Mathematical modelling of nanoparticle transport through tumours for application in radiotherapy

放射治疗是利用高能X射线杀死肿瘤中的癌细胞。电离辐射通过靶向DNA，导致链断裂和不再进一步的细胞复制，以及通过产生高活性粒子--自由基，来造成细胞损伤。辐射与氧气相互作用产生的自由基将对附近细胞膜造成结构性损害，导致细胞凋亡(Kwatra等人，2013年)。辐射主要损害正在活跃分裂的细胞，对癌细胞的影响不成比例，因为它们经常分裂。然而，辐射会影响健康细胞，因此治疗是在摧毁癌细胞和将对健康细胞的损害降至最低之间取得平衡(癌症背后的科学，2014)。因此，提高放射治疗的效率和靶向性是一个非常感兴趣的领域。一种特别的途径是通过使用放射增敏剂，即增强放射治疗效果的惰性试剂。Xarion Healthcare开发了一种纳米氧化钛颗粒，能够增强肿瘤内自由基的产生，从而提高放射治疗的有效性和改善治疗结果。颗粒由掺有稀土金属的氧化钛组成，X射线与颗粒的相互作用导致水和氧的裂解产生自由基。利用低氧、低氧、特别感兴趣的肿瘤区域中的颗粒，因为低氧细胞目前对辐射的抵抗力是高氧细胞的3倍(Rockwell等人，2009年)。使用异种移植小鼠模型的研究表明，与不使用颗粒的放疗联合使用时，这些颗粒可以将肿瘤的再生长减少三倍以上(Wakefield等人，2018年)。选择的给药方法是直接瘤内注射；这比传统的输注方法有优势，包括减少系统毒性、改善清除和更高的肿瘤摄取率(Hainfeld等人，2019年)。然而，注射后纳米颗粒在肿瘤内的确切分布仍然不清楚，只知道它将是异质的(Su等人，2010年)。这在小鼠模型中问题不大，因为它们的尺寸很小，但当放大到人类肿瘤的大小时可能会引起问题。纳米颗粒传输的数学模型与固体肿瘤内流体流动的计算模型相结合可以帮助克服这一问题。以前已经有大量研究对治疗药物进入肿瘤的输送进行建模(Koumoutasakos等人，2013年；詹等人，2014年)，尽管这些研究主要集中在大分子药物的输送上。大分子制剂的输送模型不适用于纳米颗粒，因为它们与细胞表面会发生强烈的相互作用，导致颗粒沉积。以前对直接注射后纳米颗粒分布的模拟结果与实验结果进行比较的研究表明，在考虑颗粒-表面相互作用和不考虑颗粒-表面相互作用时存在较大差异时，两者具有很好的一致性(SU，2010)。该项目将开发一个多尺度模型来跟踪纳米颗粒在肿瘤中的分布。这将通过与Xarion提供的体内异种移植数据进行比较来验证。经过验证的模型将用于评估各种注射因素(注射速度、注射位置、纳米颗粒浓度)对纳米颗粒在肿瘤内分布的影响。找到最优的注射参数集将使Xarion能够进入药物开发的下一个阶段，即临床试验。

Radiation therapy is the use of high energy X-rays to kill cancer cells in a tumour. The ionizing radiation causes cellular damage both by targeting DNA, causing strand breaks and no further cell replication, and by the generation of highly reactive particles, free radicals. Free radicals generated from the radiation's interaction with oxygen will cause structural damage to nearby cell's membranes resulting in apoptosis (Kwatra et al., 2013). Radiation mainly damages cells that are actively dividing, disproportionately affecting cancer cells as they divide frequently. However, the radiation will affect healthy cells and so treatment is a balance between destroying the cancer cells while minimising damage to healthy cells (The Science behind Cancer, 2014).As such, improving the efficiency and targeting of radiation therapy is an area of keen interest. One particular avenue is through the use of radiosensitizers, inert agents that enhance the effects of radiotherapy. Xerion Healthcare has developed a titanium oxide nanoparticle capable of enhancing the generation of free radicals within the tumour thereby increasing radiotherapy's effectiveness and improving treatment outcomes. The particles consist of titanium oxide dosed with rare earth metals, X-ray interaction with the particles leads to the generation of free radicals by the splitting of water as well as oxygen. Making use of the particles in poorly oxygenated, hypoxic, tumour regions of particular interest, as hypoxic cells are currently 3 times more resistant to radiation than well oxygenated cells (Rockwell et al., 2009). The particles have been shown, using xenograft mouse models, to reduce tumour regrowth by more than three times when used in conjunction with radiotherapy versus radiotherapy without the particles (Wakefield et al., 2018).The delivery method chosen is direct intratumoral injection; this has advantages over traditional infusion methods, including reduced systemic toxicity, improved clearance and higher tumour uptake (Hainfeld et al., 2019). However, the exact distribution of nanoparticles within the tumour post-injection remains unclear, only that it will be heterogeneous (Su et al., 2010). This is less of a problem in murine models due to their small size but can cause issues when scaling up to the size of a human tumour.Mathematical modelling of nanoparticle transport combined with computational modelling of fluid flow within a solid tumour can help to overcome this problem. There has been significant previous research into modelling the delivery of therapeutic agents into tumours (Koumoutasakos et al., 2013; Zhan et al., 2014) although much of this focuses on the delivery of macromolecular agents. Delivery models of macromolecular agents are not applicable to nanoparticles due to their small size, as strong interactions with cell's surface can occur resulting in particle deposition. Previous studies comparing simulation and experimental results of nanoparticle distribution after direct injection showed good agreement when accounting for particle-surface interactions and large discrepancies when not (Su, 2010).This project will develop a multi-scale model to track nanoparticle distribution within a tumour. This will be validated through comparison with in vivo xenograft data provided by Xerion. The validated model will be used to assess the effect of various injection factors (injection rate, location of injection, nanoparticle concentration) on the intratumoral distribution of nanoparticles. Finding the optimal set of injection parameters will enable Xerion to progress to the next stage of drug development, clinical trials.