Multiscale modelling and mathematical methods for brain development, trauma, and diseases

The human brain is an organ of extreme complexity, the object of ultimate intellectual egocentrism, and a source of endless scientific challenges. At the basic functional level, the goal of many scientific enquiries is to understand the functions that result from the interaction of about 86 billion neurons with 100 trillion connections. From this perspective, the problem consists of connecting the biochemical and electrophysiological behavior of brain cells with the overall behavior of networks of connected cells. The ultimate goal is to translate the resulting macroscopic electrophysiological behavior into the functional dimension where direct relations can be established with neuronal response and, ultimately, behavior. Despite an overwhelming interest and major research initiatives on how our brain operates, comparatively little is known about how the brain functions at the physical and mechanical levels. Recent findings have directly linked major brain development, mechanisms, and diseases to the mechanical response of the brain both at the cellular and tissue levels. Various factors contribute to this poor state of knowledge. First, the brain is a fully enclosed organ that is particularly difficult to probe physically. Second, viewed as a solid, it is extremely soft and its mechanical response is heavily influenced by a fluid phase and multiple charged molecules found in its cells and in the extracellular matrix. A holistic mathematical analysis requires a fully coupled multi-field theory, which needs to be calibrated and validated experimentally. Further, most brain pathologies depend on many different factors and their physical manifestation may be conveniently ignored by focusing on genetics and cellular function as the primary driver. Nonetheless, the last decade has seen fundamental advances in different areas of brain mechanics and has revealed that one of the reasons that brain mechanics is particularly exciting is that it involves extreme scales: the extremely soft scale associated with neurosurgery; the extremely hard scale associated with the skull; the extremely slow scale associated with brain development and, the extremely fast scale associated with traumatic brain injury; the extremely small scales of protein aggregation within axons leading to cell death and the relatively extremely large scale of the brain itself where neuro-degeneratives processes take place. A mathematical theory needs to reconcile all these different scales within a unified theory. The objective of the proposed research is to develop the mathematical theory and tools to approach many questions related to brain mechanics. It will use the basic physical principles underlying brain function to address a number of problems and challenges appearing in normal and pathological situations. At the mathematical level, it requires the coupling of solid, fluid, electrochemical, and electromechanical components together with a theory of growth and remodelling. My aim is to build a general multiscale theoretical framework of brain mechanics linking molecular, cellular, tissue, and organ scales. Using these theories, I will tackle a number of fundamental questions in situations and pathologies where mechanics play a key role and where modeling can improve our understanding and predicting capabilities. These include brain development, brain folding, skull growth, brain surgery, traumatic brain injury, brain swelling, and neuro-degenerative diseases.