From Radiation Dose to Cellular Dynamics: A Discrete Model for Simulating Cancer Therapy

TL;DR

This work addresses radiotherapy dose optimization by moving from continuum tissue descriptions to discrete, mechanobiologically coupled cells. It introduces a framework that couples CellSim3D with a Monte Carlo radiation beam and the Linear-Quadratic survival model, where the survival probability is $S(D) = e^{-(\alpha D + \beta D^2)}$ and death probability per cell is $D_n = 1 - S_n(D)$, plus phagocytosis and dual cell types. The study analyzes inter-cellular force distributions and validates the approach against experimental force measurements and PC-3 prostate cancer data, finding strong qualitative agreement and tail-level quantitative matches. This framework enables exploration of fractionated dose, dose inhomogeneities, and tissue radiosensitivity heterogeneity, with future extensions to include cell migration and metastasis.

Abstract

Radiation therapy is one of the most common cancer treatments, and dose optimization and targeting of radiation are crucial since both cancerous and healthy cells are affected. Different mathematical and computational approaches have been developed for this task. The most common mathematical approach, dating back to the late 1970's, is the linear-quadratic (LQ) model for the survival probability given the radiation dose. Most simulation models consider tissue as a continuum rather than consisting of discrete cells. While reasonable for large-scale models (e.g., human organs), continuum approaches necessarily neglect cellular-scale effects, which may play a role in growth, morphology, and metastasis of tumors. Here, we propose a method for modeling the effect of radiation on cells based on the mechanobiological \textsc{CellSim3D} simulation model for growth, division, and proliferation of cells. To model the effect of a radiation beam, we incorporate a Monte Carlo procedure into \textsc{CellSim3D} with the LQ model by introducing a survival probability at each beam delivery. Effective removal of dead cells by phagocytosis was also implemented. Systems with two types of cells were simulated: stiff slowly proliferating healthy cells and soft rapidly proliferating cancer cells. For model verification, the results were compared to prostate cancer (PC-3 cell line) data for different doses and we found good agreement. In addition, we simulated proliferating systems and analyzed the probability density of the contact forces. We determined the state of the system with respect to the jamming transition and found very good agreement with experiments.

Figures (4)

• Figure 1: Distribution of the normalized contact force of dead cells in the packed (red) and open (blue) spatial configurations. The shaded area contains the three curves with three different fractions of dead cells in the final frame of the simulation, being $D_1 \approx 20$%, $D_2 \approx 40$% and $D_3 \approx 60$%, while the solid line is the median of the three. The broken line is an exponential fit using Eq. \ref{['eq:fitExp']} on the tail, whose parameters are summed up in Tab. \ref{['tab:slopes']}.
• Figure 2: Distribution of the normalized contact force of alive cells in the packed (black) and open (golden) spatial configurations without the beam (i.e. $100$% alive cells). The broken lines in the tail and the red and blue shaded area, plotted for reference, follow the same convention of Fig. \ref{['fig:dead']}.
• Figure 3: Percentage of surviving cells in our simulations (dashed lines), labeled with their $\alpha$ and $\beta$ parameters (Table \ref{['tab:abprost']}), and experimental data (solid lines) taken from Kiprianou et al.prost_l1 (orange), Russell et al.prost_l2 (magenta) and Yun et al.prost_l3 (olive green).
• Figure 4: Mass density projected along all three orthogonal planes ($zy$-, $zx$-, and $yx$-planes) both at the beam hit (left panels), and at the end (right panels) of the open-boundary simulation with 60.9% of alive cells at the final step. Blue represents alive cells and red the dead cells. Proliferation tends to push the dead cells into clusters as the system evolves. The units on the axes are expressed in the natural length scale of the model (see Table \ref{['tab:params']}). A qualitatively similar spatial segregation of live and dead populations has been observed experimentally in 3D bioprinted tumor constructs combining cancer cells and cancer-associated fibroblasts, where confocal live/dead staining reveals clustered distributions of nonviable cells within the tissue Baka2023.