Theoretical derivation of blood velocity from TOF-MRA based artery centerline

[2607.16498] Theoretical derivation of blood velocity from TOF-MRA based artery centerline Skip to main content Search Submit Donate Log in Physics > Medical Physics arXiv:2607.16498 (physics) [Submitted on 17 Jul 2026 ( v1 ), last revised 24 Aug 2026 (this version, v4)] Title: Theoretical derivation of blood velocity from TOF-MRA based artery centerline Authors: Abrar Faiyaz View PDF Abstract: Time-of-flight magnetic resonance angiography (TOF-MRA) is widely used for nonin-vasive visualization of arterial anatomy, but extracting hemodynamics like blood velocity typically requires supplementary phase-contrast scans, tagging or multi-TE images. This study proposes a novel, physics-informed computational framework to extract variable fluid velocity directly from standard TOF-MRA signal profiles. We analytically expand the approach-to-steady-state Bloch equations to include convective flow, establishing a mathematical relationship between the spatial decay of longitudinal magnetization and fluid velocity. The velocity derivation was further extended to pointwise estimation over a 1-D centerline, overcoming the limitations of constant-velocity assumptions. To validate and solve this problem, a MATLAB (R2025b) simulation framework was developed to model fluid flow in two variable-geometry flowing tube cases, i.e., continuous narrowing and focal stenosis, under synthetic scanner noise. A global inverse optimization approach utilizing Dual-Tikhonov regularization was applied to stably invert the ill-posed transit time integral, actively penalizing high-frequency numerical ringing while preserving structural curves. The computational simulations successfully recovered ground-truth point-wise velocities, tracking gradual hemodynamic accelerations and sharp stenotic jets. This theoretical framework and the example centerline TOF-MRA signal intensity pro-vide a robust mathematical proof-of-concept that quantitative, localized functional he-modynamic metrics can be extracted from standard structural MRA imaging, establishing a foundation for advanced flow quantification without requiring additional scan time. Subjects: Medical Physics (physics.med-ph) ; Mathematical Physics (math-ph) Cite as: arXiv:2607.16498 [physics.med-ph] (or arXiv:2607.16498v4 [physics.med-ph] for this version) https://doi.org/10.48550/arXiv.2607.16498 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Abrar Faiyaz [ view email ] [v1] Fri, 17 Jul 2026 20:37:52 UTC (1,217 KB) [v2] Tue, 21 Jul 2026 14:12:23 UTC (1,218 KB) [v3] Thu, 23 Jul 2026 15:22:28 UTC (2,324 KB) [v4] Mon, 24 Aug 2026 18:44:21 UTC (3,710 KB) Full-text links: Access Paper: View PDF view license Current browse context: physics.med-ph < prev | next > new | recent | 2026-07 Change to browse by: math math-ph math.MP physics References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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