一类生物流体力学模型的稳定性

在研究颅内压集中参数模型的基础上，改进自适应的龙格-库塔法对一类生物流体力学模型进行数值模拟。通过合理控制计算量，得到了微分方程近似解的局部截断误差的估计。使用矩阵特征值分析微分方程的稳定性，在实际生理范围内变化模型参数，得到特征值随参数变化的关系，指出模型中存在实部为正的特征值。文章还讨论了控制矩阵特征值的变化对数值方法稳定步长的影响，并得到步长的取值范围。通过理论分析。得到控制方程的解随时间的发展和模型中生理参数的选取相关。分析了特征值变化的稳定性和参数的关系，并对模型进行改进，讨论其稳定性的情况。

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..