Numerical simulation of blood and interstitial flow through a solid tumor.

Area of Science:

• Biophysics
• Mathematical Biology
• Oncology

Background:

• Solid tumors exhibit irregular vasculature, impacting blood flow and drug delivery.
• Understanding plasma leakage is crucial for predicting tumor growth and treatment efficacy.

Purpose of the Study:

• To develop a theoretical framework for blood flow and plasma leakage in solid tumors.
• To analyze the influence of vascular architecture and interstitial properties on plasma extravasation.

Main Methods:

• Modeling the tumor capillary bed as a bifurcating tree with deterministic and random parameters.
• Applying Sterling's law for plasma leakage and Darcy's law for interstitial flow.
• Solving coupled integral and differential equations using numerical discretization and iterative methods.

Main Results:

• Quantified the effect of interstitial hydraulic and vascular permeability on fractional plasma leakage.
• Demonstrated that fractional leakage peaks at a specific vascular tree bifurcation grade.
• The model provides insights into pressure distribution within tumor vasculature and interstitium.

Conclusions:

• The developed theoretical framework accurately describes blood flow and plasma leakage in tumor vasculature.
• Interstitial and vascular permeability are key determinants of plasma extravasation.
• Optimal vascular tree structure exists for minimizing or maximizing plasma leakage, with implications for drug delivery strategies.