Topological Complexity Determines the Frequency of Branching Variations in the Celiac Trunk-Superior Mesenteric Artery System.

Background: Variations in the anatomical branching patterns of the celiac trunk and superior mesenteric artery (SMA) directly affect vascular identification, surgical planning, and risk of intraoperative vascular injury. However, despite the extensive classification of these variations, the principles governing the occurrence of certain branching patterns remain unclear.

Methods: We analyzed 28 branching subtypes of the celiac trunk-SMA system described by Adachi. Each branching pattern was quantified relative to the standard configuration by using Node-Shift (relative displacement of branching nodes), Edge-Gain (number of additional branches), and Edge-Loss (number of missing branches). The relationships between these topological parameters and branching frequency were examined using linear, log-linear, and exponential regression models.

Results: Branching frequency consistently decreased as topological complexity increased. In subtypes without branch loss, the branching frequency showed a strong exponential decline with increasing Node-Shift and Edge-Gain (R² = 0.979). When all subtypes were included, the exponential model maintained a similarly high explanatory power (R² = 0.979), whereas the linear and log-linear models showed a limited fit. Branch loss was exclusively associated with very-low-frequency patterns.

Conclusions: Arterial branching variations do not arise in a purely random manner and are consistent with the probabilistic constraints of developmental and anatomical pattern formation.