Relating DirectedMotion Strength to Pressure in CPM

[David Dolgitzer]

Hello,

I am attempting to simulate micropipette aspiration (MPA) on a single cell using CPM. My approach involves defining a custom boundary that represents the pipette as two protruding lines with a measurable width. Within this pipette region, I apply a local DirectedMotion, which, based on visual observation and initial analysis, effectively mimics aspiration.

However, I am struggling with correlating the strength of DirectedMotion to an actual pressure value. I can measure the velocity of a cell subjected to a given DirectedMotion strength and then estimate the pressure using Stokes’ law, assuming a known media viscosity. But this velocity is highly variable between simulation runs, and any changes to the cell properties (such as volume or surface constraint strengths) affect how the cell responds to DirectedMotion. This means I need to run multiple simulations to determine an average velocity for each parameter set, which is both tedious and impractical.

My questions:

1. Is there an alternative way to model local pressure in CPM other than using DirectedMotion?

2. If not, is there a known or more systematic way to relate DirectedMotion strength to pressure?

Any insights or suggestions would be greatly appreciated!

Best,

David

[Lutz Brusch]

Hi David,

yes, you can apply DirectedMotion locally by using an expression as function of position (or a Global/Field as mask) to limit the strength parameter to the inside of the pipette. 

Your observed dependency on the other energy contributions from volume and surface constraint strengths is typical for CPM since motion results from individual updates to lattice nodes which locally deform the cell with or against the volume and surface constraints. This is especially useful when you model a narrow pipette compared to the cell diameter. There the CPM cell shape approaches an equilibrium with a cell protrusion that extends a certain distance into the pipette and that distance becomes a function of DirectedMotion strength (~pressure) over surface constraint strength. 

Regarding variable observables across repeated runs with the same parameter set, you may measure the velocity from the displacement after a longer time interval such that the dynamics averages during a single run already. On the other hand, you will always observe some variability and quantifying this (from multiple runs) is interesting data. To automate the statistical analysis, please see the R code shared by Earvin on Dec 5th 2024 in another conversation in this group.

For a systematic relation between CPM strength parameters versus force and pressure please see
- Rens E. G. and Edelstein-Keshet L. (2019) From energy to cellular forces in the Cellular Potts Model: An algorithmic approach. PLOS Comp. Biol. 15(12), e1007459. https://doi.org/10.1371/journal.pcbi.1007459
- Magno R., Grieneisen V. A. and Marée A. F. M. (2015) The biophysical nature of cells: potential cell behaviours revealed by analytical and computational studies of cell surface mechanics. BMC Biophysics 8, 8. https://doi.org/10.1186/s13628-015-0022-x

Best,
Lutz

for Morpheus.lab

[David Dolgitzer]

Thank you so much!

David