Oncolytic viruses (OV) are viruses that can replicate selectively within cancer cells and destroy them. While the past few decades have seen significant progress re- lated to the use of these viruses in clinical contexts, the degree of success of viral oncolytic therapies is currently dampened by the relatively low level of understand- ing of the complex spatio-temporal tumour-OV dynamic interactions, whose main characteristics are yet to be deciphered. In this work, we present a novel multiscale moving boundary modelling for the tumour-OV interactions, which is based on cou- pled systems of partial differential equations both at macro-scale (tissue-scale) and at micro-scale (cell-scale) that are connected through a double feedback link. At the macro-scale, we account for the coupled dynamics of uninfected cancer cells, OV-infected cancer cells, extracellular matrix (ECM) and oncolytic viruses. At the same time, at the micro scale, we focus on essential dynamics of urokinase plasminogen activator (uPA) system which is one of the important proteolytic systems responsible for the degradation of the ECM, with notable influence in cancer invasion. While sourced by the cancer cells that arrive during their macro-dynamics within the outer proliferating rim of the tumour, the uPA micro-dynamics is crucial in determining the movement of the macro-scale tumour boundary (both in terms of direction and displacement magnitude). In this investigation, we consider several scenarios for the macro-scale tumour-OV interactions. While assuming the usual modelling context of reaction-diffusion- taxis coupled PDEs, these scenarios gradually explore the influence of the ECM taxis over the tumour - OV interaction, in the form of haptotaxis of both uninfected and infected cells populations as well as the indirect ECM taxis for the oncolytic virus. The complex tumour-OV interactions are also investigated numerically through the development a new multiscale moving boundary computational framework. Furthermore, as there is increasing biological evidence that a sub-class of viruses that contain fusion proteins (triggering the formation of syncytia) can lead to better on- colytic results, we continue our investigation by exploring several scenarios for the complex dynamics of syncytia formation in the presence of tumour - fusogenic virus interactions. Since the details of the tumour dynamics following syncytia formation are not fully understood, we consider a modelling and computational approach to describe the effect of a fusogenic oncolytic virus within the multiscale dynamics of a spreading tumour. For the parameter regimes that we considered, the numerical investigation shows that a tumour reduction can be obtained in terms of choosing different viral burst rates and death rates for individually-infected tumour cells in a comparison with syncytia structures. Furthermore, we investigate the impact that the type of syncytia diffussive transport (i.e., with either constant or density dependent coefficient) has upon the outcome of the oncolytic viral therapy. Finally, we study the local existence and uniqueness of solutions by using Banach fixed point theorem for several macroscopic and microscopic models. To achieve this, we take advantage of essential mathematical concepts involving the theory of semigroups, the sectorial operator, the lipschitzianity properties, space embeddings for Holder continuous functions, the triangle inequality, the continuity of the norm, and the property of the Lebesgue Integral and Bochner Integral.
|Date of Award||2020|
|Sponsors||Saudi Arabian Cultural Bureau & Umm Al-Qura University|
|Supervisor||Dumitru Trucu (Supervisor) & Ping Lin (Supervisor)|