Magnetomotive ultrasound imaging is the identification of tissue in which magnetic nanoparticle tracers are present by detecting a magnetically induced motion. Although the nanoparticles have a magnetization that depends nonlinearly on the external magnetic field, this has often been neglected and the presence of resulting higher harmonics in the detected motion has not been reported yet. Here, the magnetization of nanoparticles in gelatin was modeled according to the Langevin-theory of superparamagnetism. This nonlinear relationship has a fundamental effect on the resulting force and motion. However, the magnetic field must contain regions with a strong magnetic gradient and a low absolute magnetic field to allow the significant generation of higher harmonics in the force. To validate the model, a magnetomotive setup that has a constant magnetic gradient on one axis superimposed by a homogeneous time-varying magnetic field was used. After magnetic characterization of the nanoparticles and calculations of the expected displacement in the setup, experiments were conducted. A laser Doppler vibrometer was used to quantify the small displacements at higher harmonics. The experimental results followed theoretical predictions. Deviations between model and experiment were attributed to a simplified mechanical modeling and temperature rise during measurements. It is concluded that in magnetomotive techniques the nonlinear magnetization of nanoparticles must generally be considered to reconstruct quantitative parameters, to achieve optimum matching of fields and particles, or to exploit nanoparticle magnetization for tissue characterization. Additionally, with the presented experimental setup, the magnetization properties of nanoparticles can be determined by magnetomotive techniques alone.

中文翻译：

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磁动技术中纳米粒子非线性力的建模和测量。

磁动力超声成像是通过检测磁感应运动来识别存在磁性纳米粒子示踪剂的组织。尽管纳米颗粒的磁化强度非线性地依赖于外部磁场，但通常被忽略，并且尚未报道在检测到的运动中会产生更高的谐波。在这里，明胶中纳米颗粒的磁化是根据超顺磁性的Langevin理论建模的。这种非线性关系对所产生的力和运动产生根本影响。但是，磁场必须包含具有强磁梯度和低绝对磁场的区域，以允许在力中大量产生高次谐波。为了验证模型，使用磁通势装置，其在一个轴上具有恒定的磁梯度，并由均匀的时变磁场叠加。在对纳米颗粒进行磁性表征并计算设置中的预期位移后，进行了实验。激光多普勒振动计用于量化高次谐波下的小位移。实验结果遵循理论预测。模型和实验之间的差异归因于简化的机械建模和测量过程中的温度上升。结论是，在磁动力技术中，通常必须考虑纳米粒子的非线性磁化以重建定量参数，实现场和粒子的最佳匹配或利用纳米粒子磁化来进行组织表征。