Brain Metastasis Response to Stereotactic Radio Surgery: A Mathematical Approach

Abstract

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 the side effects of treatment. No mathematical model-based quantitative biomarkers have been determined for estimating prognosis. As a first step toward that goal, we describe a mathematical model of growth and response of brain metastasis to stereotactic radio surgery. The mathematical model incorporates some biological mechanisms involved in BM growth and response to SRS and allows the observed dynamics to be accurately described.

Radiation necrosis after radiation therapy treatment of brain metastases: A computational approach

“…From typical cell sizes [46], the carrying capacity of a single voxel was estimated to be K = 2 × 10 5 cells, assuming similar sizes for tumor and healthy cells (* 10-12 μm). Basal rates of tumor cell division, death and migration were chosen using Bayesian criteria based on the doubling times estimations [47] and imaging data from real BMs in [28]. The value k = 2 was taken, i.e.…”

“…Mechanistic mathematical models have been used to study the growth of untreated metastasis in different scenarios [21][22][23], the interaction between primary and secondary tumors [24], cancer metastasis networks [25][26][27], and, and, in recent years, the response to treatment [28][29][30][31][32][33][34]. However only a few of them have studied specifically brain metastases [23,28,29,33,34].…”