Simulations
Interactive physics-based models of confluent biological tissue. Each simulation runs directly in the browser — adjust parameters in real time and observe how the tissue responds.
Model 01 · Quasi-Static · Simple Shear
2D Voronoi Tissue Under Simple Shear
A quasi-static (AQS) model of a confluent monolayer deformed in simple shear. Cell shapes emerge from the Voronoi tessellation of N = 100 particle centers. Each cell resists area changes, capturing cell incompressibility, and has a preferred perimeter set by the competition between cortical contractility and line tension at junctions. The ratio of the preferred perimeter to the square root of the preferred area, p₀, is the key parameter that control tissue rigidity. At each strain step of δγ = 0.001, particle positions are sheared affinely and relaxed to a local energy minimum. Yielding is purely mechanical — there is no thermal noise — and occurs through system-spanning cascades of T1 neighbor exchanges.
What you can study
- Yield stress and the jamming transition
- T1 avalanche statistics
- Mechanical memory and oscillatory training
- Stress–strain curves and hysteresis
- Fatigue under cyclic loading
Model 02 · Active Vertex Model · Dual-Role Adhesion
Vertex Model with Dual-Role Cell–Cell Adhesion
A 2D active vertex model of N = 100 polygonal cells whose edges meet at trivalent vertices. Each cell resists area changes, capturing incompressibility, and has a preferred perimeter governed by the balance of cortical contractility and line tension; the ratio of target perimeter to cell size, p₀, controls where the tissue sits relative to the rigidity transition. Cell–cell adhesion enters through two independent channels: energetic adhesion (p₀) lowers the effective line tension at shared junctions; viscous adhesion (B) introduces frictional resistance to differential sliding at junctions, slowing relative motion.
What you can study
- Dual role of adhesion in tissue fluidity
- Jamming and unjamming transitions
- Viscous dissipation and effective tissue viscosity
- Collective cell migration
Model 03 · Active Brownian Particles · Homeostasis
Active Cells with Voronoi Geometry and Homeostasis
N₀ = 900 active Brownian particles evolve in a 30σ × 30σ periodic domain. Each particle self-propels at speed v₀ along a slowly rotating orientation with rotational diffusion Dr, and repels neighbors through a soft contact force. Cell shapes emerge from the Voronoi tessellation of particle centers — no energy function governs cell geometry; shape is a purely geometric consequence of packing. Homeostasis is enforced stochastically: a cell divides along its principal inertia axis when its area becomes sufficiently large, and undergoes apoptosis when it becomes too small, with rates k_div and k_apo set by the user.
What you can study
- Cell area distributions and their statistical form
- Effect of motility, cell division and apoptosis on spatial order and heterogeneity