Numerical Modeling of Long Bone Adaptation due to Mechanical Loading: Correlation with Experiments

The process of external bone adaptation in cortical bone is modeled mathematically using finite element (FE) stress analysis coupled with an evolution model, in which adaptation response is triggered by mechanical stimulus represented by strain energy density. The model is applied to experiments in which a rat ulna is subjected to cyclic loading, and the results demonstrate the ability of the model to predict the bone adaptation response. The FE mesh is generated from micro-computed tomography (μCT) images of the rat ulna, and the stress analysis is carried out using boundary and loading conditions on the rat ulna obtained from the experiments [Robling, A. G., F. M. Hinant, D. B. Burr, and C. H. Turner. J. Bone Miner. Res. 17:1545–1554, 2002]. The external adaptation process is implemented in the model by moving the surface nodes of the FE mesh based on an evolution law characterized by two parameters: one that captures the rate of the adaptation process (referred to as gain); and the other characterizing the threshold value of the mechanical stimulus required for adaptation (referred to as threshold-sensitivity). A parametric study is carried out to evaluate the effect of these two parameters on the adaptation response. We show, following comparison of results from the simulations to the experimental observations of Robling et al. (J. Bone Miner. Res. 17:1545–1554, 2002), that splitting the loading cycles into different number of bouts affects the threshold-sensitivity but not the rate of adaptation. We also show that the threshold-sensitivity parameter can quantify the mechanosensitivity of the osteocytes.     

A fiber matrix model for fluid flow and streaming potentials in the canaliculi of an osteon

A theoretical model is developed to predict the fluid shear stress and streaming potential at the surface of osteocytic processes in the lacunar-canalicular porosity of an osteon when the osteon is subject to mechanical loads that are parallel or perpendicular to its axis. The theory developed in Weinbaumet al. (31) for the flow through a proteoglycan matrix in a canaliculus is employed in a poroelastic model for the osteon. Our formulation is a generalization of that of Petrovet al. (17). Our model predicts that, in order to satisfy the measured frequency dependence of the phase and magnitude of the SGP in macroscopic bone samples, the fiber spacing in the fluid annulus must lie in the narrow range 6–7 nm typical of the spacing of GAG sidechains along a protein monomer. The model predictions for the local SGP profiles in the osteon agree with the experimental observations of Starkebaumet al. (24). The theory predicts that the pore pressure relaxation time, τ_d, for a 150–300 μm diameter osteon with the foregoing matrix structure is approximately 0.03–0.13 sec, and that the amplitude of the mean fluid shear stress on the membrane of the osteocytic process at the mean areal radius of the osteon has a maximum at 28 Hz if τ_d = 0.06 sec. This maximum, which is independent of the magnitude of the loading, could be importantin vivo since the recent experiments of Turneret al. (28) and McLeodet al. (15) have a peak in the strain frequency spectrum between 20 and 30 Hz that also appears to be independent of the type (magnitude) of loading. Numerical predictions for the amplitude of the average fluid shear stress on the osteocytic membrane at the mean areal radius of the osteon show that the fluid shear stress associated with the low amplitude 20–30 Hz spectral strain component is at least as large as the average fluid shear stress associated with the high amplitude 1 Hz stride component, although the latter loading is an order of magnitude larger, and has a magnitude that lies within the middle of the range, 6–30 dynes/cm², where fluid shear stresses in tissue culture studies with osteoblast monolayers have elicited an intracellular Ca⁺⁺ response (31). The implications of these results for intracellular electrical communication are discussed.     

