The role of computational models in mechanobiology of growing bone

Endochondral ossification, the process by which long bones grow in length, is regulated by mechanical forces. Computational models, specifically finite element models, have been used for decades to understand the role of mechanical loading on endochondral ossification. This perspective outlines the stages of model development in which models are used to: 1) explore phenomena, 2) explain pathologies, 3) predict clinical outcomes, and 4) design therapies. As the models progress through the stages, they increase in specificity and biofidelity. We give specific examples of models of endochondral ossification and expect models of other mechanobiological systems to follow similar development stages.Peer ReviewedPostprint (published version

Effect of growth plate geometry and growth direction on prediction of proximal femoral morphology

AbstractMechanical stimuli play a significant role in the process of endochondral growth. Thus far, approaches to understand the endochondral mechanical growth rate have been limited to the use of approximated location and geometry of the growth plate. Furthermore, growth has been simulated based on the average deflection of the growth plate or of the femoral neck. It has also been reported in the literature that the growth plate lies parallel to one of the principal stresses acting on it, to reduce the shear between epiphysis and diaphysis. Hence the current study objectives were (1) to evaluate the significance of a subject-specific finite element model of the femur and growth plate compared to a simplified growth plate model and (2) to explore the different growth direction models to better understand proximal femoral growth mechanisms. A subject-specific finite element model of an able-bodied 7-year old child was developed. The muscle forces and hip contact force were computed for one gait cycle and applied to a finite element model to determine the specific growth rate. Proximal femoral growth was simulated for two different growth direction models: femoral neck deflection direction and principal stress direction. The principal stress direction model captured the expected tendency for decreasing the neck shaft angle and femoral anteversion for both growth plate models. The results of this study suggest that the subject-specific geometry and consideration of the principal stress direction as growth direction may be a more realistic approach for correct prediction of proximal femoral growth morphology

Small scale fracture of bone to understand the effect of fibrillar organization on toughness

Fracture toughness is a critical component of bone quality and derives from the hierarchical arrangement of collagen and mineral from the molecular level to the whole bone level. Molecular defects, disease, and age affect bone toughness, yet there is currently no treatment to address deficits in toughness. Toughening mechanisms occur at every length scale, making it difficult to isolate the influence of specific components. Most experimental studies on the fracture behaviour of bone use milled samples of bone or whole bones. Toughness deficits can be identified but may be caused by a multitude of parameters across length-scales, making it difficult to develop targeted therapies. Herein, we measure the toughness of bone in micropillars where porosity and heterogeneities are minimized, allowing us to determine the role of fibril anisotropy on fracture toughness. Double cantilever beam micromechanical tests were conducted in a scanning electron microscope on 4x6x15 mm pillars of mouse bone femorae produced in the longitudinal and transverse orientations. Subsequent transmission electron microscopy of the fractured pillars revealed a role of the local organization of the mineralized collagen fibrils in influencing crack propagation. We demonstrate that fibril orientation is a critical factor in deflection during crack propagation, significantly contributing to fracture toughness

Studies of chain substitution caused sub-fibril level differences in stiffness and ultrastructure of wildtype and oim/oim collagen fibers using multifrequency-AFM and molecular modeling

Molecular alteration in type I collagen, i.e., substituting the α2 chain with α1 chain in tropocollagen molecule, can cause osteogenesis imperfecta (OI), a brittle bone disease, which can be represented by a mouse model (oim/oim). In this work, we use dual-frequency Atomic Force Microscopy (AFM) and incorporated with molecular modeling to quantify the ultrastructure and stiffness of the individual native collagen fibers from wildtype (+/+) and oim/oim diseased mice humeri. Our work presents direct experimental evidences that the +/+ fibers have highly organized and compact ultrastructure and corresponding ordered stiffness distribution. In contrast, oim/oim fibers have ordered but loosely packed ultrastructure with uncorrelated stiffness distribution, as well as local defects. The molecular model also demonstrates the structural and molecular packing differences between +/+ and oim/oim collagens. The molecular mutation significantly altered sub-fibril structure and mechanical property of collagen fibers. This study can give the new insight for the mechanisms and treatment of the brittle bone disease

Ex vivo determination of bone tissue strains for an in vivo mouse tibial loading model

AbstractPrevious studies introduced the digital image correlation (DIC) as a viable technique for measuring bone strain during loading. In this study, we investigated the sensitivity of a DIC system in determining surface strains in a mouse tibia while loaded in compression through the knee joint. Specifically, we examined the effect of speckle distribution, facet size and overlap, initial vertical alignment of the bone into the loading cups, rotation with respect to cameras, and ex vivo loading configurations on the strain contour maps measured with a DIC system.We loaded tibiae of C57BL/6 mice (12 and 18 weeks old male) up to 12N at 8N/min. Images of speckles on the bone surface were recorded at 1N intervals and DIC was used to compute strains. Results showed that speckles must have the correct size and density with respect to the facet size of choice for the strain distribution to be computed and reproducible. Initial alignment of the bone within the loading cups does not influence the strain distribution measured during peak loading, but bones must be placed in front of the camera with the same orientation in order for strains to be comparable. Finally, the ex vivo loading configurations with the tibia attached to the entire mouse, or to the femur and foot, or only to the foot, showed different strain contour maps.This work provides a better understanding of parameters affecting full field strain measurements from DIC in ex vivo murine tibial loading tests

