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In this chapter the electrical analogy developed previously is employed in ladder network models. Mathematical concepts are used to show that in the limit (i.e. for a sufficient number of airways) such ladder networks converge to a lumped impedance with a fractional-order term. Symmetric and asymmetric lung structures are discussed. Validation of the model in mid-range (4–48 Hz) and low-range (0.9–10 Hz) frequencies is provided on real life measurements in healthy individuals.

This chapter provides the reader with insight for selecting the best candidate model to characterize the impedance and further validation in clinical studies. An analysis of the modeling performance of several candidate fractional-order models on the respiratory impedance is necessary, in order to decide which model is most suitable in the frequency range of interest. The models are presented on an evolutionary basis from the most simple to the most complex representation. The model delivering the least modeling errors and having the least number of parameters is then selected as the best candidate to model the input impedance in various frequency range intervals. Once the selection is performed, the ability of the FO model in classifying between healthy and pathologic patient data needs to be assessed. The investigated clinical groups are twofold: (i) adults and (ii) children. In the adult group are healthy volunteers and patients a priori diagnosed with chronic obstructive pulmonary disease and with kyphoscoliosis. In the children group are healthy volunteers, and patients a priori diagnosed with asthma and with cystic fibrosis. All the measurements have been performed using the forced oscillation lung function test.

The developments on the electrical ladder network in previous chapters is used as a mathematical basis to introduce the analogy to mechanical parametric models. The mechanical analogy serves as a theoretical basis for analyzing viscoelastic properties in the lung tissue. A relation between the lumped fractional-order model parameters and viscoelasticity bridges the two worlds of mathematical and physiological concepts. We conclude the chapter with the implications of these models in pathology and their ability to describe structural changes in the respiratory airways and tissue.

This chapter provides a basic knowledge of anatomy and structure of the lungs, necessary to understand further developments in this book. The morphology plays an important role here, so a great deal of attention has been given to its implications in fractal analysis. The mechanical properties of the lungs are the result of a dynamic interplay between structure, active and passive breathing, all due to variations in pressure between the mouth and the alveoli. Evaluation of these properties give information upon the work of breathing and consequent diagnosis, with classification of respiratory diseases. Airway remodeling becomes important since the dynamics of the lungs and its intrinsic properties change with these structural alterations. An overview of the non-invasive lung function tests is also provided, since it helps the reader to understand the clinical significance of the mechanical work of respiration.

From the previous chapter we have seen that parametric models with FO terms may be more efficient in estimating frequency dependent respiratory impedance values. It is therefore necessary to provide a link between the anatomy and morphology of the respiratory tract and the appearance of the fractional orders and their values. Hence, this chapter lays the mathematical basis for the genesis of such FO models.

This chapter treats the basic principles of estimating the respiratory impedance from measurements performed with the forced oscillation lung function test. First, the non-parametric identification of the respiratory impedance is presented by means of spectral analysis. Next, a comparison with most representative parametric models from the literature for assessing respiratory input impedance shows that FO models are more efficient than integer-order models. It is also shown that the FO model in four parameters available from the literature is limited to the low frequency range of estimated impedance, whereas a model in two FO terms is more efficient at mid-range frequencies.

This chapter describes the non-linear effects in the respiratory signals and in the related measurement instrumentation during FOT tests. In order to do so, some improvements are brought to the classical FOT device and a mechanical, piston-based prototype FOT device is introduced. This prototype overcomes the limitations of the loudspeaker and allows generation of multisine signals below 4 Hz. The principle of sending detection lines in the frequency domain for characterizing odd and even non-linear contributions from a non-linear system are introduced to the reader as a theoretical basis for the further discussion of this chapter. Two detection methods are presented: a robust method based on multiple measurements and a fast method based on a single measurement. After having discussed the pitfalls of non-linear distortions from the measuring device itself, we discuss the non-linear contributions in the respiratory signals: pressure and flow. The non-linear effects are further quantified by means of a novel evaluation index. Then the variations in this novel index are analyzed in groups of asthma patients, COPD patients, and healthy volunteers. Finally, the link between the non-linear distortions and the lumped fractional order model parameters is introduced, thus completing the puzzle of this book.