Testing non-linearity and directedness of interactions between neural groups in the macaque inferotemporal cortex

Information processing in the visual cortex depends on complex and context sensitive patterns of interactions between neuronal groups in many differen t cortical areas. Methods used to date for disentangling this functional co nnectivity presuppose either linearity or instantaneous interactions, assum ptions that are not necessarily valid. In this paper a general framework th at encompasses both linear and non-linear modelling of neurophysiological t ime series data by means of Local Linear Non-linear Autoregressive models ( LLNAR) is described. Within this framework a new test for non-linearity of time series and for non-linearity of directedness of neural interactions ba sed on LLNAR is presented. These tests assess the relative goodness of tit of linear versus non-linear models via the bootstrap technique. Additionall y, a generalised definition of Granger causality is presented based on LLNA R that is valid for both linear and non-linear systems. Finally, the use of LLNAR for measuring non-linearity and directional influences is illustrate d using artificial data, reference data as well as local field potentials ( LFPs) from macaque area TE. LFP data is well described by the linear varian t of LLNAR. Models of this sort, including lagged values of the preceding 2 5 to 60 ms, revealed the existence of both uni- and bi-directional influenc es between recording sites. (C) 1999 Elsevier Science B.V. All rights reser ved.