Stability for a Kind of Biofluidmechanical Models

The stability of a kind of biomechanical models with lump parameters was discussed. Based on a lumped parametric model of intracranial pressure, an adaptive Runge-Kutta method had been revised for numerical simulation. The local truncated error estimation of the approximately solution could be obtained with reasonable computational cost. Eigenvalues of the matrix were presented to analyze the stability of the equations in the model. The relations between the variations of eigenvalues and parameters in the matrix were shown. The existing of eigenvalue with positive real part leads to the instability of solutions. The influences on the stabilized step lengths by the eigenvalues of the matrix were also studied and the maximum length of the step was calculated. It is found that the developing trends of the numerical results depend on the selection of the clinical data in the model. The connection between the preferences and the stability on the variation of eigenvalues was further considered on the characteristics of the spectrum and Wilkinson conditional values. The model is improved and its stability is also contemplated. In conclusion, the applicability of the hemodynamics model is summarized and the considerations for ulterior amelioration are provided..