Organizational
Requirements
! Instructor contact
! MATLAB
! Signal Processing for Neuroscientists
! Cartoon Guide to Statistics (optional)
! Class List
! [email protected], 310-980-7453. Suite 17-369 NPI
! Please include NITP in the subject line of emails
! Sections and TAs
! Kevin McEvoy [email protected]
! Web site (http://ccn.ucla.edu/wiki/index.php/Principles_of_Neuroimaging_A) is a Wiki
! Pre-Requisites
! Username: NITP Password: 2007Problem Sets
! Due one week after assignment (usually)
" Basic Statistics
" Programming
" Integral Calculus
" Functional Neuroanatomy
! Send via email to Kevin and Mark
! NITP in Subject Line
! Midterm and Final
©2010 Mark Cohen, all rights reserved
www.brainmapping.org
1
©2010 Mark Cohen, all rights reserved
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Schedule (http://ccn.ucla.edu/wiki/index.php/Class_Schedule)
Week Topic
1 ! Orientation to Neuroimaging, Neurons, Brains
2 ! Linear Systems
3 ! Noise
4 ! Electricity and Electronics
5 ! Electrophysiology and Stats review
6 ! Advanced Statistics
7 ! Real-World Circuits
8 ! Getting your hands dirty
9 ! tbd
10! tbd
11! FINALS
Topics To Be Scheduled:
Spike Measurement and Analysis
Point Spread Functions
Principles of Optical Neuroimaging and Microscopy
Exploratory Data Analysis
Loose ends
©2010 Mark Cohen, all rights reserved
www.brainmapping.org
the UCLA Neuroimaging Training Program
! NIH-Sponsored Program Promoting
Multidisciplinary Training
Neuroscience, Statistics, Mathematics, Physics,
Engineering Computer Sciences
! Five Graduate Fellowships (including non-US
nationals)
! Annual Summer Advanced Fellowship
! Only Three Such Programs Funded
©2008 Mark Cohen, all rights reserved
www.brainmapping.org
3
©2008 Mark Cohen, all rights reserved
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How to Apply for Training
! NITP Will Prepare a Certificate for students
completing the requirements. This does not
depend on receipt of a fellowship.
! Pre-requisites:
" Integral Calculus
" Basic Statistics
" Electricity and Magnetism
" Computer Programming (any language)
" Functional Neuroanatomy
! Discuss with Home Department
! Contact Mark Cohen
©2008 Mark Cohen, all rights reserved
www.brainmapping.org
2
Topics
• anatomy of single neurons
• resting and action potentials
• transmission of signals
• chemical and electrical synapses
• information coding
• BOLD and unit activity
• EEG & SITE
• MR-visible effects
Neuronal Anatomy
and Electrical Activity
Mark S. Cohen
UCLA Psychiatry, Neurology, Radiology, Psychology,
Biomedical Engineering, Biomedical Physics
Suite 17-369 NPI
Cohen
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©2010 Mark Cohen, all rights reserved
Cohen
Types of Neurons
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©2010 Mark Cohen, all rights reserved
Resting Potential
Dendrites
Soma (cell body)
Typical:
-90 < resting potential < -60 mV
Axon
Axon terminals
Cohen
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©2010 Mark Cohen, all rights reserved
Cohen
Development of the Membrane Potential
– +
+
–
+
+
–
+
–
+
– +
–
+
–
Cohen
©2010 Mark Cohen, all rights reserved
+
–
–
Development of the Membrane Potential
– +
–
–
+
+
–
+
+
–
+
–
+
–
– +
+
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www.brainmapping.org
©2010 Mark Cohen, all rights reserved
+
– +
–
©2010 Mark Cohen, all rights reserved
+
–
+
–
Cohen
–
–
–
+
www.brainmapping.org
+
+
–
– +
Development of the Membrane Potential
– +
+
–
+
+
–
+
–
+
– +
–
+
–
+
Nernst Potential
@37°C
–
–
–
Observed Ion Concentrations
+
+
[Na+] 460 mM
p B [B]
p ymV
[y]in
RT10 mM p A [A]out[K+]
[K+]
400 mM
out p y [x]in-95
– +
RT [Cinside ]
ln
F
[Coutside ] +
[C
]
! 27mV ln inside
[Coutside ]
–
3 Na+ out
Cohen
Structure of the Cell Membrane
©2010 Mark Cohen, all rights reserved
Glycoprotein
5 nm
V
Polar
Head
Axon
Ringer’s Sol’n
Cholesterol
Carbohydrate
in
i
Nonpolar
Tail
Cytoplasm
-50
-100
Taken from Human Biology by Daniel Chiras
www.brainmapping.org
Current and Voltage
Sodium Permeability
Transient conductance increase
mV
Potassium Permeability
Voltage-dependent conductance
0
Neurons are REFRACTORY
after each Action Potential
-50
Membrane Potential
-100
1 ms
Cohen
©2010 Mark Cohen, all rights reserved
Cohen
©2010 Mark Cohen, all rights reserved
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Sodium Leakage with Action Potentials
100
50
“Action Potential”
0
Cytoskeletal Filament
Note: E-field is >10 MV/m!
