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