Mathematical modelling of bone adaptation of the metacarpal subchondral bone in racehorses

In Thoroughbred racehorses, fractures of the distal limb are commonly catastrophic. Most of these fractures occur due to the accumulation of fatigue damage from repetitive loading, as evidenced by microdamage at the predilection sites for fracture. Adaptation of the bone in response to training loads is important for fatigue resistance. In order to better understand the mechanism of subchondral bone adaptation to its loading environment, we utilised a square root function defining the relationship between bone volume fraction \((f_{BM} )\) and specific surface \((S_v )\) of the subchondral bone of the lateral condyles of the third metacarpal bone (MCIII) of the racehorse, and using this equation, developed a mathematical model of subchondral bone that adapts to loading conditions observed in vivo. The model is expressed as an ordinary differential equation incorporating a formation rate that is dependent on strain energy density. The loading conditions applied to a selected subchondral region, i.e. volume of interest, were estimated based on joint contact forces sustained by racehorses in training. For each of the initial conditions of \(f_{BM} \) we found no difference between subsequent homoeostatic \(f_{BM} \) at any given loading condition, but the time to reach equilibrium differed by initial \(f_{BM} \) and loading condition. We found that the observed values for \(f_{BM} \) from the mathematical model output were a good approximation to the existing data for racehorses in training or at rest. This model provides the basis for understanding the effect of changes to training strategies that may reduce the risk of racehorse injury.     

Concept and development of an orthotropic FE model of the proximal femur

PURPOSE: In contrast to many isotropic finite-element (FE) models of the femur in literature, it was the object of our study to develop an orthotropic FE "model femur" to realistically simulate three-dimensional bone remodelling. METHODS: The three-dimensional geometry of the proximal femur was reconstructed by CT scans of a pair of cadaveric femurs at equal distances of 2mm. These three-dimensional CT models were implemented into an FE simulation tool. Well-known "density-determined" bony material properties (Young's modulus; Poisson's ratio; ultimate strength in pressure, tension and torsion; shear modulus) were assigned to each FE of the same "CT-density-characterized" volumetric group.In order to fix the principal directions of stiffness in FE areas with the same "density characterization", the cadaveric femurs were cut in 2mm slices in frontal (left femur) and sagittal plane (right femur). Each femoral slice was scanned into a computer-based image processing system. On these images, the principal directions of stiffness of cancellous and cortical bone were determined manually using the orientation of the trabecular structures and the Haversian system. Finally, these geometric data were matched with the "CT-density characterized" three-dimensional femur model. In addition, the time and density-dependent adaptive behaviour of bone remodelling was taken into account by implementation of Carter's criterion. RESULTS: In the constructed "model femur", each FE is characterized by the principal directions of the stiffness and the "CT-density-determined" material properties of cortical and cancellous bone. Thus, on the basis of anatomic data a three-dimensional FE simulation reference model of the proximal femur was realized considering orthotropic conditions of bone behaviour. CONCLUSIONS: With the orthotropic "model femur", the fundamental basis has been formed to realize realistic simulations of the dynamical processes of bone remodelling under different loading conditions or operative procedures (osteotomies, total hip replacements, etc).     

Influence of the change in stem length on the load transfer and bone remodelling for a cemented resurfaced femur

The effect of a short-stem femoral resurfacing component on load transfer and potential failure mechanisms has rarely been studied. The stem length has been reduced by approximately 50% as compared to the current long-stem design. Using 3-D FE models of natural and resurfaced femurs, the study is aimed at investigating the influence of a short-stem resurfacing component on load transfer and bone remodelling. Applied loading conditions include normal walking and stair climbing. The mechanical role of the stem along with implant–cement and stem–bone contact conditions was observed to be crucial. Shortening the stem length to half of the current length (long-stem) led to several favourable effects, even though the stress distributions in the implant and the cement were similar in both the cases. The short-stem implant led not only to a more physiological stress distribution but also to bone apposition (increase of 20–70% bone density) in the superior resurfaced head, when the stem–bone contact prevailed. This also led to a reduction in strain concentration in the cancellous bone around the femoral neck–component junction. The normalised peak strain in this region was lower for the short-stem design as compared to that of the long-stem one, thereby reducing the initial risk of neck fracture. The effect of strain shielding (50–75% reduction) was restricted to a small bone volume underlying the cement, which was approximately half of that of the long-stem design. Consequently, bone resorption was considerably less for the short-stem design. The short-stem design offers better prospects than the long-stem resurfacing component.     

