Phenomenological modelling of some mechanisms in schizophrenia

The paper shows how mechanisms being important factors in the development and treatment of schizophrenia can be modelled in terms of differential equations in order to understand better the interplay of these mechanisms. As an example, the nigrostriatal loop is chosen which is an essential part of the basic model presented by Carlsson. In the beginning, piecewise linear functions are used to demonstrate the mathematical procedures and to show that even such approximations can explain qualitative features. This is the case in particular in the neighbourhood of the operating point, which is shown to be an adequate concept in a situation of missing data on all complicated details. The simplified picture can be improved step by step. For instance, we calculate the occupation of receptors by dopamine and other ligands, and show how the operating point varies between healthy persons and schizophrenics (without and with neuroleptics). Different causes of the hypoactivity of striatal output can be discussed. That the modelling methods presented here can be applied to mechanisms in the mesoaccumbal system and in the cortex as well shall be shown in a forthcoming paper.