Geometric optimization of implants: the potential of hollowed Voronoi scaffolds

The regeneration of massive bone loss remains a major surgical challenge, where the limitations of autografts and allografts — donor site morbidity and immunological risks — necessitate the search for high-performance synthetic alternatives. In this context, bone tissue engineering (BTE) relies on 3D porous structures acting as temporary extracellular matrices. While regular lattice architectures are well-documented, biomimetic structures based on Voronoi diagrams offer a stochastic morphology closer to trabecular bone, promoting better stress distribution and osseointegration.

This study focuses specifically on a geometric innovation: the use of hollow cylindrical struts within Voronoi structures manufactured by stereolithography (SLA). The objective is to quantify the influence of varying the internal radius of these cylinders on the mechanical performance of the scaffold. The authors explore the critical balance between a lightweight design, promoting nutrient transport, and maintaining sufficient compressive stability. The tested hypothesis suggests that by optimizing the ratio between internal and external radii, it is possible to adjust the implant stiffness to match that of native cancellous bone while avoiding the stress shielding phenomenon.

Design and manufacturing of devices

This in vitro study evaluated the mechanical performance of biomimetic hollow cylindrical scaffolds, designed by parametric modeling (Grasshopper/Rhinoceros 7) and manufactured by stereolithography (SLA). Samples were produced using a bio-based photopolymer resin (Anycubic) featuring a flexural strength of 40–60 MPa and a tensile strength of 35–55 MPa.

Geometric parameters and experimental groups

The design is based on open-cell Voronoi structures, optimized to maintain a constant porosity of approximately 63% (relative density of 0.37) and a total volume of 95 mm³. Three experimental groups were defined according to the internal radius (r) of the hollow cylinder:

• Cylinder I: Internal radius of 0.5 mm.
• Cylinder II: Internal radius of 1.0 mm.
• Cylinder III: Internal radius of 1.5 mm.

To compensate for the loss of material related to the increase in the internal radius and to maintain the physical weight unchanged, the number of "seed points" (seeds) of the Voronoi structure was dynamically adjusted for each model.

Mechanical analysis protocol

All scaffolds presented a height (H) of 12 mm and an external diameter (D) of 6.54 mm, complying with ASTM D695 standards with an aspect ratio of 1.83 to prevent premature macroscopic buckling. The evaluation of structural integrity was performed through experimental compression tests to measure compressive stress resistance and energy absorption capacity.

Mechanical performance and compression behavior

Experimental analysis of hollow cylindrical scaffolds reveals a direct correlation between internal geometric parameters and structural robustness. The results show that increasing the internal radius significantly reduces the mechanical properties of biomimetic devices.

Comparison of configurations and energy absorption

The study highlights notable differences depending on the chosen internal diameter:

• Compression resistance: Models with the smallest internal diameter (Cylinder I) exhibit the highest resistance to compression stress.
• Energy absorption: Structures with a small internal radius exhibit superior energy absorption capacity, essential for supporting mechanical bone loads.
• Structural stability: Although the relative density was kept constant at 37% for all models, the wall thickness resulting from a smaller internal radius optimizes load transfer and limits stress concentrations.

In qualitative terms, stereolithography (SLA) manufacturing has achieved high geometric precision, respecting an aspect ratio of 1.83 (height 12 mm / diameter 6.54 mm) to prevent any premature macroscopic buckling during testing. The authors confirm that optimizing the internal radius is the primary lever for balancing the implant's lightness and its compressive stability.

Analysis of geometric transition and mechanical compromise

The study demonstrates that modifying the internal radius (from 0.5 to 1.5 mm) of hollow cylindrical spacers within a Voronoi structure directly impacts stability under compression. The results are clear: as the internal radius increases, the resistance to compressive stress and the energy absorption capacity decrease. For the practitioner, this highlights that the quest for scaffold lightness has an immediate mechanical cost that must be calibrated according to the reconstruction site.

The interest of this biomimetic approach lies in its ability to mimic the stochastic architecture of trabecular bone. By maintaining an overall porosity of approximately 63%, the authors manage to remain within the low stiffness ranges of native cancellous bone. This is a crucial point for limiting the stress shielding phenomenon, a known factor in peri-implant bone resorption when the device is too rigid compared to the surrounding bone.

Limits and clinical perspective

However, although the use of a bio-based resin by stereolithography (SLA) offers remarkable geometric precision, these data come from experimental compression tests. The study focuses on pure mechanical performance and does not document here the in vivo cellular biological response or the biodegradation kinetics in a real physiological environment.

Nevertheless, compared to classic regular lattice structures, the hollow Voronoi design allows for a more homogeneous stress distribution. This fine modulation of the internal/external radius ratio offers a serious path for designing custom supports, capable of withstanding transient loads while optimizing the space required for vascularization and osseointegration.

Summary of results

This study demonstrates that increasing the internal radius of Voronoi scaffolds (from 0.5 to 1.5 mm) significantly reduces their mechanical strength, despite maintaining a porosity of 63%. Structures with the smallest internal diameter (0.5 mm) exhibit the highest resistance to compressive stress and superior energy absorption capacity, which are essential for bone regeneration in load-bearing sites.

In concrete terms, for the practitioner:

• Geometric optimization: For your bone reconstructions, keep in mind that the internal diameter of the spacers is a critical lever; prefer reduced diameters to maximize mechanical stability without compromising the porosity necessary for vascularization.
• Voronoi Advantage: Prioritize these biomimetic architectures which, unlike simple cubic networks, mimic the stochastic morphology of trabecular bone, thus limiting the stress shielding phenomenon.
• SLA Customization: Stereolithography technology now allows for the adjustment of wall thickness in biodegradable supports (bio-sourced resin) to perfectly balance structural integrity and biocompatibility according to the defect to be filled.

Technical lexicon of the study

Voronoi structures: Biomimetic architectures characterized by a heterogeneous and stochastic pore distribution, designed to mimic the complex morphology of natural trabecular bone and optimize mechanical stress distribution.

Stereolithography (SLA): High-precision additive manufacturing technique using UV-cured photopolymers (resins), allowing the production of complex porous geometries with interconnected pore networks.

Hollow cylindrical scaffolds: Three-dimensional supports whose struts possess a hollow core, a design allowing for the modulation of wall thickness and the balancing of structural lightness with load-bearing capacity.

Stress shielding: A phenomenon where an excessively rigid implant absorbs most of the mechanical stress, depriving the adjacent bone of stimulus and causing its resorption. Voronoi structures aim to reduce this risk by adapting rigidity.

Trabecular bone (or cancellous bone): Internal bone tissue characterized by high porosity (50-90%), whose irregular morphology serves as a biological model for the design of scaffolds promoting vascularization and osseointegration.

Energy absorption: Mechanical capacity of a scaffold to dissipate energy under compressive stress, a crucial parameter to ensure the stability of the biodegradable support during fracture repair.

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