A time-resolved experimental-mathematical model for predicting the response of glioma cells to single-dose radiation therapy

Integr Biol (Camb). 2021 Jul 8;13(7):167-183. doi: 10.1093/intbio/zyab010.


Purpose: To develop and validate a mechanism-based, mathematical model that characterizes 9L and C6 glioma cells' temporal response to single-dose radiation therapy in vitro by explicitly incorporating time-dependent biological interactions with radiation.

Methods: We employed time-resolved microscopy to track the confluence of 9L and C6 glioma cells receiving radiation doses of 0, 2, 4, 6, 8, 10, 12, 14 or 16 Gy. DNA repair kinetics are measured by γH2AX expression via flow cytometry. The microscopy data (814 replicates for 9L, 540 replicates for C6 at various seeding densities receiving doses above) were divided into training (75%) and validation (25%) sets. A mechanistic model was developed, and model parameters were calibrated to the training data. The model was then used to predict the temporal dynamics of the validation set given the known initial confluences and doses. The predictions were compared to the corresponding dynamic microscopy data.

Results: For 9L, we obtained an average (± standard deviation, SD) Pearson correlation coefficient between the predicted and measured confluence of 0.87 ± 0.16, and an average (±SD) concordance correlation coefficient of 0.72 ± 0.28. For C6, we obtained an average (±SD) Pearson correlation coefficient of 0.90 ± 0.17, and an average (±SD) concordance correlation coefficient of 0.71 ± 0.24.

Conclusion: The proposed model can effectively predict the temporal development of 9L and C6 glioma cells in response to a range of single-fraction radiation doses. By developing a mechanism-based, mathematical model that can be populated with time-resolved data, we provide an experimental-mathematical framework that allows for quantitative investigation of cells' temporal response to radiation. Our approach provides two key advances: (i) a time-resolved, dynamic death rate with a clear biological interpretation, and (ii) accurate predictions over a wide range of cell seeding densities and radiation doses.

Keywords: brain cancer; computational biology; mathematical modeling; oncology; radiotherapy.

Publication types

  • Research Support, N.I.H., Extramural
  • Research Support, Non-U.S. Gov't

MeSH terms

  • Glioma* / radiotherapy
  • Humans
  • Models, Theoretical