Transient ischemic attacks (TIAs) and secondary ischemic strokes remain heavily burdened by delayed microvascular failure occurring downstream of patent epicranial arteries. While clinical protocols prioritize macrovascular recanalization and systemic antiplatelet therapy, they overlook the hydrodynamic and electrodynamic breakdown of the neurovascular unit (NVU). In this paper, we formulate a non-equilibrium hydrodynamic and information-theoretic model governing the mechanical shielding of the blood-brain barrier (BBB). We model the luminal endothelial glycocalyx layer (EGL) as an active, fractional viscoelastic porous matrix operating under Brinkman-extended momentum transport coupled to pulsatile Navier-Stokes luminal flow. Under physiological conditions, the EGL acts as a mechanical low-pass filter, dissipating high-frequency systolic wall shear stress (WSS) harmonics and preserving eNOS phosphorylation (Ser1177) and trans-endothelial electrical resistance (TEER). When the glycocalyx sheds under acute oxidative or hemodynamic stress, apical lipid bilayers are directly subjected to destructive high-shear spikes. This mechanical denudation triggers an immediate drop in the bioenergetic Signal-to-Noise Ratio (SNR_bio < 3.0 dB), collapses Shannon channel capacity (C → 0), and exposes sub-endothelial ligands, precipitating platelet adhesion, leukocyte plugging, and delayed micro-thrombosis. Within the Science 4.0 framework, we propose targeted pre-reperfusion electrodynamic shielding and nano-vectorized matrix restoration to quench mechanical entropy production, prevent BBB disruption, and eradicate the biophysical triggers of secondary TIA cascades.