Department of Mathematics, Indian Institute of Technology Kharagpur, Kharagpur, West Bengal 721 302, India.
Microvasc Res. 2010 Sep;80(2):209-20. doi: 10.1016/j.mvr.2010.05.002. Epub 2010 May 18.
The present investigation deals with finding the trajectories of the drug dosed magnetic carrier particle in a microvessel with two-phase fluid model which is subjected to the external magnetic field. The radius of the microvessel is divided into the endothelial glycocalyx layer in which the blood is assumed to obey Newtonian character and a core and plug regions where the blood obeys the non-Newtonian Herschel-Bulkley character which is suitable for the microvessel of radius 50 microm. The carrier particles, bound with nanoparticles and drug molecules are injected into the vascular system upstream from malignant tissue, and captured at the tumor site using a local applied magnetic field. The applied magnetic field is produced by a cylindrical magnet positioned outside the body and near the tumor position. The expressions for the fluidic force for the carrier particle traversing in the two-phase fluid in the microvessel and the magnetic force due to the external magnetic field are obtained. Several factors that influence the magnetic targeting of the carrier particles in the microvasculature, such as the size of the carrier particle, the volume fraction of embedded magnetic nanoparticles, and the distance of separation of the magnet from the axis of the microvessel are considered in the present problem. An algorithm is given to solve the system of coupled equations for trajectories of the carrier particle in the invasive case. The trajectories of the carrier particle are found for both invasive and noninvasive targeting systems. A comparison is made between the trajectories in these cases. Also, the present results are compared with the data available for the impermeable microvessel with single-phase fluid flow. Also, a prediction of the capture of therapeutic magnetic nanoparticle in the impermeable microvasculature is made for different radii, distances and volume fractions in both the invasive and noninvasive cases.
本研究旨在寻找在外磁场作用下，载药磁性载体颗粒在具有两相流模型的微管中的轨迹。微管的半径被分为内皮糖萼层，其中血液被假定为服从牛顿特性，以及核心和塞流区域，其中血液服从适用于半径为 50 微米的微管的非牛顿 Herschel-Bulkley 特性。载体颗粒与纳米颗粒和药物分子结合后被注入到恶性组织上游的血管系统中，并使用局部施加的磁场在肿瘤部位捕获。施加的磁场是由位于体外和靠近肿瘤位置的圆柱形磁铁产生的。获得了载体颗粒在微管两相流中穿越的流体力和外部磁场产生的磁力的表达式。本问题考虑了影响载体颗粒在微血管中磁靶向的几个因素，例如载体颗粒的大小、嵌入磁性纳米颗粒的体积分数以及磁铁与微管轴的分离距离。给出了一种用于求解载体颗粒侵入性轨迹的耦合方程组的算法。找到了载体颗粒在侵入性和非侵入性靶向系统中的轨迹。比较了这些情况下的轨迹。此外，将本研究结果与单相流不可渗透微管的可用数据进行了比较。还对侵入性和非侵入性情况下不同半径、距离和体积分数的不可渗透微血管中治疗性磁性纳米颗粒的捕获进行了预测。
