Effects of homogeneous and heterogeneous changes in the lung periphery on spirometry results

Investigation of tracer gas transport in a new numerical model of lung acini

Obstructive pulmonary diseases are associated with considerable morbidity. For an early diagnosis of these diseases, inert gas washouts can potentially be used. However, the complex interaction between lung anatomy and gas transport mechanisms complicates data analysis. In order to investigate this interaction, a numerical model, based on the finite difference method, consisting of two lung units connected in parallel, was developed to simulate the tracer gas transport within the human acinus. Firstly, the geometries of the units were varied and the diffusion coefficients (D) were kept constant. Secondly, D was changed and the geometry was kept constant. Furthermore, simple monoexponential growth functions were applied to evaluate the simulated data. In 109 of the 112 analyzed curves, monoexponential function matched simulated data with an accuracy of over 90%, potentially representing a suitable numerical tool to predict transport processes in further model extensions. For total flows greater than 5 × 10−4 ml/s, the exponential growth constants increased linearly with linear increasing flow to an accuracy of over 95%. The slopes of these linear trend lines of 1.23 µl−1 (D = 0.6 cm2/s), 1.69 µl−1 (D = 0.3 cm2/s), and 2.25 µl−1 (D = 0.1 cm2/s) indicated that gases with low D are more sensitive to changes in flows than gases with high D.

Graphical abstract

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.

Quantitative Assessment of the Airway Response to Bronchial Tests Based on a Spirometric Curve Shift

OBJECTIVE

Although spirometry is the most common pulmonary function test, there is no method to quantitatively infer about airway resistance or other properties from the flow-volume curves. Recently, an identifiable inverse model for forced expiration was proposed, as well as the idea to deduce changes in airway resistances and compliances from spirometric curve evolution. The aim of this work was to combine the above advances in a method for assessing the airway response to bronchial tests from a spirometric curve shift.

METHODS

The approach is based on the differential measurement of the degree, site of maximal effect and width of changes, further recalculated into relative changes in the distribution of airway resistances (δR_g) and compliances (δC_g) along the bronchial tree. To this end, appropriate models were identified using the pre- and post-test spirometry data. The accuracy was validated using sets of data simulated by the anatomy and physiology based models. Finally, the method was used to analyze the bronchodilation tests of three asthmatic subjects.

RESULTS

The expected errors in assessing the degree, site and width of changes in the zone of conducting airways were 6.3%, 2.4 generations and 22%, respectively, and for δR_g and δC_g were 5-10% and 13-16%, respectively. The analyses of clinical data indicated a significant reduction in resistances and an increase in compliances of airway generations 8-12, consistent with clinical knowledge.

CONCLUSION

An unprecedented method to plausibly transforming the spirometry data into the site and degree of changes in airway properties has been proposed.

SIGNIFICANCE

The method can be used to deduce about the effects of bronchial tests, as well as to monitor changes in the airways between visits or to investigate how inhaled pharmaceuticals affect the bronchi.