Mechanobiological modeling of endochondral ossification: an experimental and computational analysis

Chondrocyte hypertrophy in the growth plate promotes stress anisotropy affecting long bone development through chondrocyte column formation

The length of long bones is determined by column formation of proliferative chondrocytes and subsequent chondrocyte hypertrophy in the growth plate during bone development. Despite the importance of mechanical loading in long bone development, the mechanical conditions of the cells within the growth plate, such as the stress field, remain unclear owing to the difficulty in investigating spatiotemporal changes within dynamically growing tissues. In this study, the mechanisms of longitudinal bone growth were investigated from a mechanical perspective through column formation of proliferative chondrocytes within the growth plate before secondary ossification center formation using continuum-based particle models (CbPMs). A one-factor model, which simply describes essential aspects of a biological signaling cascade regulating cell activities within the growth plate, was developed and incorporated into CbPM. Subsequently, the developmental process and maintenance of the growth plate structure and resulting bone morphogenesis were simulated. Thus, stress anisotropy in the proliferative zone that affects bone elongation through chondrocyte column formation was identified and found to be promoted by chondrocyte hypertrophy. These results provide further insights into the mechanical regulation of multicellular dynamics during bone development.

Contributions of cell behavior to geometric order in embryonic cartilage

During early development, cartilage provides shape and stability to the embryo while serving as a precursor for the skeleton. Correct formation of embryonic cartilage is hence essential for healthy development. In vertebrate cranial cartilage, it has been observed that a flat and laterally extended macroscopic geometry is linked to regular microscopic structure consisting of tightly packed, short, transversal clonar columns. However, it remains an ongoing challenge to identify how individual cells coordinate to successfully shape the tissue, and more precisely which mechanical interactions and cell behaviors contribute to the generation and maintenance of this columnar cartilage geometry during embryogenesis. Here, we apply a three-dimensional cell-based computational model to investigate mechanical principles contributing to column formation. The model accounts for clonal expansion, anisotropic proliferation and the geometrical arrangement of progenitor cells in space. We confirm that oriented cell divisions and repulsive mechanical interactions between cells are key drivers of column formation. In addition, the model suggests that column formation benefits from the spatial gaps created by the extracellular matrix in the initial configuration, and that column maintenance is facilitated by sequential proliferative phases. Our model thus correctly predicts the dependence of local order on division orientation and tissue thickness. The present study presents the first cell-based simulations of cell mechanics during cranial cartilage formation and we anticipate that it will be useful in future studies on the formation and growth of other cartilage geometries.

Can pelvic tilt cause cam morphology? A computational model of proximal femur development mechanobiology

Cam deformity of the proximal femur is a risk factor for early osteoarthritis. While cam morphology is related to mechanical force at a formative time in skeletal growth, the specific problematic forces contributing to the development of cam morphology remain unknown. Individuals with femoroacetabular impingement syndrome exhibit an increased anterior pelvic tilt during walking, which alters their hip joint forces. This study aims to investigate the influence of altered joint force caused by anterior pelvic tilt on proximal femur epiphyseal growth and the potential association between increased anterior pelvic tilt and the development of cam morphology. A computational model is utilized to simulate the endochondral ossification in the proximal femur and predict cam formation. Cartilage growth and ossification patterns for a gait cycle with and without anterior pelvic tilt were modeled. The simulated growth results indicated an increased alpha angle (53° for typically developing to 68° for anterior pelvic tilt) and aspherical femoral head in the model with anterior pelvic tilt. We conclude that anterior pelvic tilt may be sufficient to cause the formation of the cam morphology. Identifying the critical mechanical conditions that increase the risk of cam deformity could help prevent this condition by adjusting the physical activities before skeletal maturity.

