On February 5, 2024, Beatriz Ocaña-Tienda, presented her PhD thesis entitled "Mathematical insights into brain metastases".

Her thesis explored brain metastases (BMs) through various mathematical tools and methodologies, such as data analysis, medical image processing, agent-based and differential equation modeling, and statistical analysis, with the goal of providing practical tools that can be implemented in clinical settings. 

First, she investigated the initiation and development of these metastatic lesions at the microscopic level. A discrete mathematical model, calibrated with data from a mouse model, helped her to reveal the processes underlying the formation of BMs. Transitioning to the macroscopic scale, her study of untreated and treated brain metastases revealed unique growth patterns using scaling laws, specifically the von Bertalanffy equation, in combination with clinical data. In addition, her research explored the growth dynamics of radiation necrosis, allowing for a more precise differentiation between tumor progression and the effects of this condition. 

The thesis also introduced novel criteria for assessing treatment response by using volumetric measurements of BMs. These criteria exhibited better classification accuracy, evaluation of all lesions, and earlier detection of recurrences compared to one-dimensional criteria. Volumetric measurements also allow to obtain quantitative biomarkers from routine MRI scans. The proportion of necrosis and the regularity of lesion surfaces emerged as prognostic indicators. Finally, the release of the largest BM dataset is a significant achievement that allows for additional research and the enhancement of automated segmentation algorithms. These advancements can accelerate disease assessment, improving diagnosis and follow-up. 

In essence, Beatriz's thesis depicts a broad view that combines various mathematical tools. Her research has generated valuable insights into the complex nature of brain metastases, and this multidisciplinary approach sets the stage for improved diagnostic and therapeutic strategies that promise better care and outcomes for patients facing the challenges of brain metastases.