Would it be possible to have isoelasticity lines for volume-deformation plots?

[MartaUrb]

Do we have volume information for the E modulus from numerical simulations? It would be cool to be able to plot the volume against deformation with isoelasticity lines.

Although I am starting to doubt that the rotation of the contour gives an accurate estimate of volume. From the numerical simulations in the square channel it seems like the cell is actually taking some shape that has more of a square with rounded edges cross section rather than circular one in the axis perpendicular to the flow direction....

[paulmueller]

Yes, it should be possible to compute deformation-vs-volume isoelasticity lines.

Indeed, the shape of the cross-section perpendicular to the channel axis might not be rotationally symmetric. However, I think that the effect on volume will be small. Which numerical simulations are you referring to?

[EDIT 2020-05-04: I withdraw my statement on the effect on volume]

The only thing that I am unsure about are the conversion rules of deformation-volume isoelasticity lines for different flow rates, channel widths, or medium viscosities.

@chrherold How big would the effort be to extract the volume in addition to the area from the simulations? I guess they would have to be run again...

[chrherold]

I do not have the volume information but the guys who did the simulation should.

One would have to decide to either

• take the volume as constant during simulation (which is assumed for the simulations)
  This way one only needs to match the deformation points along the deformation path with the original volume which I guess could be done very fast.

• consider the "real life" effect that the convex hull has on the data as is done for the area. For this, one needs the shapes of in every data point which as far as I know was saved in the previous simulations.

@paulmueller It might well be that conversion is the same as in area deformation plots. But this is half-guessed.

@MartaUrb could you ask the guys for the data?

[paulmueller]

I'm transferring this to dclab, because it fits better here.
@MartaUrb Did you get back from Aland's group yet?

[MartaUrb]

Hi. I actually haven't asked. I am asking Lucas right now.

[paulmueller]

Just a quick update:

1. The new FEM simulations are now online and everything is much more transparent than before: https://doi.org/10.6084/m9.figshare.12155064.v2 🥳
2. I used these simulation results to create a new LUT (dclab 0.24.0), which is slightly larger and reproduces the old LUT with a maximal relative error of 0.1%.
3. I realized that the LUT is combined of numerical and analytical data.
4. I also realized that we compute the volume in dclab from the raw contour (not the convex contour, as it is done for area). This is something that might be important. We might think about adding a convex volume feature. What do you think? [EDIT 2020-05-04: This discussion was continued via private channels, we are still considering it]
5. To compute the volume-deformation isoelastics, I need to:
   • Generate a volume-deformation LUT from the FEM simulations on figshare
   • Find out what the volume values were for the analytical part of the LUT (Have to take a look at the Matlab scripts given to me by Christoph) - Extracting the simulation parameters was straight forward. Turns out that the resulting isoelasticity lines were cropped manuall (first 15 points and last point).
   • Maybe perform a pixelation correction for volume (as it is currently done for deformation). I first have to investigate how large the pixelation error in the Young's modulus could become. Ironically, for the convex volume, this pixelation effect appears to be negligible.
   • Investigate how volume-deformation isoelastics transform for different channel sizes, viscosities, and flow rates. Volume scales with (L'/L)³ - this is defined by the characteristic length scales described in Alexander Mietkes diploma thesis.
   • Implement volume-deformation pixelation correction in dclab
   • Test volume-deformation isoelastics (including pixelation correction)

[paulmueller]

I just added a script (ec97923, https://github.com/ZELLMECHANIK-DRESDEN/dclab/blob/master/scripts/pixelation_correction.py) for visualizing the pixelation effects (reproducing the figures in the arXiv paper https://arxiv.org/abs/1704.00572 by @chrherold and doing the same thing for volume). It also quantifies the errors made when computing the emodulus (or determining the corrected isoelastics for that matter).

Conclusion

• I can confirm that a change in the area does not significantly affect the emodulus computation via the LUT.
• This is also true for volume.
• For volume-deformation isoelastics (note that this does not affect the LUT, because the LUT is always area_um-deform), I have to add a pixelation correction function in dclab. This function is already hard-coded in pixelation_correction.py and just needs to be copied over to dclab (maybe some other logic is necessary, but the job is done mostly).
• Side note: If you have been following the discussions about volume and how it might or might not change with flow rate or other parameters, know this: The convex volume (i.e. volume computed from the convex contour) might be a much better approximation of the actual event volume than the regular volume (computed from the raw contour) as implemented in dclab. This is material for an ongoing discussion and should not be discussed here.