Mathematical models and computational strategies for understanding and recreating glioblastoma progression in microfluidic devices. Towards a scientific machine learning approach 

 Jacobo Ayensa Jiménez is a postdoctoral researcher at the Institute for Health Reearch Aragon, focused on Artificial Intelligence solutions in Healthcare and in Mathematical Modelling of tumour microenvironments, incorporating elements of Machine Learning. He received his M.Sc. in Mathematics and M.Eng. in Civil Engineering at the CFIS center, in the Polytechnic University of Catalonia. J. Ayensa began his professional career in the research department of Abengoa (Abengoa Research) working on the uncertainty incorporation in mechanical system designs, such as CSPP troughs and heliostats, while attending a M.Eng. in Advanced Design in Mechanical Engineering in the University of Seville. Later, he moved to the academic world where he obtained his Ph.D. in Mechanical Engineering at the Aragon Institute of Engineering Research, recognized with the Extraordinary Doctorate Award. During his Ph.D, he participated in Data Science projects in collaboration with the Aragon Institute of Technology and in international Data Science competitions, achieving outstanding results (top 2%), and he completed a stay with Prof. Eamonn Gaffney at the Mathematical Institute in University of Oxford. 

 In silico models are invaluable tools that complement in vitro experiments to improve our understanding of complex biological phenomena such as cancer evolution. We present a mathematical framework to study the dynamical progression of glioblastoma, the most common and lethal brain cancer, in microfluidic devices, the most biomimetic in vitro cell culture technique nowadays. The approach allows the use of both analytical and computational tools, including some elements of statistical analysis and machine learning, made possible thanks to the High-throughput character of these experimental platforms. Depending on the data availability, many strategies are possible, ranging from purely knowledge-based solutions to data-driven, and hence completely model-free ones. In particular, we dwell on hybrid approaches, which combine physics-based knowledge and data-driven elements, showing how they allow us to broaden our understanding of glioblastoma progression by unraveling the mathematical structure of some unknown hidden biological mechanisms, which in turn can be exploited for the design of future experiments or preclinical tests.