Fractional order models of the human respiratory system

The fractional calculus is a generalization of classical integer-order integration and derivation to fractional (non-integer) order operators. Fractional order (FO) models are those models which contain such fractional order operators. A common representation of these models is in frequency domain, due to its simplicity. The dynamical systems whose model can be approximated in a natural way using FO terms, exhibit specific features, such as viscoelasticity, diffusion and a fractal structure; hence the respiratory system is an ideal application for FO models. Although viscoelastic and diffusive properties were intensively investigated in the respiratory system, the fractal structure was ignored. Probably one of the reasons is that the respiratory system does not pose a perfect symmetry, hence failing to satisfy one of the conditions for being a typical fractal structure. In the 70s, the respiratory impedance determined by the ratio of air-pressure and air-flow, has been introduced in a model structure containing a FO term. It has also been shown that the fractional order models outperform integer-order models on input impedance measurements. However, there was a lack of underpinning theory to clarify the appearance of the fractional order in the FO model structure. The thesis describes a physiologically consistent approach to reach twofold objectives: 1. to provide a physiologically-based mathematical explanation for the necessity of fractional order models for the input impedance, and 2. to determine the capability of the best fractional order model to classify between healthy and pathological cases. Rather than dealing with a specific case study, the modelling approach presents a general method which can be used not only in the respiratory system application, but also in other similar systems (e.g. leaves, circulatory system, liver, intestines). Furthermore, we consider also the case when symmetry is not present (e.g. deformations in the thorax - kyphoscoliose) as well as various pathologies. We provide a proof-of-concept for the appearance of the FO model from the intrinsic structure of the respiratory tree. Several clinical studies are then conducted to validate the sensitivity and specificity of the FO model in healthy groups and in various pathological groups

International Conference on Mathematical Analysis and Applications in Science and Engineering – Book of Extended Abstracts

The present volume on Mathematical Analysis and Applications in Science and Engineering - Book of Extended Abstracts of the ICMASC’2022 collects the extended abstracts of the talks presented at the International Conference on Mathematical Analysis and Applications in Science and Engineering – ICMA2SC'22 that took place at the beautiful city of Porto, Portugal, in June 27th-June 29th 2022 (3 days). Its aim was to bring together researchers in every discipline of applied mathematics, science, engineering, industry, and technology, to discuss the development of new mathematical models, theories, and applications that contribute to the advancement of scientific knowledge and practice. Authors proposed research in topics including partial and ordinary differential equations, integer and fractional order equations, linear algebra, numerical analysis, operations research, discrete mathematics, optimization, control, probability, computational mathematics, amongst others. The conference was designed to maximize the involvement of all participants and will present the state-of- the-art research and the latest achievements.info:eu-repo/semantics/publishedVersio

Proceedings of the 96th Annual Virginia Academy of Science Meeting, 2018

Proceedings of the 96th Annual Virginia Academy of Science Meeting, May 23-25, 2018, at Longwood University, Farmville, Virginia

Modeling And Simulation Of Soft Bodies

As graphics and simulations become more realistic, techniques for approximating soft body objects, that is, non-solid objects such as liquids, gases, and cloth, are becoming increasingly common. The proposed generalized soft body method encompasses some specific cases of other existing models enabling simulation of a variety of soft body materials by parameter adjustment. This research presents a general method of soft body model and simulation in which parameters for body control, surface deformation, volume control, and gravitation, can be adjusted to simulate different types of soft bodies. In this method, the soft body mesh structure maintains configuration among surface points while fluid modeling deforms the details of the surface. To maintain volume, an internal pressure is approximated by simulated molecules within the soft body. Free fall motion of soft body is generated by gravitational field. Additionally, a constraint is specified based on the property of the soft body being modeled. There are several standard methods to control soft body volume. This work illustrates the simplicity of simulation by selecting a mass-spring system for the deformation of the connected points of a three-dimensional mesh, while an internal pressure force acts upon the surface triangles. To incorporate fluidity, smooth particles hydrodynamics (SPH) is applied where surface points are considered as free moving particles interacting with neighboring surface points within a SPH radius. Because SPH is computationally expensive, it requires an efficient method to determine neighboring surface points. Collision detection with soft bodies and other rigid body objects also requires such fast neighbor detection. To determine the neighboring surface point, Axis Aligned Bounding Box (AABB), Octree, and a partitioning and hashing schemes iv have been investigated and the result shows that the partitioning and hashing scheme provides the best frame rate. Thus a fast partitioning and hashing scheme is used in this research to reduce both computational time and the memory requirements. The proposed soft body model aims to be applied in several types of soft body application depending on the specific types of soft body deformation. The work presented in this dissertation details experiments with a variety of visually appealing fluid-like surfaces and organic materials animated at interactive speeds. The algorithm is also used to implement animated space-blob creatures in the Galactic Arms Race video game and a human lung simulation, demonstrating the effectiveness of the algorithm in both an actual video game engine and a medical application. The simulation results show that the general model of the soft body can be applied to several applications by adjusting the soft body parameters according to the appearance results

Engineering Education and Research Using MATLAB

MATLAB is a software package used primarily in the field of engineering for signal processing, numerical data analysis, modeling, programming, simulation, and computer graphic visualization. In the last few years, it has become widely accepted as an efficient tool, and, therefore, its use has significantly increased in scientific communities and academic institutions. This book consists of 20 chapters presenting research works using MATLAB tools. Chapters include techniques for programming and developing Graphical User Interfaces (GUIs), dynamic systems, electric machines, signal and image processing, power electronics, mixed signal circuits, genetic programming, digital watermarking, control systems, time-series regression modeling, and artificial neural networks