A computational model for the joint onset and 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.

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.

Computational model of a synovial joint morphogenesis

Joints enable the relative movement between the connected bones. The shape of the joint is important for the joint movements since they facilitate and smooth the relative displacement of the joint's parts. The process of how the joints obtain their final shape is yet not well understood. Former models have been developed in order to understand the joint morphogenesis leaning only on the mechanical environment; however, the obtained final anatomical shape does not match entirely with a realistic geometry. In this study, a computational model was developed with the aim of explaining how the morphogenesis of joints and shaping of ossification structures are achieved. For this model, both the mechanical and biochemical environments were considered. It was assumed that cartilage growth was controlled by cyclic hydrostatic stress and inhibited by octahedral shear stress. In addition, molecules such as PTHrP and Wnt promote chondrocyte proliferation and therefore cartilage growth. Moreover, the appearance of the primary and secondary ossification centers was also modeled, for which the osteogenic index and PTHrP-Ihh concentrations were taken into account. The obtained results from this model show a coherent final shape of an interphalangeal joint, which suggest that the mechanical and biochemical environments are crucial for the joint morphogenesis process.