Choice of implicit and explicit operators for the upwind differencing method

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76274/1/AIAA-1988-624-513.pd

Numerical evaluation of a solution representing a jet in cross-flow

SIGLEAvailable from British Library Document Supply Centre- DSC:8670.19(RAE-TM-AERO--2137) / BLDSC - British Library Document Supply CentreGBUnited Kingdo

Numerical evaluation of a solution representing a jet in cross-flow

SIGLEAvailable from British Library Document Supply Centre- DSC:8670.19(RAE-TM-AERO--2137) / BLDSC - British Library Document Supply CentreGBUnited Kingdo

Effects of basal ganglia on cortical computation: A hybrid network/neural field model

The basal ganglia play a crucial role in the execution of movements, as demonstrated by the severe motor deficits that accompany neuronal degeneration in Parkinson's disease. Since motor commands originate from the cortex, an important functional question is how the basal ganglia influence cortical computation, and how this influence becomes pathological in Parkinson's disease. To explore this issue, we developed a hybrid neuronal network/neural field model. The neuronal network consisted of 9900 event-driven rule-based neurons, divided into 15 excitatory and inhibitory thalamocortical cell populations. This model was then embedded in a neural field model of the basal ganglia-thalamocortical system. This model included direct and indirect pathways via the striatum, a hyperdirect pathway via the subthalamic nucleus, thalamostriatal connections, and local inhibition in the striatum and globus pallidus. Both network and field models have been separately validated in previous work, with both shown to produce realistic firing rates and spectra. Spikes generated by the field model were used to drive the network model. Four types of drive were explored: (1) spikes drawn from a white-noise distribution; (2) spikes generated by the thalamocortical field model; (3) spikes generated by the full basal ganglia-thalamocortical field model; and (4) spikes generated by the full field model, with parameters based on parkinsonian individuals. In each case, we explored the information throughput in the network model from layer 2/3 (representing input from premotor and other cortical areas) to layer 5 (representing output to spinal cord motor neurons) using spectral Granger causality. All models had peaks in the coherence spectra at roughly 0 and 15 Hz; however, overall coherence in the white-noise model was roughly half that of the other three models, indicating that input from the thalamocortical system is the primary determinant of overall coherence. Compared to the healthy basal ganglia model, the parkinsonian model showed greater Granger causality at frequencies below 10 Hz, and less at frequencies above 10 Hz. Causality in the opposite direction (layer 5 to layer 2/3) at 5 Hz was several times times greater in the parkinsonian versus the healthy model, indicating a reversal in the direction of normal information flow. We speculate that the observed increases in Granger causality at low frequencies may be associated with tremor, while decreases at higher frequencies may contribute to bradykinesia. These results demonstrate that the brain's large-scale oscillatory environment strongly influences the information processing that occurs within its subnetworks