Maximum expiratory flow-volume curve: mathematical model and experimental results

Area of Science:

• Pulmonary Physiology
• Mathematical Modeling
• Respiratory Medicine

Background:

• Maximum expiratory flow-volume (MEFV) curves are crucial for assessing lung function.
• Existing models may not fully capture the complex dynamics of airway resistance during forced expiration.
• Quantifying changes in airway resistance across different lung volumes is essential for diagnosing obstructive lung diseases.

Purpose of the Study:

• To develop a lumped parameter mathematical model simulating MEFV curves.
• To derive new parameters reflecting airway resistance dependency on expired volume during forced vital capacity (FVC) maneuvers.
• To evaluate the model's ability to differentiate between normal subjects and patients with obstructive lung diseases.

Main Methods:

• Developed a lumped parameter model using a theoretical activation function for lung pressure-volume relationships.
• Simulated MEFV curves and compared them with data from normal subjects and patients with small airways disease, asthma, and emphysema.
• Calculated new parameters, including the mean slope of resistance-expired volume curves, from the model's output.

Main Results:

• The model successfully reproduced MEFV curves for normal subjects and patients with various obstructive lung diseases.
• New parameters were calculated, quantifying the relationship between airway resistance and expired volume.
• Distinct mean slope values were observed: 0.095 L⁻¹ (normal), 0.13 L⁻¹ (small airways disease), 0.49 L⁻¹ (asthma), and 1.44 L⁻¹ (emphysema).

Conclusions:

• The developed mathematical model provides a novel approach to analyzing MEFV curves.
• Model-derived parameters may offer valuable insights into the dynamic changes in airway resistance.
• Further validation in larger patient cohorts is needed to establish the clinical utility of these new indices for diagnosing COPD.