Optimal diameter reduction ratio of acinar airways in human lungs

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.