Compare real and simulated C. elegans muscles; tune muscle model to get maximal similarity. about sibernetic HOT 13 CLOSED

According to data from the paper “A Biologically Accurate 3D Model of the Locomotion of Caenorhabditis Elegans”, Page 3, Table II (http://www.personal.utulsa.edu/~roger-mailler/publications/BIOSYSCOM2010.pdf),
maximal C. elegans single muscle cell force is equal to 2.5e-12 Neutons.
Now we need first to calculate our value of maximal muscle cell force used in Sibernetic and compare it to real one. Then, in case of significant difference, to find the reason and fix the problem.

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Great find Andrey. How is progress going on calculating the maximal force?

On 6 March 2014 12:00, a-palyanov [email protected] wrote:

According to data from the paper "A Biologically Accurate 3D Model of the
Locomotion of Caenorhabditis Elegans", Page 3, Table II (
http://www.personal.utulsa.edu/~roger-mailler/publications/BIOSYSCOM2010.pdf
),
maximal C. elegans single muscle cell force is equal to 2.5e-12 Neutons.
Now we need first to calculate our value of maximal muscle cell force used
in Sibernetic and compare it to real one. Then, in case of significant
difference, to find the reason and fix the problem.

Reply to this email directly or view it on GitHubhttps://github.com//issues/24#issuecomment-36849779
.

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First, I was not sure about how the length of the muscle is connected with the maximal force it can produce (considering that every 'segment' of the muscle contracts with a given force). I'm not sure that my explanation is clear, so here is the image and graph showing dynamics of the spring length (10 springs, from 1 to 10 segments long) changing between relaxed and contracted states (no gravity):

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Now let's build the graphs showing how relaxed length and contracted length depend from number of segments:

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Both curves above are linear. But if we subtract L_relaxed from L_contracted for all 10 (1 to 10 segments long) springs and divide each value by number of segments, we'll get the following curve:

I'm not sure about is it ok or not, but we should take it into account if we plan to calculate maximal muscle contraction force.

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Andrey - For the graph showing dynamics of the spring length (10 springs,
from 1 to 10 segments long) changing between relaxed and contracted states
can you explain it a bit more? The legend is in Russian, is the pink one 10
segments?

On 6 March 2014 13:21, a-palyanov [email protected] wrote:

First, I was not sure about how the length of the muscle is connected with
the maximal force it can produce (considering that every 'segment' of the
muscle contracts with a given force). I'm not sure that my explanation is
clear, so here is the image and graph showing dynamics of the spring length
(10 springs, from 1 to 10 segments long) changing between relaxed and
contracted states (no gravity):
[image: 21]https://f.cloud.github.com/assets/1803774/2345313/2f10c6ba-a532-11e3-8bf4-f5450bf6ea48.png

Reply to this email directly or view it on GitHubhttps://github.com//issues/24#issuecomment-36886772
.

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OK, so the curve is sublinear - indicating that as more segments are added
the muscle contracts proportionately less - am I understanding this
correctly?

On 6 March 2014 13:32, a-palyanov [email protected] wrote:

Both curves above are linear. But if we subtract L_relaxed from
L_contracted for all 10 (1 to 10 segments long) springs and divide each
value by number of segments, we'll get the following curve:
[image: 23]https://f.cloud.github.com/assets/1803774/2345372/ccbc21ec-a533-11e3-84fb-64af817cf1c6.png

I'm not sure about is it ok or not, but we should take it into account if
we plan to calculate maximal muscle contraction force.

Reply to this email directly or view it on GitHubhttps://github.com//issues/24#issuecomment-36887623
.

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@vellamike I have fixed the legend and updated that image. You are right - pink one corresponds to length = 10 segments.
"As more segments are added the muscle contracts proportionately less" - this is also true according to the observed behavior of the system.

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OK - is my understanding correct, that if you add segments the total muscle
contracts less (proportionately) ?

On 7 March 2014 00:55, a-palyanov [email protected] wrote:

@vellamike https://github.com/vellamike I have fixed the legend and
updated that image. You are right - pink one corresponds to length = 10
segments.

Reply to this email directly or view it on GitHubhttps://github.com//issues/24#issuecomment-36956957
.

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Yes, especially at low lengths.

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One more set of runs - now with various gravity, from 0 to 9*g:

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Test scene for stuff above is the following:

this structure is similar to the muscle tissue used in Sibernetic worm body model - same distances between neighbour particles, same structure of elastic connections, same coefficient of rigidity - so we can get all necessary muscle model parameters via making experiments with this scene.

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Let's consider the case when L=1 segment (at picture above there are 10 segments).
Relaxed length = 3.38e-06 m
Contracted length = 2.28e-06 m
then delta_l = 1.1e-06 m
Contraction force of a single muscle fiber connecting two particles = 4.225e-11 N (all fibers of a single muscle contract simultaneously in current model)
Rigidity coefficient of a single spring = 1.95e-05 N/m
Then simulated elastic tissue rigidity coefficient = contraction_force / delta_l = 3.84e-05 N/m
In the current model worm body shell elastic tissue differs from muscles only by the fact that muscles can contract when receive activating signal. Other structural properties are identical.

Now let's try to calculate Young's modulus of this elastic tissue to compare with its value for real biological worm body shell (1.3 ± 0.3 MPa)

In our case
F = 4.225e-11 N
Lo = 3.38e-06 m
delta_L = 1.1e-06 m
Ao = (2*3.38e-06 m)^2 = 4.57e-11 m2
and finally E = 2.83 Pa (vs real value = (1.3 ± 0.3 MPa))
So, something is significantly wrong here...

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