sibernetic
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Worm body modelling and mechanics - parameters, values etc.
One statement about worm body is the following: "The stiffness of the body is due to both high elastic modulus of its cuticle (the Young Modulus, E = 10–400 MPa, is comparable to rubber). Using measured viscoelasticity, it is possible to estimate the muscle power that is required to bend the body itself or to push the body against surroundings. In environments that pose little resistance (e.g., water), most muscle power is used to drive the bending of a stiff body. Only when the viscosity of surroundings increases by ~100-fold does the muscle power needed to push against the environment begin to compare with the power needed to bend the body. For over a ~10,000-fold increase in environmental viscosity, the muscle power varies by less than twofold [72]. Hence, the C. elegans motor circuit operates in low gear, pushing the animal through high resistance environments, and exhibiting little acceleration in low resistance environments." (source: https://scholar.harvard.edu/files/aravisamuel/files/zhen_curr_opin_neurobiol_2015.pdf)
Another one contains significanlty different values: "Despite the high stiffness measurements reported for the worm cuticle, an analysis based on the bending moments observed in the worm’s undulatory swimming gait leads to a significantly lower estimate for the Young’s modulus for the entire worm, 3.77 kPa (14); the mechanical loading in this experiment was provided by the worm’s own muscles as it swims, complicating interpretation and possibly underlying the low modulus value. Another recent study measured the worm’s bending modulus using deflection of the entire body under actuation from a single point (26). Calculating the Young’s modulus of the worm’s body yields a value ranging from 110 kPa to 1.3 MPa, depending on whether the worm is modeled as a uniform cylinder or cylindrical shell (26). The large range of reported values highlights our poor understanding of the mechanical properties of C. elegans. There is a clear need for elucidating the role of the cuticle, as well as the interplay of internal and external pressure, in the mechanics of the whole worm." (source: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4407266/)
Here I plan to discuss parameters, values and other stuff related to worm body modelling, and keep the history of progress on this, especially related to Sibernetic worm models.
Authors of the second paper mentioned in the previous message believe that "(A) The worm can be thought of as a stack of radially symmetric springs stretched to compensate for different internal and external pressures. (Inset) After the worm is punctured with a fine needle, internal organs are rapidly expelled, indicating high internal pressure (puncture location indicated by magenta arrow). (B) The system can be reduced to a one-dimensional model containing a valve that regulates the internal pressure."
Possibly it is a good idea to get rid of worm's internal liquid (in further versions of worm body model) and replace it with springs?
Another point (right now I don't have an estimate about how important it could be): in Sibernetic we do not take into account atmospheric pressure. However, the pressure of liquid when the worm is located inside it, will act on it.
The new version of Sibernetic is available on github (development branch). A set of parameters is tuned to provide more adequate properties of worm body and its movement (swimming, crawling) for half-resolution models. Here is a video of how it looks now:
https://www.youtube.com/watch?v=IUMI7XQpNBk
And here, for comparison, is a video of a real C. elegans swimming:
https://www.youtube.com/watch?v=qDvSYxNGSNg
And a figure showing the similarity/difference between a real and simulated trace of the worm's tail during swimming:
Hey guys, I've got some incredible news for those who work with Sibernetic.
As you probably remember, when I switched from full-resolution model to half-resolution model of the worm body, I've changed the mass and size (smoothing radius) of the particles, but preserved integration time step the same (I've missed to adjust its value). The length of half-resolution worm was 0.8 mm. Recently I've found the source paper corresponding to this worm swimming video, which was without scale bar. Here is the picture with scale bar, using which I've calculated that this worm's length is about 1.1 mm: 
So I've adjusted (encreased) the mass and radius of the particles (of the same half-resolution model) once more. And at this time I've finally realized that when mass of particles grows, integration time step can be encreased (for example, in modecular dynamics simulations masses of atoms is so small that it is necessary to use integration time step of a femto-second order). So, I've started to use larger and larger values (starting from our default value of 0.5e-5 s) and found, that simulation remains stable for the values up to 2.0e-5 s.
It is 4 times more than we used before, which means that for 1.1 mm worm body Sibernetic simulation is able to work 4 times faster. The new version, I hope, will be available on github in a few days.
I've decided to investigate the dependence of simulation quality on integration time step and used the swimming scene for this. Here are the initial and final positions of the worm:
Note that it swims by itself, without any additional conditions, in the mid-water, not at the bottom and not partially floating over the surface of the liquid (densities of the liquid and worm are equal). Here are the traces of the worm tail (as on some previous pictures in this thread) - a set of curves which were obtained from simulations, which differ from each other only in the value of dt (integration time step)
:
And here are the curves for the same set of dt values, which display the dependence of how the worm's center of mass changes with the time during the same process of swimming:
I'll be glad to discuss the problem of the choice of the optimal dt value.
If you have any suggestions about additinal calculations which will make the question about the good choice of dt more clear, feel free to inform me.
@a-palyanov: I have a question -- Do we consider the weight of the worm in our simulations? Maybe it is slower when it is heavier?!
On Wed, Dec 13, 2017 at 11:21 AM, a-palyanov [email protected] wrote:
If you have any suggestions about additinal calculations which will make the question about the good choice of dt more clear, feel free to inform me.
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Sure we consider the weight, and it is quite close to the weight of a real C. elegans (since density and geometry are also the same or almost the same as real). But these 5 runs differ only in dt, weight remains exactly the same.
Actually, I mean it's exact weight when it's movement has been recorded (a fed worm vs non-fed).
On Wed, Dec 13, 2017 at 12:29 PM, a-palyanov [email protected] wrote:
Sure we consider the weight, and it is quite close to the weight of a real C. elegans. But these 5 runs differ only in dt, weight remains exactly the same.
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Also, I was reading in some paper that there is a relationship between motor neurons participating in pharynx circuit and the movenet (body wall muscles). I have to mine a little more to find out the paper.
On Wed, Dec 13, 2017 at 12:42 PM, Vahid Ghayoomie [email protected] wrote:
Actually, I mean it's exact weight when it's movement has been recorded (a fed worm vs non-fed).
On Wed, Dec 13, 2017 at 12:29 PM, a-palyanov [email protected] wrote:
Sure we consider the weight, and it is quite close to the weight of a real C. elegans. But these 5 runs differ only in dt, weight remains exactly the same.
— You are receiving this because you commented. Reply to this email directly, view it on GitHub https://github.com/openworm/sibernetic/issues/127#issuecomment-351326293, or mute the thread https://github.com/notifications/unsubscribe-auth/AGWMgDtJQ1vQx05WGXqsoFN7wbwFmyowks5s_5HygaJpZM4P_PjF .