Modeling of the lung impedance using a fractional order ladder network with constant phase elements

The self similar branching arrangement of the airways makes the respiratory system an ideal candidate for the application of fractional calculus theory. The fractal geometry is typically characterized by a recurrent structure. This study investigates the identification of a model for the respiratory tree by means of its electrical equivalent based on intrinsic morphology. Measurements were obtained from seven volunteers, in terms of their respiratory impedance by means of its complex representation for frequencies below 5 Hz. A parametric modeling is then applied to the complex valued data points. Since at low-frequency range the inertance is negligible, each airway branch is modeled by using gamma cell resistance and capacitance, the latter having a fractional-order constant phase element (CPE), which is identified from measurements. In addition, the complex impedance is also approximated by means of a model consisting of a lumped series resistance and a lumped fractional-order capacitance. The results reveal that both models characterize the data well, whereas the averaged CPE values are supraunitary and subunitary for the ladder network and the lumped model, respectively.

Effects of Soil Compaction and Organic Carbon Content on Preferential Flow in Loamy Field Soils

Abstract: Preferential flow and transport through macropores affect plant water use efficiency and enhance leaching of agrochemicals and the transport of colloids, thereby increasing the risk for contamination of groundwater resources. The effects of soil compaction, expressed in terms of bulk density (BD), and organic carbon (OC) content on preferential flow and transport were investigated using 150 undisturbed soil cores sampled from 15 × 15–m grids on two field sites. Both fields had loamy textures, but one site had significantly higher OC content. Leaching experiments were conducted in each core by applying a constant irrigation rate of 10 mm h−1 with a pulse application of tritium tracer. Five percent tritium mass arrival times and apparent dispersivities were derived from each of the tracer breakthrough curves and correlated with texture, OC content, and BD to assess the spatial distribution of preferential flow and transport across the investigated fields. Soils from both fields showed strong positive correlations between BD and preferential flow. Interestingly, the relationships between BD and tracer transport characteristics were markedly different for the two fields, although the relationship between BD and macroporosity was nearly identical. The difference was likely caused by the higher contents of fines and OC at one of the fields leading to stronger aggregation, smaller matrix permeability, and a more pronounced pipe-like pore system with well-aligned macropores.