• bending model
• biohybrid actuator
• elastomeric scaffold
• rolled bilayer
• rolled-up technology
• tubes-in-tube

The use of living materials for generating hybrid systems is an exciting and complex paradigm, which allows taking advantage of living being's unique capabilities to perform tasks in areas where artificial technologies are still limited. The engineering challenge of integrating living and artificial materials lies at the intersection of many disciplines, from mechanics to molecular biology.
A major task in this area is the fabrication of scaffolds, artificial interfaces that host the living material, providing conditions for its organization, maturation, and viability. These structures have the challenging task of matching the complex architecture found in the native environment of cells and tissue.
The use of tridimensional scaffolds provides a more natural environment for cells; it also allows the increase of the cross-sectional area, guaranteeing the generation of greater forces in biohybrid muscle systems.
The main problem with 3D scaffolds, if not properly designed, is the presence of a necrotic core in the tissue. This occurs because of the lack of oxygen, nutrients, and wastes diffusion in the central part of the 3D scaffold. The lack of vasculature systems or any other perfusion method, for constructions above 1 mm, is still one of the main challenges for biohybrid actuation, tissue engineering, and related fields.
Many different techniques have been proposed to overcome this challenge, maintaining a compromise between fabrication complexity and performance. Among them, it is worth mentioning 3D bioprinting, cell sheet stacking, salt leaching, tissue decellularization, and rolling techniques. However, these approaches are only rarely coupled with appropriate modeling and design considerations, but they are rather explored on a trial-and-error basis.
Rolled-up technology has been vastly investigated for applications in the fields of photonics, electronics, energy storage, robotics, biomedical engineering, and others. Through this technique, a flat layer of material can be bent into tridimensional structures. In the state-of-the-art, different structures as flat films of polymer materials, hydrogels, metals, semiconductors, and crystals have been rolled-up.
A specific branch of rolled-up technologies is called Strain Induced Rolling Membrane (SIRM), which allows obtaining 3D complex structures from simple 2D elastic bilayers. During fabrication, elastic energy is stored in one of the bilayer films. After bonding them together and releasing the structure, the strain mismatch drives the bilayer to roll-up, forming a scroll-like structure with an Archimedean spiral cross-section.
In this work, by using lithographic techniques, we provided such films with topographical features suitable for enhancing anisotropic cell alignment (to mimic muscle fiber orientation) and culture media diffusion. This made SIRM an ideal technique for the fabrication of complex 3D polymeric scaffolds for bio-artificial muscles (BAM).
We also developed a modified version of the classic Timoshenko’s bilayer bending model, that can predict the geometrical features of the rolled structures. By using Archimedean spirals geometry, we were able to design a bilayer with multiple rolling steps that, after rolling completely, formed a hierarchical organization, like the one that can be found in skeletal muscle tissue. We suggest that this design strategy may have good potential for the fabrication of hybrid actuators.
We validated our model by testing its ability to correctly predict the radii of structures under strain and thickness variations. We also used these results to generate and validate a proposed methodology for the design and fabrication of hierarchical multi-rolled structures. We demonstrated its feasibility by fabricating robust and complex rolled-up structures, with controlled diameter and geometry.
We hope this work will encourage new modeling-fabrication paradigms for the design of 3D structures, pushing the boundaries of biohybrid actuation and other fields in which rolled-up technologies can find interesting applications.