A global multiscale mathematical model for the human circulation with emphasis on the venous system

Area of Science:

• Physiology
• Biomedical Engineering
• Computational Science

Background:

• The human circulatory system is complex, involving arterial, venous, pulmonary, and microcirculatory components.
• Detailed modeling of the venous system, especially head and neck veins, is crucial for understanding various medical conditions.
• Existing models often lack a global, closed-loop approach or detailed venous representation.

Purpose of the Study:

• To develop a global, closed-loop, multiscale mathematical model of the entire human circulation.
• To specifically enhance the detailed description of the venous system, including intracranial and extracranial veins.
• To enable patient-specific simulations and applications in medical research, particularly for neurodegenerative diseases.

Main Methods:

• A multiscale mathematical model integrating 1D hyperbolic systems for large vessels and 0D differential-algebraic equations for other components.
• Implementation of robust, high-order accurate numerical methods for solving hyperbolic equations with variable material properties.
• Patient-specific characterization of head and neck veins using MRI data for model validation.

Main Results:

• The model successfully simulates global, closed-loop human circulation without artificial boundary conditions.
• Validation against published data for arterial and venous systems confirmed model accuracy.
• Patient-specific validation using phase-contrast MRI data demonstrated high fidelity for head and neck venous simulations.

Conclusions:

• The developed mathematical model provides a comprehensive and accurate representation of human circulation.
• Its detailed venous system modeling, especially in the head and neck, offers new avenues for medical research.
• The model holds significant potential for studying conditions with identified venous hemodynamic connections, such as neurodegenerative diseases.