©2010 Mark Cohen, all rights reserved
out
50 mV
Peripheral Protein
Integral Protein
Cohen
www.brainmapping.org
Electrical Behavior of Neurons
i
Extracellular Fluid
K+ inanions
x, y 2are
–75 mV
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©2010 Mark Cohen, all rights reserved
Cohen
+60 mV
E=
E=
Nernst Potential:
[Na+] 50 mM
!
$
ln##
&&
p
[A]
p
[B]
p
[x]
p
[y]
-45
to
-70
mV
[Cl-] F
540 mM
[Cl-]
40-100
mM
" A in B in x out y out %
[A-] 350
mM
A,B are
cations
–
Cell Volume = 9 x 10 -13 liters,
about half of which is liquid.
At 40 mM Sodium:
= 4.0 x 10-14 Moles Sodium/cell
With Each Action Potential:
ΔV = 0.13 Volt
Q = CV = 1.3 x 10-7 Coulombs /cm2
= 1.4 x 10-12 Moles/cm2
Surface Area = 2.8 x 10-5 cm2
Each AP passes 3.7 x 10-17 Moles of Na+
Na+
10 µm
C = 1µF/cm2
[Na+] is increased by 0.1% with each Action Potential!
After Hodgkin and Huxley, 1952
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Society for Psychophysiological Research. Berlin 2009
©2009 Mark Cohen, all rights reserved
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18
Sodium Potassium Pump
Cable Properties
After Matthews and van Holde: Biochemistry 2/e
"
Potassium Expelled
to Inside
!
Initial State
Pump Open to Inside
"
Extracellular
!
"
"
K+
K+
!
!
Na+
Na+
!
Na+
K+
K+
Na+ Taken from Inside
Na+
P
"
P
!
K+
P
K+
K+
Two Potassium
Ions Accepted
from Outside
"
K+
Intracellular
ATP Phosphorylates !
Subunit and Stimulates
Conformation Change
ATP
INSIDE OF CELL
!
! Na+
"
Na+
Cm rm
ri
Na+
ADP
!
Cm rm
!
Na+
Dephosphorylation
Stimulates Conformation
Change
rm
Cm rm
Na+
x
ri
ri
Vx
!x
=e "
V0
" = rm /ri
"
Na+
Na+
#2"
Sodium is Released
"
#"
2" x
"
0
For vertebrate neurons:
µm < " < mm
"
Pump Open to Outside
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©2010 Mark Cohen, all rights reserved
Cohen
Em
ri
Na+
P
! !
