Department of Mechanical Engineering, Indian Institute of Technology Delhi, New Delhi, 110016, India.
Department of Mechanical Engineering, Indian Institute of Technology Ropar, Rupnagar, Punjab, 140001, India.
Biomech Model Mechanobiol. 2022 Oct;21(5):1425-1440. doi: 10.1007/s10237-022-01599-w. Epub 2022 Jul 7.
Existing in silico models for lamellar bone adaptation to mechanical loading are unsuitable for predicting woven bone growth. This anomaly is due to the difference in mechanobiology of the woven bone with respect to that of the lamellar bone. The present study is aimed at developing an in silico bone-adaptation model for woven bone at cellular and tissue levels. The diffusion of Ca ions reaching lining cells from the osteocytic network and the bone cortex in response to a mechanical loading on the cortical bone has been considered as a stimulus. The diffusion of ions within osteocytic network has been computed with a lacunar-canalicular network (LCN) in which bone cells are uniformly arranged. Strain energy density is assumed to regulate ion flow within the network when the induced normal strain is above a threshold level. If the induced strain exceeds another higher threshold level, then the strain with a power constant is additionally assumed to regulate the stimulus. The intracellular flow of Ca ions within the LCN has been simulated using Fick's laws of diffusion, using a finite element method. The ion diffusion from bone cortex to vesicles has been formulated as a normal strain with a power constant. The stimuli reaching the surface cells are assumed to form the new bone. The mathematical model closely predicts woven bone growth in mouse and rat tibia for various in vivo loading conditions. This model is the first to predict woven bone growth at tissue and cellular levels in response to heavy mechanical loading.
现有的层状骨适应机械加载的计算模型不适合预测编织骨的生长。这种异常是由于编织骨的力学生物学与层状骨的力学生物学不同所致。本研究旨在开发一种用于细胞和组织水平编织骨适应的计算模型。皮质骨受到机械加载时，到达衬里细胞的 Ca 离子从骨细胞网络和骨皮质扩散被认为是一种刺激。在骨细胞均匀排列的腔隙-管道网络 (LCN) 中计算了离子在骨细胞网络内的扩散。当诱导的正应变超过阈值水平时，应变能密度被假设为调节网络内的离子流动。当诱导应变超过另一个更高的阈值水平时，还假设应变与幂常数一起调节刺激。使用有限元法，根据菲克扩散定律模拟了 LCN 内细胞内 Ca 离子的流动。从骨皮质到小泡的离子扩散被公式化为具有幂常数的正应变。到达表面细胞的刺激被认为是形成新骨的原因。该数学模型可以很好地预测在各种体内加载条件下小鼠和大鼠胫骨中的编织骨生长。该模型是第一个预测在组织和细胞水平上对重机械加载的反应的编织骨生长的模型。
