Milstein-Sloan-Swartz-Annual-2008 by hilen

VIEWS: 4 PAGES: 16

									Noise, Power Laws, and the Local Field Potential
Sloan-Swartz 2008 Summer Meeting

Joshua Milstein1, Florian Morman1,2, Itzhak Fried2 and Christof Koch1
Institute of Technology 2David Geffen School of Medicine and Semel Institute of Neuroscience and Human Behavior, University of California, Los Angeles
1California

Physical Motivation
Human Intracranial Recordings

Scaling Exponent () N = 106 16

546

16

Compartmental Model
To generate the membrane currents

Pyramidal hippocampal cell within rat CA1
3-D topological reconstruction

Hodgkin-Huxley Style Kinetics
o Voltage dependent Na+, K+,Ca2+ currents o 12 different processes
i (nA)

NEURON Simulation Environment
t (ms)

Used to compare intracellular to extracellular recordings
Henze (2000) & Gold (2006)

Power Laws

Power/Slope

Scale Invariance:
QuickTime™ and a decompressor are need ed to see this picture.

Earthquake Magnitude

Electron Shot Noise

Pulse Amplitude

Time

Neuron Shot Noise

Pulse Shape

Spike Timing

Stochastic Variable:

tk1

tk2 tk3

tk4

tk5

tk6

tk7

Time

Autocorrelation Function

Wiener-Kinchin Theorem:

Power Spectrum

Autocorrelation Function

Simple Case I: Uncorrelated, Slow Synaptic Pulses

Simple Case II: Sharp Spike

Pulse Amplitude

Time

Contains All Time/Frequency Dependence

White Noise

QuickTime™ an d a decompressor are need ed to see this p icture .

Independent at each timestep

Binary Sequence: 10011010011010010001001100000100010111

QuickTime™ and a decompressor are need ed to see this picture.

Brown(ian) Noise

QuickTime™ and a decompressor are need ed to see this picture.

Autocorrelation Function:

Power Spectrum:

Amplitude

Random Walk with a Threshold

QuickTime™ an d a decompressor are need ed to see this p icture .

Timestep

Spike Train

QuickTime™ and a decompressor are neede d to see this picture.

White Noise ?!?

Telegraph Process

Autocorrelation Function:

Let

and

 = -2

Summary
1. Experimental Evidence for a Universal 1/f^2 Scaling in the LFP of Humans 2. Developed a Simple Mathematical Treatment for Understanding Power Laws in the LFP 3. Brownian Noise Can Arise From Single Neuron Activity Biophysical Examples: a. Sharp spikes followed by slow decay b. UP-DOWN states of activity

** Funded by the Swartz Foundation **


								
To top