eprintid: 10196940
rev_number: 8
eprint_status: archive
userid: 699
dir: disk0/10/19/69/40
datestamp: 2024-09-16 13:05:02
lastmod: 2024-09-16 13:05:02
status_changed: 2024-09-16 13:05:02
type: article
metadata_visibility: show
sword_depositor: 699
creators_name: Todd, Lucy
creators_name: Chin, Matthew HW
creators_name: Coppens, Marc-Olivier
title: Two conjectures on 3D Voronoi structures: a toolkit with biomedical case studies
ispublished: pub
divisions: UCL
divisions: B04
divisions: F43
keywords: Science & Technology, Physical Sciences, Technology, Chemistry, Physical, Engineering, Chemical, Nanoscience & Nanotechnology, Materials Science, Multidisciplinary, Chemistry, Engineering, Science & Technology - Other Topics, Materials Science, SIZE
note: This article is licensed under a Creative Commons Attribution 3.0 Unported Licence.
abstract: 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 ±3G). 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.
date: 2024-08-27
date_type: published
publisher: ROYAL SOC CHEMISTRY
official_url: http://dx.doi.org/10.1039/d4me00036f
oa_status: green
full_text_type: pub
language: eng
primo: open
primo_central: open_green
verified: verified_manual
elements_id: 2284920
doi: 10.1039/d4me00036f
medium: Electronic-eCollection
pii: d4me00036f
lyricists_name: Chin, Ho
lyricists_name: Coppens, Marc-Olivier
lyricists_id: MHWCH87
lyricists_id: MCOPP36
actors_name: Coppens, Marc-Olivier
actors_id: MCOPP36
actors_role: owner
funding_acknowledgements: [National Cancer Institute]; CGCATF-2021/100014 [AB K Studentship]; CA278730-01 [Cancer Research UK (CRUK)]; [National Cancer Institute]; [Mark Foundation for Cancer Research via a Cancer Grand Challenges partnership]
full_text_status: public
publication: Molecular Systems Design & Engineering
volume: 9
number: 9
pagerange: 912-919
pages: 9
event_location: England
issn: 2058-9689
citation:        Todd, Lucy;    Chin, Matthew HW;    Coppens, Marc-Olivier;      (2024)    Two conjectures on 3D Voronoi structures: a toolkit with biomedical case studies.                   Molecular Systems Design & Engineering , 9  (9)   pp. 912-919.    10.1039/d4me00036f <https://doi.org/10.1039/d4me00036f>.       Green open access   
 
document_url: https://discovery.ucl.ac.uk/id/eprint/10196940/1/ToddChinCoppens_MSDE24.pdf