Two-dimensional Models of Neural Sheets

研究人员Troy研究了在模拟大脑皮层时产生的Wilson-Cowan型积分-微分方程组的动力学行为。他的目标是了解二维神经膜中神经元之间的微妙联系，这些联系负责(I)稳定旋转波的形成，以及(Ii)组织中心的存在，这些组织中心导致周期性的环状波形成并通过介质向外传播。他使用了计算技术，以及渐近分析和约化方法，使模型简化为易于处理的形式。数学和计算结果预测和验证了稳定旋转螺旋的存在，以及最近发现的大鼠大脑枕叶皮质的周期性环状波。本研究开发的技术为理解一般神经网络模型中持续模式的形成提供了新的方向。中枢神经系统中的神经元网络表现出各种持续的波形模式。它们的范围从由同步爆发的尖峰组成的振荡波到二维环状波和旋转的螺旋波。研究人员感兴趣的是了解这种二维波是如何在大脑中形成和传播的。他使用模拟和数学方法开发了有助于理解波浪形成的模型。这位研究人员和实验神经学家之间的合作研究导致了最近在大鼠皮质中发现的螺旋波。这是第一次对哺乳动物皮层中的螺旋波进行真正的验证。螺旋波被推测与大脑癫痫的发生有关。该项目的成果也包括在为学生设计的新的跨学科课程中。

Troy The investigator studies the dynamical behavior of systemsof Wilson-Cowan type integro-differential equations that arise inmodelling cortex. His goal is to understand the subtleconnections between neurons in two-dimensional neural sheets,which are responsible for (i) the formation of stable rotatingwaves, and (ii) the existence of organizing centers that causeperiodic ring-shaped waves to form and propagate outward throughthe medium. He employs computational techniques, as well asasymptotic analysis and reduction methods, which allow the modelsto simplfy to tractable forms. The mathematical and computationalresults predict and verify the existence of stable rotatingspirals, and periodic ring-shaped waves recently discovered intangential slices of occipital cortex of rat brain. Thetechniques developed in this study provide a new direction forunderstanding persistent pattern formation in general neuralnetwork models. Neuronal networks in the central nervous system exhibit avariety of persistent wave patterns. These range from oscillatorywaves consisting of synchronized bursts of spikes totwo-dimensional ring-shaped waves and rotating spirals. Theinvestigator is interested in understanding how suchtwo-dimensional waves form and propagate in the brain. He usessimulations and mathematical methods to develop models that aidin the understanding of wave formation. Cooperative researchbetween the investigator and experimental neuroscientists has ledto the recent discovery of spiral waves in rat cortex. This isthe first true verification of spiral waves in mamallian cortex.Spiral waves are conjectured to be associated with the occurenceof seizures in the brain. The results of this project are alsoincluded in the design of new interdisciplinary courses forstudents.