Mathematical modelling of nanoparticle transport through tumours for application in radiotherapy

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.