Chinese Journal of Tissue Engineering Research ›› 2026, Vol. 30 ›› Issue (27): 7167-7175.doi: 10.12307/2026.275
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Hu Zanying1, Gao Fei2
Received:2025-11-11
Accepted:2025-11-27
Online:2026-09-28
Published:2026-05-22
Contact:
Gao Fei, PhD, Doctoral supervisor, Professor, School of Physical Education, Tianjin University of Sport, Tianjin 301617, China
About author:Hu Zanying, MS, Sports Training College, Tianjin University of Sport, Tianjin 301617, China
Supported by:CLC Number:
Hu Zanying, Gao Fei. Construction and validation of a temperature prediction model for cortical bone during orthopedic surgery[J]. Chinese Journal of Tissue Engineering Research, 2026, 30(27): 7167-7175.
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5.1 模型验证 根据热电偶测试收集的数据和共轭梯度法的反演,推断出皮质骨的能量分布系数为11.7%。图14为皮质骨钻孔过程中实验确定和预测温度值的对比,发现在固定进给率的过程中,主轴转速为800,1 000 r/min时,骨温度峰值分别为41.8 ℃和52.7 ℃。在相同条件下,预测温度分别为39.8 ℃和56.8 ℃。结果表明,温度随时间逐渐升高,主轴转速的增加会导致测量位置的温度升高。 理论值和实验值之间的相对误差是以平均方根值分析得来。模型预测值在合理误差范围内与实验值之间的误差较小,最大误差p < 6%。如表3所示,误差的可能解释是实验中存在热辐射和热对流,以及测试中人为因素不可避免的影响。因此,温度预测模型能够准确体现出在皮质骨钻孔过程中一定程度的温度分布情况。"
5.2 不同深度皮质骨温度的模拟分析 数学模型建构用于预测皮质骨温度随钻孔时间在不同方向和深度上的变化。在x=2.5的位置,皮质骨温度在不同深度的分布如图15所示。以进给速度为60 mm/min、主轴速度n为1 000 r/min进行模拟。 由图15可知,钻孔深度对皮质骨温度分布有很大影响。皮质骨的温度在z=1.5 mm的深度最早升高,在z=4.5 mm的深度最慢升高,峰值出现在5 s,最大峰差为12.7 ℃,在z=2.5 mm深度皮质骨的最高峰值温度约为52.2 ℃。该数值模拟表明,在皮质骨钻孔过程中,温度测量的最佳深度为z=2.5 mm,温度与深度之间的关系是非线性的。 5.3 纺锤体速度影响皮质骨坏死的范围 根据CARTER等[59]的研究,骨保持生物活性的极限温度是50 ℃,不会发生热坏死。该研究对热影响区进行了定义及阐述,即皮质骨温度高于50 ℃的区域,为评估皮质骨潜在热损伤区域提供了可靠有力的指标。皮质骨钻孔温度场的理论模型对不同主轴转速的下沿——皮质骨向x的温度变化进行了研究,并分析主轴转速影响皮质骨热坏死的范围。 当进给速度60 mm/min、钻头直径4 mm时,主轴转速依次为800 r/min和1 000 r/min的热影响区计算结果如图16所示。主轴转速为800 r /min时,沿径向温度≥50 ℃的范围为0.68 mm (热影响区为0.68 mm);相同条件下,主轴转速为1 000 r/min时,热影响区为0.81 mm。籍此得出结论,主轴转速较大时,热影响区较大,钻削温度沿径向x呈指数下降(图16)。 5.4 不同径向位置皮质骨温度的仿真分析 在皮质骨钻孔实际测试中,安装热电偶位置可能距离孔边缘不止0.5 mm。因此,使用上述建立的数学预测模型研究x < 0.5 mm的温度变化,在主轴转速为1 000 r/min、测量时间为4 s的情况下进行仿真分析。 在实际皮质骨钻孔实验中,热电偶的安装位置可能距孔壁超过0.5 mm,为避免对钻孔过程造成干扰,确保测温稳定性,以测温点径向距离为定值(x=0.5 mm),针对测量径向距离皮质骨空隙小于0.5 mm的温度进行分析。而发生骨热损伤的高频区恰好位于关键测量区,导致该区域的温度测量难度颇大。因而,此次研究对不同径向距离(x=0,0.1,0.2,0.3 和 0.4 mm)及不同深度(z=0,1,2,3 和 4 mm)温度变化规律进行了系统分析,其结果如图17所示。 从图17的结果来看,在皮质骨钻削区域内,测温点与热源间的距离同所记录的温度值呈正相关关系,即距离越近,温度越高。在位置 x=0 mm,z=4 mm处检测到最高温度,峰值高达 86.9 ℃;此外,在深度 z=4 mm 的截面中,沿径向的温差最为显著,该截面内不同深度测量点之间的最大温差为 32.4 ℃,当径向距离为 0.4 mm 时,温度沿径向分布呈现负相关关系,即随着与钻孔中心距离的增大,刀具摩擦所产生的热量累积逐渐减小。这主要是由于皮质骨导热系数较低,热量传递存在明显的滞后效应所造成的;在持续钻削的过程中,刀具摩擦产热累积促使温度上升,在钻头持续钻削时钻透皮质骨形成通孔的时刻,温度达到峰值,而随钻削过程深入至钻头钻透皮质骨形成通孔后,热量散失显著增强,温度随之呈下降趋势。"
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