The role of osteogenic index, octahedral shear stress and dilatational stress in the ossification of a fracture callus

The exact mechanism by which mechanical stimulus regulates the healing process of a bone fracture is not understood. This has led to the development of several hypotheses that predict the pattern of differentiation of tissue during healing that may arise from characteristic fields of stress or strain at the fracture. These have so far remained unproved because data on stress fields in actual fracture tissue have been unavailable until recently. Thus the present study examines the predictive performance of the hypothesis proposed in J Orthop Res 6 (1988) 736, against measured and calculated data reported in J Biomech 33 (2000) 415, using a 2D FEM of a clinical fracture. The hypothesis was used to predict the influence of stress fields present in the Gardner et al. tissues at four temporal stages during healing. These predictions were then correlated with callus-size, rate of endochondral ossification and ossification pattern subsequently observed by Gardner et al. in the clinical fracture. Results corroborate the hypothesis that high octahedral shear stresses may increase the size of the callus during the initial phase of healing, and they also suggest that this may be true during the later stages of the fracture fixation period. However, compressive dilatational stresses were not found to inhibit endochondral ossification, as suggested by the hypothesis. Although high shear stresses were found in regions indicative of fibrous tissue as postulated by the hypothesis, this was not found to be the case for high tensile dilatational stresses. Also, contour diagrams of Osteogenic index (I) indicated only limited correlation with callus maturation and the pattern of healing. Therefore, the hypothesis was not wholly successful in predicting healing pattern.     

Finite element modeling of the growth plate in a detailed spine model

Very few computer models of the spine integrate vertebral growth plates to investigate their mechanical behavior and potential impacts on bone growth. An approach was developed to generate a finite element (FE) model of the lumbar spine and their connective tissues including the growth plate, which allowed a personalization of the geometry based on patients’ bi-planar radiographs. The geometrical validation was performed by deforming meshed vertebrae to reference vertebral specimens and comparing geometrical indices. No significant difference was found between the measured parameters, with errors under 1% in 83% of the geometrical parameters. Mechanical validation was done by simulating loading cases on a functional unit representing experimental testing on cadaveric spines. The flexibility of the functional unit remained between expected ranges of motion, but was more linear than experimental data. The mechanical behavior of the growth plate was evaluated under various loading cases: greater stresses were located in the proliferative zone for the different spinal loading cases tested. This modeling approach is a useful tool to study the effect of mechanical stresses on bone growth.     

Numerical investigation of the effects of channel geometry on platelet activation and blood damage

Thromboembolic complications in Bileaflet mechanical heart valves (BMHVs) are believed to be due to the combination of high shear stresses and large recirculation regions. Relating blood damage to design geometry is therefore essential to ultimately optimize the design of BMHVs. The aim of this research is to quantitatively study the effect of 3D channel geometry on shear-induced platelet activation and aggregation, and to choose an appropriate blood damage index (BDI) model for future numerical simulations. The simulations in this study use a recently developed lattice-Boltzmann with external boundary force (LBM-EBF) method [Wu, J., and C. K. Aidun. Int. J. Numer. Method Fluids 62(7):765–783, 2010; Wu, J., and C. K. Aidun. Int. J. Multiphase flow 36:202–209, 2010]. The channel geometries and flow conditions are re-constructed from recent experiments by Fallon [The Development of a Novel in vitro Flow System to Evaluate Platelet Activation and Procoagulant Potential Induced by Bileaflet Mechanical Heart Valve Leakage Jets in School of Chemical and Biomolecular Engineering. Atlanta: Georgia Institute of Technology] and Fallon et al. [Ann. Biomed. Eng. 36(1):1]. The fluid flow is computed on a fixed regular ‘lattice’ using the LBM, and each platelet is mapped onto a Lagrangian frame moving continuously throughout the fluid domain. The two-way fluid–solid interactions are determined by the EBF method by enforcing a no-slip condition on the platelet surface. The motion and orientation of the platelet are obtained from Newtonian dynamics equations. The numerical results show that sharp corners or sudden shape transitions will increase blood damage. Fallon’s experimental results were used as a basis for choosing the appropriate BDI model for use in future computational simulations of flow through BMHVs.     

