Department of Biomedical Engineering, Kyung Hee University, Yongin-si, Gyeonggi-do, Republic of Korea.
Biomed Eng Online. 2012 Mar 7;11:11. doi: 10.1186/1475-925X-11-11.
Magnetic nanoparticles are gaining great roles in biomedical applications as targeted drug delivery agents or targeted imaging contrast agents. In the magnetic nanoparticle applications, quantification of the nanoparticle density deposited in a specified region is of great importance for evaluating the delivery of the drugs or the contrast agents to the targeted tissues. We introduce a method for estimating the nanoparticle density from the displacement of tissues caused by the external magnetic field.
We can exert magnetic force to the magnetic nanoparticles residing in a living subject by applying magnetic gradient field to them. The nanoparticles under the external magnetic field then exert force to the nearby tissues causing displacement of the tissues. The displacement field induced by the nanoparticles under the external magnetic field is governed by the Navier's equation. We use an approximation method to get the inverse solution of the Navier's equation which represents the magnetic nanoparticle density map when the magnetic nanoparticles are mechanically coupled with the surrounding tissues. To produce the external magnetic field inside a living subject, we propose a coil configuration, the Helmholtz and Maxwell coil pair, that is capable of generating uniform magnetic gradient field. We have estimated the coil currents that can induce measurable displacement in soft tissues through finite element method (FEM) analysis.
From the displacement data obtained from FEM analysis of a soft-tissue-mimicking phantom, we have calculated nanoparticle density maps. We obtained the magnetic nanoparticle density maps by approximating the Navier's equation to the Laplacian of the displacement field. The calculated density maps match well to the original density maps, but with some halo artifacts around the high density area. To induce measurable displacement in the living tissues with the proposed coil configuration, we need to apply the coil currents as big as 104A.
We can obtain magnetic nanoparticle maps from the magnetically induced displacement data by approximating the Navier's equation under the assumption of uniform-gradient of the external magnetic field. However, developing a coil driving system with the capacity of up to 104A should be a great technical challenge.
磁性纳米粒子在生物医学应用中扮演着重要的角色，可作为靶向药物输送剂或靶向成像对比剂。在磁性纳米粒子的应用中，定量评估沉积在特定区域的纳米粒子密度对于评估药物或对比剂输送到靶向组织的情况非常重要。我们提出了一种从外部磁场引起的组织位移来估计纳米粒子密度的方法。
我们可以通过对处于活体中的磁性纳米粒子施加磁场梯度来对其施加磁力。在外部磁场下的纳米粒子会对附近的组织施加力，导致组织位移。外部磁场下的纳米粒子引起的位移场由纳维方程控制。我们使用近似方法来获得纳维方程的逆解，该解代表当磁性纳米粒子与周围组织机械耦合时的磁性纳米粒子密度图。为了在活体内部产生外部磁场，我们提出了一种线圈结构，即亥姆霍兹和麦克斯韦线圈对，它能够产生均匀的磁场梯度。我们通过有限元方法（FEM）分析来估计能够在软组织中引起可测量位移的线圈电流。
我们通过对软组织模拟体的 FEM 分析获得的位移数据，计算出了纳米粒子密度图。我们通过将纳维方程近似为位移场的拉普拉斯来获得纳米粒子密度图。计算出的密度图与原始密度图匹配良好，但在高密度区域周围存在一些晕影伪影。为了用所提出的线圈结构在活体组织中引起可测量的位移，我们需要施加高达 104A 的线圈电流。
我们可以通过在外磁场梯度均匀的假设下近似纳维方程，从磁诱导位移数据中获得磁性纳米粒子图。然而，开发具有高达 104A 容量的线圈驱动系统将是一个巨大的技术挑战。
