Understanding glioblastoma invasion using physically-guided neural networks with internal variables.

Microfluidic capacities for both recreating and monitoring cell cultures have opened the door to the use of Data Science and Machine Learning tools for understanding and simulating tumor evolution under controlled conditions. In this work, we show how these techniques could be applied to study Glioblastoma, the deadliest and most frequent primary brain tumor. In particular, we study Glioblastoma invasion using the recent concept of Physically-Guided Neural Networks with Internal Variables (PGNNIV), able to combine data obtained from microfluidic devices and some physical knowledge governing the tumor evolution. The physics is introduced by means of nonlinear advection-diffusion-reaction partial differential equation that models the Glioblastoma evolution for defining the network structure. On the other hand, multilayer perceptrons combined with a nodal deconvolution technique are used for learning the go or grow metabolic behavior which characterises the Glioblastoma invasion. The PGNNIV is here trained using synthetic data obtained from in silico tests created under different oxygenation conditions, using a previously validated model. The unravelling capacity of PGNNIV enables discovering complex metabolic processes in a non-parametric way, thus giving explanatory capacity to the networks, and, as a consequence, surpassing the predictive power of any parametric approach and for any kind of stimulus. Besides, the possibility of working, for a particular tumor, with different boundary and initial conditions, permits the use of PGNNIV for defining virtual therapies and for drug design, thus making the first steps towards in silico personalised medicine. Author summary: In this work, we apply Physically-Guided Neural Networks with Internal Variables (PGNNIV) to the understanding of the Glioblastoma evolution process. We explain the metabolic changes between the proliferative and migrative activity of Glioblastoma cell cultures by using the go or grow activation functions as a pair of internal variables, whose dependence on the oxygen level is unravelled by some building blocks of the whole PGNNIV. Due to its model-free nature, our method is able to identify different classical mechanistic approaches and to outperform cell culture evolution predictions, as we demonstrate in the paper. Unlike Biologically-Informed Neural Networks we can assimilate data obtained from different boundary conditions and under different external stimuli to simulate the tumor progression under arbitrary conditions. We demonstrate this ability by comparing the predictions with different boundary conditions, resulting in different oxygenation conditions. This flexibility enables the use of our proposed method for personalised medical purposes, as the cell culture metabolic information, for a particular tumor, is encapsulated in a sub-network and may be used for arbitrary in silico tests. [ABSTRACT FROM AUTHOR]