TY  - JOUR
VL  - 9
SP  - 912
PB  - ROYAL SOC CHEMISTRY
JF  - Molecular Systems Design & Engineering
A1  - Todd, Lucy
A1  - Chin, Matthew HW
A1  - Coppens, Marc-Olivier
Y1  - 2024/08/27/
N2  - 3D Voronoi scaffolds are widely applied in the field of additive manufacturing as they are known for their light weight structural resilience and share many topological similarities to various natural (bone, tumours, lymph node) and synthetic environments (foam, functionally gradient porous materials). Unfortunately, the structural design features that promote these topological similarities (such as the number of vertices) are often unpredictable and require the trial and error of varying design features to achieve the desired 3D Voronoi structure. This article provides a toolkit, consisting of equations, based on over 12 000 3D Voronoi structures. These equations allow design features, such as the number of generating points (G), to be efficiently and accurately predicted based on the desired structural parameters (within ą3G). Based on these equations we are proposing, to the best of our knowledge, two new mathematical conjectures that relate the number of vertices or edges, and the average edge length to G in Voronoi structures. These equations have been validated for a wide range of parameter values and Voronoi network sizes. A design code is provided allowing any of over 12 000 structures to be selected, easily adjusted based on user requirements, and 3D printed. Biomedical case studies relevant to T-cell culturing, bone scaffolds and kidney tumours are presented to illustrate the design code.
ID  - discovery10196940
UR  - http://dx.doi.org/10.1039/d4me00036f
N1  - This article is licensed under a Creative Commons Attribution 3.0 Unported Licence.
KW  - Science & Technology
KW  -  Physical Sciences
KW  -  Technology
KW  -  Chemistry
KW  -  Physical
KW  -  Engineering
KW  -  Chemical
KW  -  Nanoscience & Nanotechnology
KW  -  Materials Science
KW  -  Multidisciplinary
KW  -  Chemistry
KW  -  Engineering
KW  -  Science & Technology - Other Topics
KW  -  Materials Science
KW  -  SIZE
TI  - Two conjectures on 3D Voronoi structures: a toolkit with biomedical case studies
SN  - 2058-9689
AV  - public
IS  - 9
EP  - 919
ER  -