Trabecular bone ontogeny in the human proximal femur

Ontogenetic changes in the human femur associated with the acquisition of bipedal locomotion, especially the development of the bicondylar angle, have been well documented. The purpose of this study is to quantify changes in the three-dimensional structure of trabecular bone in the human proximal femur in relation to changing functional and external loading patterns with age. High-resolution X-ray computed tomography scan data were collected for 15 juvenile femoral specimens ranging in age from prenatal to approximately nine years of age. Serial slices were collected for the entire proximal femur of each individual with voxel resolutions ranging from 0.017 to 0.046 mm depending on the size of the specimen. Spherical volumes of interest were defined within the proximal femur, and the bone volume fraction, trabecular thickness, trabecular number, and fabric anisotropy were calculated in three dimensions. Bone volume fraction, trabecular number, and degree of anisotropy decrease between the age of 6 months and 12 months, with the lowest values for these parameters occurring in individuals near 12 months of age. By age 2-3 years, the bone volume, thickness, and degree of anisotropy increase slightly, and regions in the femoral neck become more anisotropic corresponding to the thickening of the inferior cortical bone of the neck. These results suggest that trabecular structure in the proximal femur reflects the shift in external loading patterns associated with the initiation of unassisted walking in infants.     

Targeted regeneration of bone in the osteoporotic human femur

We have recently developed image processing techniques for measuring the cortical thicknesses of skeletal structures in vivo, with resolution surpassing that of the underlying computed tomography system. The resulting thickness maps can be analysed across cohorts by statistical parametric mapping. Applying these methods to the proximal femurs of osteoporotic women, we discover targeted and apparently synergistic effects of pharmaceutical osteoporosis therapy and habitual mechanical load in enhancing bone thickness.     

Mechanical properties of metaphyseal bone in the proximal femur

We used a three-point bending test to investigate the structural behavior of 123 rectangular flat plate specimens harvested from the metaphyseal shell of the cervical and intertrochanteric regions of five fresh/frozen human proximal femora. For comparison purposes, 36 specimens of similar geometry were also fabricated from bone of the femoral diaphysis. All specimens were oriented in either the local longitudinal or transverse directions. The mean longitudinal elastic modulus was 9650 +/- 2410 (SD) MPa and demonstrated a 24% decrease from that measured for the diaphysis (12500 +/- 2140 MPa) using the same testing technique. However, the transverse elastic moduli did not differ significantly between the proximal (5470 +/- 1720 MPa) and diaphyseal (5990 +/- 1520 MPa) specimens. The globally averaged values for the ultimate tensile strengths of the metaphyseal shell were 101 +/- 26 MPa in the longitudinal and 50 +/- 12 MPa in the transverse directions. These compared with diaphyseal values of 128 +/- 16 MPa and 47 +/- 12 MPa, respectively. While these differences were largely due to the reduced density of the proximal specimens, a slight decrease in transverse anisotropy for the proximal specimens was also noted by comparing the ratio of longitudinal to transverse moduli (1.76) and tensile strength (2.02) to the diaphyseal values (2.09 and 2.71, respectively). Use of these data should lead to improved performance of analytical models for the proximal femur, and thus help focus increased attention on the structural contribution of trabecular bone to the strength and rigidity of the proximal femur.     

Compressive properties of trabecular bone in the distal femur

Early loosening and implant migration are two problems that lead to failures in cementless (press-fit) femoral knee components of total knee replacements. To begin to address these early failures, this study determined the anterior-posterior mechanical properties from four locations in the human distal femur. Thirty-three cylindrical specimens were removed perpendicular to the press-fit surface after the surgical cuts on 10 human cadaveric femurs (age 71.5+/-14.2 years) had been made. Compression testing was performed that utilized methods to reduce the effects of end-artifacts. The bone mineral apparent density (BMAD), apparent modulus of elasticity, yield and ultimate stress, and yield and ultimate strain were measured for 28 cylindrical specimens. The apparent modulus, yield and ultimate stress, and yield and ultimate strain each significantly differed (p<0.05) in the superior and inferior locations. Linear and power law relationships between superior and inferior mechanical properties and BMAD were determined. The inferior apparent modulus and stresses were higher than those in the superior locations. These results show that the press-fit fixation characteristics of the femoral knee component differ on the anterior shield and posterior condyles. This information will be useful in the assignment of mechanical properties in finite element models for further investigations of femoral knee components. The property-density relations also have applications for implant design and preoperative assessment of bone strength using clinically available tools.     

