Modelling inert gas exchange in tissue and mixed-venous blood return to the lungs

Analysis of the effect of inert gas on alveolar/venous blood partial pressure by using the operator splitting method

This study aims to investigate how inert gas affects the partial pressure of alveolar and venous blood using a fast and accurate operator splitting method (OSM). Unlike previous complex methods, such as the finite element method (FEM), OSM effectively separates governing equations into smaller sub-problems, facilitating a better understanding of inert gas transport and exchange between blood capillaries and surrounding tissue. The governing equations were discretized with a fully implicit finite difference method (FDM), which enables the use of larger time steps. The model employed partial differential equations, considering convection-diffusion in blood and only diffusion in tissue. The study explores the impact of initial arterial pressure, breathing frequency, blood flow velocity, solubility, and diffusivity on the partial pressure of inert gas in blood and tissue. Additionally, the effects of anesthetic inert gas and oxygen on venous blood partial pressure were analyzed. Simulation results demonstrate that the high solubility and diffusivity of anesthetic inert gas lead to its prolonged presence in blood and tissue, resulting in lower partial pressure in venous blood. These findings enhance our understanding of inert gas interaction with alveolar/venous blood, with potential implications for medical diagnostics and therapies.

Effect of first order chemical reactions through tissue-blood interface on the partial pressure distribution of inhaled gas

Gas exchange is an essential process to get fresh oxygenated air from the environment. In the human respiratory system, partial pressure is responsible for exchanging gas between tissue-blood capillary (inter capillary). However, the mechanisms of partial pressure distribution in the human respiratory system remain incompletely understood in terms of inter-capillary transmission with tissue porosity and reactive boundary conditions. In this paper, we worked on the spatial (radial) and temporal variations of inhaled gas partial pressure through inter capillary. We assumed that the tissue of alveoli is porous and the material of blood capillary is absorptive and reactive and gas could bear linear first-order kinetic reactions, one is reversible among the material of blood capillary and the other is irreversible into the surrounding tissue. Mathematical modeling is done by using diffusion equation; and the effect of various dimensionless parameters e.g. the Damkohler number (DA), phase partitioning number (α), dimensionless absorption number (Γ) are analyzed. Numerical simulation shows that an increment in porosity does not change convection speed but the diffusion of gas increases in alveolar tissue, resultantly, partial pressure gradient of the gas decreases in tissue and increases in blood capillary. However, by increasing the breathing rate, the partial pressure of the gas inside the blood first decreases, and after some time it increases gradually with the breathing rate. Additionally, the dispersion coefficient advanced toward its steady-state in a short time at absorption rate Γ≤ 0.1 and Damkohler number 1≤DA≤10, while long-time dispersion is achieved at porosity ϵ = 0.9, absorption rate Γ = 1, and phase exchange rate 10<DA≤100. Ultimately, the findings of this study can be helpful for a better understanding of dispersion through human lung affected by aging and various lung diseases.

Lung heterogeneity and deadspace volume in acute respiratory distress syndrome animals using the inspired sinewave test

The acute respiratory distress syndrome is associated with a high rate of morbidity and mortality, as patients undergoing mechanical ventilation are at risk of ventilator-induced lung injuries.

OBJECTIVE

To measure the lung heterogeneity and deadspace volume to find safer ventilator strategies. Then, the ventilator settings could offer homogeneous ventilation and theoretically equalise and reduce tidal strain/stress in the lung parenchyma.

APPROACH

The Inspired Sinewave Test (IST) is a non-invasive lung measurement tool, which does not require patients' cooperation. The IST can measure the effective lung volume, pulmonary blood flow and deadspace volume. We developed a computational simulation of the cardiopulmonary system to allow lung heterogeneity to be quantified using data solely derived from the IST. Then, the method to quantify lung heterogeneity using two IST tracer gas frequencies (180s and 60s) was introduced and experimented in the simulation lungs and in animal models. Thirteen anaesthetised pigs were studied with the IST, both before and after experimental lung injury (saline-lavage ARDS model). The deadspace volume is compared between IST and the SF_{6} Washout method.

RESULTS

The IST could measure the lung heterogeneity using two frequencies tracer gases. Furthermore, the value of IST ventilation heterogeneity in ARDS lungs were higher than in control lungs at PEEP 10cmH_{2}O (AuC=0.85, p<0.001). Deadspace volume values measured by the IST has a strong relationship with the measured values of the SF_{6} (9mL bias and limits of agreement from -79mL to 57mL in control animals).

SIGNIFICANCE

the potential impact of the IST technique in the identification of ventilation and perfusion heterogeneity during ventilator support.

Inert gas transport in blood and tissues

This article establishes the basic mathematical models and the principles and assumptions used for inert gas transfer within body tissues-first, for a single compartment model and then for a multicompartment model. From these, and other more complex mathematical models, the transport of inert gases between lungs, blood, and other tissues is derived and compared to known experimental studies in both animals and humans. Some aspects of airway and lung transfer are particularly important to the uptake and elimination of inert gases, and these aspects of gas transport in tissues are briefly described. The most frequently used inert gases are those that are administered in anesthesia, and the specific issues relating to the uptake, transport, and elimination of these gases and vapors are dealt with in some detail showing how their transfer depends on various physical and chemical attributes, particularly their solubilities in blood and different tissues. Absorption characteristics of inert gases from within gas cavities or tissue bubbles are described, and the effects other inhaled gas mixtures have on the composition of these gas cavities are discussed. Very brief consideration is given to the effects of hyper- and hypobaric conditions on inert gas transport.

Inert gas clearance from tissue by co-currently and counter-currently arranged microvessels

To elucidate the clearance of dissolved inert gas from tissues, we have developed numerical models of gas transport in a cylindrical block of tissue supplied by one or two capillaries. With two capillaries, attention is given to the effects of co-current and counter-current flow on tissue gas clearance. Clearance by counter-current flow is compared with clearance by a single capillary or by two co-currently arranged capillaries. Effects of the blood velocity, solubility, and diffusivity of the gas in the tissue are investigated using parameters with physiological values. It is found that under the conditions investigated, almost identical clearances are achieved by a single capillary as by a co-current pair when the total flow per tissue volume in each unit is the same (i.e., flow velocity in the single capillary is twice that in each co-current vessel). For both co-current and counter-current arrangements, approximate linear relations exist between the tissue gas clearance rate and tissue blood perfusion rate. However, the counter-current arrangement of capillaries results in less-efficient clearance of the inert gas from tissues. Furthermore, this difference in efficiency increases at higher blood flow rates. At a given blood flow, the simple conduction-capacitance model, which has been used to estimate tissue blood perfusion rate from inert gas clearance, underestimates gas clearance rates predicted by the numerical models for single vessel or for two vessels with co-current flow. This difference is accounted for in discussion, which also considers the choice of parameters and possible effects of microvascular architecture on the interpretation of tissue inert gas clearance.