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‫מגיש‪ :‬עמית שבתאי‬
‫מנחה‪ :‬בני הוכנר‬
Abstract
Octopus vulgaris has been studied for more than 50 years,
but it has proven to be a very complicated creature.
The research group focus is understanding the way the
octopus moves, so this knowledge will be used, for
example, in the field of robotics.
It has been discovered that the octopus has a stereotypical
reaching movement.
The goal was to understand the mechanisms that generate
those movements and create a dynamic
computer model.
Octopus
Belongs to the Cephalopoda.
The only one with a brain.
An octopus is composed mainly of
muscles.
Arms uses:
sensing, chemotaxis, movement,
catching pray …
There is no preferred arm.
Special abilities:
change color, change body texture,
jet propulsion, ink ejection, regenerate.
Octopus is muscular hydrostat.
Degrees of freedom
Degree of freedom - The relative movement between two parts that
can be describes with one parameter.
Skeleton imposes a constraint on the number of
degrees of freedom.
The human hand has 7 degrees of freedom.
The octopus has a virtually infinite number of
degrees of freedom.
e=mc^2?
How can a movement
be calculated?!?!
Reaching movement
It was found (Guetfruind et al. 1996) that
the octopus has a stereotypical active
reaching movement (not whip like).
b.Bend
propogation
a. Bend
formation
It can be described as such:
a. A bend is formed somewhere along
the arm (suckers towards target).
b. The bend propagates from the
base part of the arm to it’s tip.
The part of the arm proximal to the
bend remains extended.
(Gutfreund et al. 1996)
Reaching movement
The bend of a normal reaching movement advances in a
slightly curved manner in a single linear plane.
(Gutfreund et al. 1996)
Velocity profile
Tangential velocity- bend advance in x,y,z axis (in 3D).
The velocity profile of the octopus has bell shaped characteristics:
Velocity stats:
(Gutfreund et al. 1996)
min
16 cm/sc
max
61 cm/sc
mean
35 cm/sc
sd
9.5 cm/sc
Embedded Reaching movement
•
•
•
The total number of neurons in an octopus is 5*108 .
In the arms, there are 3.5*108 neurons.
There are 3.8*105 motor neurons in each arm.
•
This information led to the assumption that the reaching movement of the
octopus is embedded in the arm itself.
Evoked Reaching movement
Arm extensions can be elicited in denervated
arms by electrical stimulation of the arm axial
nerve cord or by tactile stimulation of the skin
or suckers,
suggesting that a major part of this voluntary
movement is controlled by a motor program
that is confined to the arm’s neuromuscular
system. (Sumbre et al. 2001)
a. Arm cross section:
b. Axial nerve cord:
(Sumbre et al. 2001)
The Reaching Model
Our group has devised a dynamic computer model to simulate the
reaching movement of the octopus in 2D (3D is now the goal).
The model has a similar velocity profile like the normal reaching
movement.
There are several parameters that can be changed:
gravity, friction in water (drag), activation force …
OOW Movement Goals
1.
Analyze differences In Water and OOW environments for the
octopus, and its implications.
2.
Characterizing the bend point position in space, velocity profile,
duration.
3.
Understand the mechanism behind the reaching movement in
general.
4.
Comparison to the Reaching Dynamic Model.
OOW- Methods
The octopus’s movements were videotaped
on two cameras.
For each experiment a calibration body was used,
in order to integrate the data from the two
cameras into three dimensions.
During the OOW experiment, one of the octopus’s
arms was held by the experimenter.
OOW Environment
In OOW environment some parameters are not the same as in water:
1.
2.
No drag force OOW.
No buoyancy. Buoyancy force = (Density) (Volume)
Nm
Gm m
Gravitation force.
F 
G  6.67 *10
Kg
r
OOW movement is probably energetically costly.
2
3.
4.
g
1
2
2
11
2
OOW – Bend pos. in Space
The bend position in space in normal reaching movement is in a single
linear plane, with slightly curved path.
The bend position in OOW reaching movement is in three dimension.