An anti-Hick’s effect for exogenous, but not endogenous, saccadic eye movements

Previously, we have shown that the reaction times (RTs) of exogenously generated saccadic eye movements decrease with an increase in the number of response alternatives (Lawrence et al. in J Vis 8(26):1–7, 2008; Lawrence and Gardella in Exp Brain Res 195(3):413–418, 2009). Because this pattern of RTs is in the direction opposite that predicted by Hick (Q J Exp Psychol 4:11–26, 1952), we termed the effect an “anti-Hick’s” effect. In the present study, we examined whether this effect characterizes saccades in general, or only those saccades that are exogenously generated. An anti-Hick’s effect was found for exogenous, but not for endogenous, saccades. These results demonstrate a clear dissociation between exogenously and endogenously generated saccades and place an important constraint on the anti-Hick’s effect.     

CNTO 95, a fully human anti αv integrin antibody, inhibits cell signaling, migration, invasion, and spontaneous metastasis of human breast cancer cells

CNTO 95 is a fully human monoclonal antibody that recognizes αv integrins. Previous studies have shown that CNTO 95 exhibits both anti-tumor and anti-angiogenic activities (Trikha M et al., Int J Cancer 110:326–335, 2004). In this study we investigated the biological activities of CNTO 95 on breast tumor cells both in vitro and in vivo. In vitro treatment with CNTO 95 decreased the viability of breast tumor cells adhering to vitronectin. CNTO 95 inhibited tumor cell adhesion, migration, and invasion in vitro. CNTO 95 treatment also induced tyrosine dephosphorylation of focal adhesion kinase (FAK), and the docking protein paxillin that recruits both structural and signaling molecules to focal adhesions (Turner CE, Int J Biochem Cell Biol 30:955–959, 1998; O’Neil GM et al., Trends Cell Biol 10:111–119, 2000). These results suggest that CNTO 95 inhibits breast tumor cell growth, migration and invasion by interruption of αv integrin mediated focal adhesions and cell motility signals. In vivo studies of CNTO 95 were conducted in an orthotopic breast tumor xenograft model. Treatment with CNTO 95 resulted in significant inhibition of both tumor growth and spontaneous metastasis of MDA-MB-231 cells to the lungs. CNTO 95 also inhibited lung metastasis in a separate experimental (tail vein injection) model of metastasis. The results presented here demonstrate the anti-tumor and anti-metastatic activities of CNTO 95 in breast cancer models and provide insight into the cellular and molecular mechanisms mediating its inhibitory effects on metastasis.     

Fluid mechanics of arterial stenosis: Relationship to the development of mural thrombus

In this study, we analyzed blood flow through a model stenosis with Reynolds numbers ranging from 300 to 3,600 using both experimental and numerical methods. The jet produced at the throat was turbulent, leading to an axisymmetric region of slowly recirculating flow. For higher Reynolds numbers, this region became more disturbed and its length was reduced. The numerical predictions were confirmed by digital particle image velocimetry and used to describe the fluid dynamics mechanisms relevant to prior measurements of platelet deposition in canine blood flow (R.T. Schoephoersteret al., Atherosclerosis and Thrombosis 12:1806–1813, 1993). Actual deposition onto the wall was dependent on the wall shear stress distribution along the stenosis, increasing in areas of flow recirculation and reattachment. Platelet activation potential was analyzed under laminar and turbulent flow conditions in terms of the cumulative effect of the varying shear and elongational stresses, and the duration platelets are exposed to them along individual platelet paths. The cumulative product of shear rate and exposure time along a platelet path reached a value of 500, half the value needed for platelet activation under constant shear (J. M. Ramstacket al., Journal of Biomechanics 12: 113–125, 1979).     

Temporal uncertainty does not affect response latencies of movements produced during startle reactions

