Derivation of closed-form expression for the cerebral circulation models

Area of Science:

• Cardiovascular physiology
• Biomedical engineering
• Mathematical modeling

Background:

• Anastomosing vascular networks, such as the circle of Willis, present analytical challenges.
• Existing mathematical models fail to adequately analyze cerebral circulation loops.

Purpose of the Study:

• To present the theoretical basis of a novel mathematical model for cerebral circulation loops.
• To provide a new analytical method for understanding hemodynamics in the circle of Willis.

Main Methods:

• Development of a new model for cerebral circulation loops.
• Analytical solution of transmission line equations derived from linearized Navier-Stokes and arterial wall deformation equations.
• Computation of hemodynamic parameters using the developed model.

Main Results:

• The new model provides an analytical solution for cerebral circulation loops.
• Simulation results show satisfactory agreement with experimental data.
• The analytical solution offers higher accuracy compared to numerical methods.

Conclusions:

• The proposed model offers a more accurate analytical approach to studying cerebral circulation loops.
• This work advances the understanding of hemodynamics within the circle of Willis.
• The model has potential applications in diagnosing and treating cerebrovascular diseases.