Entropy 2014, 16(7), 3689-3709; doi:10.3390/e16073689
Article

Searching for Conservation Laws in Brain Dynamics—BOLD Flux and Source Imaging

1,* email and 2email
Received: 1 May 2014; in revised form: 26 June 2014 / Accepted: 27 June 2014 / Published: 3 July 2014
(This article belongs to the Special Issue Entropy in Human Brain Networks)
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.
Keywords: brain dynamics; brain networking; conservation law; functional MRI; fMRI; mental imagery; motor imagery; synchronization
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MDPI and ACS Style

Voss, H.U.; Schiff, N.D. Searching for Conservation Laws in Brain Dynamics—BOLD Flux and Source Imaging. Entropy 2014, 16, 3689-3709.

AMA Style

Voss HU, Schiff ND. Searching for Conservation Laws in Brain Dynamics—BOLD Flux and Source Imaging. Entropy. 2014; 16(7):3689-3709.

Chicago/Turabian Style

Voss, Henning U.; Schiff, Nicholas D. 2014. "Searching for Conservation Laws in Brain Dynamics—BOLD Flux and Source Imaging." Entropy 16, no. 7: 3689-3709.

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