Table 3 Example studies applying mathematical modeling to study the effectiveness of temporal and spatial fractionations of radiotherapy
From: Mathematical modeling in radiotherapy for cancer: a comprehensive narrative review
Authors | Radiotherapy type | Mathematical model used | Method and scale | Key findings |
|---|---|---|---|---|
Remigio et al. [96] | Fractionated radiotherapy | LQ model | ODE, temporal | Fractionated radiotherapy results in the tumor cell population being predominantly in the G1 cell cycle, reducing resistant cells in the S phase. This may reduce cancer relapses |
Haldar et al. [97] | Dose fractionation regimen | Mathematical fitting between organ at risk (OAR) and prescription dose | Regression | Evaluated OAR dosing to adopt a new fractionation regimen |
Taylor et al. [98] | Hypofractionation | Iso-survival BED | Stochastic ODE, temporal | Hypofractionation results in more efficient cell killing than previously estimated, ensuring tumor control |
Krieger et al. [99] | Hypofractionated/single field flash | Phenomenological model and BED | ODE, temporal | Found that hypofractionated single field transmission plans provided the most clinical benefit |
Böhlen et al. [100] | Flash/hypofractionation | LQ and LQL models | LQ | Quantified the minimal normal tissue sparing required by FLASH to compensate for hypofractionation |
Kuznetsov et al. [101] | Hyperfractionated radiotherapy | Antitumor effect model | PDE, spatial–temporal | Found significant treatment efficacy gains for low-malignancy tumors using protracted hyperfractionated protocols |
Moore et al. [102] | Personalized, ultra-fractionated stereotactic adaptive radiotherapy (PULSAR) | Statistical analysis on preclinical experiments | Experimental | Spaced radiation treatments 10 + days apart and combined with immune checkpoint blockade to exploit the synergistic effect |
Cahoon et al. [103] | Spatially fractionated radiotherapy (SFRT) | Probabilistic Monte Carlo model, NTCP (LKB) model, and EUD model | PDE, spatial–temporal | Analyzed survival of cells and bystander effect in SFRT |
Cho et al. [104] | SFRT | Radio-immune response model and boundary behavior | ODE, temporal | Demonstrated that heterogeneous dose distribution in SFRT can drastically improve tumor cell killing compared to homogeneous dose distribution |