Mathematical Modelling of the Spatial Dynamics of Oncolytic Viruses in Cancer Tissue
Creators: Baabdulla, Arwa Abdulla
Publisher: name: University of Alberta Library
Year: 2024

<p>In this thesis, we explore the spatial dynamics of viral infection within tissue through mathematical modelling, aiming to understand the impact of virus spread on both cancerous and healthy tissue. Specifically, we investigate how spatial patterning and heterogeneity influence viral infection levels. Our primary focus is on oncolytic viruses in cancer tissue, where viruses are employed to directly target and eliminate cancer cells while also stimulate the immune system to target virus-infected cells, thereby eradicating cancerous tissue. </p>

<p>In Chapter 2, we employ the Fisher-KPP reaction-diffusion model and the homogenization method to investigate spatial dependencies within virus load data obtained from a checkerboard experiment. Our analysis of the impact of spatial complexity among heterogeneous populations on viral load is based on the application of an innovative cell-printing method introduced by Hesung Now, Ju An Park, Woo-Jong Kim, Sungjune Jung, and Joo-Yeon Yoo. Contrary to a simplistic arithmetic summation of individual cellular activities, our model analysis, confirmed by experimental results, reveals a more intricate relationship in total virus load. Notably, our model not only elucidates observed virus load data but also predicts values not captured in experiments. Furthermore, we employ numerical techniques to examine the spatial distribution of viral load across the periodic domain using our mathematical model. This analysis illustrates how spatial heterogeneity influences cell responses to virus infection, emphasizing the importance of considering spatial arrangement rather than extrapolating measurements solely from isolated cell populations to heterogeneous mixtures of cells.</p>

<p>In Chapters 3 and Chapter  4, we investigate viral spatial oscillation patterns in cancer tissue resulting from a Hopf bifurcation, exploring their clinical relevance and intricate characteristics. Our analysis involves a bifurcation study of a spatially explicit reaction-diffusion model aimed at uncovering spatio-temporal patterns in virus infection. We consider two types of virus-tumor interactions: mass-action (Chapter  3) and Michaelis–Menten kinetics (Chapter 4). The desirable pattern for tumor eradication is the hollow ring pattern, and we identify precise conditions for its occurrence. Furthermore, we determine the minimum speed of traveling invasion waves for both cancer and oncolytic viruses. Our 2-D numerical simulations unveil complex spatial interactions in virus infection, revealing a novel phenomenon characterized by periodic peak splitting in mass-action case.</p>

<p>In Chapter 5, we probe into the oncolytic potential of the reovirus, specifically examining both the wild type T3wt and its mutated variant, SV5. Through in vitro experiments, SV5 demonstrates superior capabilities in spreading within cancer cell cultures, resulting in larger plaque sizes in cell monolayer experiments compared to T3wt. A significant contributing factor to this enhanced performance lies in the reduced binding affinity of SV5 to cells compared to T3wt. To comprehend the interplay between the binding process and virus spread for both variants, we employ a reaction-diffusion model. Our computational results reveal the presence of an optimal binding rate corresponding to an optimal viral invasion wave speed, influencing the overall spread of the virus. This identification provides a rationale for the observed larger plaque size in SV5. Additionally, we investigate the impact of burst size and binding rate on plaque size, revealing the optimal binding rates corresponding to each burst size. This underscores the significance of burst size alongside binding rate, emphasizing that the role of burst size is crucial and cannot be overlooked.  </p>

<p>We close with a conclusion (Chapter 6), where we evaluate our results in the context of current scientific development and hint at ideas for future studies.</p>