Age and Sex Differences in Load-Induced Tibial Cortical Bone Surface Strain Maps

Bone adapts its architecture to the applied load; however, it is still unclear how bone mechano-adaptation is coordinated and why potential for adaptation adjusts during the life course. Previous animal models have suggested strain as the mechanical stimulus for bone adaptation, but yet it is unknown how mouse cortical bone load-related strains vary with age and sex. In this study, full-field strain maps (at 1 N increments up to 12 N) on the bone surface were measured in young, adult, and old (aged 10, 22 weeks, and 20 months, respectively), male and female C57BL/6J mice with load applied using a noninvasive murine tibial model. Strain maps indicate a nonuniform strain field across the tibial surface, with axial compressive loads resulting in tension on the medial side of the tibia because of its curved shape. The load-induced surface strain patterns and magnitudes show sexually dimorphic changes with aging. A comparison of the average and peak tensile strains indicates that the magnitude of strain at a given load generally increases during maturation, with tibias in female mice having higher strains than in males. The data further reveal that postmaturation aging is linked to sexually dimorphic changes in average and maximum strains. The strain maps reported here allow for loading male and female C57BL/6J mouse legs in vivo at the observed ages to create similar increases in bone surface average or peak strain to more accurately explore bone mechano-adaptation differences with age and sex

Age and Sex Differences in Load-Induced Tibial Cortical Bone Surface Strain Maps

Bone adapts its architecture to the applied load; however, it is still unclear how bone mechano-adaptation is coordinated and why potential for adaptation adjusts during the life course. Previous animal models have suggested strain as the mechanical stimulus for bone adaptation, but yet it is unknown how mouse cortical bone load-related strains vary with age and sex. In this study, full-field strain maps (at 1 N increments up to 12 N) on the bone surface were measured in young, adult, and old (aged 10, 22 weeks, and 20 months, respectively), male and female C57BL/6J mice with load applied using a noninvasive murine tibial model. Strain maps indicate a nonuniform strain field across the tibial surface, with axial compressive loads resulting in tension on the medial side of the tibia because of its curved shape. The load-induced surface strain patterns and magnitudes show sexually dimorphic changes with aging. A comparison of the average and peak tensile strains indicates that the magnitude of strain at a given load generally increases during maturation, with tibias in female mice having higher strains than in males. The data further reveal that postmaturation aging is linked to sexually dimorphic changes in average and maximum strains. The strain maps reported here allow for loading male and female C57BL/6J mouse legs in vivo at the observed ages to create similar increases in bone surface average or peak strain to more accurately explore bone mechano-adaptation differences with age and sex

Local mechanical stimuli correlate with tissue growth in axolotl salamander joint morphogenesis

Movement-induced forces are critical to correct joint formation, but it is unclear how cells sense and respond to these mechanical cues. To study the role of mechanical stimuli in the shaping of the joint, we combined experiments on regenerating axolotl (Ambystoma mexicanum) forelimbs with a poroelastic model of bone rudiment growth. Animals either regrew forelimbs normally (control) or were injected with a transient receptor potential vanilloid 4 (TRPV4) agonist during joint morphogenesis. We quantified growth and shape in regrown humeri from whole-mount light sheet fluorescence images of the regenerated limbs. Results revealed significant differences in morphology and cell proliferation between groups, indicating that TRPV4 desensitization has an effect on joint shape. To link TRPV4 desensitization with impaired mechanosensitivity, we developed a finite element model of a regenerating humerus. Local tissue growth was the sum of a biological contribution proportional to chondrocyte density, which was constant, and a mechanical contribution proportional to fluid pressure. Computational predictions of growth agreed with experimental outcomes of joint shape, suggesting that interstitial pressure driven from cyclic mechanical stimuli promotes local tissue growth. Predictive computational models informed by experimental findings allow us to explore potential physical mechanisms involved in tissue growth to advance our understanding of the mechanobiology of joint morphogenesis.This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement no. 841047 and the National Science Foundation under grant no. 1727518. J.J.M. has been also funded by the Spanish Ministry of Science and Innovation under grant no. DPI2016-74929-R, and by the local government Generalitat de Catalunya under grant no. 2017 SGR 1278. K.L. was supported by a Northeastern University Undergraduate Research and Fellowships PEAK Experiences Award.Peer ReviewedPostprint (published version

An Investigation of the Mineral in Ductile and Brittle Cortical Mouse Bone

Bone is a strong and tough material composed of apatite mineral, organic matter, and water. Changes in composition and organization of these building blocks affect bone's mechanical integrity. Skeletal disorders often affect bone's mineral phase, either by variations in the collagen or directly altering mineralization. The aim of the current study was to explore the differences in the mineral of brittle and ductile cortical bone at the mineral (nm) and tissue (µm) levels using two mouse phenotypes. Osteogenesis imperfecta model, oim(-/-) , mice have a defect in the collagen, which leads to brittle bone; PHOSPHO1 mutants, Phospho1(-/-) , have ductile bone resulting from altered mineralization. Oim(-/-) and Phospho1(-/-) were compared with their respective wild-type controls. Femora were defatted and ground to powder to measure average mineral crystal size using X-ray diffraction (XRD) and to monitor the bulk mineral to matrix ratio via thermogravimetric analysis (TGA). XRD scans were run after TGA for phase identification to assess the fractions of hydroxyapatite and β-tricalcium phosphate. Tibiae were embedded to measure elastic properties with nanoindentation and the extent of mineralization with backscattered electron microscopy (BSE SEM). Results revealed that although both pathology models had extremely different whole-bone mechanics, they both had smaller apatite crystals, lower bulk mineral to matrix ratio, and showed more thermal conversion to β-tricalcium phosphate than their wild types, indicating deviations from stoichiometric hydroxyapatite in the original mineral. In contrast, the degree of mineralization of bone matrix was different for each strain: brittle oim(-/-) were hypermineralized, whereas ductile Phospho1(-/-) were hypomineralized. Despite differences in the mineralization, nanoscale alterations in the mineral were associated with reduced tissue elastic moduli in both pathologies. Results indicated that alterations from normal crystal size, composition, and structure are correlated with reduced mechanical integrity of bone