Previous research has shown that a startle ‘go’ stimulus, presented at a constant latency with respect to a warning stimulus, is capable of eliciting an intended voluntary movement in a simple reaction time (RT) task at very short latencies without involvement of the cerebral cortex (Carlsen et al. in Exp Brain Res 152:510–518, 2003; J Motor Behav 36:253–264, 2004a; Exp Brain Res 159:301–309 2004b; Valls-Solé et al. in J Physiol 516:931–938, 1999). The purpose of the present experiment was to determine the effect of temporal uncertainty on response latency during an RT task that comprised a startle stimulus. Participants were required to perform an active 20° wrist extension movement in response to an auditory tone that was presented 2,500 to 5,500 ms after a warning stimulus, in 1,000 ms increments. On certain trials the control auditory stimulus (80 dB) was unexpectedly replaced by the startle stimulus (124 dB). When participants were startled the intended voluntary movement was initiated at approximately 70 ms, regardless of foreperiod duration. The magnitude and invariance of response latencies to the startle stimulus suggest that the intended movement had indeed been prepared prior to the arrival of the imperative go stimulus, within 2.5 s of the warning stimulus. Furthermore, there was no evidence that the prepared movement decayed over a period of at least 3 s.     

Connecting filament mechanics in the relaxed sarcomere

By examining the mechanical properties of single unactivated myofibrils it has been shown that shortening and stretching of sarcomeres occurs in stepwise fashion, and that steps are seen also in the relaxed state (Yang et al. (1998) Biophys J 74: 1473–1483; Blyakhman et al. (2001) Biophys J 81: 1093–1100; Nagornyak et al. (2004) J. Muscle. Res. Cell Motil. 25: 37–43). The latter are inevitably associated with connecting filaments. Here, we carried out measurements on single myofibrils from rabbit psoas muscle to investigate steps in unactivated specimens in more detail. Myofibrils were stretched and released in ramp-like fashion. For the single sarcomere the time course of length change was consistently stepwise. We found that in the unactivated myofibrils, step size depended on initial sarcomere length, diminishing progressively with increase of initial sarcomere length, whereas in the case of activated sarcomeres, step size was consistently 2.7 nm.     

Sensitivity of patient-specific vertebral finite element model from low dose imaging to material properties and loading conditions

Patient-specific modeling could help in predicting vertebral osteoporotic fracture. The accuracy requirement for input data available in clinical routine is related to the model sensitivity. The objective of this study is to assess the relative impact of material properties and of loading conditions on vertebral strength using a finite element model. Fourteen subject-specific vertebral finite element models were used to investigate the effect of material properties and loading conditions. A design of experiment was set to study three parameters: Young’s moduli of trabecular bone and cortico-trabecular bone (outer 3 mm of the vertebra), and load location. Cortico-trabecular bone modulus variation from 270 to 478 MPa made fracture load vary from 22 to 51%, depending on other parameters. Trabecular bone modulus variation from 115 to 258 MPa made fracture load vary from 11 to 43%. Displacing load location by 1 cm resulted in a mean decrease of 48–60% of the fracture load. Anterior bending induced strain concentration in vertebral anterior wall. Material properties of both type of bone have about the same effect. Load location is the most sensitive. Effort should be made to take into account patients’ specific load distribution regarding its sagittal balance, in addition to bone properties.     

Mesh Morphing and Response Surface Analysis: Quantifying Sensitivity of Vertebral Mechanical Behavior

Vertebrae provide essential biomechanical stability to the skeleton. In this work novel morphing techniques were used to parameterize three aspects of the geometry of a specimen-specific finite element (FE) model of a rat caudal vertebra (process size, neck size, and end-plate offset). Material properties and loading were also parameterized using standard techniques. These parameterizations were then integrated within an RSM framework and used to produce a family of FE models. The mechanical behavior of each model was characterized by predictions of stress and strain. A metamodel was fit to each of the responses to yield the relative influences of the factors and their interactions. The direction of loading, offset, and neck size had the largest influences on the levels of vertebral stress and strain. Material type was influential on the strains, but not the stress. Process size was substantially less influential. A strong interaction was identified between dorsal–ventral offset and dorsal–ventral off-axis loading. The demonstrated approach has several advantages for spinal biomechanical analysis by enabling the examination of the sensitivity of a specimen to multiple variations in shape, and of the interactions between shape, material properties, and loading.     

