A nonlinear multi-scale model for blood circulation in a realistic vascular system

Area of Science:

• Computational biology
• Physiology
• Medical modeling

Background:

• Numerical models are vital for understanding physiology and improving medical diagnostics and treatments.
• Accurate simulation of blood flow distribution is crucial for organ function assessment.

Purpose of the Study:

• To develop a nonlinear multi-scale model framework for simulating blood flow distribution in an organ's entire vascular system.
• To couple macroscopic and microscopic vascular models for comprehensive physiological representation.

Main Methods:

• A quasi one-dimensional vascular graph model (Poiseuille's Law) for larger vessels.
• A porous media model (Darcy's Law) for smaller vessels and capillary beds.
• Coupling of models with pressure correction for elasticity and junction pressure drops, defining blood perfusion.

Main Results:

• The model demonstrates a strong dependence on the structural parameters of both large vessels and capillary beds.
• Numerical experiments confirm the model's ability to provide realistic organ blood circulation patterns.
• The model is sufficiently complex for physiological accuracy yet flexible for incorporating local effects.

Conclusions:

• The developed multi-scale model offers a realistic and flexible approach to simulating organ blood flow.
• Its straightforward numerical implementation allows for accessible simulations on standard desktop computers.
• This framework advances computational tools for physiological research and clinical applications.