# Flow mechanisms of the air-blood barrier

## TL;DR

This paper introduces a new fluid mechanics model for the air-blood barrier in the lungs, offering insights into pulmonary edema and potential clinical applications.

## Contribution

The first mathematical model of the air-blood barrier's fluid mechanics, including active epithelial reabsorption and new insights into interstitial fluid pressure.

## Key findings

- The model calculates interstitial fluid pressure and critical capillary pressure, which align with clinical and experimental data.
- Active epithelial reabsorption enhances alveolar-lymphatic and alveolar-capillary clearance of edema.
- The model explains how distant alveolar lymphatics function and why they are sparse.

## Abstract

The air-blood barrier protects the lung from blood/serum entering the air spaces, i.e., from “drowning in your own fluids”. Failure leads to pulmonary edema, a regularly fatal complication during the Covid-19 pandemic which claimed 7 million lives worldwide. Finding no mathematical models for the underlying fluid mechanics, we created the first. Governing flow equations for alveolar capillary, interstitium, and alveolus are coupled by crossflows at the capillary and epithelial membranes and end-exit flows to the lymphatics. Case examples include normal/recovery, cardiogenic pulmonary edema, acute respiratory distress syndrome, effects of positive end expiratory pressure, and a wide range of parameter values for permeability of the membranes and interstitial matrix. Previously unknown membrane fluid shear stresses calculate to values that affect cell function in many systems. We add active epithelial reabsorption which has two effects: shifting streamlines to favor alveolar-lymphatic clearance and adding to the direct alveolar-capillary clearance. Simple algebraic equations are derived for the interstitial fluid pressure, pi, membrane crossflow velocities and the critical capillary pressure, pcrit, above which edema occurs. For validation, the pcrit predictions fit clinical definitions and flow calculations of lymphatic vs capillary clearance match animal experimental data. For decades the value of pi has been imposed as an input, whereas we calculate the value as an output. They don’t agree. Since the space is too small for measurements, the ability to calculate pi and pcrit offers new insights, questions long-held beliefs, and opens applications from physiological studies to personalized clinical care.

Our fluid mechanics model of the air-blood barrier provides a new conceptual framework for developing and clearing pulmonary edema. It can be used to organize data, motivate experimental investigations, interpret cause-effect relationships, understand the physical basis of disease, suggest therapies, follow interventions, and personalize care. Parameter values for the anatomy and physiology of the alveolar-capillary-interstitial layers are incorporated into fluid physics equations. We predict the alveolar interstitial pressure, which can’t be measured, uncovering several misunderstandings in pulmonary physiology and medicine. Validation is achieved by deriving an equation for the critical alveolar capillary blood pressure leading to edema and calculations of alveolar edema clearance flow rate both directly to the capillary and to the lymphatic route. Both agree with clinical and experimental measurements. The flow mechanism to lymphatics resolves a puzzle, since 1896, as to how alveolar lymphatics function from so far away, and explains the paucity of lymphatics since direct clearance to the capillary is the major route by far.