Mechanobiology of human pisiform formation as a model for endochondral ossification.

The role of mechanical stimuli in promoting endochondral ossification during somatic growth and maturation remains an active area of research. This study employs a pisiform model of endochondral ossification to investigate the potential role of mechanobiological signals in the appearance and development of ossification centers and to develop theoretical applications to the primate basicranium. We constructed finite element models based on the structure of a human pisiform within the flexor carpi ulnaris tendon. The pisiform was assigned initial material properties of hyaline cartilage, and tendon properties were based on in situ observations drawn from the literature. A macaque growth model was used to simulate increased load over time as a function of body mass. A load case of uniaxial tension from the tendon was applied over 208 iterations, to simulate weekly growth over a 4-year span. The mechanical signal was defined as shear stress. Element stresses were evaluated in each iteration, with elements exceeding the yield threshold subsequently assigned a higher elastic modulus to mimic mechanically driven mineralization. Three unique mineralization rates were tested. Regardless of rate, all ossification simulations predict a pisiform with heterogeneous stiffness through alternating periods of material stasis and active mineralization/ossification. Assuming metabolic processes underlying endochondral ossification are similar throughout the body, our model suggests that a mechanical signal alone is an insufficient stimulus in the etiology of bone formation through endochondral ossification. Consequently, given the general validity of the simulation, endochondral ossification cannot be fully explained in terms of mechanical stimuli.

Efficacy of shear strain gradients as an osteogenic stimulus.

The question of which mechanical variables are responsible for inducing osteogenic activity is unresolved despite extensive experimental and theoretical investigation. Candidate variables include strain magnitude, loading frequency, the interaction of magnitude and frequency (strain rate), and strain gradients. An additional challenge is discerning the coordination of periosteal and endosteal expansion during growth, and whether this coordination (or lack thereof) is fully dependent or partially independent of the local mechanical environment. In this study, under the assumption that calculated stresses correspond to relative strain magnitudes, we specify alternative growth algorithms of bone cross-sectional size and geometry to explore skeletal growth under alternative scenarios of osteogenic activity that are tracking 1) an attractor stress, 2) local stress magnitude or 3) steepness of stress gradients. These developmental simulations are initiated from two initial geometries (symmetrical and asymmetrical ellipses) under a time-varying torsional load whose magnitude is proportional to body size growth in a model primate. In addition, we model endosteal expansion under three conditions hypothesized in the literature, in which endosteal expansion is 1) independent of the mechanical milieu, 2) completely dependent on the mechanical milieu, and 3) a "hybrid" model in which intrinsic biological (independent) growth is operative early but gives way to mechanically-sensitive (dependent) growth at later ages. Three variables were recorded over each growth simulation: the safety factor (ratio of yield stress to actual stress), an efficiency ratio (invested bone area per unit of stress), and proximity to an isostress condition (an optimal design criterion in which stress is invariant throughout the structure). The attractor stress algorithm produces the most "adapted" bones in terms of mechanical competence and economy of material. Localized osteogenic activity that is guided in direct proportion to stress magnitude produces competent bones but with variable adult geometries depending on conditions of endosteal expansion. Stress gradients also produce functional but relatively inefficient bones, with widely variable safety factors during growth and heterogeneous stress fields. If, in fact, the osteocyte network monitors strain gradients to generate osteogenic signals, the resulting morphology is competent but falls well short of an optimal mechanical solution.