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

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.