Abstract
Blood-oxygen-level-dependent (BOLD) imaging is the most important noninvasive tool to map human brain function. It relies on local blood-flow changes controlled by neurovascular coupling effects, usually in response to some cognitive or perceptual task. In this contribution we ask if the spatiotemporal dynamics of the BOLD signal can be modeled by a conservation law. In analogy to the description of physical laws, which often can be derived from some underlying conservation law, identification of conservation laws in the brain could lead to new models for the functional organization of the brain. Our model is independent of the nature of the conservation law, but we discuss possible hints and motivations for conservation laws. For example, globally limited blood supply and local competition between brain regions for blood might restrict the large scale BOLD signal in certain ways that could be observable. One proposed selective pressure for the evolution of such conservation laws is the closed volume of the skull limiting the expansion of brain tissue by increases in blood volume. These ideas are demonstrated on a mental motor imagery fMRI experiment, in which functional brain activation was mapped in a group of volunteers imagining themselves swimming. In order to search for local conservation laws during this complex cognitive process, we derived maps of quantities resulting from spatial interaction of the BOLD amplitudes. Specifically, we mapped fluxes and sources of the BOLD signal, terms that would appear in a description by a continuity equation. Whereas we cannot present final answers with the particular analysis of this particular experiment, some results seem to be non-trivial. For example, we found that during task the group BOLD flux covered more widespread regions than identified by conventional BOLD mapping and was always increasing during task. It is our hope that these results motivate more work towards the search for conservation laws in neuroimaging experiments or at least towards imaging procedures based on spatial interactions of signals. The payoff could be new models for the dynamics of the healthy brain or more sensitive clinical imaging approaches, respectively.
Highlights
Understanding functional mechanisms underlying brain dynamics is essential for clinical applications such as recovery from stroke, traumatic brain injury, and disorders of consciousness.Neuronal activity in response to perceptual stimuli or cognitive tasks can be mapped by using the blood-oxygen-level-dependent (BOLD) response as a proxy signal in functional MRI experiments.Functional MRI studies have provided us with detailed insights into local functional organization of the brain
The manuscript is organized as follows: We briefly review the importance of conservation laws and mention possible hints for conservation laws affecting brain dynamics (Section 2)
We are interested in conservation laws, including non-conserved quantities described by sources and sinks, for two reasons: (i) There exists a quite general way of expressing conservation laws in spatiotemporal systems without the need to specify the specific nature of the quantity: Continuity equations explicitly relate the local change of a physical quantity to nonlocal influences, namely flow or flux terms, and to source and sink terms. (ii) On a certain level of description, the brain can be considered as a flow-equilibrium system, which naturally gives rise to a possible description by continuity equations
Summary
Understanding functional mechanisms underlying brain dynamics is essential for clinical applications such as recovery from stroke, traumatic brain injury, and disorders of consciousness. Many recent studies relate BOLD resting state networks to functional networks of the brain, for example by utilizing information theoretical concepts or other notions from physics such as small world networks [10,11,12,13,14]. Despite these efforts to link BOLD signals of the brain to physical concepts, it seems that one fundamental way of physical modeling has not been applied to functional brain imaging yet: The concept of conserved quantities and conservation laws.
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