The self-organised morphogenesis of multicellular organisms emerges not only from biochemical but also from mechanical processes, operating across spatial scales and producing symmetry breaking through mechanical instabilities. Tissues grow against constraints, buckle, fold and crease, and much of the form we see in animals follows from that.
Over the past decade, this has become a recurring theme in our laboratory. We showed that the polygonal network of creases on the naked nose of dogs, cows and ferrets emerges from constrained growth guided by an underlying pattern of blood vessels acting as ‘mechanical positional information’ (2). We showed that exacerbated sonic hedgehog signalling drives chicken reticulate scales from chemical pre-patterning into mechanical skin folding (3). We showed that the irregular head scales of crocodiles are not developmental units at all, but polygonal domains delimited by a purely mechanical compressive-folding process (4) — and, more recently, that chemical and mechanical patterning operate in different regions of the tortoise head (5).
Every one of those studies rested on the same engine: a finite element formulation that we developed and extended project after project. And every one of them required to edit and recompile source code. That is a severe practical barrier.
This is why we built NewtonBioMorphX, published today in Computer Physics Communications. It is a GPU-accelerated, open-source application that brings all of these functionalities together behind an extensive graphical interface.
A GPU-accelerated engine
The mechanics run on NVIDIA GPUs, and a single solver unifies growth, multilayer interactions, plasticity, viscoelasticity and contact.
An interactive graphical interface
Geometries are generated inside the application (box, disk, tube, cone, sphere, torus) or imported as a mesh. Material properties, growth rates and boundary conditions are then assigned layer by layer, in a coordinate basis adapted to the geometry. Tissues can be reinforced by anisotropic, collagen-like passive fibres and driven by active, actin-like contractile filaments. Crucially, every property and growth rate can be specified either as a constant or as a function of space and time, so that gradients of stiffness, compressibility or growth can be imposed across a domain and their consequences observed directly.
Real-time rendering
While the simulation runs, the domain can be sectioned or clipped, and the distributions of shear stress, plastic deformation, growth, pressure, node velocities, and fibre orientations can be displayed and switched at any moment — so that symmetry breaking is watched as it happens, not reconstructed afterwards. Results export to VTK and PLY for downstream analysis in ParaView, VisIt, Blender or Python, and MP4 movies can be recorded directly from the rendering window.
For research and for teaching
The application ships with twelve ready-to-run presets, meant to be worked through in order: they progressively introduce the capabilities of the framework, from a growing elastic box on a rigid substrate to a fibre-reinforced tube that reproduces the polygonal pattern of scales on the face and jaws of crocodilians. The article further illustrates the versatility of the approach through parameter-gradient plots, in which folding regimes are swept in a single simulation. And because no code has to be written or recompiled, the principles of mechanical patterning can be demonstrated during a lecture, and the students can then explore them themselves, hands on the software.
NewtonBioMorphX is free and open source
The project page carries the user manual — as a PDF and as an online interactive version — together with the Windows and Linux executables and the full source code:
➔ NewtonBioMorphX project page
You will need an NVIDIA GPU with CUDA support and an up-to-date driver (R560 or newer recommended).
Additional information is available in the original article
NewtonBioMorphX: A computational framework for simulating tissue-scale mechanics of morphogenesis
Jahanbakhsh & Milinkovitch
Computer Physics Communications 2026: 110452 (2026)
DOI: 10.1016/j.cpc.2026.110452