A fast numerical method for oxygen supply in tissue with complex blood vessel network

Area of Science:

• Biomedical Engineering
• Computational Biology
• Physiology

Background:

• Angiogenesis is vital in pathological processes like tumor growth and wound healing.
• Tissue oxygen levels, influenced by blood flow, diffusion, and cellular consumption, drive angiogenesis.
• Simulating oxygen fields in large-scale angiogenesis models is computationally challenging.

Purpose of the Study:

• To develop a fast numerical method for simulating oxygen supply in tissues with complex vasculature.
• To overcome the bottleneck in large-scale modeling of angiogenesis and related physiological processes.

Main Methods:

• An implicit finite-difference scheme was used to compute the oxygen field.
• An oxygen source distribution technique and post-processing method were employed for accuracy with large mesh sizes.
• The method allows for accurate oxygen field evaluation in centimeter-scale, fully vascularized tissues.

Main Results:

• The new method achieves computational complexity slightly above linear with respect to mesh points.
• It maintains sufficient numerical accuracy using square meshes with large mesh sizes.
• The convergence order is slightly lower than second order with respect to mesh size.

Conclusions:

• A fast and accurate numerical method for oxygen field simulation in complex vascular networks has been developed.
• This method enables accurate, large-scale modeling of oxygen supply in centimeter-scale tissues.
• It has significant implications for research in tumor growth, wound healing, and other angiogenesis-related conditions.