A parametric analysis of fixation post shape in tibial knee prostheses

A primary concern of total knee replacement (TKR) is aseptic loosening of the tibial component, which may be caused by shielding of mechanical stresses in the bone and may require subsequent revision surgery. A three-dimensional (3D) finite element (FE) model has been developed to study bone and interface stresses for four different tibial prosthesis designs. The model described here incorporates orthotropic and heterogeneous bone properties with physiologically representative loading conditions. Results from this model indicate that stress distribution is affected by the incorporation of anisotropy and spatial variation of bone properties. All bone properties were mapped from published data to characterize their anisotropy and heterogeneity. Physiological loading was incorporated by mapping experimentally determined contact patterns. Convergence testing was performed to ensure model accuracy. In terms of interface forces, a tapered post decreased post shear while slightly increasing post compression compared to a cylindrical post; a post of elliptical cross-section increased post shear and decreased post compression. In terms of cancellous bone stress, tapered and elliptical posts both relieved compression compared to a cylindrical post, while a tapered post also produced increased peripheral stress. The inclusion of medial and lateral pegs in addition to a central fixation post caused localized stress shielding in the periphery of the pegs. In general, all implant models caused a reduction of cancellous bone stress plus high compression beneath the central fixation posts.     

Prediction of multiaxial mechanical behavior for conventional and highly crosslinked UHMWPE using a hybrid constitutive model

The development of theoretical failure, fatigue, and wear models for ultra-high molecular weight polyethylene (UHMWPE) used in joint replacements has been hindered by the lack of a validated constitutive model that can accurately predict large deformation mechanical behavior under clinically relevant, multiaxial loading conditions. Recently, a new Hybrid constitutive model for unirradiated UHMWPE was developed Bergstr?m et al., (Biomaterials 23 (2002) 2329) based on a physics-motivated framework which incorporates the governing micro-mechanisms of polymers into an effective and accurate continuum representation. The goal of the present study was to compare the predictive capability of the new Hybrid model with the J(2)-plasticity model for four conventional and highly crosslinked UHMWPE materials during multiaxial loading. After calibration under uniaxial loading, the predictive capabilities of the J(2)-plasticity and Hybrid model were tested by comparing the load-displacement curves from experimental multiaxial (small punch) tests with simulated load-displacement curves calculated using a finite element model of the experimental apparatus. The quality of the model predictions was quantified using the coefficient of determination (r(2)). The results of the study demonstrate that the Hybrid model outperforms the J(2)-plasticity model both for combined uniaxial tension and compression predictions and for simulating multiaxial large deformation mechanical behavior produced by the small punch test. The results further suggest that the parameters of the HM may be generalizable for a wide range of conventional, highly crosslinked, and thermally treated UHMWPE materials, based on the characterization of four material properties related to the elastic modulus, yield stress, rate of strain hardening, and locking stretch of the polymer chains. Most importantly, from a practical perspective, these four key material properties for the Hybrid constitutive model can be measured by relatively simple uniaxial tension or compression tests.     

Mathematical modeling of fracture healing in mice: comparison between experimental data and numerical simulation results

The combined use of experimental and mathematical models can lead to a better understanding of fracture healing. In this study, a mathematical model, which was originally established by Bailón-Plaza and van der Meulen (J Theor Biol 212:191–209, 2001), was applied to an experimental model of a semi-stabilized murine tibial fracture. The mathematical model was implemented in a custom finite volumes code, specialized in dealing with the model’s requirements of mass conservation and non-negativity of the variables. A qualitative agreement between the experimentally measured and numerically simulated evolution in the cartilage and bone content was observed. Additionally, an extensive parametric study was conducted to assess the influence of the model parameters on the simulation outcome. Finally, a case of pathological fracture healing and its treatment by administration of growth factors was modeled to demonstrate the potential therapeutic value of this mathematical model.     

