Statistical physics of cerebral embolization leading to stroke

TL;DR

This paper models embolic stroke as a phase transition in cerebral blood flow, using a minimal network model to analyze how emboli cause congestion and critical behavior.

Contribution

It introduces a minimal bifurcating tree model with flow-weighted interactions to study embolic stroke as a non-equilibrium phase transition.

Findings

Flow correlation time peaks at critical embolus density

Identifies an order parameter based on blockage overlap

Shows stroke dynamics resemble phase transition phenomena

Abstract

We discuss the physics of embolic stroke using a minimal model of emboli moving through the cerebral arteries. Our model of the blood flow network consists of a bifurcating tree, into which we introduce particles (emboli) that halt flow on reaching a node of similar size. Flow is weighted away from blocked arteries, inducing an effective interaction between emboli. We justify the form of the flow weighting using a steady flow (Poiseuille) analysis and a more complicated nonlinear analysis. We discuss free flowing and heavily congested limits and examine the transition from free flow to congestion using numerics. The correlation time is found to increase significantly at a critical value, and a finite size scaling is carried out. An order parameter for non-equilibrium critical behavior is identified as the overlap of blockages' flow shadows. Our work shows embolic stroke to be a feature of the cerebral blood flow network on the verge of a phase transition.