Classification of cerebrovascular pathologies in real-time using nonlinear ODE-based surrogate model

Abstract In this paper we consider the coefficient inverse problem for a second-order nonlinear ODE surrogate model describing hemodynamic parameters during intraoperative neurosurgical measurements. This mathematical model of cerebral hemodynamics is based on the generalized Van der Pol–Duffing equation and described the local interaction of the velocity and pressure of blood flow in cerebral vessels. For each patient, the coefficients of this equation are individual and are determined from clinical data in real-time by solving the coefficient inverse problem. We apply the gradient method for optimization of the cost functional with the analytical finding of initial guess to get the coefficients by clinical data obtained during neurosurgical operation in the vicinity of arterial pathologies. A good initial guess is based on the analytical Fourier method. Statistical analysis of clinical data has shown that the surrogate model equation is sensitive to different types of pathology, which allows intraoperative monitoring of the patient’s condition and assessment of the type of pathology in real time. Numerical results are presented and it is shown that the proposed mathematical model and numerical method predict clinical data well.