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We developed a mathematical model to simulate the growth of tumor volume andits response to a single fraction of high dose irradiation. We made several keyassumptions of the model. Tumor volume is composed of proliferating (ordividing) cancer cells and non-dividing (or dead) cells. Tumor growth rate (ortumor volume doubling time, Td) is proportional to the ratio of the volumes oftumor vasculature and the tumor. The vascular volume grows slower than thetumor by introducing the vascular growth retardation factor, theta. Uponirradiation the proliferating cells gradually die over a fixed time periodafter irradiation. Dead cells are cleared away with cell clearance time, Tcl.The model was applied to simulate pre-treatment growth and post-treatmentradiation response of rat rhabdomyosarcoma tumor and metastatic brain tumors offive patients who were treated by Gamma Knife stereotactic radiosurgery(GKSRS). By selecting appropriate model parameters, we showed the temporalvariation of the tumors for both the rat experiment and the clinical GKSRScases could be easily replicated by the simple model. Additionally, theapplication of our model to the GKSRS cases showed that the alpha-value, whichis an indicator of radiation sensitivity in the LQ model, and the retardationfactor theta could be predictors of the post-treatment volume change. Sincethere is a large statistical uncertainty of this result due to the small samplesize, a future clinical study with a larger number of patients is needed toconfirm this finding.

A kinetic model of tumor growth and its radiation response with an application to Gamma Knife stereotactic radiosurgery