A mathematical model for filtration and macromolecule transport across capillary walls

Area of Science:

• Physiology
• Biophysics
• Mathematical Biology

Background:

• Metabolic substrates are delivered via microvessel filtration, a process complicated by flow-transport coupling due to plasma protein osmotic pressure.
• The microvessel wall's composite structure, featuring an inner glycocalyx layer and an outer endothelial cell layer, significantly impacts macromolecule sieving.

Purpose of the Study:

• To develop and validate a mathematical model for microvessel transport that accounts for the distinct properties of the glycocalyx and endothelial cell layers.
• To investigate the relationship between hydrostatic pressure, osmotic pressure, and volumetric/solute flux within microvessels.

Main Methods:

• A two-layer membrane model representing the microvessel wall (glycocalyx and endothelial cells).
• Application of mass conservation and thermodynamic principles to derive coupled second-order ordinary differential equations for pressures.
• Obtaining analytical solutions for hydrostatic and osmotic pressures under piecewise constant layer properties.

Main Results:

• The model predicts that flow reversal in microvessels is not possible under steady-state conditions unless hydrostatic pressure drops below physiological levels.
• Analytical solutions for pressures align with experimental observations.
• Variations in volumetric and solute flux with reduced hydrostatic pressure qualitatively match literature findings.

Conclusions:

• The two-layer microvessel wall model provides accurate predictions of pressure and flux dynamics, consistent with experimental data.
• A simplified single-layer model yields inconsistent pressure distributions, highlighting the importance of the distinct glycocalyx and endothelial layers.
• The findings challenge the notion of flow reversal and offer insights into microvascular transport mechanisms.