【Paper author】

Shunsuke Kamiya　Graduate School of Arts and Sciences, University of Tokyo
Shuntaro Sasai　Araya, Inc
Masafumi Oizumi　Graduate School of Arts and Sciences, University of Tokyo

【Key points of this study】

• We propose a method to quantify the control cost required to transition from one state of the brain to another and to find the most efficient control input. The proposed method was applied to fMRI data while humans were performing various cognitive tasks to identify brain regions that contribute to the control of brain states.
• The control cost quantification method in this study is the first method that can evaluate the cost of control by taking into account the effects of noise on brain activity, which has been ignored by previous methods.
• By quantifying the cost of control as the brain transitions from one state to another, it may become possible to quantitatively assess how much load various cognitive tasks place on humans, mental fatigue, etc.

【Research Overview】

Shunsuke Kamiya, a graduate student at the University of Tokyo Graduate School of Arts and Sciences, Masafumi Oizumi, Associate Professor, and Shuntaro Sasai, CRO and Director of Research and Development at Araya Inc, proposed a novel mathematical method to quantify the control cost required to control the transition of brain activity states.

We are able to perform a variety of cognitive and behavioral tasks every day. Why is the brain able to achieve various cognitive and behavioral tasks? From the perspective of the brain's "control," the brain is able to properly control its own state and switch to various states. Quantifying the "cost" required to control the transition from one state to another and identifying brain regions that play an important role in controlling state transitions is considered important in understanding how the brain realizes cognitive and behavioral tasks.

Although there have been studies quantifying the cost of controlling brain state transitions, the problem was that they did not consider the fact that brain activity contains noise and behaves in a stochastic manner. In this study, we propose a new method that quantifies the control cost by considering the probabilistic behavior of brain activity. We applied this method to fMRI data collected while human subjects performed various cognitive tasks and identified brain regions that contribute to the control of brain states.

This study aims to quantify the "difficulty of controlling the transition from one brain state to another." Using this research as a starting point, in the future, it may provide new understanding of seemingly unrelated phenomena such as the workload and mental fatigue of human cognitive tasks, or mental illness, from a unified perspective of control. Additionally, this research provides a theoretical foundation for studies that aim to transition the brain to a specific state by applying external input.

The work was published in the American scientific journalJournal of Neuroscience: January 11, 2023.

【Research content and results】

Research Background

　The brain is a highly complex dynamical network that flexibly transitions to various states to execute a myriad of functions.In this regard, the brain can be considered a system that modulates its internal states to desired states, in accordance with the function the individual needs to perform .Among the many transitions that bring the system into the various states it requires, some state transitions are more difficult to control than others, depending on the dynamical properties of the neuronal systems. In other words, controlling transitions to some states incurs greater “costs” than controlling transitions to others. By evaluating the control cost, we can theoretically predict what control inputs to the brain are most efficient and which brain regions play an important role in control.

Previous studies have proposed an approach using control theory to evaluate the control cost of brain activity and have been applied in many studies (Gu et al, Nature Communications, 2015). However, despite being a strong approach, this framework does not take account of an important property of neural activity: it neglects noise or stochasticity in neural systems. In reality, overlooking the stochasticity of neural systems may result in an inaccurate estimation of the control costs.

Research content

In this study, we propose a novel framework to quantify control costs in linear stochastic neural systems. The research team first proposed quantifying the control cost in probabilistic neural systems by how much the distribution differs between the uncontrolled process and the controlled process towards a desired state(Fig. 1, Fig. 2). The distance between the two probability distributions can be quantified by the Kullback-Leibler divergence (KL divergence) measure.By considering control cost based on KL divergence, it is possible to take into account the probabilistic behavior of brain activity.The research team first proposed quantifying the control cost in probabilistic neural systems based on how much the distribution of the uncontrolled process differs from the desired state with control. By using KL divergence as a measure of control cost, it is possible to take into account the probabilistic behavior of brain activity.However, since there can be multiple controlled processes, the control cost can take various values.The research team considered the process that is closest to the uncontrolled process, that is the process where KL divergence is minimum, as the optimal control process and found the minimum control cost and optimal control input accordingly.

