A phenotype-structured mathematical model for the influence of hypoxia on oncolytic virotherapy

TL;DR

This work addresses how tumour hypoxia influences oncolytic virotherapy by developing a phenotype-structured, spatially resolved PDE-PIDE model that couples tumour epigenetic heterogeneity with a diffusing virus and oxygen field. The framework tracks uninfected cells with a trait $y\in[0,1]$, infection via $\beta(y)$, growth $P(y,\rho)$, and oxygen-driven selective pressure $S(y,O)$, enabling analysis of both standard and hypoxia-targeting viruses under stationary and dynamic oxygen. A formal asymptotic analysis yields equilibrium relations in the spatially homogeneous case, complemented by extensive numerical simulations that reveal hypoxia dampens standard-virus efficacy but enhances hypoxia-targeting viruses in low-oxygen regions, guiding personalized virus selection. Overall, the study highlights the pivotal role of spatial oxygen distributions and tumor evolution in virotherapy outcomes and motivates adaptive, environment-aware treatment strategies that may combine different virus types or therapies to overcome resistance.

Abstract

The effectiveness of oncolytic virotherapy is significantly affected by several elements of the tumour microenvironment, which reduce the ability of the virus to infect cancer cells. In this work, we focus on the influence of hypoxia on this therapy and develop a novel continuous mathematical model that considers both the spatial and epigenetic heterogeneity of the tumour. We investigate how oxygen gradients within tumours affect the spatial distribution and replication of both the tumour and oncolytic viruses, focusing on regions of severe hypoxia versus normoxic areas. Additionally, we analyse the evolutionary dynamics of tumour cells under hypoxic conditions and their influence on susceptibility to viral infection. Our findings show that the reduced metabolic activity of hypoxic cells may significantly impact the virotherapy effectiveness; the knowledge of the tumour's oxygenation could, therefore, suggest the most suitable type of virus to optimise the outcome. The combination of numerical simulations and theoretical results for the model equilibrium values allows us to elucidate the complex interplay between viruses, tumour evolution and oxygen dynamics, ultimately contributing to developing more effective and personalised cancer treatments.

Figures (11)

• Figure 1: Graphical representation of trade-offs involving proliferation rate (row 1), hypoxia-resistance features (row 2) and infectivity potential rate (row 3) in the case of standard (left) and hypoxia-specific (right) viruses. The correspondence with the values assumed by epigenetic variable $y\in [0,1]$ are indicated. These represent the cell potentiality, which effective effect on the cell phenotype is determined according to the environmental condition and the evolutionary scenarios.
• Figure 2: Numerical solution of Eq. \ref{['eq:equilibria_hyp']} showing the equilibria in different oxygen conditions. The parameters in panel (a) take the values listed in Table \ref{['tab:parameters']}. In panel (b), the values of $\beta_M$ and $\beta_m$ are switched to reproduce the situation of oncolytic viruses that specifically target hypoxic cells. In both cases, $\varphi(O^\infty)$ ranges between $0$ and $1$.
• Figure 3: Results of the numerical simulation without viral infection for stationary oxygenation, for three spatially homogeneous oxygen condition: $O=O_M$ (solid lines), $O=\frac{O_M+O_m}{2}$ (dashed lines), and $O=O_m$ (dot-dashed lines). We plot the solutions at time $t^*=1500\;$h. Only the horizontal section is shown to facilitate the comparison. The blue lines in the left plot represent the profile of uninfected cancer cells $U(t^*,\boldsymbol{x})$. In the right plot, the green lines show the average epigenetic trait $\mu(t^*,\boldsymbol{x})$ and the light-blue lines show the fittest trait selected by the environment $\varphi(O(t^*,\boldsymbol{x}))$.
• Figure 4: Results of the numerical simulations for stationary oxygen under physiological hypoxia, at times $t=500\;$h (panel (a)), $t=1500\;$h (panel (b)), and $t=2500\;$h (panel (c)). First column shows $U(t^*,\boldsymbol{x})$ in blue, $I(t^*,\boldsymbol{x})$ in red, and $\rho(t^*,\boldsymbol{x})$ in purple. The dotted lines show the theoretical approximation of asymptotic equilibria (using correspondent colours), obtained by solving Eq. \ref{['eq:equilibria_hyp']}. The second column provides the average epigenetic trait $\mu(t^*,\boldsymbol{x})$ in green and $\varphi(O(t^*,\boldsymbol{x}))$ in light blue. Vertical grey lines indicate the position of a wave-front moving with speed $\sqrt{D_{\boldsymbol{x}}Kp(\varphi(O))/2}$ (with $\varphi(O)$ equal respectively to $0$, $0.5$ and $1$).
• Figure 5: Results of the numerical simulations for stationary oxygen at time $t^*$, corresponding to approximately $1800\;$h after viral injection, for three spatially homogeneous oxygen conditions: $O=O_M$ (solid lines, panel (a)), $O=\frac{O_M+O_m}{2}$ (dashed lines, panel (b)), and $O=O_m$ (dot-dashed lines, panel (c)). All the graphical elements have the same meaning as in Fig. \ref{['fig:time_evolution']}. Only the horizontal section is shown to facilitate the comparison. Note that $\bar{y}(t^*,\boldsymbol{x})=1$ in panel (c) (i.e., the maximum value is on the boundary of $Y$).