Deep Breaths: A Dynamic Network Model of Respiration

Abstract

Respiratory disorders like Cystic Fibrosis and Chronic Obstructive Pulmonary Disease are characterized by alterations in the mechanical properties of airway tissues and secretions, leading to difficulties in breathing. However, a quantitative connection between these different factors remains lacking. We develop a statistical model of the lung as a branched network, with different branches opening at rates and pressure thresholds that are determined by physiological factors. Such a model allows us to examine how various factors (e.g. rheology of airway mucus lining, elasticity of airway tissue, breathing rate) affect the distribution of branch openings and overall breathing dynamics. We find that lung opening characteristics depend strongly on both breathing rate and branch opening rate. Under certain circumstances, different branches open simultaneously as cooperative \avalanches". Moreover: (i) In fast-opening airways, faster breathing promotes larger avalanches; (ii) In slow-opening airways, faster breathing promotes larger avalanches only up to a threshold breathing rate, above which faster breathing suppresses avalanche formation; (iii) Above this threshold breathing rate, avalanches and total lung opening are suppressed in slower opening airways; (iv) Below this threshold breathing rate, the airway opening rate appears to not affect the opening behavior. By abstracting away circumstantial properties which vary from patient to patient, such as the geometries and mechanical properties of individual lungs, our in silico approach allows for a more general, fundamental understanding of the airways, which in turn is key for advising approaches to treatment.