Modelling spatiotemporal properties of directionally sensitive multi-input single-output systems

The dynamics of directionally tuned linear multi-input single-output systems varies generally as a function of the spatial orientation of the inputs. A linear system receiving directionally specific inputs is represented by a linear combination of the respective input transfer functions. The input-output behaviour of such systems can be described by a vector transfer function which specifies the polarization directions of the system in real space. These directions, which can be either one (undirectional vector transfer function) or two (bidirectional vector transfer function) but never three, are obtained by computing the eigenvectors and eigenvalues of the system matrix that is defined by the gain and phase values of the system's response to harmonic stimulation directed along three orthogonal directions in space. The spatial tuning behaviour is determined by the quadratic form associated with the system matrix. Neuronal systems with bidirectional vector transfer functions process input information in a plane-specific way and exhibit novel characteristics, very much different from those of systems with unidirectional vector transfer functions.