Using Multi-scale Agent Based Model For The Bone Regeneration Mechanism Research

Osteogenetic microenvironment is a complex constitution in which extracellular matrix(ECM) molecules, stem cells and growth factors each interact to direct the coordinate regulation of bone tissue development. Importantly, angiogenesis improvement and revascularization are critical for osteogenesis during bone tissue regeneration processes. Bone reconstruction is a complex physiological process exhibiting the nonlinear characteristics in the relative material and boundary condition. The interaction between the external environment and internal factors makes a dynamic balance between osteoclasts and osteoblasts to impact the bone formation. Recently, bone reconstruction already becomes a popular research focus in the clinical study due to its importance in the human health area. Nonetheless, because the microenvironment of bone growth is very complicated, it is costly to develop the in vivo/in vitro bone reconstruction experiments to investigate the bone formation process in detail. For this reason, this study proposed such an in silicon mathematics model that not only can simulate the bone reformation process under the mechanical stimulation with related experimental design, but also can predict the bone mass change with respect to various growth factors after we optimized and validated the model by the experimental training and testing data.In previous studies, we established a systems biology model, and quantitatively explored the combinatorial effects of delivered cytokines from hydrogels on final bone density. We hypothesized that: 1) bone regeneration was driven by transcription factors Runx2 and Osterix, which responded to released cytokines, such as Wnt, BMP2, and TGFb, drove the development of osteoblast lineage, and contributed to bone mass generation; and 2) the osteoclast lineage, on the other hand, governed the bone resorption, and communications between these two lineages determined the dynamics of bone remodeling. In our model, we firstly developed a systematic model composed of a system of ordinary differential equations(ODEs) to describe the intracellular signaling pathway to regulate osteogenic differentiation. And then, we combined the intracellular signaling pathway with intercellular signaling pathway to control osteoclast differentiation. Next, we integrated the intracellular and intercellular signaling pathways into the cellular population dynamics described by a set of stochastic differential equations(SDEs) to simulate bone healing and remodeling. The unknown coefficients in the intracellular signaling pathway were estimated by fitting them to the dynamic experimental data using optimization algorithm. Finally, we investigated the response of cellular population dynamics to therapies of single or combined cytokines as well as quantitatively evaluated the combination effect of cytokines by Loewe and Bliss indexes. Simulation results revealed that the Wnt/BMP2 combinations released from hydrogels showed best control of bone regeneration and synergistic effects, and suggested optimal dose ratios of given cytokine combinations released from hydrogels to most efficiently control the long-term bone remodeling. We revealed the characteristics of cytokine combinations of Wnt/BMP2, which could be used to guide the design of in vivo bone scaffolds and the clinical treatment of some diseases such as osteoporosis.In the next study, we improved the model. We developed a three-dimensional(3D) multi-scale system model to study cell response to growth factors released from a 3D biodegradable porous calcium phosphate(CaP) scaffold. Our model reconstructed the 3D bone regeneration system and examined the effects of pore size and porosity on bone formation and angiogenesis. The present study was designed to develop a computational systems model of bone regeneration within a 3D porous biodegradable CaP scaffold by simulating osteogenesis in response to growth factor release, based on molecular mechanisms and incorporating angiogenesis and nutrient transportation. We first reconstructed the 3D bone regeneration system, and then investigated the effects of pore size and porosity on growth factor release, angiogenesis, and bone formation. Finally, we examined whether the combination of BMP2, Wnt and VEGF promoted angiogenesis and bone formation better than single growth factors at the same doses. The results suggested that scaffold porosity played a more dominant role in affecting bone formation and angiogenesis compared with pore size, while the pore size could be controlled to tailor the growth factor release rate and release fraction. Furthermore, a combination of gradient VEGF with BMP2 and Wnt released from the multi-layer scaffold promoted angiogenesis and bone formation more readily than single growth factors. These results demonstrated that the developed model can be potentially applied to predict vascularized bone regeneration with specific scaffold and growth factors.Herein we developed a novel approach to investigate the mechanism of bone regeneration in a porous biodegradable calcium phosphate(CaP) scaffold by combination of a multi-scale agent based model, experimental optimization of key parameters and experimental data validation for the predictive power of the model. The beauty of the study is that the impact of the mechanical stimulation on the bone regeneration in a porous biodegradable CaP scaffold is considered, experimental design is used to explore the optimal combination of the growth factor loaded on the porous biodegradable CaP scaffold for promoting of the bone regeneration and the model test/analysis is carried out by experimental data, data mining algorithm and related sensitive analysis.Results discover that the mechanical stimulation has great impact on the bone regeneration in a porous biodegradable CaP scaffold and the optimal combination of the growth factors that are encapsulated into nano-spheres and loaded into porous biodegradable CaP scaffolds layer by layercan mostly promote the bone regeneration. Further, the model is robust and is able to predict the development of bone regeneration under the specified condition.