Cm
"
Vx/Vo
"
Voltage/Pressure Analogy
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©2010 Mark Cohen, all rights reserved
Cohen
Cable Properties
Extracellular
rm
Cm rm
Intracellular
ri
x
Cm rm
ri
rm
Cm
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©2010 Mark Cohen, all rights reserved
Cohen
Propagation of the Action Potential
V1
V2
V3
10
V4
V1
V3
V1
0
0
0
V4
thresh
V4
V2
0
0
0
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V3
0
V2
©2010 Mark Cohen, all rights reserved
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V3
V4
0
thresh
thresh
Resulting Velocity ~1-3m/sec
Cohen
20 msec
V2
thresh
thresh
thresh
15
Propagation of the Action Potential
V1
thresh
5
©2010 Mark Cohen, all rights reserved
Cohen
Em
ri
For vertebrate neurons:
0.5 msec < $ < 5 msec
0
ri
Cm
ri
V
Current
Cm rm
Resulting Velocity ~1-3m/sec
Cohen
©2010 Mark Cohen, all rights reserved
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thresh
Propagation of the Action Potential
V1
V2
V3
Propagation of the Action Potential
V4
V1
V1
V3
V1
0
0
0
thresh
V2
0
thresh
V2
V4
V2
0
0
0
V4
0
thresh
thresh
Resulting Velocity ~1-3m/sec
V2
V3
Propagation of the Action Potential
V4
V1
V1
V3
V1
0
0
0
thresh
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©2010 Mark Cohen, all rights reserved
Cohen
Propagation of the Action Potential
V1
V2
V3
0
thresh
V2
V4
V2
0
0
0
V4
0
thresh
thresh
Resulting Velocity ~1-3m/sec
V2
V3
Propagation of the Action Potential
V4
V1
V1
V3
V1
0
0
0
thresh
V2
0
thresh
V2
V4
V2
0
0
0
©2010 Mark Cohen, all rights reserved
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V4
V3
V4
0
thresh
thresh
Resulting Velocity ~1-3m/sec
Cohen
V3
thresh
thresh
thresh
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©2010 Mark Cohen, all rights reserved
Cohen
Propagation of the Action Potential
V1
thresh
Resulting Velocity ~1-3m/sec
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©2010 Mark Cohen, all rights reserved
Cohen
V4
V3
thresh
thresh
thresh
thresh
Resulting Velocity ~1-3m/sec
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©2010 Mark Cohen, all rights reserved
Cohen
V4
V3
thresh
thresh
thresh
V3
Resulting Velocity ~1-3m/sec
Cohen
©2010 Mark Cohen, all rights reserved
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thresh
Propagation of the Action Potential
V1
V2
V1
V3
Myelin Sheath
V4
V3
0
0
thresh
thresh
V2
V4
0
0
thresh
thresh
100 Å
Resulting Velocity ~1-3m/sec
Cohen
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©2010 Mark Cohen, all rights reserved
Nodes of Ranvier
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©2010 Mark Cohen, all rights reserved
Cohen
Saltatory Conduction
Internode:
High Membrane Resistance
Long Spatial Constant
Short Time Constant
Efficient Electrotonic Conduction
Myelin
Axon
Node:
Low Membrane Resistance
High Membrane Current Flow
Fires Action Potential
Action Potential Regeneration
Cohen
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©2010 Mark Cohen, all rights reserved
White and Gray Matter
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©2010 Mark Cohen, all rights reserved
Cohen
EPSP’s: Excitatory Post-Synaptic Potentials
Trans-Calossal
Fibers
Muscle end plate potentials
Recorded in low Ca2+ / high Mg2+
Boyd & Martin, 1956
Optic
Radiations
20
Arcuate Fibers
# of Observations
16
12
Amplitudes are quantized
and display a Poisson
distribution
8
4
After: Catani, et al., NeuroImage 17:77, 2002
0
0
0.4
0.8
1.2
1.6
2.0
2.4
2.8
Measured Potential (mV)
Cohen
©2010 Mark Cohen, all rights reserved
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Cohen
©2010 Mark Cohen, all rights reserved
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Reversal Potential
Outward
200
Neural Synapse
38 mV
Vset
Synaptic vesicles
Synaptic Bouton
–
+
+
0 nA
Golgi Complex
iout
Neuron
Synaptic vesicles
Extra-cellular fluid
Mitochondrion
-120 mV
0
2
Dendritic Spine
4
6
