AP (R2=0.3018), and SI (R2=0.6445) directions (p<0.05).

Direct perfusion measurements of cancellous bone anisotropic permeability

More extensive characterization of trabecular connectivity and intertrabecular space will be instrumental in understanding disease states and designing engineered bone. This project presents an experimental protocol to define the directional dependence of transport properties as measured from healthy cancellous bone when considered as a biologic, porous medium. In the initial design phases, mature bovine bone was harvested from the femoral neck (n=6 cylinders) and distal condyle (n=4 cubes) regions and used for "proof of concept" experimentation. A power study on those results led to the presented work on 20 cubic samples (mean volume=4.09cm(3)) harvested from a single bovine distal femur. Anisotropic intrinsic permeabilities (k(i)) were quantified along the orthogonal anatomic axes (i=medial-lateral, anterior-posterior, and superior-inferior) from each individual cubic bone sample. Using direct perfusion measurements, permeability was calculated based upon Darcy's Law describing flow through porous media. The maximum mean value was associated with the superior-inferior orientation (4.65x10(-10)m(2)) in comparison with the mean anterior-posterior (4.52x10(-10)m(2)) and medial-lateral (2.33x10(-10)m(2)) direction values. The results demonstrate the anisotropic (p=0.0143) and heterogeneous (p=0.0002) nature of the tissue and encourage the ongoing quantification of parameters within the established poroelastic models.