COUPLED FINITE ELEMENT: ANALYTICAL MODEL TO PREDICT DEFECT INFILLING BY OSTEOCHONDRAL PROGENITOR CELLS

Summary Statement A coupled finite element - analytical model is presented to predict and to elucidate a clinical healing scenario where bone regenerates in a critical-sized femoral defect, bounded by periosteum or a periosteum substitute implant and stabilised via an intramedullary nail. Introduction Bone regeneration and maintenance processes are intrinsically linked to mechanical environment. However, the cellular and subcellular mechanisms of mechanically-modulated bone (re-) generation are not fully understood. Recent studies with periosteum osteoprogenitor cells exhibit their mechanosensitivity in vitro and in situ . In addtion, while a variety of growth factors are implicated in bone healing processes, bone morphogenetic protein-2 (BMP-2) is recognised to be involved in all stages of bone regeneration. Furthermore, periosteal injuries heal predominantly via endochondral ossification mechanisms. With this background in mind, the current study aims to understand the role of mechanical environment on BMP-2 production and periosteally-mediated bone regeneration. The one-stage bone transport model [1] provides a clinically relevant experimental platform on which to model the mechanobiological process of periosteum-mediated bone regeneration in a critical-sized defect. Here we develop a model framework to study the cellular-, extracellular- and mechanically-modulated process of defect infilling, governed by the mechanically-modulated production of BMP-2 by osteoprogenitor cells located in the periosteum. Methods Material properties of the healing callus and periosteum contribute to the strain stimulus sensed by osteoprogenitor cells therein. Using a mechanical finite element model, periosteal surface strains are first predicted as a function of callus properties. Strains are then input to a mechanistic mathematical model, where mechanical regulation of BMP-2 production mediates rates of cellular proliferation, differentiation and extracellular matrix (ECM) production, to predict healing outcomes. A parametric approach enables the spatial and temporal prediction of tissue regeneration via endochondral ossification. Predictions are compared with experimental, micro-computed tomographic and histologic, measures of cartilage and mineralised bone tissue regenerates. Model Predictions in Light of Experimental Case Studies: A validated baseline model predicts defect healing via cellular egression, extracellular matrix production and endochondral ossification, using parameters optimised to mimic experimental outcome measures at initial and final stages of healing. To elucidate which predictive model paramenters result in the intrinsic differences in experimental outcomes between defects bounded by either periosteum in situ or a periosteum substitute implant, model parameters are then varied by orders of magnitude to determine which factors exert dominant influence on achievement of experimentally relevant ECM area outcomes. Considering the complete set of parameters relevant to healing, the rate of osteoprogenitor to osteoblast differentiation, as well as rates of chondrocyte and osteoblast proliferation must be reduced and ECM production by chondrocytes must be increased from baseline, to achieve healing outcomes analogous to those observed in experiments. Discussion/Conclusion The novel model framework presented here integrates a mechanistic feedback system, based on the mechanosensitivity of periosteal osteoprogenitor cells, which allows for modeling and prediction of tissue regeneration on multiple length and time scales.