Development of continuum-based particle models of cell growth and proliferation for simulating tissue morphogenesis

Biological tissues acquire various characteristic shapes through morphogenesis. Tissue shapes result from the spatiotemporally heterogeneous cellular activities influenced by mechanical and biochemical environments. To investigate multicellular tissue morphogenesis, this study aimed to develop a novel multiscale method that can connect each cellular activity to the mechanical behaviors of the whole tissue by constructing continuum-based particle models of cellular activities. This study proposed mechanical models of cell growth and proliferation that are expressed as volume expansion and cell division by extending the material point method. By simulating cell hypertrophy and proliferation under both free and constraint conditions, the proposed models demonstrated potential for evaluating the mechanical state and tracing cells throughout tissue morphogenesis. Moreover, the effect of a cell size checkpoint was incorporated into the cell proliferation model to investigate the mechanical behaviors of the whole tissue depending on the condition of cellular activities. Consequently, the accumulation of strain energy density was suppressed because of the influence of the checkpoint. In addition, the whole tissues acquired different shapes depending on the influence of the checkpoint. Thus, the models constructed herein enabled us to investigate the change in the mechanical behaviors of the whole tissue according to each cellular activity depending on the mechanical state of the cells during morphogenesis.

Computational model of endochondral ossification: Simulating growth of a long bone

Mechanical loading is a crucial factor in joint and bone development. Using a computational model, we investigated the role of mechanics on cartilage growth rate, ossification of the secondary center, formation of the growth plate, and overall bone shape. A computational algorithm was developed and implemented into finite element models to simulate the endochondral ossification for symmetric and asymmetric motion in a generic diarthrodial joint. Under asymmetric loading condition the secondary center ossifies asymmetrically leaning toward the external load and results in tilted growth plate. Also the mechanics seems to have greater influence in the early onset of the ossification of the secondary center rather than later progression of the center. While previous models have simulated select stages of skeletal development, our model can simulate growth and ossification during the entirety of post-natal development. Such computational models of skeletal development may provide insight into specific loading conditions that cause bone and joint deformities, and the required timing for rehabilitative repair.

Biomechanical Study of the Development of Long Bones: Finite Element Structure Synthesis of the Human Second Proximal Phalanx Under Growth Conditions

Torsional loads are a possible mechanical explanation for the architecture of long bone. Finite element structure synthesis (FESS) has previously successfully been used as a deductive technique using Wolff's Law by applying expected loads to an unspecific homogeneous solid and eliminating stress free parts to verify muscle forces. The extended approach presented in this article includes further mechanobiological rules to model the development from a cartilage model to a finger bone. In contrast to former computational models, simulation of processes leading to both external growth and internal differentiation are included. Combined axial and torsional loads synthesize a complete human secondary proximal phalanx model comparable to form and internal structure to that observed in vivo. While the computational model is very sensitive to initial alterations of loads, changes after growth have a minor effect as observed in animal models. Predictions of cartilage growth and ossification during FESS showed significant similarities to ontogeny indicating the importance of mechanical factors for the morphogenesis of bone during growth. Anat Rec, 302:1389-1398, 2019. © 2018 Wiley Periodicals, Inc.

A novel mechanobiological model can predict how physiologically relevant dynamic loading causes proteoglycan loss in mechanically injured articular cartilage

Cartilage provides low-friction properties and plays an essential role in diarthrodial joints. A hydrated ground substance composed mainly of proteoglycans (PGs) and a fibrillar collagen network are the main constituents of cartilage. Unfortunately, traumatic joint loading can destroy this complex structure and produce lesions in tissue, leading later to changes in tissue composition and, ultimately, to post-traumatic osteoarthritis (PTOA). Consequently, the fixed charge density (FCD) of PGs may decrease near the lesion. However, the underlying mechanisms leading to these tissue changes are unknown. Here, knee cartilage disks from bovine calves were injuriously compressed, followed by a physiologically relevant dynamic compression for twelve days. FCD content at different follow-up time points was assessed using digital densitometry. A novel cartilage degeneration model was developed by implementing deviatoric and maximum shear strain, as well as fluid velocity controlled algorithms to simulate the FCD loss as a function of time. Predicted loss of FCD was quite uniform around the cartilage lesions when the degeneration algorithm was driven by the fluid velocity, while the deviatoric and shear strain driven mechanisms exhibited slightly discontinuous FCD loss around cracks. Our degeneration algorithm predictions fitted well with the FCD content measured from the experiments. The developed model could subsequently be applied for prediction of FCD depletion around different cartilage lesions and for suggesting optimal rehabilitation protocols.