Pérez García, Victor M.. Pérez Beteta, Julián. León Triana, Odelaisy. Albillo Labarra, José David. Arana Fernández de Moya, Estanislao. Pérez Romasanta, Luis. 

Brain metastases (BMs) are cancer cells that spread to the brain from primary tumors in other organs. Up to 35\% of adult cancer patients develop BMs. The treatment of BM patients who have well-controlled extracranial disease and a small number of lesions consists of localized doses of radiation (Stereotactic Radio Surgery - SRS). Estimating prognosis among BM patients may allow treatments to be chosen that balance durability of intracranial tumor control with quality of life and side effects of treatment. No mathematical-model-based quantitative biomarkers have been developed for prognosis estimation. As a first step towards that task in this work we put forward a mathematical model of growth and response of brain metastasis to stereotactic radio surgery. The mathematical model incorporates a few biological mechanisms involved in BM growth and response to SRS and allows to describe accurately the different observed dynamics.