Bifurcations in adaptive vascular networks: Toward model calibration

Area of Science:

• Mathematical modeling
• Vascular biology
• Network dynamics

Background:

• Transport networks are vital for biological and technological systems.
• Vascular network adaptation involves dynamic structural adjustments to blood flow and pressure.
• Local feedback mechanisms operate on various timescales in mammalian vasculature.

Purpose of the Study:

• To test the hypothesis that the cost exponent (γ) for vascular systems is 1/2.
• To assess the consistency of a mathematical model of vascular network adaptation with experimental data.
• To determine if measured flow networks align with physical reality and adaptive dynamic models.

Main Methods:

• Bifurcation analysis of a triangular network motif with fluctuating demand.
• Numerical simulations on network topologies from rodent brain perivascular networks.
• Comparison of model predictions with experimental data.

Main Results:

• The cost exponent (γ) is found to be closer to 1 than to 1/2 for model-data consistency.
• The adaptive dynamic model captures certain aspects of vascular network formation.
• The model's predictions align better with experimental data when γ approaches 1.

Conclusions:

• The mathematical model provides insights into vascular network adaptation dynamics.
• The study suggests limitations in the current model and proposes future research directions.
• Findings contribute to understanding adaptive transport networks and mammalian vasculature.