The prediction of viscous losses and pressure drop in models of the human airways

Algebraic approximation of the distributed model for the pressure drop in the respiratory airways

The complexity of the human respiratory system causes that one of the main methods of analyzing the dynamic pulmonary phenomena and interpreting experimental results are simulations of its computational models. Among the most compound elements of these models, apart from the bronchial tree structure, is the phenomenon of flow limitation in flexible bronchi, which causes them to collapse with increasing flow, thus their properties, such as resistance, compliance and inertance, are highly nonlinear and time-varying. Commonly, this phenomenon is ignored, or a distributed model for the airway pressure drop is applied, simulated with a modified numerical solver of this differential equation (ODE). The disadvantages of this solution are the problems with taking into account the inherent singularity of the model and the long computation time due to iterative nature of the ODE procedure. The aim of the work was to derive an algebraic approximation of this distributed model, suitable for implementation in continuous dynamic models, to validate it by comparing the results of simulations with the respiratory system model including approximate and original (ODE solver) numerical procedures, as well as to evaluate possible acceleration of calculations. All simulations, including spontaneous breathing, mechanical ventilation with the optimal ventilatory waveform and forced expiration, proved that algebraic approximation yielded results negligibly differing from the ODE solution, and shortened the computation time by an order. The proposed approach is an attractive alternative in the case of computer implementations of pulmonary models, where simulations of flows and pressures in the complex respiratory system are of primary importance.

Modeling of the Transport and Exchange of a Gas Species in Lungs With an Asymmetric Branching Pattern. Application to Nitric Oxide

Over the years, various studies have been dedicated to the mathematical modeling of gas transport and exchange in the lungs. Indeed, the access to the distal region of the lungs with direct measurements is limited and, therefore, models are valuable tools to interpret clinical data and to give more insights into the phenomena taking place in the deepest part of the lungs. In this work, a new computational model of the transport and exchange of a gas species in the human lungs is proposed. It includes (i) a method to generate a lung geometry characterized by an asymmetric branching pattern, based on the values of several parameters that have to be given by the model user, and a method to possibly alter this geometry to mimic lung diseases, (ii) the calculation of the gas flow distribution in this geometry during inspiration or expiration (taking into account the increased resistance to the flow in airways where the flow is non-established), (iii) the evaluation of the exchange fluxes of the gaseous species of interest between the tissues composing the lungs and the lumen, and (iv) the computation of the concentration profile of the exchanged species in the lumen of the tracheobronchial tree. Even if the model is developed in a general framework, a particular attention is given to nitric oxide, as it is not only a gas species of clinical interest, but also a gas species that is both produced in the walls of the airways and consumed within the alveolar region of the lungs. First, the model is presented. Then, several features of the model, applied to lung geometry, gas flow and NO exchange and transport, are discussed, compared to existing works and notably used to give new insights into experimental data available in the literature, regarding diseases, such as asthma, cystic fibrosis, and chronic obstructive pulmonary disease.

Modeling Inspiratory Flow in a Porcine Lung Airway

Inspiratory flow in a multigeneration pig lung airways was numerically studied at a steady inlet flow rate of 3.2 × 10-4 m3/s corresponding to a Reynolds number of 1150 in the trachea. The model was validated by comparing velocity distributions with previous measurements and simulations in simplified airway geometries. Simulation results provided detailed maps of the axial and secondary flow patterns at different cross sections of the airway tree. The vortex core regions in the airways were visualized using absolute helicity values and suggested the presence of secondary flow vortices where two counter-rotating vortices were observed at the main bifurcation and in many other bifurcations. Both laminar and turbulent flows were considered. Results showed that axial and secondary flows were comparable in the laminar and turbulent cases. Turbulent kinetic energy (TKE) vanished in the more distal airways, which indicates that the flow in these airways approaches laminar flow conditions. The simulation results suggested viscous pressure drop values comparable to earlier studies. The monopodial asymmetric nature of airway branching in pigs resulted in airflow patterns that are different from the less asymmetric human airways. The major daughters of the pig airways tended to have high airflow ratios, which may lead to different particle distribution and sound generation patterns. These differences need to be taken into consideration when interpreting the results of animal studies involving pigs before generalizing these results to humans.