Structured Flows on Manifolds as guiding concepts in brain science

Viktor Jirsa (1)

1 INS - Institut de Neurosciences des Systèmes

Any discussion of brain repair, rehabilitation, and functional recovery imperatively requires a working definition of "function" (Jirsa et al. 2019). If such definition is not explicitly provided, which is more common than not, then the precedent statement still remains valid and is implied by the choice of methods applied in the investigation. An illustrative and recent example is the use of resting state paradigms in modern neuroscience, in which spa-tiotemporal brain activity is recorded using neuroimaging techniques such as functional MRI or EEG and then cast into a measure, e.g., functional connectivity, which captures the Pearson correlation of brain activations. Measures assign a value on the relationship between two brain regions in a systematic way, which implicitly evokes an underlying model and understanding of brain function. Functional connectivity assumes that the co-variation of brain activations in time is related in a meaningful way to brain function. What does meaningful refer to in this case? Here meaning can be assigned in two ways. Either it can be linked to a causal description of brain activity, as only the latter provides us with entry points for interventions in case of brain dysfunction, and ultimately brain repair. The juxtaposition of empirical brain data and a causal description thereof is commonly performed through the building of a mechanistic brain model. Once one or multiple key mechanisms are identified, then the actual confrontation between empirical data and model is made by the parameters in the model. In fact, this is what any scientific interrogation reduces to at this stage. The assignment of values (whether through explicit numbers, parameter ranges, or co-dependent subsets) to model parameters establishes the critical link between our understanding (aka the model) and the real-world (aka the data). It will generally not be unique, but degenerate in the sense that the brain exhibits the one-to-many and many-to-one behavior well-known from complex systems. Virtually indistinguishable network activity patterns can for instance arise from many distinct biophysical mechanisms

Domaines: Neurosciences; Informatique [cs]; Sciences cognitives; Sciences du Vivant [q-bio]

Viktor Jirsa. Structured Flows on Manifolds as guiding concepts in brain science. Selbstorganisation – ein Paradigma für die Humanwissenschaften, Springer Fachmedien Wiesbaden; Springer Fachmedien Wiesbaden, pp.89-102, 2020, ⟨10.1007/978-3-658-29906-4_6⟩. ⟨hal-02527445⟩