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This paper introduces a stochastic hemodynamic system to describe the brain neural activity based on the balloon model. A continuous-discrete extended Kalman filter is used to estimate the nonlinear model states. The stability, controllability and observability of the proposed model are described based on the simulation and measurement data analysis. The observability and controllability characteristics are in- troduced as significant factors to validate the preference of different hemodynamic factors to be considered for diagnosis and monitoring in clinical applications. This model also can be efficiently applied in any monitoring and control platform include brain and for study of hemodynamics in brain imaging modalities such as pulse oximetry and functional near infrared spectroscopy. The work is on progress to extend the proposed model to cover more hemodynamic and neural brain signals for real-time <i>in-vivo</i> application

Efficient hemodynamic states stimulation using fNIRS data with the extended Kalman filter and bifurcation analysis of balloon model