Geometry-Controlled Diffusion in Bicontinuous Cubic Lipid Net-works: Network Topology, Tortuosity, and Pore-Scale Constric-tion Effects

Triply periodic minimal surface (TPMS) architectures - Gyroid, Diamond, and Primitive - are increasingly used as delivery matrices for therapeutic agents. Although point-tracer diffusion and geodesic tortuosity (tau) describe solvent transport through their aqueous nanochannels, practical drug delivery requires accounting for finite-sized solutes. We present a unified computational framework that combines discrete lattice random walks with periodic Euclidean distance transforms and domain erosion. By mapping local clearance from lipid boundaries, we quantify both the effective diffusion coefficient (D_eff) and the macroscopic size-dependent sieving factor K_s(rho) over a range of normalized tracer radii (rho = r/R_ch). Our results decouple structural tortuosity from excluded-volume partition effects, providing a rigorous 3D generalization of classical hindrance theory tailored to the complex topology of TPMS matrices. Comparison with experimental water self-diffusion data shows that the geometric point-tracer model systematically overpredicts the observed diffusivity; the residual offset is consistent with a bound-water contribution, though we do not claim a quantitative scaling law (the correlation rests on only five data points and is reported descriptively). All simulations are reported in dimensionless units; a physical length scale is required to map normalized sieving to absolute drug radii. Using a typical monoolein gyroid lattice constant (a ~ 10 nm) as an illustrative conversion, water's hydrodynamic radius corresponds to rho ~ 0.12 (with the Marching Cubes-corrected R_ch), where steric hindrance is negligible (K_s ~ 1), whereas drug-sized payloads (rho >= 0.3) experience substantial steric exclusion.