Movement 6_1
OOW – Velocity profile
Velocity profile for normal reaching was calculated using
Tangential velocity formula.
dx 2 dy 2 dz 2
Vtan  (
dt
) (
dt
) (
dt
)
BUT,
base
The nonlinear nature of the OOW reaching movement makes this
formula inadequate. Another was used:
( xbend  x fp )2  ( ybend  y fp )2  ( zbend  z fp )2
V
dt
(which I term Euclidian velocity)
Reaching movement Velocity profile table:
Normal
Mean peak vel. (cm/sec)
num of movements
Upwards
OOW 1
OOW 2
35.24±9.55
28.1±10.74
7.88±2.59
15.94±5.5
83
17
23
13
OOW – movement duration
Reaching movement duration table:
Normal
Mean dur. (sec)
num of
movements
Upwards
OOW 1
OOW 2
1.02±0.42
1.11±0.38
0.97±0.4
1.03±0.34
83
17
23
13
Correction of arm base during OOW
reaching movement- two mechanisms
rotated_plane_expr3\day3\rotated_shot1_2.cor
rotated_plane_expr3\day3\rotated_shot1_2.cor
15
15
10
10
90° view of the bend
point as a function of
time
5
0
5
0
-5
-5
-10
base
10
5
time
base
0
-10
5
0
time
place in space
place in space
Tan vel.
Euc vel.
The advance of the
bend point is
independant of the
base correction
Bell shaped velocity profile?
• When using the Euclidian velocity profile on normal
reaching movements, the first phase was gone.
• This implies that this phase is due to a correction of the
base of the arm.
Euc vel profile
(Tan-Euc) vel profile
OOW – The Model
The parameters of the model were modified:
1. The octopus’s arm base is directed upwards.
2. The Drag force is eliminated.
3. No buoyancy OOW.
The activation forces were modified on need.
Fetch movement
• It is interesting to see another kind of movement-the fetch
movement, and understand how this movement can be
generated.
In water reach
(no gravity)
OOW reach
(gravity)
In water OOW
Movement dur.
0.8 sec
0.72 sec
Circadian Rhythms
Amit Shabtay
2004
The Clock in our Lives
• In 1729, DeMarain described a daily rhythmic opening and
closing of the leaves of a heliotrope plant.
• What was very interesting, is that this rhythm persisted, even
in the absence of light.
• Since then it has been discovered that this “clock” is present
in almost all eukaryotic life.
• Another kind of clock was found- a timer, on which we will
not elaborate.
Definitions
• Free run- only darkness conditions.
• Circadian time- the inner cycle of the animal, which is
usualy != 24 hours cycle.
• Solar time- 24 hours cycle of the sun.
• Citegeber time- artificial cycle given to the animal.
• All these cycles are normalized to 24 hours cycle.
Experimental Data
Solar time
Free run
Reseting the Clock
What about
blind people?
There are Many “Clocks”
•
The signal from the SCN travels to the
entire body, and affects many
functions of it.
Phase Response Curve
Next night will be earlier
Next night will be postponed
There is a delay in the
response of the clock
Two oscillating proteins
A few Words about Skeletal muscles
A skeletal muscle is a muscle that is
connected to the skeleton (as opposed to
the heart muscle or smooth muscle)
Always work in maximum tension
Length-Tension curves
The skeletal muscle has two kinds of forces- passive
force and active force
The Importance of Closed circle
Control
Mission
1a neurons
Calc firing rate
Check Sit.
Spindle
Activate muscle
α Motoneurons
Adding Load
Load is added,
Spindle is stretched
α Motoneurons cause
the muscle to contract.
Spindle is relaxed
Spindle is
stretched again.
Two Variable Equation
Firing motoneurons as a
function of muscle length
Muscle length as a function
of firing motoneurons
Two Variable Equation
Matching axes
Firing motoneurons as a
function of muscle length
Muscle length as a function
of firing motoneurons
Two Variable Equation
Joining graphs
Working
point
Correcting Errors
Correction
Error
‫תיקון‬
 ‫הגבר‬
‫שגיאה‬
Correcting Errors
Time of
error
Correcting Errors
When the amplification
is too high, oscillations
can occur
Stable Feedback System
•
The feedback system will always be stable if these three
conditions are met:
1. Amplification < 1
2. Short delays
3. Slow response to changes
Response
Firing rate
of mn α
Delay
Muscle
length
time
Returning to Working Point
Short delays,
Fast response
Returning to Working Point
Short delays,
Slow response