Physics-Informed Operator Learning for Pulsatile Milk Flow in Distal Generations of a Bifurcated Mammary Duct Network

Authors

Olapojoye, A. O., Nosratinia, A., Hassanipour, F.

Abstract

Pulsatile milk transport through the lactating mammary ductal tree involves complex interactions between pressure gradients, wall compliance, and non-Newtonian rheology across spatial scales that span nearly two orders of magnitude in lumen radius. Direct experimental characterization of flow in distal ductal generations remains infeasible due to their sub-millimeter caliber, leaving the hemodynamic environment of the secretory ductules largely unknown. We present a two-stage physics-informed operator-learning framework that extends validated flow predictions from three instrumented duct generations to twenty generations of a bifurcated mammary network. A Physics-Informed Neural Network (PINN) trained against particle image velocimetry measurements across seven ducts achieved R^2 = 0.924-0.997. A Deep Operator Network (DeepONet) distilled from the PINN and refined through physics-constrained training on the governing one-dimensional fluid-structure interaction equations achieved R^2(u) = 0.857-0.985 across all validated ducts, with predictions for Generations 4-20 obtained by supplying Murray's Law geometry and mass-conservation-scaled boundary conditions to the frozen operator. Three biophysically significant findings emerge: a mean velocity plateau of 0.14-0.18 m/s across Generations 4-13 produced by Cross shear-thinning compensation offsetting Murray-branching deceleration; a non-monotonic pulsatility index that declines from 0.048 at Generation 1 to a minimum of 0.039 at Generation 5 before rising monotonically to 1.37 at Generation 20 as progressive wall stiffening drives the most distal ductules into a microcirculation-like hemodynamic regime; and a brief elastic-recoil transition zone at Generations 4-5 where mean axial pressure drop reverses sign. To the authors' knowledge, these results provide the first quantitative characterization of pulsatile milk flow across the full hierarchy of a bifurcated mammary ductal tree using a physics-informed operator-learning framework with implications for ductal mechanobiology, milk ejection mechanics, and mastitis pathogenesis.

Preprint server: bioRxiv
The authors list and abstract were imported from bioRxiv on 17 Jun 2026.

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