Energy informed transit time distribution modelling for enhanced characterization of cerebral cortical vascular networks

OBJECTIVE: Energetic optimality has long been used to explain vascular design, but many analyses treat hydraulic costs in isolation and neglect oxygen delivery. The objective of this study is to examine whether local cerebral bifurcation geometry can be interpreted through an energetic principle that explicitly accounts for oxygen delivery. APPROACH: We study an idealised, geometrically constrained arterial bifurcation using an objective that combines viscous dissipation, volume maintenance, and oxygen extraction via a simple wall mass-transfer description. The model is optimised over branching angle and child radius asymmetry under a generalised Murray-type relationship. MAIN RESULTS: The optimal angle shows a broad, shallow minimum around 30-45°, consistent with classical equal-radius benchmarks near 37.5° and indicating limited sensitivity to angle within this range. Across the parameter regime examined, oxygen extraction in the parent segment is near complete, so geometry primarily influences the energetic cost. Moderately asymmetric bifurcations can remain energetically efficient, whereas highly asymmetric configurations tend to push solutions toward boundary designs, reflecting increased viscous losses for very small child vessels. SIGNIFICANCE: The results suggest that local bifurcation geometry can be interpreted through an energetic principle that explicitly accounts for oxygen delivery and may provide useful priors for larger network models incorporating transit-time-based metrics.