Real-Time Finite Element Monitoring of Sub-Dermal Tissue Stresses in Individuals with Spinal Cord Injury: Toward Prevention of Pressure Ulcers

Patients with a spinal cord injury (SCI) are susceptible to deep tissue injury (DTI), a necrosis in excessively deformed muscle tissue overlying bony prominences, which, in wheelchair users, typically occurs in the gluteus muscles under the ischial tuberosities. Recently, we developed a generic real-time, subject-specific finite element (FE) modeling method to provide monitoring of mechanical conditions in deep tissues deformed between bony prominences and external surfaces. We previously employed this method to study internal tissue loads in plantar tissues of the foot [Yarnitzky, G., Z. Yizhar, and A. Gefen. J. Biomech. 39:2673–2689, 2006] and in muscle flaps of residual limbs in patients who underwent transtibial amputation (Portnoy, S., G. Yarnitzky, Z. Yizhar, A. Kristal, U. Oppenheim, I. Siev-Ner, and A. Gefen. Ann. Biomed. Eng. 35:120–135, 2007). The goal of the present study was to adapt the method to study the time-dependent mechanical stresses in glutei of patients with SCI during wheelchair sitting, continuously in real-time, and to compare the trends of internal tissue load data with those of controls. Prior to human studies, the real-time FE model—adapted to study the buttocks during sitting—was validated by comparing its predictions to data from a physical phantom of a buttocks and to non-real-time, commercial FE software. Next, real-time, subject-specific, FE models were built for six participating subjects (3 patients with SCI, 3 controls) based on their individual anatomies from MRI scans. Subjects were asked to sit normally in a wheelchair, on a ROHO cushion, and to watch a 90 min movie. Continuous interface pressure measurements from a pressure mat were used as subject-specific boundary conditions for real-time FE analyses of deep muscle stresses. Highest peaks of compression, shear and von Mises stresses throughout the trial period, and averages of peaks of these stresses were recorded over the trial for each individual. These parameters generally had 3-times to 5-times greater values in patients with SCI compared with controls. Likewise, stress doses, defined as the integration of peak compression stress over time, were ∼35-times and ∼50-times greater in the subjects with SCI, the values referring to the highest of all peaks recorded throughout the trial, and to average of peaks over the trial, respectively. We believe that by allowing—for the first time—practical and continuous monitoring of internal tissue loads in patients with motosensory deficits, without any risk or interruption to their lifestyle, and either at the clinical setting or at home, the present method can make a substantial contribution to the prevention of severe pressure ulcers and DTI.     

Influence of Spreading and Contractility on Cell Detachment

Cell adhesion is a key phenomenon that affects fundamental cellular processes such as morphology, migration, and differentiation. In the current study, an active modelling framework incorporating actin cytoskeleton remodelling and contractility, combined with a cohesive zone model to simulate debonding at the cell–substrate interface, is implemented to investigate the increased resistance to detachment of highly spread chondrocytes from a substrate, as observed experimentally by Huang et al. (J. Orthop. Res. 21: 88–95, 2003). 3D finite element meshes of the round and spread cell geometries with the same material properties are created. It is demonstrated that spread cells with a flattened morphology and a larger adhesion area have a more highly developed actin cytoskeleton than rounded cells. Rounded cells provide less support for tension generated by the actin cytoskeleton; hence, a high level of dissociation is predicted. It is revealed that the more highly developed active contractile actin cytoskeleton of the spread cell increases the resistance to shear deformation, and subsequently increases the shear detachment force. These findings provide new insight into the link between cell geometry, cell contractility, and cell–substrate detachment.     

Persistent tubular conduction in vacuolated amphibian skeletal muscle following osmotic shock