Functional adaptation of cancellous bone in human proximal femur predicted by trabecular surface remodeling simulation toward uniform stress state

Two-dimensional simulation of trabecular surface remodeling was conducted for a human proximal femur to investigate the structural change of cancellous bone toward a uniform stress state. Considering that a local mechanical stimulus plays an important role in cellular activities in bone remodeling, local stress nonuniformity was assumed to drive trabecular structural change to seek a uniform stress state. A large-scale pixel-based finite element model was used to simulate structural changes of individual trabeculae over the entire bone. As a result, the initial structure of trabeculae changed from isotropic to anisotropic due to trabecular microstructural changes caused by surface remodeling according to the mechanical environment in the proximal femur. Under a single-loading condition, it was shown that the apparent structural property evaluated by fabric ellipses corresponded to the apparent stress state in cancellous bone. As is observed in the actual bone, a distributed trabecular structure was obtained under a multiple-loading condition. Through these studies, it was concluded that trabecular surface remodeling toward a local uniform stress state at the trabecular level could naturally bring about functional adaptation phenomenon at the apparent tissue level. The proposed simulation model would be capable of providing insight into the hierarchical mechanism of trabecular surface remodeling at the microstructural level up to the apparent tissue level.     

Patient-specific finite-element analyses of the proximal femur with orthotropic material properties validated by experiments

Patient-specific high order finite-element (FE) models of human femurs based on quantitative computer tomography (QCT) with inhomogeneous orthotropic and isotropic material properties are addressed. The point-wise orthotropic properties are determined by a micromechanics (MM) based approach in conjunction with experimental observations at the osteon level, and two methods for determining the material trajectories are proposed (along organs outer surface, or along principal strains). QCT scans on four fresh-frozen human femurs were performed and high-order FE models were generated with either inhomogeneous MM-based orthotropic or empirically determined isotropic properties. In vitro experiments were conducted on the femurs by applying a simple stance position load on their head, recording strains on femurs' surface and head's displacements. After verifying the FE linear elastic analyses that mimic the experimental setting for numerical accuracy, we compared the FE results to the experimental observations to identify the influence of material properties on models' predictions. The strains and displacements computed by FE models having MM-based inhomogeneous orthotropic properties match the FE-results having empirically based isotropic properties well, and both are in close agreement with the experimental results. When only the strains in the femoral neck are being compared a more pronounced difference is noticed between the isotropic and orthotropic FE result. These results lay the foundation for applying more realistic inhomogeneous orthotropic material properties in FEA of femurs.     

Sex differences in bone resorption in the mouse femur

Summary In male and female dd-mice at 4, 7, and 14 weeks of age and in 7 and 14-week-old mice gonadectomized at 4 weeks of age, the number of osteoclasts and the number and size of bone resorption areas along the surface of bone trabeculae in the distal metaphysis of the femur were determined. Osteoclasts were counted at the light-microscopic level in paraffin sections of decalcified femora. The number and size of the bone resorption areas were examined by scanning electron microscopy of femora after removing organic material by means of KOH and NaOCl treatment. In untreated mice, the number of osteoclasts and the number and size of bone resorption areas showed no sex differences at 4 weeks of age but were larger in females than males at 7 and 14 weeks of age. In gonadectomized mice, the number of osteoclasts and the bone resorption areas increased in males and decreased in females. The results of the gonadectomy experiments suggest that bone resorption in young adult mice is stimulated by female sex hormone and inhibited by male sex hormone.     

Quantification of ovine bone adaptation to altered load: morphometry, density, and surface strain

Mechanical loading in the sheep proximal radius was increased by ulnar osteotomy (Group O), decreased by Steinmann pinning (Group P) and unaltered in sham operated controls (Group C). A series of intravenous fluochromes was given to label bone formation and the adaptive response was measured at intervals up to 24 weeks. Surface strains, measured in an in vitro rig, were reduced in Group P and increased significantly in Group O. Cross-sectional area (CSA) peaked in all groups at 6 weeks consistent with a regional acceleratory phenomenon (RAP) and the formation of fibrolamellar bone of low density. In Groups C and P the extent of the RAP was related to the degree of operative trauma and the newly-formed bone was subsequently resorbed. In Group P, CSA fell below control levels suggesting negative adaptation. The increase in area was sustained in Group O and bone density increased due to mineralisation and infilling. Periosteal labelling of the scaffold of parallel-fibred bone peaked at 10 weeks, followed by labelling of lamellar bone filling the gaps in the structure. This adaptive response reduced surface strains to near normal levels by 24 weeks in Group O. Positive adaptation was distinguished from the non-specific RAP due to surgical trauma. The adaptive response is both 'intelligent', in that it utilises and adds to the RAP, and accurate, as no further increase in cross-sectional area was required after 6 weeks.     