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©2010 Mark Cohen, all rights reserved
Postsynaptic Membrane
Presynaptic Membrane
8 msec
From: http://www.driesen.com/synapse.htm
After Magleby and Stevens, 1972
Cohen
Synaptic Cleft
Synaptic Cleft
-15 mV
200
Inward
Microtubules
epsp’s result from increased K
+ and Na+ conductance, with
%Na+ > %K+
Cohen
Synapses by EM
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©2010 Mark Cohen, all rights reserved
Synaptic Mechanism (movie)
Flat Vesicles
Delay from Presynaptic
Action Potential to
Post-synaptic Voltage
Change is ! 0.5 msec
Round Vesicles
Mitochondria
Synaptic Density
200 nm
Atlas of Ultrastructural Neurocytology
http://synapses.mcg.edu/atlas/1_6_1.stm
Cohen
©2010 Mark Cohen, all rights reserved
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Cohen
Synaptic Vesicles
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©2010 Mark Cohen, all rights reserved
Neurotransmitters
Small Molecules:
Acetylcholine
Serotonin
Histamine
Epinephrine
Norepinephrine
Dopamine
Adenosine
ATP
Nitric Oxide
Amino Acids
Aspartate
Gamma-aminobutyric Acid
Glutamate
Glycine
Exocytosis of Transmitter requires Ca2+
Peptides
Angiotensin II
Bradykinin
Beta-endorphin
Bombesin
Calcitonin
Cholecystokinin
Enkephalin
Dynorphin
Insulin
Galanin
Gastrin
Glucagon
GRH
GHRH
From: Matthews, G. Neurobiology: Molecules, Cells and Systems 2nd edn
Cohen
©2010 Mark Cohen, all rights reserved
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Cohen
©2010 Mark Cohen, all rights reserved
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Motilin
Neurotensin
Neuropeptide Y
Substance P
Secretin
Somatostatin
Vasopressin
Oxytocin
Prolactin
Thyrotropin
THRH
Luteinizing Hormone
Vasoactive Intestinal Peptide
!
…and many others
Electrical Synapses
Gap Junction Microstructure
Gap Junction
Channel
Connexon
NH3+
Connexon
Subunit
Gap
Junction
COO–
Intercellular Gap
50 nm
50 nm
Cohen
©2010 Mark Cohen, all rights reserved
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Gap Junctions have
no synaptic delay,
and may act as
simple resistance or
as electrical rectifiers
Modified from: http://aids.hallym.ac.kr
Cohen
SpatioTemporal Summation of psp’s
©2010 Mark Cohen, all rights reserved
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Integration of Inputs
Single epsp
2 mV
0
8 ms
12
Electrotonic properties of cells
can result in spatial
information zones within cells
6
0
-2
Summated epsp’s
http://www.oseplus.de/Images/jpg/Synapse1.jpg
Cohen
©2010 Mark Cohen, all rights reserved
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Cohen
Dendritic Spines
©2010 Mark Cohen, all rights reserved
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How Do Neurons Encode
Action Potentials are Identical!
1. Firing Rate: Ranges up to 1000 spikes/
second
2. Labeled Channels: Each neuron has
different information content
3. Modification of Synaptic Efficacy
4. Firing Synchrony
5. Transmitter Identity
1 µm
Atlas of Ultrastructural Neurocytology
Cohen
©2010 Mark Cohen, all rights reserved
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Cohen
©2010 Mark Cohen, all rights reserved
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Place Encoding - Basilar Membrane
Inhibition
V
20kHz
t
-60
Frequency
-70
K+ efflux
-80
20Hz
0
5
10
15 ms
Reversal potential of Cl– is near the
resting potential. Therefore, its
inhibition may be silent.
Cohen
©2010 Mark Cohen, all rights reserved
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Cohen
Pre-Synaptic Inhibition
Cl– influx
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©2010 Mark Cohen, all rights reserved
How does BOLD relate to neural firing?
Energy Demands in Transmission
Pre-synaptic:
Transmitter Synthesis
Exocytosis
Transmitter re-uptake
Inhibitory Synapse
Post-Synaptic
Maintenance of membrane potential after ion leakage
Excitatory: Removal of Sodium (Na/K pump)
Inhibitory: ???
