Characteristic of all conifer needles, the transfusion tissue mediates the radial transport of water and sugar between the endodermis and axial vasculature. Physical constraints imposed by the needle's linear geometry introduce two potential extravascular bottlenecks where the opposition of sugar and water flows may frustrate sugar export: one at the vascular access point and the other at the endodermis. We developed a network model of the transfusion tissue to explore how its structure and composition affect the delivery of sugars to the axial phloem. To describe extravascular transport with cellular resolution, we construct networks from images of Pinus pinea needles obtained through tomographic microscopy, as well as fluorescence and electron microscopy. The transfusion tissue provides physically distinct pathways for sugar and water, reducing resistance between the vasculature and endodermis and mitigating flow constriction at the vascular flank. Dissipation of flow velocities through the transfusion tissue's branched structure allows for bidirectional transport of an inbound diffusive sugar flux against an outbound advective water flux across the endodermis. Our results clarify the structure-function relationships of the transfusion tissue under conditions free of physiological stress. The presented model framework is also applicable to different transfusion tissue morphologies in other gymnosperms.