The application of the linear quadratic model to compensate the effects of prolonged fraction delivery time on a Balb/C breast adenocarcinoma tumor: An in vivo study

Abstract

Purpose To investigate the effect of increasing the overall treatment time as well as delivering the compensating doses on the Balb/c breast adenocarcinoma (4T1) tumor.

Materials and methods A total of 72 mice were divided into two aliquots (classes A and B) based on the initial size of their induced tumor. Each class was divided into a control and several treatment groups. Among the treatment groups, group 1 was continuously exposed to 2 Gy irradiation, and groups 2 and 3 received two subfractions of 1 Gy over the total treatment times of 30 and 60 min, respectively. To investigate the effect of compensating doses, calculated based on the developed linear quadratic model (LQ) model, the remaining two groups (groups 4 and 5) received two subfractions of 1.16 and 1.24 Gy over the total treatment times of 30 and 60 min, respectively. The growing curves, Tumor Growth Time (TGT), Tumor Growth Delay Time (TGDT) and the survival of the animals were studied.

Results For class A (tumor size ≤ 30 mm³), the average tumor size in the irradiated groups 1–5 was considerably different compared to the control group as one unit (day) change in time, by amount of −160.8, −158.9, +39.4 and +44.0, respectively. While these amounts were +22.0, +17.9, −21.7 and −0.1 for class B (tumor size ≥ 400 mm³). For the class A of animals, the TGT and TGDT parameters were significantly lower (0 ≤ 0.05) for the groups 2 and 3, compared to group 1. There was no significant difference (p > 0.05) between groups 1, 4 and 5 in this class. There was no significant difference (p > 0.05) between all the treated groups in class B.

Conclusions Increasing total treatment time affects the radiobiological efficiency of treatment especially in small-sized tumor. The compensating doses derived from the LQ model can be used to compensate the effects of prolonged treatment times at in vivo condition.

Keywords:

• Intensity Modulated Radiation Therapy (IMRT)
• tumor size
• compensating dose
• fractionation
• breast adenocarcinoma

Acknowledgements

This study was carried out as a PhD project by S.N. at Tarbiat Modares University (Tehran, Iran) and was supported financially by this university. The authors wish to express their sincere thanks to Professor Z. S. Hasan and his colleagues at the Immunology Department of Tarbiat Modares University for providing substantial technical help and access to their lab facilities. Our special thanks is also expressed to the staff of Shahid Fayazbakhsh General Hospitals (Tehran, Iran), especially Dr Mohsen Bakhshande for providing access and technical help for irradiating the samples at different stages of the project using their Co-60 machine.

Declaration of interest

The authors report no conflict of interest. The authors alone are responsible for the content and writing of the paper.