Abstract Magnetic susceptibility of structurally intact bone may play a role in low frequency (below 10 kHz), low field (below 10 mT amplitude) pulsed electromagnetic field (LF PEMF) treatment of fracture non-unions and an adjunct to cervical fusion surgery, approved by the U.S Food and Drug Administration (FDA). The aim of this study was to determine if a difference in PEMF treatment results in measurable differences in the bone magnetic susceptibility using a model of structurally intact rat vertebrae. We measured bone volume magnetic susceptibility by a custom built mechanical resonator comprising a diametrically-polarized NdFeB permanent dipole magnet cylinder (25.4×25.4 mm, height by diameter) rotated about its axis by a stepper motor at even intervals from 53 to 63 RPM, acting as a source of a local, oscillating magnetic field (mean field of 95 mT, gradient of 12 T/m) on an intact laboratory rat lumbar vertebrae (n=21, from tissue repository from past studies on LF PEMF treatment in vivo) suspended 26.0 mm from magnet axis on a thin line of 80 mm nominal length forming a pendulum of nominal eigenfrequency of 100 Hz. The vertebra motion was captured by a video camera and the geometrical center of its 2D image motion was analyzed by ImagePro® and MATLAB® routines. The amplitude of bone oscillations (at twice the angular frequency of the rotating magnet) showed a characteristic pattern of resonance with the magnet rotational frequency. The amplitude maximum agreed with that calculated from a model of forced, damped harmonic oscillator and the diamagnetic tension force acting on bone. The calculated mean volume magnetic susceptibility (SI) of -was on the order of magnitude of literature value (|χ|≈10-5) . The results point to the bone site-specific aspect of LF PEMF therapy and provide experimental and theoretical basis for a novel, rational method of designing next generation of effective LF PEMF therapies.

中文翻译：

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测量结构完整骨磁化率的机械谐振器

摘要 结构完整骨的磁化率可能在低频（低于 10 kHz）、低场（低于 10 mT 振幅）脉冲电磁场​​ (LF PEMF) 治疗骨折不愈合和颈椎融合手术的辅助手段中发挥作用，已获批准由美国食品和药物管理局 (FDA) 批准。本研究的目的是使用结构完整的大鼠椎骨模型确定 PEMF 治疗的差异是否会导致骨磁化率的可测量差异。我们通过定制的机械谐振器测量骨体积磁化率，该谐振器包括一个径向极化的 NdFeB 永磁偶极磁体圆柱体（25.4 × 25.4 毫米，直径高度），由步进电机以 53 到 63 RPM 的均匀间隔绕其轴旋转，作用作为当地的一个来源，完整的实验室大鼠腰椎（n = 21，来自过去对体内 LF PEMF 治疗的研究的组织库）上的振荡磁场（平均磁场为 95 mT，梯度为 12 T/m）悬浮在磁轴上 26.0 mm 处80 mm 标称长度的细线，形成标称特征频率为 100 Hz 的钟摆。椎骨运动由摄像机捕获，其 2D 图像运动的几何中心由 ImagePro® 和 MATLAB® 例程分析。骨振荡的幅度（旋转磁体角频率的两倍）显示出与磁体旋转频率共振的特征模式。振幅最大值与根据受迫阻尼谐振子模型和作用在骨骼上的抗磁张力计算的结果一致。计算出的平均体积磁化率 (SI) 处于文献值的数量级 (|χ|≈10-5)。结果指向LF PEMF疗法的骨部位特异性方面，并为设计下一代有效LF PEMF疗法的新颖、合理的方法提供实验和理论基础。