A Mathematical Model of Cancer Stem Cell Kinetics and Response to Radiation Therapy
Zhong H, Barton K, Movsas B, and Chetty I. A mathematical model of cancer stem cell kinetics and response to radiation therapy. Med Phys 2017; 44(6):2995.
Purpose: To model the dynamic equilibrium of different cell compartments for quantification of tumor response to radiotherapy. Methods: Cancer cells were divided into three groups: cancer stem cells (CSCs), differentiated cancer cells (DCCs) and dead cells (DCs). Cell transitions between these groups were modeled using a set of ordinary differential equations. The solution of these equations was used to generate a discrete model. This model was applied to three patients with squamous-cell lung cancer. For each patient, treatment doses and dates were imported into the model to calculate the number of total tumor cells. 33 CBCT images were acquired for each patient. Tumor volumes were measured on each of these images. Based on published data, the half time to resolve dead cells was assumed to be 5 days, the potential cell doubling time set to 6.2 days, and the 2 Gy-survival fraction of differentiated squamous cells set to 0.87. Other parameters were derived by minimizing the difference between the computed and measured tumor volumes. Results: For the three patients, the developed model showed the fitting errors of 1.4, 2.3 and 2.7%, which are smaller than the errors of 5.7, 3.1 and 3.6% produced by a 2-compartment model generally used for kinetic modeling. Tumor growth within the first few treatment fractions for two of the patients was simulated successfully with the new model, but not with the 2-compartment model. The half time of programmed cell death for DCCs is 1.1 days, the survival fraction of CSCs under 2 Gy is 0.97, and the probability for the symmetric division of CSCs is 0.508. Conclusion: Cancer stem cells have been included in a new kinetic model for quantification of cell transition and response to radiotherapy. The model derived parameters show that CSCs are more radio-resistant than DCCs, which is consistent to published results.