Mathematical modelling of nanoparticle transport through tumours for application in radiotherapy

放射治疗是使用高能X射线杀死肿瘤中的癌细胞。电离辐射通过靶向DNA（导致链断裂和没有进一步的细胞复制）和通过产生高反应性颗粒（自由基）来引起细胞损伤。由辐射与氧的相互作用产生的自由基将对附近的细胞膜造成结构损伤，导致细胞凋亡（Kwatra等人，2013年）。辐射主要损害活跃分裂的细胞，不成比例地影响癌细胞，因为它们经常分裂。然而，放射线会影响健康细胞，因此治疗是在破坏癌细胞的同时最大限度地减少对健康细胞的损害之间取得平衡（The Science behind Cancer，2014）。因此，提高放射治疗的效率和靶向是一个非常感兴趣的领域。一个特别的途径是通过使用放射增敏剂，惰性剂，增强放射治疗的效果。Xerion Healthcare开发了一种氧化钛纳米颗粒，能够增强肿瘤内自由基的生成，从而提高放射治疗的有效性并改善治疗效果。该颗粒由添加了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气分解产生自由基。在氧合不良、缺氧的肿瘤区域中利用颗粒是特别感兴趣的，因为缺氧细胞目前对辐射的抗性是氧合良好细胞的3倍（Rockwell等人，2009年）。使用异种移植物小鼠模型，已经显示当与放射疗法结合使用时，与没有颗粒的放射疗法相比，颗粒减少肿瘤再生长超过三倍（韦克菲尔德等人，2018).所选择的递送方法是直接瘤内注射;这具有优于传统输注方法的优点，包括降低的全身毒性、改善的清除率和更高的肿瘤摄取（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，只是它将是异质的（Su等人，2010年）。这在小鼠模型中问题较小，因为它们的尺寸较小，但当按比例放大到人类肿瘤的尺寸时可能会引起问题。纳米颗粒运输的数学建模结合实体肿瘤内流体流动的计算建模可以帮助克服这个问题。先前已经有大量研究对治疗剂递送到肿瘤中进行建模（Koumoutasakos等人，2013; Zhan等人，2014），尽管其中大部分集中在大分子试剂的递送上。大分子药剂的递送模型由于其小尺寸而不适用于纳米颗粒，因为可能发生与细胞表面的强烈相互作用，导致颗粒沉积。以前的研究比较了直接注射后纳米颗粒分布的模拟和实验结果，在考虑颗粒-表面相互作用时显示出良好的一致性，而在不考虑颗粒-表面相互作用时则显示出很大的差异（Su，2010）。这将通过与Xerion提供的体内异种移植物数据进行比较进行验证。经验证的模型将用于评估各种注射因素（注射速率、注射位置、纳米颗粒浓度）对纳米颗粒瘤内分布的影响。找到最佳的注射参数将使Xerion能够进入药物开发的下一阶段，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.