How can a scaffold vary one physical cue while preserving others? The authors parameterized three-dimensional strut-based meta-biomaterials, ran 44,837 numerical homogenization simulations and optimized pairs that contrast Poisson’s ratio or relative mass density. Selected designs were fabricated by PolyJet printing and two-photon polymerization; mechanical and permeability measurements tested the predictions. Decoupling is approximate: permeability was excluded from the density-pair average, and measured density-pair stiffnesses differ more than predicted. Independently testing scaffold effec

Nature Communications · 2026

A scaffold’s shape changes how it feels, how much space it leaves, and how fluid moves through it. Can we change one of those cues while keeping the others similar?

Yarali and colleagues searched 44,837 simulated designs, then printed and tested selected structures. Their answer lives in carefully chosen pairs.

Architecture sets the response.

The challenge. Scaffold properties are linked. Making a structure denser may also make it stiffer and change its pores. That makes individual cues difficult to study.

The approach. Adjust strut angle, length and diameter, then find pairs with a large difference in one property and small average differences in the others.

01 / The paired experiment

One push. Two responses.

Start with the Poisson’s-ratio pair. Compress both structures and watch their width. Then change the target cue, or compare predictions with measurements.

Pair I · Two structures with opposite Poisson’s-ratio signs and approximately preserved companion properties.

At 0.50% compression, P#I1 narrows by 0.055% while P#I2 widens by 0.045%. Opposite lateral responses; predicted stiffness differs by 18.95%.

What else changes?

The Poisson’s-ratio sign flips, while other descriptors remain approximately similar. The average deviation across the other properties is 14.04%.

Deviations reproduce the paper’s tables. E0 is the elastic modulus of the solid printing material. Bars compare values within each row.

Average companion-property deviation: 14.04% (all properties in Table 3). The selected cue is excluded from this average.

Choose your comparison.

To study the effect of density on cells, which comparison best follows this paper’s design strategy?

Select a strategy to reveal why separating cues matters.

02 / From a design to a specimen

Millimetres to micrometres.

The architecture is scalable. PolyJet printing supplied the large specimens for paired tests. Two-photon polymerization demonstrated that these lattices can also be made at the microscale.

Conceptual laser-writing sequence. The experiment used stitched blocks and a 5 × 5 × 5 array of 300 µm unit cells.

Write a lattice with light.

A focused femtosecond laser polymerizes IP-Q photoresist by two-photon absorption. The researchers used a Nanoscribe Photonic Professional GT+ in a dip-in configuration to print 1.5 mm specimens.

Microscale: 1.5 mm specimen · 300 µm unit cells · Nanoscribe GT+ and IP-Q.

Better pairs, clearer questions.

Cells encounter scaffold mechanics, pore geometry and fluid transport together. If researchers can vary one cue while holding the others closer, they can ask which cue drives a biological response.

This paper establishes the computational design framework and tests selected physical properties. It proposes using these paired scaffolds in future cell experiments to isolate effects such as Poisson’s ratio or density.

03 / See the physical evidence

The structures, for real.

Look from the large printed lattices to microscale electron micrographs. The supplementary material makes the link between mathematical geometry and fabrication tangible.

Explore the design space.

Supplementary Video 1 · generating the geometry. The unit-cell architecture changes as its geometric inputs vary. Three design variables—strut angle θ, length L and diameter d—supply the search space for the optimization.

Ebrahim Yarali et al. · Supplementary material. Complete video; content unmodified, format converted to WebM. CC BY-NC-ND 4.0.

Watch it compress.

Supplementary Video 11 · compression of P#I1. The real printed auxetic specimen narrows under compression. Playback is shown at 4× speed in the authors’ original video.

Ebrahim Yarali et al. · Supplementary material. Complete video; content unmodified, format converted to WebM. CC BY-NC-ND 4.0.

Source figures: Ebrahim Yarali et al., Nature Communications (2026), Figure 5 and Supplementary Figure 5. Reproduced unmodified under CC BY-NC-ND 4.0. The interactive teaching models are original interpretations of the reported geometry and data.

Continue with the research

Decoupling mechanical and morphometric properties in meta-biomaterials

Ebrahim Yarali, Urs Staufer, Lidy E. Fratila-Apachitei, Abdulrahman Al-Sanea, Reza Mahdavi, Amir A. Zadpoor, Angelo Accardo & Mohammad J. Mirzaali.

Nature Communications (2026). DOI: 10.1038/s41467-026-77121-y.