The transverse (T-)tubules primarily function in conducting the action potentials that initiate excitation– contraction coupling in skeletal muscle but may additionally subserve longer-term roles in volume regulation, membrane fusion and other trafficking processes. Osmotic shock thus both electrically detaches the T-tubules from surface membrane (‘detubulation’) and produces tubular vacuolation. The present experiments separated these effects. An established, reference osmotic shock protocol that exposed muscles to Ca²⁺/Mg²⁺-Ringer and gradual cooling to 10°C after 18 min in glycerol–Ringer accomplished significant detubulation (77.5 ± 13.15%, mean ± SEM; n = 4). In contrast, a test protocol conducted entirely at room temperature using Mg²⁺-rather than Ca²⁺/Mg²⁺-Ringer yielded reduced (P < 0.05, post hoc Duncan's multiple range test) detubulation indices (1.67 ± 1.67%, n = 6) statistically indistinguishable from findings in fibres spared osmotic shock. Yet both osmotic shocks caused a formation of closed vacuoles, demonstrated by Sulphorhodamine B trapping, that occupied statistically similar fractions of total fibre volume (reference procedure: 14.38 ± 2.7%, n = 6; test procedure: 13.36 ± 2.00%, n = 22) in turn higher than determinations in control fibres (P < 0.05). The findings reconcile reports associating detubulation with vacuolation in osmotically shocked muscle [S. Nik-Zainal et al. (1999) J Muscle Res Cell Motil 20: 45–53; K.N. Khan et al. (2000) J Muscle Res Cell Motil 21: 79–90] with the persistence of tubular electrical activity in extensively vacuolated amphibian fibres following fatigue [J. Lannergren and H. Westerblad (1987) Acta Physiol Scand 129: 311–318; J. Lannergren et al. (1999) J Muscle Res Cell Motil 20: 19–32]. Furthermore test protocols produced higher densities of open vacuoles (13.38 ± 2.33%, n = 9) than did reference protocols (6.66 ± 1.63%, n = 20) contrary to their possible involvement in the electrophysiological changes. Abolition of tubular electrophysiological activity thus either follows or is independent of tubular vacuolation whilst sharing some of its underlying osmotic mechanisms. This revised version was published online in July 2006 with corrections to the Cover Date.     

Computational modelling of the mechanical environment of osteogenesis within a polylactic acid–calcium phosphate glass scaffold

A computational model based on finite element method (FEM) and computational fluid dynamics (CFD) is developed to analyse the mechanical stimuli in a composite scaffold made of polylactic acid (PLA) matrix with calcium phosphate glass (Glass) particles. Different bioreactor loading conditions were simulated within the scaffold. In vitro perfusion conditions were reproduced in the model. Dynamic compression was also reproduced in an uncoupled fluid-structure scheme: deformation level was studied analyzing the mechanical response of scaffold alone under static compression while strain rate was studied considering the fluid flow induced by compression through fixed scaffold. Results of the model show that during perfusion test an inlet velocity of 25 μm/s generates on scaffold surface a fluid flow shear stress which may stimulate osteogenesis. Dynamic compression of 5% applied on the PLA–Glass scaffold with a strain rate of 0.005 s^?1 has the benefit to generate mechanical stimuli based on both solid shear strain and fluid flow shear stress on large scaffold surface area. Values of perfusion inlet velocity or compression strain rate one order of magnitude lower may promote cell proliferation while values one order of magnitude higher may be detrimental for cells. FEM–CFD scaffold models may help to determine loading conditions promoting bone formation and to interpret experimental results from a mechanical point of view.     

Mechanobiological Predictions of Femoral Anteversion in Cerebral Palsy

Many morphological changes occur during development of the proximal femur. The anteversion angle is a measure of the rotation of the neck of the femur around the diaphysis. In normal development anteversion is 30 degrees at birth and decreases to 15 degrees by skeletal maturity. In children with cerebral palsy (CP) anteversion often increases slightly and remains high throughout development. Previous models have proposed that cyclic hydrostatic stress decreases the growth rate while cyclic octahedral shear stress increases the growth rate. In this study we also examine changes in the growth direction caused by deformation of the developing cartilage. Using these mechanobiological principles we considered the influence of mechanical loads on the formation of the anteversion angle in normal and CP development. Loads were applied to a three-dimensional finite element model of the proximal femur. From the resulting stresses and deformations at the growth front we calculated the growth rate and growth direction and simulated the progression of the growth front over 6 months. The model predicted a decrease in anteversion angle (-2 degrees over 6 months) under normal-loading conditions, and an increase in anteversion (+ 1 degrees over 6 months) under CP-loading conditions. These results compare well with observations during skeletalgenesis, in which the anteversion angle decreases rapidly in the first few years of normal growth and may increase in children with CP.