Mathematical models of motion detection in the fly's visual cortex
| dc.contributor.committeeChair | Martin, Clyde F. | |
| dc.contributor.committeeMember | Dayawansa, Wijesuriya P. | |
| dc.contributor.committeeMember | Sun, Shan | |
| dc.creator | Chen, Baili | |
| dc.date.accessioned | 2016-11-14T23:16:18Z | |
| dc.date.available | 2011-02-18T20:34:27Z | |
| dc.date.available | 2016-11-14T23:16:18Z | |
| dc.date.issued | 2005-12 | |
| dc.degree.department | Mathematics | en_US |
| dc.description.abstract | Visual motion detection is one of the most active areas in neuroscience today. In this work, we study the mechanism of motion detection in the fly's visual cortex. The work consists of three parts: First, investigate how the direction signals of the moving objects are encoded in the visual cortex of a fly. Several differential equations are derived to model the dendrites which carry information to the tangential cells in the visual cortex of a fly and to model the dynamics in the synaptic inputs. One of these equations can be reduced to an asymmetric forced van-der-pol equation. Studying this equation in detail, it is found that when the parameters are within certain range, there exists a periodic solution. By tracing the trajectory of this solution together with solving the other differential equations, a conclusion is drawn which can explain how the visual system of the fly encodes the motion signal like the change of the direction. The second part of the work aims to find out the mechanism underlying the ¡°vector addition¡± as stated in ¡°population vector¡± hypothesis. Mathematical models are built to model a decending neuron and two tangential cells. Partial differential equations are derived and solved to find out the relation between the input and output of the decending neuron. We come to the conclusion that if the visual cortex of the fly does perform vector addition, this ability should be mainly attributed to the special arrangement of the synaptic locations on the dendrites. In the third part of the work, we propose a hypothesis about how the brain of a fly reconstruct motion trajectory based on the firing rates of the neurons in the brain. | |
| dc.format.mimetype | application/pdf | |
| dc.identifier.uri | http://hdl.handle.net/2346/14190 | en_US |
| dc.language.iso | eng | |
| dc.publisher | Texas Tech University | en_US |
| dc.rights.availability | Unrestricted. | |
| dc.subject | Visual cortex | en_US |
| dc.subject | Differential equations | en_US |
| dc.subject | Motion detection | en_US |
| dc.subject | Modeling | en_US |
| dc.title | Mathematical models of motion detection in the fly's visual cortex | |
| dc.type | Dissertation |