SLIDE 1
Brain areas
3 2 1
Fundamentals of Computational Neuroscience 2e December 27, 2009 - - PowerPoint PPT Presentation
Fundamentals of Computational Neuroscience 2e December 27, 2009 - - PowerPoint PPT Presentation
Fundamentals of Computational Neuroscience 2e December 27, 2009 Chapter 5: Cortical organizations and simple networks Brain areas Dorsal 3 1 2 Parietal lobe Frontal lobe Occipital Caudal Rostral lobe Temporal lobe Cerebellum
SLIDE 2
SLIDE 3
Hierarchical connectivity
V3 V3A PO V4t DP VIP 7a CITv MSTd V1 V2 VP PIP VOT PITv PITd MSTl AITv STPa TF FST TH AITd FEF CITd V4 MT STPp LIP 46
SLIDE 4
Layered cortex
I I I I II II II II III III III III IV IV IV IV V V V V VI VI VI VI
I II III IV V VI
- A. Different staining techniques
Golgi Nissl Weigert
{
{
{
{
{
{
- B. Variation in cortex
SLIDE 5
Layered cortical architecture
I II III IV V VI
Subcortex Cortex Subcortex Thalamus 2/3 2/3 4 4 6 6
V2 V1 LGN
SLIDE 6
Cortical maps
left eye left eye right eye right eye
- A. Ocular dominance columns
- B. Relation between ocular dominance
and orientation columns
1 2 3 4 5 6 1 2 3 4 5 6
Left visual field Right V1
Fovea
- C. Topographic map of the visual field
in primary visual cortex
- D. Somatosensory map
Genitals Toes Foot Leg Hip Teeth, gums, and jaw T
- n
g u e Lower lip Upper lip F a c e Nose Eye T h u m b Index Middle Ring F i n g e r s Little Hand W r i s t F
- r
e a r m Elbow A r m Shoulder Hand Neck Trunk abdominal
1cm
SLIDE 7
Neuronal chains
- A. Linear chain
- B. Diverging--converging chain
SLIDE 8
Netlets
0.25 0.5 0.75 1 0.25 0.5 0.75 1 0.25 0.5 0.75 1 0.25 0.5 0.75 1
Fraction of active neurons at t Fraction of active neurons at t Fraction of active neurons at t +1 Fraction of active neurons at t +1
Θ =1 Θ =2 Θ =3 Θ =4 Θ = 5 Θ =6
Saturation Steady state Saturation Steady state
Θ =1 Θ = 2 Θ =3 Θ = 4 Θ = 5
- A. Without inhibitory neurons
- B. With inhibitory neurons
SLIDE 9
Random networks with axonal delay
500 1000 500 1000 800 Time [ms] Neuron number
20 40 60 80 100 Frequency (Hz) Power
- A. Spike trains in random network
- B. Power spectrum in random network
20 40 60 80 100 0.5 1 1.5 Frequency [Hz] Power
a b e c d
9 m s 5ms 1 m s 1 m s 5ms 8ms
a e d c b a e d c b
9 8 4 1
a e d c b
3 9 8 7
- C. Spike activation with axonal delay
8 5 1 9 5 1
Time [ms] Time [ms] Time [ms]
10 9 8 1 from Izhikevich 2003/2006
SLIDE 10
1 % Created by Eugene M. Izhikevich, February 25, 2003 2 % Excitatory neurons Inhibitory neurons 3 Ne=800; Ni=200; 4 re=rand(Ne,1); ri=rand(Ni,1); 5 a=[0.02*ones(Ne,1); 0.02+0.08*ri]; 6 b=[0.2*ones(Ne,1); 0.25-0.05*ri]; 7 c=[-65+15*re.ˆ2;
- 65*ones(Ni,1)];
8 d=[8-6*re.ˆ2; 2*ones(Ni,1)]; 9 S=[0.5*rand(Ne+Ni,Ne),-rand(Ne+Ni,Ni)]; 10 11 v=-65*ones(Ne+Ni,1); % Initial values of v 12 u=b.*v; % Initial values of u 13 firings=[]; % spike timings 14 15 for t=1:1000 % simulation of 1000 ms 16 I=[5*randn(Ne,1);2*randn(Ni,1)]; % thalamic input 17 fired=find(v>=30); % indices of spikes 18 if ˜isempty(fired) 19 firings=[firings; t+0*fired, fired]; 20 v(fired)=c(fired); 21 u(fired)=u(fired)+d(fired); 22 I=I+sum(S(:,fired),2); 23 end; 24 v=v+0.5*(0.04*v.ˆ2+5*v+140-u+I); 25 v=v+0.5*(0.04*v.ˆ2+5*v+140-u+I); 26 u=u+a.*(b.*v-u); 27 end; 28 plot(firings(:,1),firings(:,2),’.’);
SLIDE 11