Qualitative simulation of physiological dynamical models involving second-order derivatives

Qualitative simulation of dynamical models is a promising new subject in the field of artificial intelligence, especially suitable for the analysis of clinical and physiological problems. The major limitation of this method, however, consists in the excessive number of alternative solutions arising when systems of order higher than one are simulated. In particular, many solutions produced in the course of qualitative reasoning are inconsistent, i.e. they have no real physical significance. The present study analyses how a second-order dynamical model can be qualitatively simulated, avoiding the occurrence of inconsistent solutions. This is made possible by including additional qualitative constraints in the model, i.e., constraints which do not merely arise from causal links between quantities, but depend on the peculiar nature of mathematical equations. In particular, we suggest the use of some constraints on the second time derivatives of state variables, evaluated at those instants when the first time derivatives become zero. A simple example, concerning qualitative simulation of a second-order compartmental model is presented and discussed.