Estimation of hidden state variables of the intracranial system using constrained nonlinear Kalman filters

Impeded by the rigid skull, direct assessment of physiological variables of the intracranial system is difficult. A hidden state estimation approach is designed in the present work to facilitate the estimation of unobserved variables from available clinical measurements including intracranial pressure (ICP) and cerebral blood flow velocity (CBFV). The estimation algorithm is based on a modified nonlinear intracranial mathematical model, whose parameters are first identified in an offline stage using a nonlinear optimization paradigm. Following the offline stage, an online filtering process is performed using a nonlinear Kalman filter-like state estimator that is equipped with a new way of deriving the Kalman gain using the physiological constraints on the state variables. It is shown in the present work that changes of nominal radii of the proximal and distal cerebral arterial vascular beds could be tracked by using the proposed hidden state estimator.