News Release

Research team builds framework to quantify brain’s control costs

Deepens understanding of brain functions from the control perspective

Peer-Reviewed Publication

University of Tokyo

Comparison of deterministic and stochastic state transitions in the brain from the perspective of control theory

image: The previous framework (left) fails to take into account noises of the brain. The brain state transitions were written as point-to-point, the dynamics as deterministic, and the control cost as the integral of the squared control input. In the current framework (right), the research team introduced a stochastic model, in which brain state transitions were considered as probability distribution to probability distribution, dynamics as stochastic process, and the control cost as KL divergence. view more 

Credit: Shunsuke Kamiya, The University of Tokyo

The brain performs various cognitive and behavioral functions in everyday life, flexibly transitioning to various states to carry out these functions. Scientists view the brain as a system that performs these numerous functions by controlling its states. To better understand the properties of this control in the brain, scientists look for ways to estimate the difficulty of control, or control cost, when the brain transitions from one state to another. So a team of researchers undertook a study to quantify such control costs in the brain, and was successful in building a framework that evaluates these costs.

Controlling transitions to some states incurs greater “costs” than controlling transitions to others. With the development of a framework for quantifying transition costs, scientists will have a way to evaluate the difficulty of the shifts between various brain states. Possibly, they might also have a quantifiable measure for explaining cognitive loads, sleep-wake differences, habituation of cognitive tasks and psychiatric disorders.

The work is published in the Journal of Neuroscience.

The team worked to build a novel framework to quantify control cost that takes account of stochasticity, or the randomness, of neural activity. This stochasticity has been ignored in previous studies. The current control paradigm in neuroscience uses a deterministic framework that is unable to consider stochasticity. But it is well known that the neural dynamics are stochastic and the noise is ubiquitous throughout the whole brain. “In this work, we addressed the issue of stochasticity and first proposed a novel theoretical framework that quantifies the control cost taking account of the stochastic fluctuations of the neural dynamics,” said Shunsuke Kamiya, a doctoral student in the Graduate School of Arts and Sciences at the University of Tokyo.

In their study, the researchers established the analytical expression of the stochastic control cost, which enabled them to compute the cost in high-dimensional neural data. By the analytical expression, they discovered that the optimal control cost can be decomposed into the costs to control the mean and covariance. “This decomposition enables us to investigate how various brain areas differently contribute to controlling the transitions from one brain state to another,” said Kamiya.

The researchers also identified the significant brain regions for the optimal control in cognitive tasks in human whole-brain imaging data. They examined the significant brain regions in the optimal control of transitions from the resting state to seven cognitive task states, using human whole-brain imaging data of 352 healthy adults. They found that, with these different transitions, the lower visual areas commonly played a significant role in controlling the means, while the posterior cingulate cortex commonly played a significant role in controlling the covariances. The posterior cingulate cortex is the upper part of the limbic lobe, that region of the brain that plays an important role in memory and emotional behaviors.

In this study, the team only considered the optimal control cost where brain state transitions are controlled in an optimal manner, with minimization of stochastic control cost. However, in real neural systems, it is not likely that state transitions are controlled in an optimal manner. “An intriguing future direction will be to compare the optimally controlled dynamics and the actual dynamics using neural data during tasks,” said Masafumi Oizumi, associate professor in the Graduate School of Arts and Sciences at the University of Tokyo.

Looking ahead to future research, Oizumi explains that the ultimate goal of his lab is to understand the connection between brain dynamics and human behaviors, cognitions and consciousness. “For example, we suspect that the decrease of controllability in the brain dynamics may be related to mental fatigue or the loss of consciousness. We expect that control theoretical perspective will provide a new insight to this goal,” said Oizumi.



The research is funded by grants from the Japan Society for the Promotion of Science KAKENHI, Japan Science and Technology Agency Moonshot, Japan Science and Technology Agency CREST.


Related links

Oizumi Lab:

Graduate School of Arts and Sciences:


About the University of Tokyo

The University of Tokyo is Japan's leading university and one of the world's top research universities. The vast research output of some 6,000 researchers is published in the world's top journals across the arts and sciences. Our vibrant student body of around 15,000 undergraduate and 15,000 graduate students includes over 4,000 international students. Find out more at or follow us on Twitter at @UTokyo_News_en

Disclaimer: AAAS and EurekAlert! are not responsible for the accuracy of news releases posted to EurekAlert! by contributing institutions or for the use of any information through the EurekAlert system.