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Aneurysm Morphology Based on Conformal Geometry.

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Title: Aneurysm Morphology Based on Conformal Geometry.
Authors: Liu, Yuanpeng1 (AUTHOR), Zhao, Zhou1 (AUTHOR), Fang, Siyu2 (AUTHOR), Liu, Donglian2 (AUTHOR), Sadasivan, Chander3 (AUTHOR), Tassiopoulos, Apostolos3 (AUTHOR), Chen, Shikui4 (AUTHOR), Gu, Xianfeng1 (AUTHOR) gu@cs.stonybrook.edu
Source: International Journal for Numerical Methods in Biomedical Engineering. May2026, Vol. 42 Issue 5, p1-13. 13p.
Subjects: Aortic aneurysms, Conformal geometry, Image segmentation, Hodge theory, Aneurysms, Endovascular aneurysm repair, Conformal mapping, Riemann surfaces
Abstract: Several morphological parameters such as aortic neck length, angulation, or centerline curvature have previously been evaluated to define "hostile" anatomies that predispose to poor outcomes after endovascular aneurysm repair. In this study, we present a new method for classifying aneurysm morphologies using their conformal structures. The conformal structure of a surface is determined by its Riemannian metric, and conformal mappings between surfaces with complex topologies preserve their conformal structures. To classify aneurysm shapes, the aortic aneurysm is first segmented from CT scans and represented as a discrete surface. Next, holomorphic differential forms are computed based on the discrete Hodge Theory. The aneurysm surface can be conformally mapped onto a pair of planar rectangles with an aortic bifurcation point by integrating a special holomorphic differential. This canonical configuration gives the conformal invariants, or "conformal fingerprints," which can then be used to classify aneurysm morphologies. This novel methodology shows promise in providing an improved understanding of aneurysm morphologies, which can aid in better predicting and managing potential complications after endovascular aneurysm repair. [ABSTRACT FROM AUTHOR]
Copyright of International Journal for Numerical Methods in Biomedical Engineering is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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DbLabel: Engineering Source
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PubType: Academic Journal
PubTypeId: academicJournal
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  Label: Title
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  Data: Aneurysm Morphology Based on Conformal Geometry.
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  Data: <searchLink fieldCode="AR" term="%22Liu%2C+Yuanpeng%22">Liu, Yuanpeng</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Zhao%2C+Zhou%22">Zhao, Zhou</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Fang%2C+Siyu%22">Fang, Siyu</searchLink><relatesTo>2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Liu%2C+Donglian%22">Liu, Donglian</searchLink><relatesTo>2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Sadasivan%2C+Chander%22">Sadasivan, Chander</searchLink><relatesTo>3</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Tassiopoulos%2C+Apostolos%22">Tassiopoulos, Apostolos</searchLink><relatesTo>3</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Chen%2C+Shikui%22">Chen, Shikui</searchLink><relatesTo>4</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Gu%2C+Xianfeng%22">Gu, Xianfeng</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> gu@cs.stonybrook.edu</i>
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  Data: <searchLink fieldCode="JN" term="%22International+Journal+for+Numerical+Methods+in+Biomedical+Engineering%22">International Journal for Numerical Methods in Biomedical Engineering</searchLink>. May2026, Vol. 42 Issue 5, p1-13. 13p.
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  Data: <searchLink fieldCode="DE" term="%22Aortic+aneurysms%22">Aortic aneurysms</searchLink><br /><searchLink fieldCode="DE" term="%22Conformal+geometry%22">Conformal geometry</searchLink><br /><searchLink fieldCode="DE" term="%22Image+segmentation%22">Image segmentation</searchLink><br /><searchLink fieldCode="DE" term="%22Hodge+theory%22">Hodge theory</searchLink><br /><searchLink fieldCode="DE" term="%22Aneurysms%22">Aneurysms</searchLink><br /><searchLink fieldCode="DE" term="%22Endovascular+aneurysm+repair%22">Endovascular aneurysm repair</searchLink><br /><searchLink fieldCode="DE" term="%22Conformal+mapping%22">Conformal mapping</searchLink><br /><searchLink fieldCode="DE" term="%22Riemann+surfaces%22">Riemann surfaces</searchLink>
– Name: Abstract
  Label: Abstract
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  Data: Several morphological parameters such as aortic neck length, angulation, or centerline curvature have previously been evaluated to define "hostile" anatomies that predispose to poor outcomes after endovascular aneurysm repair. In this study, we present a new method for classifying aneurysm morphologies using their conformal structures. The conformal structure of a surface is determined by its Riemannian metric, and conformal mappings between surfaces with complex topologies preserve their conformal structures. To classify aneurysm shapes, the aortic aneurysm is first segmented from CT scans and represented as a discrete surface. Next, holomorphic differential forms are computed based on the discrete Hodge Theory. The aneurysm surface can be conformally mapped onto a pair of planar rectangles with an aortic bifurcation point by integrating a special holomorphic differential. This canonical configuration gives the conformal invariants, or "conformal fingerprints," which can then be used to classify aneurysm morphologies. This novel methodology shows promise in providing an improved understanding of aneurysm morphologies, which can aid in better predicting and managing potential complications after endovascular aneurysm repair. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of International Journal for Numerical Methods in Biomedical Engineering is the property of Wiley-Blackwell and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
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      – Type: doi
        Value: 10.1002/cnm.70177
    Languages:
      – Code: eng
        Text: English
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      Pagination:
        PageCount: 13
        StartPage: 1
    Subjects:
      – SubjectFull: Aortic aneurysms
        Type: general
      – SubjectFull: Conformal geometry
        Type: general
      – SubjectFull: Image segmentation
        Type: general
      – SubjectFull: Hodge theory
        Type: general
      – SubjectFull: Aneurysms
        Type: general
      – SubjectFull: Endovascular aneurysm repair
        Type: general
      – SubjectFull: Conformal mapping
        Type: general
      – SubjectFull: Riemann surfaces
        Type: general
    Titles:
      – TitleFull: Aneurysm Morphology Based on Conformal Geometry.
        Type: main
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          Name:
            NameFull: Liu, Yuanpeng
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            NameFull: Zhao, Zhou
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            NameFull: Fang, Siyu
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            NameFull: Liu, Donglian
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            NameFull: Sadasivan, Chander
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            NameFull: Tassiopoulos, Apostolos
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            NameFull: Chen, Shikui
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            NameFull: Gu, Xianfeng
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            – D: 01
              M: 05
              Text: May2026
              Type: published
              Y: 2026
          Identifiers:
            – Type: issn-print
              Value: 20407939
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              Value: 42
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              Value: 5
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            – TitleFull: International Journal for Numerical Methods in Biomedical Engineering
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