Multi-scale modelling of nanoparticle delivery and heat transport in vascularised tumours.

IF 0.8 4区 数学 Q4 BIOLOGY Mathematical Medicine and Biology-A Journal of the Ima Pub Date : 2022-12-02 DOI:10.1093/imammb/dqac009
Tahani Al Sariri, Raimondo Penta
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引用次数: 3

Abstract

We focus on modelling of cancer hyperthermia driven by the application of the magnetic field to iron oxide nanoparticles. We assume that the particles are interacting with the tumour environment by extravasating from the vessels into the interstitial space. We start from Darcy's and Stokes' problems in the interstitial and fluid vessels compartments. Advection-diffusion of nanoparticles takes place in both compartments (as well as uptake in the tumour interstitium), and a heat source proportional to the concentration of nanoparticles drives heat diffusion and convection in the system. The system under consideration is intrinsically multi-scale. The distance between adjacent vessels (the micro-scale) is much smaller than the average tumour size (the macro-scale). We then apply the asymptotic homogenisation technique to retain the influence of the micro-structure on the tissue scale distribution of heat and particles. We derive a new system of homogenised partial differential equations (PDEs) describing blood transport, delivery of nanoparticles and heat transport. The new model comprises a double Darcy's law, coupled with two double advection-diffusion-reaction systems of PDEs describing fluid, particles and heat transport and mass, drug and heat exchange. The role of the micro-structure is encoded in the coefficients of the model, which are to be computed solving appropriate periodic problems. We show that the heat distribution is impaired by increasing vessels' tortuosity and that regularization of the micro-vessels can produce a significant increase (1-2 degrees) in the maximum temperature. We quantify the impact of modifying the properties of the magnetic field depending on the vessels' tortuosity.

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血管化肿瘤中纳米颗粒传递和热传递的多尺度建模。
我们专注于模拟由氧化铁纳米粒子磁场驱动的癌症热疗。我们假设这些颗粒通过从血管外渗进入间隙与肿瘤环境相互作用。我们从达西和斯托克斯关于间质和液体血管室的问题开始。纳米颗粒的平流扩散发生在两个腔室中(以及肿瘤间质的吸收),与纳米颗粒浓度成正比的热源驱动系统中的热扩散和对流。所考虑的系统本质上是多尺度的。邻近血管之间的距离(微观尺度)远小于肿瘤的平均大小(宏观尺度)。然后,我们应用渐近均质化技术来保留微观结构对热量和粒子的组织尺度分布的影响。我们推导了一种新的均质偏微分方程(PDEs)系统,描述血液运输、纳米颗粒输送和热运输。新模型包括一个双达西定律,以及描述流体、颗粒和热传递以及质量、药物和热交换的两个PDEs双平流-扩散-反应系统。微观结构的作用被编码在模型的系数中,这些系数是通过求解适当的周期问题来计算的。我们发现,增加血管的弯曲度会损害热分布,微血管的正则化会使最高温度显著升高(1-2度)。我们量化了根据血管弯曲度改变磁场特性的影响。
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来源期刊
CiteScore
2.20
自引率
0.00%
发文量
15
审稿时长
>12 weeks
期刊介绍: Formerly the IMA Journal of Mathematics Applied in Medicine and Biology. Mathematical Medicine and Biology publishes original articles with a significant mathematical content addressing topics in medicine and biology. Papers exploiting modern developments in applied mathematics are particularly welcome. The biomedical relevance of mathematical models should be demonstrated clearly and validation by comparison against experiment is strongly encouraged. The journal welcomes contributions relevant to any area of the life sciences including: -biomechanics- biophysics- cell biology- developmental biology- ecology and the environment- epidemiology- immunology- infectious diseases- neuroscience- pharmacology- physiology- population biology
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