Excitatory Synapse
©2010 Mark Cohen, all rights reserved
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Cohen
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©2010 Mark Cohen, all rights reserved
Logothetis results
Average
BOLD
Normalized Response
Logothetis Results
LFP = 40-130 Hz
MUA = 300-1500 Hz
Normalized Response
Cohen
Contrast
Time
On!
Post
Stim
BOLD
Pre !
Normalized Response
LFP * hrf
Logothetis, et al., Nature 412:152, 2001
Time
Cohen
©2010 Mark Cohen, all rights reserved
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Cohen
©2010 Mark Cohen, all rights reserved
LFP/MUA
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Types of Neurons
Presumed Origin of the EEG
+
+
+
–
+
–
–
–
–
Skin
Bone
CSF
–
Axon
©2010 Mark Cohen, all rights reserved
Cohen
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Many Neurons are Not “Seen” by EEG
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©2010 Mark Cohen, all rights reserved
Cohen
General Limitations in EEG Localization
Skin
Bone
Bone
•
•
•
•
•
CSF
Deeper Sources Show Weaker Signals
Magnitude Depends on Dipole Orientation
Magnitude Depends on Temporal Synchrony
Magnitude Depends on Spatial Coherence
Conductivity of Body Tissues (CSF, scalp) Blur the Scalp
Potentials
SITE = Simultaneous Imaging for
Tomographic Electrophysiology
©2010 Mark Cohen, all rights reserved
Cohen
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EEG at Rest
Cohen
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©2010 Mark Cohen, all rights reserved
Alpha Mapping
Fp2-F8
F8-T4
T4-T6
Average Power (µV2)
Fp1-F7
F7-T3
T3-T5
T5-O1
100µV
spectral power in the alpha
band
predicted BOLD
response
1.6
T6-O2
Fp2-F4
1 sec
F4-C4
C4-P4
P4-O2
Fp1-F3
1.4
1.2
1
0.8
0.6
0.4
0.2
F3-C3
0
C3-P3
0
0
P3-O1
25
50
1
©2010 Mark Cohen, all rights reserved
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100
125
2
150
175
3
time (sec)
time (minutes)
EKG
Cohen
75
Cohen
©2010 Mark Cohen, all rights reserved
www.brainmapping.org
200
225
4
250
SITE of Resting Alpha
EEG-fMRI Issues
• Scalp Potentials are Proportional to the Derivative of
the Voltage, whereas fMRI is Proportional to the
Integral of the Firing
• The Action Potential, per se, Is Probably Invisible to
BOLD
• The Rhythmic Structures in the EEG May Depend More
on Synchronous Firing than on High Firing Rate
• The BOLD Signal is Likely Associated with the PostSynaptic Neurons
R
Goldman (2002) NeuroReport 13(18):2487
Cohen
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©2010 Mark Cohen, all rights reserved
Cohen
MR-Lucent Neurophysiology
Energetic Demands!
©2010 Mark Cohen, all rights reserved
www.brainmapping.org
Thanks.
(BOLD, ASL)
Transmitter Synthesis, Exocytosis, Metabolism
Na+/K+ Pump
Cohen
[Na+]"
Imaging
Glucose Metabolism"
Spectroscopy
Extracellular Currents (?) "
Phase Disturbance
Anisotropic Diffusion"
DTI, etc…
Neural Constituents (NAA) "
Spectroscopy
©2010 Mark Cohen, all rights reserved
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Cohen
The Neural Membrane
©2010 Mark Cohen, all rights reserved
Anatomy of a single neuron
Dendrites
Observed Capacitance: 1 µF/cm2
Since:
C!
www.brainmapping.org
1.1k
4"d # 10 $12
Soma (cell body)
If k (the dielectric constant) is about 6,
then d ! 5 x 10-7cm = 50 Å.
Axon
If P.D. ! 0.1 Volt, then the E field is
"
2 x 107 V/m !
Schwann Cells
©EnchantedLearning.com
Axon terminals
Cohen
©2010 Mark Cohen, all rights reserved
www.brainmapping.org
Cohen
©2010 Mark Cohen, all rights reserved
www.brainmapping.org