A HYBRID ASYMPTOTIC-NUMERICAL STUDY OF A MODEL FOR INTRACRANIAL-PRESSURE DYNAMICS

Lumped parameter, compartmental models of the human intracranial syste m are studied through development of a hybrid asymptotic-numerical tec hnique. Dimensionless variables are introduced so that disparate time scales can be identified, and analysis shows that the system of model equations varies over both a fast and a slow time scale. On the fast t ime scale, the 5 x 5 system of equations may be decoupled to give a re duced 3 x 3 system combined with two conservation laws for the cerebro spinal fluid and brain compartmental volumes, respectively, The stiffn ess condition of the reduced system is shown to be considerably improv ed over that of the original system, For the general nonlinear problem , a uniformly valid asymptotic approximation for large time is derived by a hybrid asymptotic-numerical technique. In the special case of th e linear problem, where compliances and resistances are assumed to be constants, the uniform approximation for large time is obtained analyt ically. To verify accuracy, both asymptotic and hybrid asymptotic-nume rical results are compared with direct numerical integration of the fu ll system. Physiological interpretations of the results are also given .