Vibration exercise for treatment of osteoporosis: a theoretical model
Vibration exercise for treatment of osteoporosis: a theoretical model
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DOI：
10.1243/09544119jeim439
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发表时间：
2008-10-01
期刊：
影响因子：
1.8
通讯作者：
Harrigan, J. J.
中科院分区：
文献类型：
--
作者：
Aleyaasin, M.;Harrigan, J. J.
运用Wolff的应变性骨重塑理论，从理论上探讨了肌肉振动训练对骨质疏松症的矫形康复作用。有限振幅振动通过肌肉传递到骨骼的重构方程对应于一个缓慢时变的非线性动力学系统。该缓慢时变系统由具有随所施加振动的频率振荡的快速变化系数的Riccatti方程支配。平均技术用于确定传递到骨骼的有效力。该力用连接肌肉的刚度和阻尼参数表示。分析结果预测，为了获得骨加固，振动的频率和振幅不应超过规定的水平。此外，低频振动不会充分刺激骨骼以引起显著的重塑。本文的理论模型证实了振动锻炼及其对康复的影响的临床建议。在数值示例中，该模型预测，由于卧床休息而导致骨量减少的股骨将通过振动而完全愈合，该振动包括在250天的时间段内以30 Hz的频率施加的2g的加速度。
Orthopaedic rehabilitation of osteoporosis by muscle vibration exercise is investigated theoretically using Wolff's theory of strain-induced bone 'remodelling'. The remodelling equation for finite amplitude vibration to be transmitted to the bone via muscle corresponds to a slowly time-varying non-linear dynamic system. This slowly time-varying system is governed by a Riccatti equation with rapidly varying coefficients that oscillate with the frequency of the applied vibration. An averaging technique is used to determine the effective force transmitted to the bone. This force is expressed in terms of the stiffness and damping parameters of the connected muscle. The analytical result predicts that, in order to obtain bone reinforcement, the frequency and amplitude of vibration should not exceed specified levels. Furthermore, low-frequency vibration does not stimulate the bone sufficiently to cause significant remodelling. The theoretical model herein confirms the clinical recommendations regarding vibration exercise and its effects on rehabilitation. In a numerical example, the model predicts that a femur with reduced bone mass as a result of bed rest will be healed completely by vibration consisting of an acceleration of 2g applied at a frequency of 30 Hz over a period of 250 days.