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Inclusion of interactions in mathematical modelling of implant assisted magnetic drug targeting

机译：将相互作用包括在植入物辅助磁性药物靶向的数学模型中

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摘要

Drug delivery technologies are an important area within biomedicine. Targeted drug delivery aims to reduce the undesired side effects of drug usage by directing or capturing the active agents near a desired site within the body. This is particularly beneficial in, for instance, cancer chemotherapy, where the side effects of general (systemic) drug administration can be severe. One approach to targeted drug delivery uses magnetic nanoparticles as the constituents of carriers for the desired active agent. Once injected into the body, the behaviour of these magnetic carriers can be influenced and controlled by magnetic fields. In implant assisted magnetic drug targeting systems a magnetic implant, typically a stent, wire or spherical seed can be used to target sites deep within the body as the implant acts as a focus for the resulting magnetic force. This can be easily understood as the force depends on the gradient of the magnetic field and the gradient near the implant is large. In designing such a system many factors need to be considered including physical factors such as the size and nature of the implants and carriers, and the fields required. Moreover, the range of applicability of these systems in terms of the regions of the vasculature system, from low blood velocity environments, such as capillary beds to higher velocity arteries, must be considered. Furthermore, assessment criteria for these systems are needed. Mathematical modelling and simulation has a valuable role to play in informing in vitro and in vivo experiments, leading to practical system design. Specifically, the implant assisted magnetic drug targeting systems of Aviles, Ebner and Ritter are considered within this review, and two dimensional mathematical modelling is performed using the open source C++ finite volume library OpenFOAM. In the first system treated, a large ferromagnetic particle is implanted into a capillary bed as a seed to aid collection of single domain nanoparticles (radius 20-100 nm). The Langevin function is used to calculate the magnetic moment of the particles, and the model is further adapted to treat the agglomeration of particles known to occur in these systems. This agglomeration can be attributed to interparticle interactions and here the magnetic dipole-dipole and hydrodynamic interactions for two mutually interacting nanoparticles are modelled, following Mikkelsen et al. who treated two particle interactions in microfluidic systems, with low magnetic field (0.05 T). The resulting predicted performance is found to both increase and decrease significantly depending on initial positions of the particles. Secondly, a ferromagnetic, coiled wire stent is implanted in a large arterial vessel. The magnetic dipole-dipole and hydrodynamic interactions for multiple particles are included. Different initial positions are considered and the system performance is assessed. Inclusion of these interactions yields predictions that are in closer agreement with the experimental results of Aviles et al. We conclude that the discrepancies between the non interacting theoretical predictions and the corresponding experimental results can (as suggested by Aviles et al.) be largely attributed to interparticle interactions and the consequent agglomeration.
机译：药物输送技术是生物医学中的重要领域。有针对性的药物输送旨在通过将活性剂引导或捕获到体内所需部位附近来减少药物使用的不良副作用。这在例如癌症化疗中特别有益，在癌症化疗中，一般（全身）给药的副作用可能很严重。靶向药物递送的一种方法使用磁性纳米颗粒作为所需活性剂的载体成分。一旦注入人体，这些磁性载体的行为就会受到磁场的影响和控制。在植入物辅助的磁性药物靶向系统中，磁性植入物（通常是支架，金属丝或球形种子）可用于靶向体内深处的部位，因为植入物可作为产生的磁力的焦点。这很容易理解，因为力取决于磁场的梯度，植入物附近的梯度很大。在设计这样的系统时，需要考虑许多因素，包括物理因素，例如植入物和载体的尺寸和性质以及所需的领域。此外，必须考虑这些系统在脉管系统区域方面的适用范围，从低血流速度的环境（例如毛细血管床）到高速动脉。此外，需要这些系统的评估标准。数学建模和仿真在通知体外和体内实验中起着重要作用，从而导致了实用的系统设计。具体而言，在本次审查中考虑了Aviles，Ebner和Ritter的植入物辅助磁性药物靶向系统，并使用开源C ++有限体积库OpenFOAM执行了二维数学建模。在第一个处理过的系统中，将大的铁磁颗粒作为种子植入毛细管床中，以帮助收集单畴纳米颗粒（半径20-100 nm）。 Langevin函数用于计算粒子的磁矩，并且该模型还适用于处理已知在这些系统中发生的粒子的团聚。这种团聚可以归因于粒子间的相互作用，在这里，按照Mikkelsen等人的方法，对两个相互相互作用的纳米粒子的磁偶极-偶极子和流体动力相互作用进行了建模。他们用低磁场（0.05 T）处理了微流体系统中的两个粒子相互作用。发现所得的预测性能显着增加和降低，这取决于颗粒的初始位置。其次，将铁磁线圈支架植入大型动脉血管中。包括多个粒子的磁偶极-偶极子和流体动力学相互作用。考虑不同的初始位置，并评估系统性能。包括这些相互作用产生的预测与Aviles等人的实验结果更加一致。我们得出的结论是，非相互作用的理论预测与相应的实验结果之间的差异（如Aviles等人所暗示）可以很大程度上归因于粒子间的相互作用以及随之而来的团聚。

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