Effect of Bronchial Blood Flow on Respiratory Heat Exchange: A Mathematical Analysis for Infectious Diseases

Abstract

The present study aims to mathematically analyze the role of bronchial blood flow on heat transfer in respiratory infections. In general, the exchange of heat transfer in various infectious diseases like COVID-19 caused by SARS-CoV-2 has adversely affected respiration by reducing the physiological efficiency of the human respiratory tract. The mechanism of heat exchange through airway walls with the bronchial blood circulation still needs to be thoroughly studied for infectious diseases. In this article, a three-dimensional (3D) spatio-temporal theoretical model is developed to estimate the possible role of bronchial blood on heat exchange during breathing. The local description of the model is presented in a comprehensive and consistent dimensionless framework to explicitly state the actual physiological background. The global description is framed by a multicompartment-based approach, and the algorithm is solved using an advanced numerical scheme to ensure computational tractability. The numerical study elucidates the role of inhalation air temperature, breathing cycles, blood perfusion rate, and mucosal hydration. The outcomes of the algorithm estimate the parameters of the isothermal saturation boundary (ISB), which is defined as the position in the respiratory tract where the temperature of inhaled air comes in equilibrium with the body core saturation temperature. The derived results help to understand the pathophysiological threshold limits and recommend the values to evaluate respiratory distress. With the variations of inspiratory flow conditions, it is observed that the ISB position shifts to the distal branches with the increment in inhalation temperature, breathing rate and virus infection, and decrement in blood perfusion rate. The two antiparallel effects are observed: inhalation of cold air transmits the viral infection, and inhalation of warm air produces thermal injury. However, both can be well controlled by suitable ventilation rates. The observed threshold values may be helpful in clinical trials to correlate the anatomic configuration with pathophysiology.