Data_Sheet_1_Modeling Osteocyte Network Formation: Healthy and Cancerous Environments.pdf

Advanced cancers, such as prostate and breast cancers, commonly metastasize to bone. In the bone matrix, dendritic osteocytes form a spatial network allowing communication between osteocytes and the osteoblasts located on the bone surface. This communication network facilitates coordinated bone remodeling. In the presence of a cancerous microenvironment, the topology of this network changes. In those situations, osteocytes often appear to be either overdifferentiated (i.e., there are more dendrites than healthy bone) or underdeveloped (i.e., dendrites do not fully form). In addition to structural changes, histological sections from metastatic breast cancer xenografted mice show that number of osteocytes per unit area is different between healthy bone and cancerous bone. We present a stochastic agent-based model for bone formation incorporating osteoblasts and osteocytes that allows us to probe both network structure and density of osteocytes in bone. Our model both allows for the simulation of our spatial network model and analysis of mean-field equations in the form of integro-partial differential equations. We considered variations of our model to study specific physiological hypotheses related to osteoblast differentiation; for example predicting how changing biological parameters, such as rates of bone secretion, rates of cancer formation, and rates of osteoblast differentiation can allow for qualitatively different network topologies. We then used our model to explore how commonly applied therapies such as bisphosphonates (e.g., zoledronic acid) impact osteocyte network formation.

晚期癌症（如前列腺癌与乳腺癌）常发生骨转移。在骨基质中，树突状骨细胞可形成空间网络，实现骨细胞（osteocyte）与骨表面成骨细胞（osteoblast）之间的信号交流，该网络可协调骨重建过程。当存在癌性微环境时，该网络的拓扑结构会发生改变：此时骨细胞往往呈现过度分化（即树突数量多于健康骨骼）或分化不足（即树突无法完全形成）的状态。除结构改变外，转移性乳腺癌异种移植小鼠的组织学切片显示，健康骨与癌性骨的单位面积骨细胞数量存在显著差异。我们提出了一种整合成骨细胞与骨细胞的基于智能体的随机模型，可用于探究骨内网络结构与骨细胞密度。该模型既支持本研究空间网络模型的仿真，也可用于分析积分偏微分方程（integro-partial differential equations）形式的平均场方程（mean-field equations）。我们通过调整模型变体，研究与成骨细胞分化相关的特定生理学假说，例如预测改变骨分泌速率、癌症形成速率、成骨细胞分化速率等生物学参数，如何使网络拓扑结构产生质性差异。随后我们利用该模型，探究了双膦酸盐类药物（bisphosphonates，如唑来膦酸（zoledronic acid））等常用疗法对骨细胞网络形成的影响。