THE RELATION BETWEEN RESONANT FREQUENCIES AND TORSIONAL STIFFNESS OF LONG BONES INVITRO - VALIDATION OF A SIMPLE BEAM MODEL
THE RELATION BETWEEN RESONANT FREQUENCIES AND TORSIONAL STIFFNESS OF LONG BONES INVITRO - VALIDATION OF A SIMPLE BEAM MODEL
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DOI：
10.1016/0021-9290(93)90032-a
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发表时间：
1993-06-01
影响因子：
2.4
通讯作者：
LAMMENS, J
中科院分区：
文献类型：
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作者：
LOWET, G;VANAUDEKERCKE, R;LAMMENS, J
对动物长骨进行了振动分析实验和冲击扭转试验，验证了基于共振频率预测扭转刚度的简单梁模型。对142块切除的长骨进行了两种相互垂直的弯曲振动模式的共振频率数据评估。同一骨骼的扭转刚度已通过冲击扭转试验确定。利用简单的梁模型，推导了梁的共振频率与扭转刚度之间的理论关系。如果已知总骨量和骨长，则由此推导出的公式允许从共振频率计算扭转刚度。线性回归分析显示，绵羊股骨（r2 = 0.63, n = 24）、狗股骨（r2 = 0.94, n = 34）、狗胫骨（r2 = 0.79, n = 18）和猴子桡骨（r2 = 0.77, n = 66）的扭转刚度实测值与计算值具有较强的相关性。研究发现，这种线性关系不仅适用于一种骨类型。对所有骨的组合数据进行线性回归分析，结果表明所有骨的扭转刚度测量值与计算值之间的整体线性关系相同（r2 = 0.98, n = 142）。这意味着同一梁模型适用于研究的不同骨类型。然而，从共振频率计算刚度需要知道总骨量、骨密度和长度。从体内应用的角度出发，研究了用总骨矿物质含量（TBMC）作为骨密度指标的可行性。总骨量与总骨矿物质含量呈良好的线性相关。利用TBMC数据计算的扭转刚度与实测扭转刚度之间的相关性仍然非常令人满意。最后，从单个标本中观察到左右骨的特性之间具有良好的线性相关性。这些结果表明共振频率与体外骨力学性能之间存在简单的关系。在充分考虑体内效应（肌肉、皮肤、关节等）对振动行为的影响的情况下，研究结果为共振频率技术用于骨折愈合监测和骨质疏松评价的可行性提供了前景。
The results of vibration analysis experiments and impact torsion tests performed on excised animal long bones were used to validate a simple beam model for the prediction of torsional stiffness from resonant frequencies. Resonant frequency data on two mutually perpendicular bending vibration modes of 142 excised long bones were evaluated. Torsional stiffness of the same bones had been determined by an impact torsion test. Using a simple beam model, a theoretical relation between resonant frequencies and torsional stiffness was derived. If total bone mass and bone length are known, the formula thus derived allows one to calculate torsional stiffness from resonant frequencies.Linear regression analysis shows a strong correlation between the measured and the calculated torsional stiffness for sheep femora (r2 = 0.63, n = 24), dog femora (r2 = 0.94, n = 34), dog tibiae (r2 = 0.79, n = 18) and monkey radii (r2 = 0.77, n = 66). It was found that this linear relation was valid not within one bone type alone. Linear regression analysis on the combined data of all bones demonstrated that all bones obeyed the same global linear relation between measured and the calculated torsional stiffness (r2 = 0.98, n = 142). This implies that one and the same beam model is valid for the different bone types investigated. The calculation of stiffness from resonant frequencies, however, requires total bone mass, m, and length to be known. In view of in vivo applications, the feasibility of using total bone mineral content (TBMC) as a measure for m was investigated. A good linear correlation was found between total bone mass and total bone mineral content. The correlation between torsional stiffness using TBMC data and measured torsional stiffness was still highly satisfying. Finally, a good linear correlation was observed between the properties of left and right bone from a single specimen. These results demonstrate a simple relation between resonant frequencies and bone mechanical properties in vitro. Under the condition that in vivo effects (muscles, skin, joints, etc.) on the vibrational behaviour can be accounted for properly, the results are promising as to the feasibility of the resonant frequency technique for fracture healing monitoring and osteoporosis evaluation.