Figure 1. Schematic of our framework for quantification of control costs in the brain in linear stochastic systems. We model a brain state to follow a certain probability distribution π0 at time t = 0 (left, blue ellipse). In uncontrolled dynamics, the brain state stays in the same distribution (right, blue trajectory and blue ellipse). However, in a state transition, the brain dynamics changes so that it reaches a target distribution πT at time t = T (gold ellipse). We call this altered trajectory the controlled process (gold trajectory). To evaluate how close the controlled process is to the uncontrolled one, we use the KL divergence between the two processes as the cost function, marginalized with the initial and the target distributions (blue square). The distributions of the processes are defined on a path space, the space composed of Rn valued continuous functions defined on [0, T].

Figure 2. Comparison of deterministic and stochastic state transitions in a brain from the perspective of control theory. The Previous framework column describes the deterministic model of state transitions. The Proposed framework column explains the stochastic model of brain state transitions. Here, the uncontrolled process (blue arrow) and a controlled process (gold arrow) are given as stochastic processes. A brain state transition is viewed as a shift from an n-dimensional probability distribution to another. As a control cost, the KL divergence between the two processes is examined.

In this study, we proposed a new framework for quantifying the control cost of brain activity by considering the probabilistic behavior of the brain activity, which has been ignored in previous studies. To make the control cost mathematically tractable, we modeled the dynamics of brain activity using linear probabilistic differential equations. By using the linear model, we were able to successfully obtain the analytical solution of the optimal control cost. Additionally, we mathematically proved that this optimal cost can be decomposed into two terms: one that controls the average change in brain activity and the other that controls the change in correlation between different brain regions (more specifically, the change in covariance).

Our team applied the proposed method to fMRI data from the Human Connectome Project (HCP) and calculated the optimal control cost while identifying brain regions that play an important role in state transitions. As a result, we found that the low-level visual field is important for controlling the average brain activity, while the posterior cingulate cortex is important for controlling the correlation between brain regions (covariance)(Fig. 3).

Figure 3. This study shows the important brain regions for controlling the transition from a resting state to a cognitive task. One of the benefits of the new framework in this study is that it can identify the brain regions that play an important role in controlling the average and the covariance of brain activity during state transitions. The figures on the left and center show the regions that contribute to the control of the average and the covariance, respectively. The figure on the right shows the regions that contribute to the control of the overall probability distribution, which is the sum of the average and the covariance. The numbers in the figures indicate how many of the 7 cognitive tasks in the Human Connectome Project identified the same brain regions as important. The darkly colored regions are considered to be important brain regions that are common to different 7 cognitive tasks.

Social Significance/Future Plans

　By quantifying the cost of controlling the brain's transition from one state to another, it may become possible to quantify the cognitive load and mental fatigue of performing a certain cognitive task. Additionally, the proposed framework may provide theoretical predictions for clinical applications such as determining the most efficient external inputs (such as magnetic or electrical stimulation) for transitioning the brain to a desired state.

Acknowledgments

This research was supported by JSPS Grants-in-Aid for Scientific Research (JP22J23428, JP18H02713, JP20H05712), JST Moonshot-type R&D project JPMJMS2012, and JST CREST JPMJCR1864.

【Comments from Project Manager】

The new perspective of evaluating the brain's state transition cost (control cost) is innovative and has theoretical potential. Although the research approach is mathematical, it has the possibility of providing quantitative evaluations such as mental fatigue. This research is truly a moonshot project in the sense that it has the potential to solve human problems based on solid science and pave the way for the future. In this study, we used fMRI data, but in the future, we hope that the research will evolve through approaches such as using brainwaves measured by non-invasive BMI, which is also being studied in the same project.

Moonshot Goal 1
Realization of a society in which human beings can be free from limitations of body, brain, space, and time by 2050 Project Manager: Ryota Kanai

【Papers】

Journal: The Journal of Neuroscience (January 11)
Title of paper: Optimal Control Costs of Brain State Transitions in Linear Stochastic Systems
Authors: Shunsuke Kamiya, Genji Kawakita, Shuntaro Sasai, Jun Kitazono, and Masafumi Oizumi*.
DOI Number: 10.1523/JNEUROSCI.1053-22.2022

【Contact】

Masafumi Oizumi, Associate Professor
The University of Tokyo, Graduate School of Arts and Sciences Department of General Systems Studies
E-mail: c-oizumi@g.ecc.u-tokyo.ac.jp

【Related links】

PRESS RELEASE
Graduate School of Arts and Sciences, University of Tokyo, Oizumi Lab
Moonshot Goal 1 Kanai Project
Shuntaro Sasai