Modelling dynamic changes in blood flow and volume in the cerebral vasculature

Area of Science:

• Neuroscience
• Biomedical Engineering
• Computational Fluid Dynamics

Background:

• The cerebral microvasculature is crucial for brain function, supplying blood and nutrients.
• Current in-vivo human imaging is limited to millimeter scales, necessitating mathematical models for interpretation.
• Modeling the dense network of cerebral vessels (approx. 10,000 per mm³ voxel) is computationally intensive, especially for dynamic changes.

Purpose of the Study:

• To rigorously justify simplifications in mathematical models of cerebral microvasculature.
• To determine the validity of approximations across different generations and sizes of cerebral blood vessels.
• To provide a simplified yet rigorous framework for modeling dynamic cerebral blood flow and volume.

Main Methods:

• Analysis of governing equations for blood flow and volume changes in the cerebral microvasculature.
• Evaluation of proposed mathematical approximations, including neglecting advection and assuming quasi-steady state for blood volume.
• Application of validated approximations to solve flow fields within cerebral vascular networks.

Main Results:

• Two approximations (neglecting advection, quasi-steady state blood volume) are valid throughout the cerebral vasculature.
• Two additional approximations (first-order differential relationship for flow/pressure, static pressure matching at nodes) are valid for vessels < 1 mm diameter.
• The validated approximations enable a simplified yet rigorous approach to solving dynamic flow fields, comparable to alternative methods.

Conclusions:

• A framework is established for modeling cerebral blood flow and volume at sub-millimeter scales.
• The validated simplifications enhance computational efficiency for dynamic modeling of the cerebral vasculature.
• This approach offers greater insight into cerebral blood flow and volume dynamics, particularly below human imaging resolution.