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22nd November

Spatial processing in the spine and motor cortex
Spatial processing in motor cortex: population vectors

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Neurons have broad tuning to preferred reach direction
The broad tuning of firing rate to ‘preferred’ reaching direction is a cosine curve
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1988)

Neuron i would have a preferred reaching direction if di, i
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preferred directions can be thought of as unit
vectors di
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So how do
we understand it?
The simplest thing to do is to take the firing rate weighted vector sum of preferred directions- this is the
definition of population vecotr
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d = ∑ifidi
Or firing rate weighted vector average, i
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each spike ‘votes’ for its cell’s

preferred direction
So this is a good way of averaging across all the noisy neurons to get a good
estimate overall of which direction the neurons are encoding
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These are with 10 degrees of each
other, the population vector is not exact
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Mental rotation of a population vector
A neuron might fire at a high rate when the monkey is reaching in a particular direction because it’s getting
proprioceptive information from the limb when it’s reaching in that direction, or the neuron could fire when
monkey is reaching in a direction because the neuron plays a part in the calculation of direction of
movement
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At the beginning, a small population vector points to the direction of
the LED, as time goes on, the vector increases in size and point at 90o away from the LED
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So he concluded that
this population of motor cortex neurons play a role in planning the direction of movement,
not simply a feedback signal of the direction movement from proprioception
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Population vectors
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Can also be applied to other neurons that are tuned to broadly represent a value,
e
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place cells, head direction cells
Each place cell has a preferred location, which could be a vector, so a rat’s location is well predicted
by firing rate weighted vector average of preferred locations:

It would give an estimate of the rat’s location but this doesn’t work as well as reaching movement
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If the average of all the preferred locations of place cells, each one weighted by firing rate of that
cell, there will be a bias towards the centre of the box
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Unlike for reaching, all the values are covered, and as it is a circular variable, there is no central
tendency
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The population vector is only actually the best optimal estimator when the tuning is a cosine
function
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Evaluation of population vectors
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Easy way to combine many rough estimates to get a more precise estimate
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Population vector occurs in many parts of the brain, e
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pitch, light, direction, location etc
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Spatial processing in the spine: convergent force fields
Problems in control of limb movement (even if you know the direction
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22nd November
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Unknown muscle tensions
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Solution: in the spine?

Bizzi et al
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He was interested in how that force changed according to different starting locations
The start of the arrow shows starting point of frog leg, arrow shows direction of movement, size
shows amplitude of force
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This is
expected
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They were called convergent force fields, CFF
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In other words, if the leg was already at the equilibrium position
to start with, stimulation of lateral neuropil region would produce no movement
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This
shows that there is complicated wiring, maybe from evolution and a bit during development, to take a blob
of activity caused by glutamate in the spinal cord, and produce a movement always towards the same
location
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All the equilibrium positions are
usually at the edge of the limb’s possible movements
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Maybe you can move your leg to any position by combining convergent force fields?

Equilibrium point control hypothesis
So combine one CFF with another to form an intermediate equilibrium position, by taking the average vector
in each location
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This is potentially very useful, so if
you will your leg to go anywhere, you can take it there from any position, just by giving the right amount of
relative activation to different CFF generators, with equilibrium positions around the edge of the work space,
by combining them, the leg can move to any intermediate position
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of CFF generators rather than a bunch of complicated
combinations of motor units
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Temporal element

Bizzi drops glutamate into the spine at time zero, CFF takes a while to develop
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But then over time, the CFF
develops and the equilibrium position goes outwards, then fading away again and coming back
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Then if he let go of the leg (not
holding it) the actual trajectory is quite similar to the predicted trajectory
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Bizzi have also done experiments where the leg moves up and down and the same results have been found
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It might not be as
relevant for primates because primates have more direct projections form the CNS to individual muscles
without much processing in the spine
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However, gross movements of the limbs may still have control from spinal cord using
equilibrium point control
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If this is true, this should be stimulated in a simple way
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, (1996)
Wanted to see if they could make a neural network, simple feed forward two layer network, where the
inputs are motor cortical neurons, these neurons should project to a small number of CFF generators,
simulating what’s going on in the spine
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e
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22nd November
They didn’t try to see if these connections could be
learnt by genetic algorithms or some unsupervised
learning algorithm during development, they just wanted
to see if there were connection weights possible to make
this network work, so they used lots of simulations
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He demonstrated that the motor cortical population
vector (15 neurons) could be connected to 4 CFF
generators so as to control a 6 muscle artificial arm
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The
motor cortical neurons gave input to the artificial neural
network and the movement of the monkey and the
movement of the robot arm were very similar
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Brain machine interface
Taking brain signals and move prosthetic devices
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2003
They took recordings form a primate’s brain, they included local field potentials and other electrical signals
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In this experiment, the task was to move the joystick and squeeze it
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The location of joystick is yellow, target location is green circle
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When he’s got there, he has to learn to squeeze the joystick at
a certain strength, so the yellow dot expands to the red amount, which is between the red circles
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After learning, a robot arm is introduced that is controlled by the monkey- brain control
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After a few trials of ‘brain
control’, the monkey realises it doesn’t have to move his arm, and it stops moving his arm
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This is
pretty cool

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