Paper & poster are available on the COMSOL conference website: www.comsol.com/paper/direct...

"Within the competition to bring this field to a new level, SimuCell3D is remarkable and will mark a clear evolution of the topic."
🥁That’s what the committee said about this #SIBRemarkableOutputs 2024
👉Discover the output: tinyurl.com/53arz2rz
@iberd.bsky.social

The goal: make it easier for others to reproduce and extend these models within COMSOL.

We hope this serves as a generalizable reference for simulating collective cell behavior and pattern formation.

arxiv.org/pdf/2509.08930

This complements our earlier work introducing the DCM model 👉 bsky.app/profile/iber...

That previous paper focused on the biological questions and mathematical framework.

Here, we focus on the practical COMSOL #PIDE implementation: setup, BCs, 1D–3D, and Lagrangian reformulation for growth.

Paper: doi.org/10.1016/j.ne...

Tweetorial: x.com/DagmarIber/s...

📄 Read the full study here: doi.org/10.1101/2025...

🎯 Useful for: developmental biology, tissue engineering, pattern formation, and computational modeling

#DevBio #PatternFormation #CellMigration #Morphogenesis #ComputationalBiology

📌 Summary:

• #DCM is a rapid, robust mechanism for developmental pattern formation
• COMSOL FEM implementation makes DCM models numerically accessible
• #DCM patterning parameter ranges and timeframes
• Pattern Orientation via attraction anisotropy or directed tissue growth

👇Thread 🧵(10/11)

2. Dynamic #attraction #zones

Spatially varying cell attraction that changes with tissue growth can guide migrating cells, leading to precise large-scale patterning.

This mimics how tissues form rings, bands, or layered structures in vivo.

👇Thread 🧵(9/11)

We identify two mechanisms for guiding pattern orientation:

1. #Anisotropic #attraction
Cells pulling or migrating more strongly in one direction form aligned stripe-like patterns—e.g., during directional tissue growth.

👇Thread 🧵(8/11)

#DCM naturally leads to unoriented patterns—spots, labyrinths—similar to Turing-like systems.

But biological tissues often require oriented patterns to fulfill specific functions.

Can DCM produce stripes, too?

👇Thread 🧵(7/11)

Three key parameters drive the emergence and morphology of patterns:

• Initial density of motile cells
• Intercellular attraction strength
• Cell sensing radius

👇Thread 🧵(6/11)

Simulations and linear stability analysis allowed us to find #critical #conditions for pattern formation and predict #patterning #speed.

We show under which conditions #DCM can realistically pattern tissues in development.

👇Thread 🧵(5/11)

We developed a mathematical framework that represents a wide range of #DCM cues, e.g., chemotaxis, durotaxis, haptotaxis & a general Finite Element Method #FEM:

👉 1D, 2D, 3D
👉 arbitrary geometries & boundary conditions
👉 isotropic & anisotropic interactions
👉 fast, large-scale simulations

🧵(4/11)

To study #DCM, both discrete and continuum models have been used.

But:
👉 Discrete models are computationally expensive.

👉 Continuum models have required custom Finite Volume Method #FVM implementations—until now.

👇Thread 🧵(3/11)

During embryonic development, cellular tissues transition from uniform starting conditions into robust spatial patterns.

#DCM offers a particularly fast and versatile route to spontaneously symmetry breaks and pattern formation without tissue buckling.

🧵(2/11)

SimuCell3D … for simulating tissue mechanics with cell polarization. @iberd.bsky.social

Dimension: 3D
Software language: C++
Download: git.bsse.ethz.ch/iber/Publica...

bsky.app/profile/epim...

👩💻 Want to try it? Just a few extra lines of code vs. classic PINNs!
Code & details: git.bsse.ethz.ch/iber/Publica...

Retweet 🔄 if you’d use this for your inverse problems! #OpenScience

⚡ No plateaus here!
Classical PINNs stall. PINNverse keeps improving physics loss ∼ epoch^(-1.4) for Fisher’s equation.
Algebraic decay >> stagnation!