Shock formation and non-linear dispersion in a microvascular capillary network

Area of Science:

• Biophysics
• Fluid Dynamics
• Computational Biology

Background:

• Blood flow in microvascular networks exhibits temporal and spatial fluctuations.
• Non-linear rheological properties of capillary blood flow, including the Fåhraeus effect, Fåhraeus-Lindqvist effect, and phase-separation at bifurcations, are hypothesized to cause these fluctuations.

Purpose of the Study:

• To investigate the stability and dynamics of blood flow in a simple arcade microvascular network.
• To determine if non-linear rheological effects are sufficient to generate temporal fluctuations in blood flow.

Main Methods:

• Simulated blood flow through a simple arcade network using coupled hyperbolic partial differential equations (PDEs).
• Incorporated empirical descriptions of non-linear rheological effects, including spatially varying hematocrit distributions.
• Solved the PDE system using a characteristic-based numerical method.

Main Results:

• Under physiologically realistic conditions, a unique, linearly stable steady flow was found in the arcade network.
• Plasma skimming was observed to suppress the oscillatory decay of perturbations.
• Non-linear perturbations in hematocrit distributions can develop shocks due to the Fåhraeus effect.

Conclusions:

• The study suggests that simple microvascular networks exhibit stable, steady blood flow, challenging previous hypotheses.
• The Fåhraeus effect can induce non-linear dispersion through shock formation in hematocrit distributions.
• These findings offer a novel mechanism for understanding non-linear dynamics in microcirculation.