【摘要】 在脑血管疾病的临床实践中可以知道颅内压的变化和血液动力学的参数有着密切的关系.在颅内压脑血管动力学集中参数模型的基础上,对模型控制方程的数值解法进行改进,在计算量变化较小的情况下,得到近似解的局部截断误差估计,实现步长的自适应调整.使用矩阵特征方程分析微分方程的稳定性,通过在实际生理范围内变化模型参数,得到矩阵特征值的随参数的变化关系,指出数学模型的不足之处.还讨论了控制方程的稳定性对数值方法的重要影响,并得到步长的取值范围.通过理论分析,发现控制方程的解随时间的发展是不稳定的,解的变化和具体生理参数的选取相关.更多还原

【Abstract】 The close relations between the variation of intracranial pressure and hemodynamic parameters can be obtained from clinical practices. The numerical methods for solving the dominated equations are improved on the lumped parametric model of cerebral vascular dynamics. A estimation of local truncated errors to the approximate solution is reached without obvious additional costs. Eigenfunction of the coefficient matrix is used to analyze the stability of ordinary differential equations, so that the developing trends of eigenvalues are determined while the parameters change in terms of the medical ranges. The drawbacks of the mathematical model are pointed out for further revision. The stability of the governing equations could also impact on the reliability of numerical methods where the step length range is acquired. It is found that the solutions of the equations become instable with increasing time because they depend on time and selection of parameters. In conclusion, the applicable scopes for current hemodynamic model are summarized and novel considerations for its further improvement are given.更多还原