Mathematical modelling of the reactivity of analyzer systems during adaptation

Information processing has been successfully applied to the prediction of the adaptation characteristics of various sensory analyzers. On the basis of mathematical treatment of the experimental data available in literature, time-constant values T and of the limit parameter I infinity required for prediction of adaptation course have been obtained. Formula have been derived for determining the dependence of these parameters on the luminance and wave-length of the light, on the concentration of the solution and the temperature of the stimulus. The results of computations are compared with the experimental data obtained by various authors.     

A novel endoplasmic reticulum adaptation is critical for the long-lived Caenorhabditis elegans rpn-10 proteasomal mutant

The loss of proteostasis due to reduced efficiency of protein degradation pathways plays a key role in multiple age-related diseases and is a hallmark of the aging process. Paradoxically, we have previously reported that the Caenorhabditis elegans rpn-10(ok1865) mutant, which lacks the RPN-10/RPN10/PSMD4 subunit of the 19S regulatory particle of the 26S proteasome, exhibits enhanced cytosolic proteostasis, elevated stress resistance and extended lifespan, despite possessing reduced proteasome function. However, the response of this mutant against threats to endoplasmic reticulum (ER) homeostasis and proteostasis was unknown. Here, we find that the rpn-10 mutant is highly ER stress resistant compared to the wildtype. Under unstressed conditions, the ER unfolded protein response (UPR) is activated in the rpn-10 mutant as signified by increased xbp-1 splicing. This primed response appears to alter ER homeostasis through the upregulated expression of genes involved in ER protein quality control (ERQC), including those in the ER-associated protein degradation (ERAD) pathway. Pertinently, we find that ERQC is critical for the rpn-10 mutant longevity. These changes also alter ER proteostasis, as studied using the C. elegans alpha-1 antitrypsin (AAT) deficiency model, which comprises an intestinal ER-localised transgenic reporter of an aggregation-prone form of AAT called ATZ. The rpn-10 mutant shows a significant reduction in the accumulation of the ATZ reporter, thus indicating that its ER proteostasis is augmented. Via a genetic screen for suppressors of decreased ATZ aggregation in the rpn-10 mutant, we then identified ecps-2/H04D03.3, a novel ortholog of the proteasome-associated adaptor and scaffold protein ECM29/ECPAS. We further show that ecps-2 is required for improved ER proteostasis as well as lifespan extension of the rpn-10 mutant. Thus, we propose that ECPS-2-proteasome functional interactions, alongside additional putative molecular processes, contribute to a novel ERQC adaptation which underlies the superior proteostasis and longevity of the rpn-10 mutant.     

The fabric dependence of the orthotropic elastic constants of cancellous bone

It has been proposed that the orthotropic elastic constants of cancellous bone depend upon a tensorial measure of anisotropy called fabric as well as the tissue's structural density. Cowin (1985, Mechanics Mater, 4, 137-147; 1986, J. biomech. Engng 108, 83-88) developed explicit relationships for the elastic constant, structural density and fabric relationship. In this study the orthotropic elastic moduli, structural density, and fabric components were measured for 11 cancellous bone specimens from five bovine femora and for 75 specimens from three human proximal tibiae and fitted to these relationships using a least squares analysis. The relationships explained between 72 and 94% of the variance in the elastic constants. The relationships between the elastic constants and squared or cubed power functions of structural density had better predictive value over the entire distribution of the data than did expressions with linear functions of structural density.     

Mammalian BLM helicase is critical for integrating multiple pathways of meiotic recombination

Bloom’s syndrome (BS) is an autosomal recessive disorder characterized by growth retardation, cancer predisposition, and sterility. BS mutated (Blm), the gene mutated in BS patients, is one of five mammalian RecQ helicases. Although BLM has been shown to promote genome stability by assisting in the repair of DNA structures that arise during homologous recombination in somatic cells, less is known about its role in meiotic recombination primarily because of the embryonic lethality associated with Blm deletion. However, the localization of BLM protein on meiotic chromosomes together with evidence from yeast and other organisms implicates a role for BLM helicase in meiotic recombination events, prompting us to explore the meiotic phenotype of mice bearing a conditional mutant allele of Blm. In this study, we show that BLM deficiency does not affect entry into prophase I but causes severe defects in meiotic progression. This is exemplified by improper pairing and synapsis of homologous chromosomes and altered processing of recombination intermediates, resulting in increased chiasmata. Our data provide the first analysis of BLM function in mammalian meiosis and strongly argue that BLM is involved in proper pairing, synapsis, and segregation of homologous chromosomes; however, it is dispensable for the accumulation of recombination intermediates.     

