Physics-informed neural entangled-ladder network for inhalation impedance of the respiratory system

Abstract

Background and objectives: The use of machine learning methods for modelling bio-systems is becoming prominent which can further improve bio-medical technologies. Physics-informed neural networks (PINNs) can embed the knowledge of physical laws that govern a system during the model training process. PINNs utilise differential equations in the model which traditionally used numerical methods that are computationally complex.

Methods: We integrate PINNs with an entangled ladder network for modelling respiratory systems by considering a lungs conduction zone to evaluate the respiratory impedance for different initial conditions. We evaluate the respiratory impedance for the inhalation phase of breathing for a symmetric model of the human lungs using entanglement and continued fractions.

Results: We obtain the impedance of the conduction zone of the lungs pulmonary airways using PINNs for nine different combinations of velocity and pressure of inhalation. We compare the results from PINNs with the finite element method using the mean absolute error and root mean square error. The results show that the impedance obtained with PINNs contrasts with the conventional forced oscillation test used for deducing the respiratory impedance. The results show similarity with the impedance plots for different respiratory diseases.

Conclusion: We find a decrease in impedance when the velocity of breathing is lowered gradually by 20%. Hence, the methodology can be used to design smart ventilators to the improve flow of breathing.

Keywords: Entanglement; Inhalation; Ladder network; Lungs; Physics-informed neural network; Respiratory impedance.