A mathematical analysis on the biological zero problem in laser Doppler flowmetry

Area of Science:

• Biomedical Engineering
• Physiology
• Medical Physics

Background:

• Laser Doppler flowmetry (LDF) is crucial for measuring tissue blood flow.
• The biological zero (BZ) problem complicates accurate measurement of low blood flow rates.
• Existing methods for addressing BZ flux lack rigorous mathematical validation.

Purpose of the Study:

• To mathematically analyze and resolve the biological zero (BZ) problem in LDF.
• To define net perfusion flux and establish its relationship with BZ and normal flux.
• To develop a correct method for recovering net flux from measured LDF data.

Main Methods:

• Decomposition of moving blood cell (MBC) movement into translation and random wandering.
• Mathematical formulation of BZ and net perfusion flux based on MBC movement.
• Derivation of a formula to recover net flux from BZ and normal flux measurements.

Main Results:

• A clear definition of BZ and net perfusion flux was established.
• Subtracting BZ flux was shown to cause underestimation of net perfusion.
• A novel formula accurately recovers net flux, outperforming subtraction methods.
• A more accurate general density function for MBC speeds was introduced.

Conclusions:

• The developed mathematical approach provides an accurate solution to the BZ problem in LDF.
• The new method ensures more reliable measurement of low tissue blood flows.
• This work offers a foundation for advanced theoretical developments in LDF technology.