Naoya Fujiwara

Towards dynamical network biomarkers in neuromodulation of episodic migraine

Computational methods have complemented experimental and clinical neurosciences and led to improvements in our understanding of the nervous systems in health and disease. In parallel, neuromodulation in form of electric and magnetic stimulation is gaining increasing acceptance in chronic and intractable diseases. In this paper, we firstly explore the relevant state of the art in fusion of both developments towards translational computational neuroscience. Then, we propose a strategy to employ the new theoretical concept of dynamical network biomarkers (DNB) in episodic manifestations of chronic disorders. In particular, as a first example, we introduce the use of computational models in migraine and illustrate on the basis of this example the potential of DNB as early-warning signals for neuromodulation in episodic migraine.

Synchronization of mobile chaotic oscillator networks

We study synchronization of systems in which agents holding chaotic oscillators move in a two-dimensional plane and interact with nearby ones forming a time dependent network. Due to the uncertainty in observing other agents states, we assume that the interaction contains a certain amount of noise that turns out to be relevant for chaotic dynamics. We find that a synchronization transition takes place by changing a control parameter. But this transition depends on the relative dynamic scale of motion and interaction. When the topology change is slow, we observe an intermittent switching between laminar and burst states close to the transition due to small noise. This novel type of synchronization transition and intermittency can happen even when complete synchronization is linearly stable in the absence of noise. We show that the linear stability of the synchronized state is not a sufficient condition for its stability due to strong fluctuations of the transverse Lyapunov exponent associated with a slow network topology change. Since this effect can be observed within the linearized dynamics, we can expect such an effect in the temporal networks with noisy chaotic oscillators, irrespective of the details of the oscillator dynamics. When the topology change is fast, a linearized approximation describes well the dynamics towards synchrony. These results imply that the fluctuations of the finite-time transverse Lyapunov exponent should also be taken into account to estimate synchronization of the mobile contact networks.

The role of asymmetrical and repulsive coupling in the dynamics of two coupled van der Pol oscillators.

A system of two asymmetrically coupled van der Pol oscillators has been studied. We show that the introduction of a small asymmetry in coupling leads to the appearance of a wideband synchronization channel in the bifurcational structure of the parameter space. An increase of asymmetry and transition to repulsive interaction leads to the formation of multistability. As the result, the tip of the Arnolds tongue widens due to the formation of folds defined by saddle-node bifurcation curves for the limit cycles on the torus.

A perturbation-theoretic approach to Lagrangian flow networks

Complex network approaches have been successfully applied for studying transport processes in complex systems ranging from road, railway, or airline infrastructures over industrial manufacturing to fluid dynamics. Here, we utilize a generic framework for describing the dynamics of geophysical flows such as ocean currents or atmospheric wind fields in terms of Lagrangian flow networks. In this approach, information on the passive advection of particles is transformed into a Markov chain based on transition probabilities of particles between the volume elements of a given partition of space for a fixed time step. We employ perturbation-theoretic methods to investigate the effects of modifications of transport processes in the underlying flow for three different problem classes: efficient absorption (corresponding to particle trapping or leaking), constant input of particles (with additional source terms modeling, e.g., localized contamination), and shifts of the steady state under probability mass conservation (as arising if the background flow is perturbed itself). Our results demonstrate that in all three cases, changes to the steady state solution can be analytically expressed in terms of the eigensystem of the unperturbed flow and the perturbation itself. These results are potentially relevant for developing more efficient strategies for coping with contaminations of fluid or gaseous media such as ocean and atmosphere by oil spills, radioactive substances, non-reactive chemicals, or volcanic aerosols.

Smoothing effect for spatially distributed renewable resources and its impact on power grid robustness

In this paper, we show that spatial correlation of renewable energy outputs greatly influences the robustness of the power grids against large fluctuations of the effective power. First, we evaluate the spatial correlation among renewable energy outputs. We find that the spatial correlation of renewable energy outputs depends on the locations, while the influence of the spatial correlation of renewable energy outputs on power grids is not well known. Thus, second, by employing the topology of the power grid in eastern Japan, we analyze the robustness of the power grid with spatial correlation of renewable energy outputs. The analysis is performed by using a realistic differential-algebraic equations model. The results show that the spatial correlation of the energy resources strongly degrades the robustness of the power grid. Our results suggest that we should consider the spatial correlation of the renewable energy outputs when estimating the stability of power grids.

Development of a Numerical Method for Patient-Specific Cerebral Circulation Using 1D-0D Simulation of the Entire Cardiovascular System with SPECT Data.

The detailed flow information in the circle of Willis (CoW) can facilitate a better understanding of disease progression, and provide useful references for disease treatment. We have been developing a one-dimensional–zero-dimensional (1D–0D) simulation method for the entire cardiovascular system to obtain hemodynamics information in the CoW. This paper presents a new method for applying 1D–0D simulation to an individual patient using patient-specific data. The key issue is how to adjust the deviation of physiological parameters, such as peripheral resistance, from literature data when patient-specific geometry is used. In order to overcome this problem, we utilized flow information from single photon emission computed tomography (SPECT) data. A numerical method was developed to optimize physiological parameters by adjusting peripheral cerebral resistance to minimize the difference between the resulting flow rate and the SPECT data in the efferent arteries of the CoW. The method was applied to three cases using different sets of patient-specific data in order to investigate the hemodynamics of the CoW. The resulting flow rates in the afferent arteries were compared to those of the phase-contrastxa0magnetic resonance angiography (PC-MRA) data. Utilization of the SPECT data combined with the PC-MRA data showed a good agreement in flow rates in the afferent arteries of the CoW with those of PC-MRA data for all three cases. The results also demonstrated that application of SPECT data alone could provide the information on the ratios of flow distributions among arteries in the CoW.