Modeling of the lung impedance using a fractional-order ladder network with constant phase elements

Area of Science:

• Physiology
• Biophysics
• Applied Mathematics

Background:

• The respiratory system's fractal geometry, characterized by self-similar branching, suggests suitability for fractional calculus applications.
• Understanding respiratory system dynamics is crucial for diagnosing and treating lung diseases.

Purpose of the Study:

• To develop and validate an electrical equivalent model for the respiratory tree based on its fractal morphology.
• To apply fractional calculus theory to characterize respiratory impedance at low frequencies.

Main Methods:

• Respiratory impedance measurements were obtained from seven volunteers across a frequency range below 5 Hz.
• Parametric modeling was used to analyze complex-valued impedance data.
• Airway branches were modeled using gamma cell resistance and fractional-order capacitance (constant phase element).

Main Results:

• Both a ladder network model and a lumped model effectively characterized the respiratory impedance data.
• The fractional-order constant phase element (CPE) was successfully identified from impedance measurements.
• Averaged CPE values differed between the ladder network (supraunitary) and the lumped model (subunitary).

Conclusions:

• Fractional calculus provides a robust framework for modeling the respiratory system's electrical impedance.
• The identified models offer a novel approach to understanding lung mechanics and respiratory system dynamics.
• Further research can explore these models for clinical applications in respiratory diagnostics.