Tumor Hypoxia Heterogeneity Affects Radiotherapy: Inverse-Percolation Shell-Model Monte Carlo Simulations

Abstract

Tumor hypoxia was discovered a century ago, and the interference of hypoxia with all radiotherapies is well known. Here, we demonstrate the potentially extreme effects of hypoxia heterogeneity on radiotherapy and combination radiochemotherapy. We observe that there is a decrease in hypoxia from tumor periphery to tumor center, due to oxygen diffusion, resulting in a gradient of radiative cell-kill probability, mathematically expressed as a probability gradient of occupied space removal. The radiotherapy-induced break-up of the tumor/TME network is modeled by the physics model of inverse percolation in a shell-like medium, using Monte Carlo simulations. The different shells now have different probabilities of space removal, spanning from higher probability in the periphery to lower probability in the center of the tumor. Mathematical results regarding the variability of the critical percolation concentration show an increase in the critical threshold with the applied increase in the probability of space removal. Such an observation will have an important medical implication: a much larger than expected radiation dose is needed for a tumor breakup enabling successful follow-up chemotherapy. Information on the TME’s hypoxia heterogeneity, as shown here with the numerical percolation model, may enable personalized precision radiation oncology therapy.

Tumor Biochemical Heterogeneity and Cancer Radiochemotherapy: Network Breakdown Zone-Model

“…This paper extends our previous work [ 1 ] that correlated a tumor’s lattice heterogeneities with its radiochemotherapy efficacy, extending it now from an idealized lattice model to a more realistic network model, using a new mathematical approach. It also arrives at some recommendations towards optimized treatment protocols.…”

“…Qualitatively, the results of these network models resemble those of the lattice model [ 1 ]: A drop in the node removal (cancer kill) probability between the tumor’s external and internal zones decelerates the network’s breakdown. Quantitatively, at about 95% site (cell) destruction, we here get an order of magnitude increase in the size of the surviving network (see Results section).…”

“…When nodes are picked from the outer zone, they are always removed with probability . When they are picked from the inner zone, they are removed with a probability equal to where r is defined the same way as in [ 1 ]. It is the rate of the reduction of removal probability between the two zones in both models.…”

“…We thus apply an originally random distribution of tumor cells, with a zone-to-zone density gradient of kill probability. As a first step towards illustrating this approach, we used earlier a simple two-dimensional “onion-like” shelled lattice model [ 1 ]. We showed in that work that the “critical concentration”, for the live tumor cell network break-up, does depend strongly on the ratio of removal probabilities in the different zones.…”

Percolation in two-species antagonistic random sequential adsorption in two dimensions

“…Percolation theory itself has a broad range of applications, not only in physics and mathematics, but in materials science, ecology, biology, social sciences, and others [6][7][8]. Recent applications include vaccine allocation for achieving herd immunity [9] and radiation oncology [10].…”