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

Abstract

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.

A Multi-Compartment Model of Glioma Response to Fractionated Radiation Therapy Parameterized via Time-Resolved Microscopy Data

“…This assignment is justified as Mariotti et al (29) have measured gH2AX under both single and multi-fractionated treatment schemes and showed similar repair kinetics in response to a second dose when cells are given proper time for repair and recovery. Our previous flow cytometry experiments (10) indicate that most (> 80%) DSBs are repaired within 24 hours given the dose range we employ in the experiments. Therefore, this estimation is reasonable.…”

“…The 9L (American Type Culture Collection, ATCC) and C6 (Sigma Aldrich) cells are cultured according to the manufacturer's guidelines as previously described (10). The 9L cell line is cultured with Eagle's minimum essential medium (ATCC, VA), and the C6 cell line is cultured with Ham's F12 (Corning, NY).…”

“…To prevent cell loss when refreshing the media in the 96-well plates, we pipetted only the top 80 ml of the total 100 ml per well to minimize the disturbance to attached cells. Live and dead cells were segmented using a semi-automated pipeline consisting of a histogram Otsubased method followed by a morphology-based cell debris removal [described in detail in (10)].…”

“…This is despite the now vast biological knowledge that exists regarding DNA repair (8) and radiation-induced cell death pathways (9). To address these two limitations, we previously proposed and validated a mechanism-based time-resolved model (10) to a single-dose treatment. We now seek to extend this model to account for multiple-fraction treatment regimens.…”

The Hallmarks of Mathematical Oncology

“…However, using more complex models can result in overfitting and hence reduce the biological insight available from a model. To counter this, model selection methods such as Akaike's Information Criteria (AIC) and Bayesian Information Criteria (BIC) have been developed in order to balance the fit of a model against model complexity (see, e.g., [29]).…”