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).

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.

a. Bend formation

b.Bend propogation

(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 profileTangential velocity- bend advance in x,y,z axis (in 3D).

The velocity profile of the octopus has bell shaped characteristics:

min16 cm/sc

max61 cm/sc

mean35 cm/sc

sd9.5 cm/sc

Velocity stats:

(Gutfreund et al. 1996)

Embedded Reaching movement

• The total number of neurons in an octopus is .

• In the arms, there are neurons.

• There are motor neurons in each arm.

• This information led to the assumption that the reaching movement of the octopus is embedded in the arm itself.

85*1083.5*10

53.8*10

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 voluntarymovement is controlled by a motor programthat is confined to the arm’s neuromuscularsystem. (Sumbre et al. 2001)

b. Axial nerve cord:

a. Arm cross section:

(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.No drag force OOW.2.No buoyancy. Buoyancy force = (Density) (Volume)

3.Gravitation force. 4.OOW movement is probably energetically costly.

1 22g

Gm mF

r 116.67*10G

2

2

Nm

Kg

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.

BUT,The nonlinear nature of the OOW reaching movement makes this formula inadequate. Another was used:

(which I term Euclidian velocity)

Reaching movement Velocity profile table:

2 2 2tan ( ) ( ) ( )

dx dy dzV

dt dt dt

NormalUpwardsOOW 1OOW 2

Mean peak vel. (cm/sec)35.24±9.5528.1±10.747.88±2.5915.94±5.5

num of movements83172313

2 2 2( ) ( ) ( )bend fp bend fp bend fpx x y y z zV

dt

base

OOW – movement duration

Reaching movement duration table:

NormalUpwardsOOW 1OOW 2

Mean dur. (sec)1.02±0.421.11±0.380.97±0.41.03±0.34

num of movements

83172313

Correction of arm base during OOW reaching movement- two mechanisms

0510

-10

-5

0

5

10

15

place in space

rotated_plane_expr3\day3\rotated_shot1_2.cor

time

05

-10

-5

0

5

10

15

time

rotated_plane_expr3\day3\rotated_shot1_2.cor

place in space

90° view of the bend point as a function of time

Tan vel. Euc vel.

The advance of the bend point is independant of the base correction

base base

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.

OOW reach(gravity)

In water reach(no gravity)

In waterOOW

Movement dur.0.8 sec0.72 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

Always work in maximum tension

A skeletal muscle is a muscle that is connected to the skeleton )as opposed to the heart muscle or smooth muscle(

Length-Tension curves

The skeletal muscle has two kinds of forces- passive force and active force

The Importance of Closed circle Control

Mission

Calc firing rate

Activate muscle

Check Sit.

α Motoneurons

1a neurons

Spindle

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

Muscle length as a function of firing motoneurons

Firing motoneurons as a function of muscle length

Two Variable Equation

Matching axesMuscle length as a function of firing motoneurons

Firing motoneurons as a function of muscle length

Two Variable Equation

Joining graphs

Working point

Correcting Errors

Correction

Errorהגבר

שגיאה

תיקון

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

time

Muscle length

Firing rate of mn α

Delay

Response

Returning to Working Point

Short delays,

Fast response

Returning to Working Point

Short delays,

Slow response