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.

Application of genetic algorithms in the design of an electrical potential of fractional order

Fractional calculus (FC) is currently being applied in many areas of science and technology. In fact, this mathematical concept helps the researches to have a deeper insight about several phenomena that integer order models overlook. Genetic algorithms (GA) are an important tool to solve optimization problems that occur in engineering. This methodology applies the concepts that describe biological evolution to obtain optimal solution in many different applications. In this line of thought, in this work we use the FC and the GA concepts to implement the electrical fractional order potential. The performance of the GA scheme, and the convergence of the resulting approximation, are analyzed. The results are analyzed for different number of charges and several fractional orders.

Accounting for the dissociating properties of organic chemicals in LCIA: an uncertainty analysis applied to micropollutants in the assessment of freshwater ecotoxicity

In life cycle impact assessment (LCIA) models, the sorption of the ionic fraction of dissociating organic chemicals is not adequately modeled because conventional non-polar partitioning models are applied. Therefore, high uncertainties are expected when modeling the mobility, as well as the bioavailability for uptake by exposed biota and degradation, of dissociating organic chemicals. Alternative regressions that account for the ionized fraction of a molecule to estimate fate parameters were applied to the USEtox model. The most sensitive model parameters in the estimation of ecotoxicological characterization factors (CFs) of micropollutants were evaluated by Monte Carlo analysis in both the default USEtox model and the alternative approach. Negligible differences of CFs values and 95% confidence limits between the two approaches were estimated for direct emissions to the freshwater compartment; however the default USEtox model overestimates CFs and the 95% confidence limits of basic compounds up to three orders and four orders of magnitude, respectively, relatively to the alternative approach for emissions to the agricultural soil compartment. For three emission scenarios, LCIA results show that the default USEtox model overestimates freshwater ecotoxicity impacts for the emission scenarios to agricultural soil by one order of magnitude, and larger confidence limits were estimated, relatively to the alternative approach.

New findings on the dynamics of HIV and TB coinfection models

In this paper we study a model for HIV and TB coinfection. We consider the integer order and the fractional order versions of the model. Let α∈[0.78,1.0] be the order of the fractional derivative, then the integer order model is obtained for α=1.0. The model includes vertical transmission for HIV and treatment for both diseases. We compute the reproduction number of the integer order model and HIV and TB submodels, and the stability of the disease free equilibrium. We sketch the bifurcation diagrams of the integer order model, for variation of the average number of sexual partners per person and per unit time, and the tuberculosis transmission rate. We analyze numerical results of the fractional order model for different values of α, including α=1. The results show distinct types of transients, for variation of α. Moreover, we speculate, from observation of the numerical results, that the order of the fractional derivative may behave as a bifurcation parameter for the model. We conclude that the dynamics of the integer and the fractional order versions of the model are very rich and that together these versions may provide a better understanding of the dynamics of HIV and TB coinfection.