From Geometry to Flow Allocation: A Physics-Based Framework for Interpretable Microvascular Hemodynamics

Fiedler, Alexander; Drysch, Marius; Schmidt, Sonja Verena; Weskamp, Pia; Reinkemeier, Felix; Puscz, Flemming; Sogorski, Alexander; Lehnhardt, Marcus; Wallner, Christoph

doi:10.3390/bioengineering13091091

Open AccessArticle

From Geometry to Flow Allocation: A Physics-Based Framework for Interpretable Microvascular Hemodynamics

by

Alexander Fiedler

^†,

Marius Drysch

^†,

Sonja Verena Schmidt

,

Pia Weskamp

,

Felix Reinkemeier

,

Flemming Puscz

,

Alexander Sogorski

,

Marcus Lehnhardt

and

Christoph Wallner

^*

Department of Plastic Surgery and Hand Surgery, Burn Centre, BG University Hospital Bergmannsheil, Ruhr University Bochum, Bürkle-de-la-Camp-Platz 1, 44789 Bochum, Germany

^*

Author to whom correspondence should be addressed.

^†

These authors contributed equally to this work.

Bioengineering 2026, 13(9), 1091; https://doi.org/10.3390/bioengineering13091091 (registering DOI)

Submission received: 4 September 2026 / Revised: 14 September 2026 / Accepted: 17 September 2026 / Published: 20 September 2026

(This article belongs to the Special Issue Cardiovascular Models and Biomechanics)

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Abstract

Anastomotic angle and flow allocation change together in end-to-side junctions, complicating interpretation of angle-dependent wall shear. We used MITOS Flow Lab, a two-dimensional D2Q9 two-relaxation-time lattice-Boltzmann environment, to examine this coupling in steady, rigid-walled, Newtonian models at Re ≈ 91. Angles of 30–120° were compared under equal outlet pressures and at approximately matched branch-flow fractions of 0.25 and 0.21, achieved with angle-specific static outlet-pressure offsets. Under equal outlet pressures, the branch-flow fraction decreased from 0.356 to 0.151 across this angle range, while the minimum normalized signed recipient-floor shear increased from 0.140 to 0.450. Matching flow allocation substantially reduced angle-associated variation in this endpoint and in the sub-toe response, whereas sub-heel and sub-ostial responses remained angle dependent under the adjusted boundary conditions. This qualitative contrast persisted when the lumen resolution was increased from 32 to 64 nodes for the 0.25 target, although minimum-shear attenuation changed from approximately 83% to 74%. The 0.21 target was examined only on the production grid. These experiments demonstrate that the interpretation of angle-associated shear depends on the flow-allocation condition used for comparison. They do not identify a boundary-independent geometric effect or a causal mediation fraction. Absolute values and attenuation magnitudes remain sensitive to discretization and have not been independently validated. These controlled comparisons provide a framework for interpreting angle-associated shear together with achieved flow allocation and the specified outlet conditions.

Keywords: end-to-side anastomosis; two-dimensional modeling; flow allocation; signed wall shear; lattice Boltzmann method; computational hemodynamics; controlled numerical experiment

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MDPI and ACS Style

Fiedler, A.; Drysch, M.; Schmidt, S.V.; Weskamp, P.; Reinkemeier, F.; Puscz, F.; Sogorski, A.; Lehnhardt, M.; Wallner, C. From Geometry to Flow Allocation: A Physics-Based Framework for Interpretable Microvascular Hemodynamics. Bioengineering 2026, 13, 1091. https://doi.org/10.3390/bioengineering13091091

AMA Style

Fiedler A, Drysch M, Schmidt SV, Weskamp P, Reinkemeier F, Puscz F, Sogorski A, Lehnhardt M, Wallner C. From Geometry to Flow Allocation: A Physics-Based Framework for Interpretable Microvascular Hemodynamics. Bioengineering. 2026; 13(9):1091. https://doi.org/10.3390/bioengineering13091091

Chicago/Turabian Style

Fiedler, Alexander, Marius Drysch, Sonja Verena Schmidt, Pia Weskamp, Felix Reinkemeier, Flemming Puscz, Alexander Sogorski, Marcus Lehnhardt, and Christoph Wallner. 2026. "From Geometry to Flow Allocation: A Physics-Based Framework for Interpretable Microvascular Hemodynamics" Bioengineering 13, no. 9: 1091. https://doi.org/10.3390/bioengineering13091091

APA Style

Fiedler, A., Drysch, M., Schmidt, S. V., Weskamp, P., Reinkemeier, F., Puscz, F., Sogorski, A., Lehnhardt, M., & Wallner, C. (2026). From Geometry to Flow Allocation: A Physics-Based Framework for Interpretable Microvascular Hemodynamics. Bioengineering, 13(9), 1091. https://doi.org/10.3390/bioengineering13091091

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From Geometry to Flow Allocation: A Physics-Based Framework for Interpretable Microvascular Hemodynamics

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