title: Identifying the necrotic zone boundary in tumour spheroids with pair-correlation functions.
abstract: Automatic identification of the necrotic zone boundary is important in the assessment of treatments on in vitro tumour spheroids. This has been difficult especially when the difference in cell density between the necrotic and viable zones of a tumour spheroid is small. To help overcome this problem, we developed novel one-dimensional pair-correlation functions (PCFs) to provide quantitative estimates of the radial distance of the necrotic zone boundary from the centre of a tumour spheroid. We validate our approach on synthetic tumour spheroids in which the position of the necrotic zone boundary is known a priori It is then applied to nine real tumour spheroids imaged with light sheet-based fluorescence microscopy. PCF estimates of the necrotic zone boundary are compared with those of a human expert and an existing standard computational method.
authors.affiliation: School of Mathematical Sciences, The University of Adelaide, Adelaide, South Australia 5005, Australia saber.dini@adelaide.edu.au.
authors.forename: S
authors.identifier: 0000-0002-4613-3672
authors.initials: S
authors.lastname: Dini
authors.affiliation: School of Mathematical Sciences, The University of Adelaide, Adelaide, South Australia 5005, Australia.
authors.forename: B J
authors.initials: BJ
authors.lastname: Binder
authors.affiliation: Department of Biological Sciences (IZN, FB 15), Buchmann Institute for Molecular Life Sciences (BMLS), Goethe Universität Frankfurt am Main, 60438 Frankfurt am Main, Germany.
authors.forename: S C
authors.initials: SC
authors.lastname: Fischer
authors.affiliation: Department of Biological Sciences (IZN, FB 15), Buchmann Institute for Molecular Life Sciences (BMLS), Goethe Universität Frankfurt am Main, 60438 Frankfurt am Main, Germany.
authors.forename: C
authors.initials: C
authors.lastname: Mattheyer
authors.affiliation: Department of Biological Sciences (IZN, FB 15), Buchmann Institute for Molecular Life Sciences (BMLS), Goethe Universität Frankfurt am Main, 60438 Frankfurt am Main, Germany.
authors.forename: A
authors.initials: A
authors.lastname: Schmitz
authors.affiliation: Department of Biological Sciences (IZN, FB 15), Buchmann Institute for Molecular Life Sciences (BMLS), Goethe Universität Frankfurt am Main, 60438 Frankfurt am Main, Germany.
authors.forename: E H K
authors.initials: EH
authors.lastname: Stelzer
authors.affiliation: School of Mathematical Sciences, The University of Adelaide, Adelaide, South Australia 5005, Australia ARC Centre of Excellence for Mathematical and Statistical Frontiers, Parkville, Victoria 3010, Australia.
authors.forename: N G
authors.initials: NG
authors.lastname: Bean
authors.affiliation: School of Mathematical Sciences, The University of Adelaide, Adelaide, South Australia 5005, Australia.
authors.forename: J E F
authors.identifier: 0000-0001-5061-9563
authors.initials: JE
authors.lastname: Green
mesh_terms: D045744:Cell Line, Tumor; D003198:Computer Simulation; D006801:Humans; D008954:Models, Biological; D009336:Necrosis; D009369:Neoplasms / Q000378:metabolism* / Q000473:pathology; D018874:Spheroids, Cellular / Q000378:metabolism* / Q000473:pathology
keywords: necrotic zone; pair-correlation function; tumour spheroid