Roth B J, Basser P J, Wikswo J P
Biomedical Engineering and Instrumentation Program, National Center for Research Resources, National Institutes of Health, Bethesda, MD 20892.
IEEE Trans Biomed Eng. 1994 Aug;41(8):723-8. doi: 10.1109/10.310087.
A theoretical model of magneto-acoustic current imaging is derived, based on fundamental equations of continuum mechanics and electromagnetism. In electrically active tissue, the interaction between an applied magnetic field, B, and action currents, J, creates a pressure distribution. In the near field limit, this pressure obeys Poisson's equation, with a source term (delta x J).B. The displacement and pressure fields are calculated for a dipole (q), oriented either parallel or perpendicular to the applied magnetic field (B), at the center of an elastic, conducting sphere (radius a, shear modulus G). Surface displacements are on the order of qB/(4 pi Ga), which is about 1 nm for typical biological parameters. If the applied magnetic field is changing with time, eddy currents induced in the tissue may be larger than the action currents themselves. The frequency of the pressure and displacement arising from these eddy currents, however, is twice the frequency of the applied magnetic field, so it may be possible to eliminate this artifact by filtering or lock-in techniques. Magneto-acoustic and biomagnetic measurements both image delta x J in a similar way, although magneto-acoustic current imaging has the disadvantage that acoustic properties vary among tissues to a greater degree than do magnetic properties.
基于连续介质力学和电磁学的基本方程，推导了磁声电流成像的理论模型。在电活性组织中，外加磁场B与动作电流J之间的相互作用会产生压力分布。在近场极限下，该压力服从泊松方程，其源项为(delta x J).B。对于位于弹性导电球体（半径a，剪切模量G）中心的偶极子（q），计算其平行或垂直于外加磁场（B）方向的位移和压力场。表面位移量级为qB/(4 pi Ga)，对于典型的生物学参数，该值约为1 nm。如果外加磁场随时间变化，组织中感应的涡流可能会大于动作电流本身。然而，由这些涡流产生的压力和位移的频率是外加磁场频率的两倍，因此有可能通过滤波或锁相技术消除这种伪像。磁声测量和生物磁测量都以类似的方式对delta x J进行成像，尽管磁声电流成像的缺点是组织的声学特性比磁特性在不同组织间的变化程度更大。
