  We developed a mathematical model to simulate the growth of tumor volume and
its response to a single fraction of high dose irradiation. We made several key
assumptions of the model. Tumor volume is composed of proliferating (or
dividing) cancer cells and non-dividing (or dead) cells. Tumor growth rate (or
tumor volume doubling time, Td) is proportional to the ratio of the volumes of
tumor vasculature and the tumor. The vascular volume grows slower than the
tumor by introducing the vascular growth retardation factor, theta. Upon
irradiation the proliferating cells gradually die over a fixed time period
after irradiation. Dead cells are cleared away with cell clearance time, Tcl.
The model was applied to simulate pre-treatment growth and post-treatment
radiation response of rat rhabdomyosarcoma tumor and metastatic brain tumors of
five patients who were treated by Gamma Knife stereotactic radiosurgery
(GKSRS). By selecting appropriate model parameters, we showed the temporal
variation of the tumors for both the rat experiment and the clinical GKSRS
cases could be easily replicated by the simple model. Additionally, the
application of our model to the GKSRS cases showed that the alpha-value, which
is an indicator of radiation sensitivity in the LQ model, and the retardation
factor theta could be predictors of the post-treatment volume change. Since
there is a large statistical uncertainty of this result due to the small sample
size, a future clinical study with a larger number of patients is needed to
confirm this finding.
