ArticleThe journal of physiological sciences : JPS2012
Vascular tortuosity: a mathematical modeling perspective.
Article in The journal of physiological sciences : JPS, 2012. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 6 papers.
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6 citing papers in PubMed.
- Radiomics of the Airway (RadAr): Multi-Scale Airway Phenotyping for Disease Characterization on Routine CT Imaging.medRxiv : the preprint server for health sciences · 2026Article
- A Machine Learning Driven Approach to Quantifying Coronary Artery Tortuosity.JACC. Advances · 2026Article
- Noninvasive imaging analysis of vascular phenotypes improves prognostic stratification in primary liver cancer: a multi-cohort study.NPJ precision oncology · 2025Article
- AI-based radiomic features predict outcomes and the added benefit of chemoimmunotherapy over chemotherapy in extensive stage small cell lung cancer: A multi-institutional study.Cancer letters · 2025Article
- Characterization of Lenticulostriate Arteries and Its Associations With Vascular Risk Factors in Community-Dwelling Elderly.Frontiers in aging neuroscience · 2021Article
- Vascular amounts and dispersion of caliber-classified vessels as key parameters to quantitate 3D micro-angioarchitectures in multiple myeloma experimental tumors.Scientific reports · 2018Article
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2 authors.
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Abstract
Although vascular tortuosity is a ubiquitous phenomenon, almost no mathematical models exist to describe its shape. Given that the shape of tortuous vessel curves seems fairly uniform across orders of magnitude of vessel size and across vast differences in anatomic substrata, it is hypothesized that the shape of tortuosity is not purely random but rather is governed by physical principles. We present a mathematical model of tortuosity based on optimality principles, and show how this model can potentially be used to distinguish physiologic tortuosity from abnormal tortuosity which may exist in disease states. Using the calculus of variations, a model of tortuosity has been developed which minimizes average curvature per unit length. The model is tested against curves in normal vessels and in diseased vessels in a case of Fabry's disease. It is found that the theoretical model provides a good fit for normal vessel tortuosity. This suggests that blood vessels obey optimality principles, and curve in such a way as to minimize average curvature. The model may also be able to distinguish physiologic tortuosity from abnormal tortuosity found in disease states.
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