The fluoric origin of the bone lesion in the Pithecanthropus erectus femur

The femur of a patient autopsied 11 years ago is presented in which an osteophyte comparable to the one of the Pithecanthropus Erectus femur can be observed. Their analogous anatomopathological disposition is due to the fact that both are caused by the ossification of the tendinous insertion of the adductors of the thigh. The orifices they both present correspond to the channel of the perforating arteries which normally pierce them. This type of osteophyte is only present as a result of bone fluorosis. The autopsied patient presents a bone fluorosis of the Periostitis deformans' type, as described by the author in 1952. The femur of the Pithecanthropus was found by Eugene Dubois in some geological strata composed mainly of volcanic ash. In the Pithecanthropus, the fluoric intoxication came from the ingestion of fruits and plants impregnated with the fluorine filled volcanic ash. This volcanic fluorisis, known as Gaddur, is now seen among animals living on the volcanic region of Iceland. For these reasons we assume that the Pithecanthropus erectus suffered a bone fluorosis of the type of the Periostitis deformans, which would be the first disease known in man.     

Activation of multiple signaling modules is critical in angiotensin IV-induced lung endothelial cell proliferation

Signaling events involving angiotensin IV (ANG IV)-mediated pulmonary artery endothelial cell (PAEC) proliferation were examined. ANG IV significantly increased upstream phosphatidylinositide (PI) 3-kinase (PI3K), PI-dependent kinase-1 (PDK-1), extracellular signal-related kinases (ERK1/2), and protein kinase B-alpha/Akt (PKB-alpha) activities, as well as downstream p70 ribosomal S6 kinase (p70S6K) activities and/or phosphorylation of these proteins. ANG IV also significantly increased 5-bromo-2'-deoxy-uridine incorporation into newly synthesized DNA in a concentration- and time-dependent manner. Pretreatment of cells with wortmannin and LY-294002, inhibitors of PI3K, or rapamycin, an inhibitor of the mammalian target of rapamycin kinase and p70S6K, diminished the ANG IV-mediated activation of PDK-1 and PKB-alpha as well as phosphorylation of p70S6K. Although an inhibitor of mitogen-activated protein kinase kinase, PD-98059, but not rapamycin, blocked ANG IV-induced phosphorylation of ERK1/2, both PD-98059 and rapamycin independently caused partial reduction in ANG IV-mediated cell proliferation. However, simultaneous treatment with PD-98059 and rapamycin resulted in total inhibition of ANG IV-induced cell proliferation. These results demonstrate that ANG IV-induced DNA synthesis is regulated in a coordinated fashion involving multiple signaling modules in PAEC.     

Computational simulation of trabecular adaptation progress in human proximal femur during growth

There are a large number of clinical and experimental studies that analyzed trabecular architecture as a result of bone adaptation. However, only a limited amount of quantitative data is currently available on the progress of trabecular adaptation during growth. In this paper, we proposed a two-step numerical simulation method that predicts trabecular adaptation progress during growth using a recently developed topology optimization algorithm, design space optimization (DSO), under the hypothesis that the mechanisms of DSO are functionally equivalent to those of bone adaptation. We applied the proposed scheme to trabecular adaptation simulation in human proximal femur. For the simulation, the full trabecular architecture in human proximal femur was represented by a two-dimensional μFE model with 50 μm resolution. In Step 1, we determined a reference value that regulates trabecular adaptation in human proximal femur. In Step 2, we simulated trabecular adaptation in human proximal femur during growth with the reference value derived in Step 1. We analyzed the architectural and mechanical properties of trabecular patterns through iterations. From the comparison with experimental data in the literature, we showed that in the early growth stage trabecular adaptation was achieved mainly by increasing bone volume fraction (or trabecular thickness), while in the later stage of the development the trabecular architecture gained higher structural efficiency by increasing structural anisotropy with a relatively low level of bone volume fraction (or trabecular thickness). We demonstrated that the proposed numerical framework predicted the growing progress of trabecular bone that has a close correlation with experimental data.