Cancer fingerprints by topological data analysis. (English) Zbl 07737811
Ehrhardt, Matthias (ed.) et al., Progress in industrial mathematics at ECMI 2021. Proceedings of the 21st European conference on mathematics for industry, ECMI 2021, Wuppertal, Germany, April 13–15, 2021. Selected and reviewed papers. Cham: Springer. Math. Ind. 39, 23-29 (2022).
Summary: Topological data analysis has arisen has a promising tool to extract information on the structure of a wide variety of datasets. We analyze here its potential in two types of cancer studies. First, we compare times series of images from simulations of metastatic invasion in epithelial tissues. Calculating bottleneck distances of persistent diagrams we can characterize and classify the advancing interfaces of cellular aggregates. Second, we compare mRNA expression values for genes involved in cell cycles extracted from pancreas cancer tissue. We discuss how persistence information from different distances can provide insight on patient/gene clusters.
For the entire collection see [Zbl 1506.65002].
For the entire collection see [Zbl 1506.65002].
MSC:
| 65-XX | Numerical analysis |
Software:
clusfindReferences:
| [1] | L.L. Bonilla, A. Carpio, C. Trenado, Tracking collective cell motion by topological data analysis, PLoS Comput Biol 16 (2020) e1008407. · doi:10.1371/journal.pcbi.1008407 |
| [2] | G. Carlsson, Topology and data, Bull. Amer. Math. Soc. 46 (2009) 255-308. · Zbl 1172.62002 · doi:10.1090/S0273-0979-09-01249-X |
| [3] | A. Carpio, L.L. Bonilla, J.C. Mathews, A.R. Tannenbaum, Fingerprints of cancer by persistent homology, bioRxiv 777169, 2019 |
| [4] | A. Carpio, A. Simón, L.F. Villa, Clustering methods and Bayesian inference for the analysis of the time evolution of immune disorders, arXiv:2009.11531 2020 |
| [5] | A. Carpio, A. Simón, A. Torres, L.F. Villa, Pattern recognition in data as a diagnosis tool, Journal of Mathematics in Industry 12 (2022) 3. · Zbl 1485.62079 · doi:10.1186/s13362-022-00119-w |
| [6] | E. Cerami, J. Gao, U. Dogrusoz et al, The cBio cancer genomics portal: An open platform for exploring multidimensional cancer genomics data, Cancer Discov 2 (2012) 401-404. · doi:10.1158/2159-8290.CD-12-0095 |
| [7] | Y. Chen, F. D. Cruz, R. Sandhu, A. L. Kung, P. Mundi, et al, Poediatric sarcoma data forms a unique cluster measured via the Earth Mover’s Distance, Sci. Rep. 7 (2017) 7035. · doi:10.1038/s41598-017-07551-8 |
| [8] | M.R. McGuirl, A. Volkening, B. Sandstede, Topological data analysis of zebrafish patterns. Proc. Nat. Acad. Sci. 117 (2020) 5113-5124. · Zbl 1456.92004 · doi:10.1073/pnas.1917763117 |
| [9] | S. Moitrier, C. Blanch, S. Garcia, K. Sliogeryte et al., Collective stresses drive competition between monolayers of normal and Ras-transformed cells, Soft Matter 15 (2019) 537-545. · doi:10.1039/C8SM01523F |
| [10] | L. Kaufman, P.J. Rousseeuw, Finding groups in data: An introduction to cluster analysis, Hoboken: Wiley-Interscience, 1990. · Zbl 1345.62009 · doi:10.1002/9780470316801 |
| [11] | M. Kerber, D. Morozov, A. Nigmetov, Geometry helps to compare persistence diagrams, ACM J. Exp. Algorithmics, 22 (2017) 1.4. · Zbl 1414.68129 · doi:10.1145/3064175 |
| [12] | T. Kovacheva, A hierarchical clustering approach to find groups of objects, Proceedings of the IV Congress of Mathematicians, Macedonia; 2008. pp 359-373. |
| [13] | A.H. Rizvi, P.G. Camara, E.K. Kandror, T.J. Roberts et al., Single-cell topological RNA-seq analysis reveals insights into cellular differentiation and development, Nat. Biotech. 35 (2017) 551-560. · doi:10.1038/nbt.3854 |
| [14] | F. Sapienza, P. Groisman, M. Jonckheere, Weighted Geodesic Distance Following Fermat’s Principle. Proc 6th International Conference on Learning Representations (ICLR), 2018. |
| [15] | The ICGC/TCGA Pan-Cancer Analysis of Whole Genomes Consortium, Pan-cancer analysis of whole genomes, Nature 578 (2020) 82-93. · doi:10.1038/s41586-020-1969-6 |
| [16] | C. Topaz, L. Ziegelmeier, T. Halverson, Topological data analysis of biological aggregation models, PLoS ONE 10 (2015) e0126383. · doi:10.1371/journal.pone.0126383 |
| [17] | A. Zomorodian, G. Carlsson, Computing persistent homology. Discrete and Computational Geometry, 33 (2002) 249-274. · Zbl 1069.55003 · doi:10.1007/s00454-004-1146-y |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
