Objective:

To develop a mathematical framework explaining paradoxical regional ischemia observed
in hypertensive encephalopathy despite elevated mean arterial pressure (MAP).

Background:

Traditional hemodynamic models fail to explain why hypertensive encephalopathy causes
selective ischemic injury to deep and superficial perforators while sparing cortical vessels. Current pressure flow models focus on longitudinal pressure dynamics but cannot account for branch vessel perfusion failure at elevated MAP.

Design/Methods:

We developed a dual-pressure mathematical model distinguishing longitudinal pressure (P(ℓ)=(½)ρv(ℓ)^2) from transverse pressure (ΔP(t)=ρε(Δv(t)^2), where ε represents vessel wall elasticity and Δv(t) is transverse velocity gradient. The model predicts critical MAP thresholds (MAP(crit)) where transverse pressure collapses due to flow laminarization. Theoretical predictions were evaluated against known MRI patterns in hypertensive encephalopathy

Results:

The model demonstrates that as MAP increases, wall-proximal turbulence diminishes, causing
transverse pressure gradient collapse even with maximal elasticity (ε=1). At MAP(crit), Δv(t) → 0 leads to ΔP(t) → 0, impairing branch perfusion despite rising global cerebral blood volume. Vessels with reduced elasticity (ε < 1) show earlier collapse. This mechanism explains selective perforator vulnerability while cortical vessels remain perfused through preserved longitudinal pressure.

Conclusions:

Regional ischemia in hypertensive encephalopathy results from transverse pressure collapse,
not inadequate MAP. This dual-pressure framework reconceptualizes autoregulatory failure as structural coherence loss rather than simple pressure deficit. The model provides theoretical basis for refined pressure management protocols emphasizing vessel geometry and directional flow dynamics beyond global MAP targets.