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This paper proposed a unified analysis model based on persistent homology (PH) and graph modelling to provide a comprehensive portrait of BMs distribution. Spatial relationships are quantified through dynamic multiple-scale graphs constructed with Rips filtration. The multi-scale centrality importance and clustering coefficients are extracted to decode BMs spatial relations. Morphologic BMs characteristics are further analysed by varying radius and volume values that are considered as clinically influential factors. Finally, two-tailed proportional hypothesis testing is used for BM statistical distribution analysis.<\/jats:p>\n          <\/jats:sec>\n          <jats:sec>\n            <jats:title>Results<\/jats:title>\n            <jats:p>For spatial analysis, results have shown a statistical increase in the proportions of high-level centrality BMs at the left cerebellum (p&lt;0.01). BMs rapidly form graphs with high clustering rather than those with high centrality. For demographic analysis, the cerebellum and frontal are the top high-frequency areas of BMs with 0-4 and 5-10 radii. Statistical increases in the proportions of BMs at cerebellum (p&lt;0.01).<\/jats:p>\n          <\/jats:sec>\n          <jats:sec>\n            <jats:title>Conclusion<\/jats:title>\n            <jats:p>Results indicate that distributions of both BMs spatial relations and demographics are statistically non-random. This research offers novel insights into the BMs distribution analysis, providing physicians with the BMs demographic to guide screening and early diagnosis.<\/jats:p>\n          <\/jats:sec>","DOI":"10.1007\/s11547-025-01965-5","type":"journal-article","created":{"date-parts":[[2025,2,28]],"date-time":"2025-02-28T05:45:27Z","timestamp":1740721527000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Spatial-demographic analysis model for brain metastases distribution"],"prefix":"10.1007","author":[{"given":"Lin","family":"Zhang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tongtong","family":"Che","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bowen","family":"Xin","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shuyu","family":"Li","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Guanzhong","family":"Gong","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiuying","family":"Wang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,2,28]]},"reference":[{"issue":"1","key":"1965_CR1","doi-asserted-by":"publisher","first-page":"5","DOI":"10.1038\/s41572-018-0055-y","volume":"5","author":"AS Achrol","year":"2019","unstructured":"Achrol AS, Rennert RC, Anders C, Soffietti R, Ahluwalia MS, Nayak L, Peters S, Arvold ND, Harsh GR, Steeg PS et al (2019) Brain metastases. 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