Fractional order impedance models as rising tools for quantification of unconscious analgesia

This research focuses on modeling the diffusion process that occurs in the human body when an analgesic drug is taken up, by using fractional-order impedance models (FOIMs). We discuss the measurement of a suitable feedback signal that can be used in a model-based control strategy. With this knowledge an early dawn concept of a pain sensor is presented. The major challenges that are encountered during this development consist of identification of the patient model, validation of the pain sensor and validation of the effect of the analgesic drug

Numerical Simulation of Parallel RLC Model Using Different Fractional Derivative Operators

In the current study, the theory of fractional calculus is applied to the electric parallel RLC circuit. The aim of this article is to alter the concept of a parallel RLC circuit by applying various fractional derivative operators. A fractional RLC circuit was investigated via Caputo, Caputo-Fabrizio, and Atangana-Baleanu derivatives. The Laplace transform technique was applied to resolve the system of governing differential equations. The results for the various orders are compared to each other. When the fractional order derivative tends to be one, the system\u27s performance is found to be very slow due to a decrease in damping capacity. The results for the various orders are compared to each other. When the fractional order derivative tends to be one, the system\u27s performance is found to be very slow due to a decrease in damping capacity. The results for the various orders are compared to each other. When the fractional order derivative tends to be one, the system\u27s performance is found to be very slow due to a decrease in damping capacity

Fractional dynamics and MDS visualization of earthquake phenomena

This paper analyses earthquake data in the perspective of dynamical systems and fractional calculus (FC). This new standpoint uses Multidimensional Scaling (MDS) as a powerful clustering and visualization tool. FC extends the concepts of integrals and derivatives to non-integer and complex orders. MDS is a technique that produces spatial or geometric representations of complex objects, such that those objects that are perceived to be similar in some sense are placed on the MDS maps forming clusters. In this study, over three million seismic occurrences, covering the period from January 1, 1904 up to March 14, 2012 are analysed. The events are characterized by their magnitude and spatiotemporal distributions and are divided into fifty groups, according to the Flinn–Engdahl (F–E) seismic regions of Earth. Several correlation indices are proposed to quantify the similarities among regions. MDS maps are proven as an intuitive and useful visual representation of the complex relationships that are present among seismic events, which may not be perceived on traditional geographic maps. Therefore, MDS constitutes a valid alternative to classic visualization tools for understanding the global behaviour of earthquakes

Fractional Describing Function Analysis of PWPF Modulator

Pulse-width pulse-frequency (PWPF) modulators are widely used in spacecraft thruster control. Their dynamic characteristic is still lack of effective analysis tools. This paper presents a fractional describing function method to describe the frequency characteristics of PWPF. A frequency-dependent gain and phase shift are clearly described by fractional-order expression, and the fractional-order behaviors depict the nonlinear properties of PWPF modulators. This fractional describing function method can also be applied to other kinds of modulators

Identification for control of suspended objects in non-Newtonian fluids

This paper proposes a framework for modelling velocity profiles and suspended objects in non-Newtonian fluid environment. A setup is proposed to allow mimicking blood properties and arterial to venous dynamic flow changes. Navier-Stokes relations are employed followed by fractional constitutive equations for velocity profiles and flow. The theoretical analysis is performed under assumptions of steady and pulsatile flow conditions, with incompressible properties. The fractional derivative model for velocity and friction drag effect upon a suspended object are determined. Experimental data from such an object is then recorded in real-time and identification of a fractional order model performed. The model is determined from step input changes during pulsatile flow for velocity in the direction of the flow. Further on, this model can be employed for controller design purposes for velocity and position in pulsatile non-Newtonian fluid flow

Structural changes in the COPD lung and related heterogeneity

This paper proposes a mathematical framework for understanding how the structural changes in the COPD lung reflect in model parameters. The core of the analysis is a correlation between the heterogeneity in the lung as COPD degree changes (GOLD II, III and IV) and the nonlinearity index evaluated using the forced oscillation technique. A low frequency evaluation of respiratory impedance models and nonlinearity degree is performed since changes in tissue mechanics are related to viscoelastic properties. Simulation analysis of our model indicates a good correlation to expected changes in heterogeneity and nonlinear effects. A total of 43 COPD diagnosed patients are evaluated, distributed as GOLD II (18), GOLD III (15) and GOLD IV (10). Experimental data supports the claims and indicate that the proposed model and index for nonlinearity is well-suited to capture COPD structural changes

Mathematical Modeling and Analysis of Asthma Stability and Severity

Asthma is one of the most common chronic conditions in the United States. Asthma affects about one in fifteen people. It affects children more than adults and blacks more than whites. People with asthma experience attacks of wheezing, breathlessness, chest tightness, and coughing. Asthma can be fatal and the costs for the disease (direct and indirect) are approximated to be tens of billions of dollars each year. There is no cure for asthma. However; for most people if asthma is controlled well they can lead normal, active lives. Therefore asthma controllability is a main factor in clinical practice. In order to control asthma, the disease has to be completely understood. Asthma is very heterogeneous and this makes the exact diagnosis and control procedures difficult. To better evaluate and study asthma, mathematical tools can be very beneficial. In this study we first develop a complete system for lung impedance analysis of laboratory models of asthma. Our designed system is capable of precisely diagnosing the diseased models and predicting the severity of their condition. We also evaluate the treatment progress in mouse models of asthma. We then study an asthma database of humans including measurements of four related laboratory parameters and cluster patients based on inherent properties of the study variables. This mathematical approach clustered patients with specific characteristics and segregated the unstable asthmatic patients in a single group. Our method is very promising in predicting the instability of asthma, which is highly correlated with frequent asthma attacks and increased utilization of care

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

Analog Implementation of Fractional-Order Elements and Their Applications

With advancements in the theory of fractional calculus and also with widespread engineering application of fractional-order systems, analog implementation of fractional-order integrators and differentiators have received considerable attention. This is due to the fact that this powerful mathematical tool allows us to describe and model a real-world phenomenon more accurately than via classical “integer” methods. Moreover, their additional degree of freedom allows researchers to design accurate and more robust systems that would be impractical or impossible to implement with conventional capacitors. Throughout this thesis, a wide range of problems associated with analog circuit design of fractional-order systems are covered: passive component optimization of resistive-capacitive and resistive-inductive type fractional-order elements, realization of active fractional-order capacitors (FOCs), analog implementation of fractional-order integrators, robust fractional-order proportional-integral control design, investigation of different materials for FOC fabrication having ultra-wide frequency band, low phase error, possible low- and high-frequency realization of fractional-order oscillators in analog domain, mathematical and experimental study of solid-state FOCs in series-, parallel- and interconnected circuit networks. Consequently, the proposed approaches in this thesis are important considerations in beyond the future studies of fractional dynamic systems