Estimating the energy of dissipative neural systems

Erik D. Fagerholm; Robert Leech; Federico E. Turkheimer; Gregory Scott; Milan Brázdil

doi:10.1007/s11571-024-10166-1

Estimating the energy of dissipative neural systems

Erik D. Fagerholm^*, Robert Leech, Federico E. Turkheimer, Gregory Scott, Milan Brázdil

^*Corresponding author for this work

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Abstract

There is, at present, a lack of consensus regarding precisely what is meant by the term 'energy' across the sub-disciplines of neuroscience. Definitions range from deficits in the rate of glucose metabolism in consciousness research to regional changes in neuronal activity in cognitive neuroscience. In computational neuroscience virtually all models define the energy of neuronal regions as a quantity that is in a continual process of dissipation to its surroundings. This, however, is at odds with the definition of energy used across all sub-disciplines of physics: a quantity that does not change as a dynamical system evolves in time. Here, we bridge this gap between the dissipative models used in computational neuroscience and the energy-conserving models of physics using a mathematical technique first proposed in the context of fluid dynamics. We go on to derive an expression for the energy of the linear time-invariant (LTI) state space equation. We then use resting-state fMRI data obtained from the human connectome project to show that LTI energy is associated with glucose uptake metabolism. Our hope is that this work paves the way for an increased understanding of energy in the brain, from both a theoretical as well as an experimental perspective.

Original language	English
Journal	Cognitive Neurodynamics
Early online date	29 Aug 2024
DOIs	https://doi.org/10.1007/s11571-024-10166-1
Publication status	E-pub ahead of print - 29 Aug 2024

Keywords

Computational neuroscience
Neural energy

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Estimating the energy of_Fagerholm_publishedonline29August2024_Gold_VOR (CC BY)Final published version, 458 KBLicence: CC BY-NC-ND

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title = "Estimating the energy of dissipative neural systems",

abstract = "There is, at present, a lack of consensus regarding precisely what is meant by the term 'energy' across the sub-disciplines of neuroscience. Definitions range from deficits in the rate of glucose metabolism in consciousness research to regional changes in neuronal activity in cognitive neuroscience. In computational neuroscience virtually all models define the energy of neuronal regions as a quantity that is in a continual process of dissipation to its surroundings. This, however, is at odds with the definition of energy used across all sub-disciplines of physics: a quantity that does not change as a dynamical system evolves in time. Here, we bridge this gap between the dissipative models used in computational neuroscience and the energy-conserving models of physics using a mathematical technique first proposed in the context of fluid dynamics. We go on to derive an expression for the energy of the linear time-invariant (LTI) state space equation. We then use resting-state fMRI data obtained from the human connectome project to show that LTI energy is associated with glucose uptake metabolism. Our hope is that this work paves the way for an increased understanding of energy in the brain, from both a theoretical as well as an experimental perspective.",

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AU - Scott, Gregory

AU - Brázdil, Milan

PY - 2024/8/29

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N2 - There is, at present, a lack of consensus regarding precisely what is meant by the term 'energy' across the sub-disciplines of neuroscience. Definitions range from deficits in the rate of glucose metabolism in consciousness research to regional changes in neuronal activity in cognitive neuroscience. In computational neuroscience virtually all models define the energy of neuronal regions as a quantity that is in a continual process of dissipation to its surroundings. This, however, is at odds with the definition of energy used across all sub-disciplines of physics: a quantity that does not change as a dynamical system evolves in time. Here, we bridge this gap between the dissipative models used in computational neuroscience and the energy-conserving models of physics using a mathematical technique first proposed in the context of fluid dynamics. We go on to derive an expression for the energy of the linear time-invariant (LTI) state space equation. We then use resting-state fMRI data obtained from the human connectome project to show that LTI energy is associated with glucose uptake metabolism. Our hope is that this work paves the way for an increased understanding of energy in the brain, from both a theoretical as well as an experimental perspective.

AB - There is, at present, a lack of consensus regarding precisely what is meant by the term 'energy' across the sub-disciplines of neuroscience. Definitions range from deficits in the rate of glucose metabolism in consciousness research to regional changes in neuronal activity in cognitive neuroscience. In computational neuroscience virtually all models define the energy of neuronal regions as a quantity that is in a continual process of dissipation to its surroundings. This, however, is at odds with the definition of energy used across all sub-disciplines of physics: a quantity that does not change as a dynamical system evolves in time. Here, we bridge this gap between the dissipative models used in computational neuroscience and the energy-conserving models of physics using a mathematical technique first proposed in the context of fluid dynamics. We go on to derive an expression for the energy of the linear time-invariant (LTI) state space equation. We then use resting-state fMRI data obtained from the human connectome project to show that LTI energy is associated with glucose uptake metabolism. Our hope is that this work paves the way for an increased understanding of energy in the brain, from both a theoretical as well as an experimental perspective.

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Estimating the energy of dissipative neural systems

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