Lucy Todd, Matthew H. W. Chin and Marc-Olivier Coppens
{"title":"Two conjectures on 3D Voronoi structures: a toolkit with biomedical case studies","authors":"Lucy Todd, Matthew H. W. Chin and Marc-Olivier Coppens","doi":"10.1039/D4ME00036F","DOIUrl":null,"url":null,"abstract":"<p >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 (<em>G</em>), to be efficiently and accurately predicted based on the desired structural parameters (within ±3<em>G</em>). 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 <em>G</em> 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.</p>","PeriodicalId":91,"journal":{"name":"Molecular Systems Design & Engineering","volume":" 9","pages":" 912-919"},"PeriodicalIF":3.2000,"publicationDate":"2024-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://pubs.rsc.org/en/content/articlepdf/2024/me/d4me00036f?page=search","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Molecular Systems Design & Engineering","FirstCategoryId":"5","ListUrlMain":"https://pubs.rsc.org/en/content/articlelanding/2024/me/d4me00036f","RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"CHEMISTRY, PHYSICAL","Score":null,"Total":0}
引用次数: 0
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.
期刊介绍:
Molecular Systems Design & Engineering provides a hub for cutting-edge research into how understanding of molecular properties, behaviour and interactions can be used to design and assemble better materials, systems, and processes to achieve specific functions. These may have applications of technological significance and help address global challenges.