A mathematical model of the human respiratory system considering environmental influence
01 Apr 2020-Vol. 2216, Iss: 1, pp 060007
TL;DR: In this paper, the authors developed a sub-model to examine gas flows inside the human lungs that are a two-phase saturated elastically deformed porous media, which allowed for interaction between lung tissue and air inside the lungs.
Abstract: The paper is developing a sub-model to examine gas flows inside the human lungs that are a two-phase saturated elastically deformed porous media. This sub-model is being developed within creation of a mathematical model for the human respiratory system. There was a sub-task related to uniform compression of a thin-wall hollow sphere filled with air; having solved it, we obtained a correlation applied to determine how rapidly changes occurred in average stress of the two-phase media in the lungs. The correlation allowed for interaction between lung tissue and air inside the lungs. Further development of the mathematical model involves finding a solution to a task concerning gas filtration in a deformed saturated porous media of the lungs in its full statement, taking into account the correlation described in the given paper. There also should be a joint solution to tasks related to gas dynamics in the upper airways and filtration inside the human lungs. Results of the given research are significant from theoretical point of view as they provide a better insight into breathing mechanics and mechanisms of functional disorders accumulation under inhalation exposure to chemicals contained in inhaled air. They also have applied significance as they can be used to assess and predict individual and population health risks.
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01 Jan 2021
01 Jan 2020
Cites methods from "A mathematical model of the human r..."
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TL;DR: In this paper , the set-point modulated fuzzy PI-based model reference adaptive controller (SFPIMRAC) is delineated to control the oxygen supply to uncomforted breathing or respiratory infected patients.
Abstract: Uncontrolled breathing is the most critical and challenging situation for a healthcare person to patients. It may be due to simple cough/cold/critical disease to severe respiratory infection of the patients and resulting directly impacts the lungs and damages the alveoli which leads to shortness of breath and also impairs the oxygen exchange. The prolonged respiratory failure in such patients may cause death. In this condition, supportive care of the patients by medicine and a controlled oxygen supply is only the emergency treatment. In this paper, as a part of emergency support, the intelligent set-point modulated fuzzy PI-based model reference adaptive controller (SFPIMRAC) is delineated to control the oxygen supply to uncomforted breathing or respiratory infected patients. The effectiveness of the model reference adaptive controller (MRAC) is enhanced by assimilating the worthiness of fuzzy-based tuning and set-point modulation strategies. Since then, different conventional and intelligent controllers have attempted to regulate the supply of oxygen to respiratory distress patients. To overcome the limitations of previous techniques, researchers created the set-point modulated fuzzy PI-based model reference adaptive controller, which can react instantly to changes in oxygen demand in patients. Nonlinear mathematical formulations of the respiratory system and the exchange of oxygen with time delay are modeled and simulated for study. The efficacy of the proposed SFPIMRAC is tested, with transport delay and set-point variations in the devised respiratory model.
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TL;DR: In this paper, a hypo-elasticity model based on the objective corotational rate of the Kirchhoff stress defined by the spin tensor is proposed and the simplest relationship between hypo elasticity and elasticity can be established.
Abstract: Recently these authors have proved [46, 47] that a smooth spin tensor Ωlog can be found such that the stretching tensor D can be exactly written as an objective corotational rate of the Eulerian logarithmic strain measure ln V defined by this spin tensor, and furthermore that in all strain tensor measures only ln V enjoys this favourable property This spin tensor is called the logarithmic spin and the objective corotational rate of an Eulerian tensor defined by it is called the logarithmic tensor-rate In this paper, we propose and investigate a hypo-elasticity model based upon the objective corotational rate of the Kirchhoff stress defined by the spin Ωlog, ie the logarithmic stress rate By virtue of the proposed model, we show that the simplest relationship between hypo-elasticity and elasticity can be established, and accordingly that Bernstein's integrability theorem relating hypo-elasticity to elasticity can be substantially simplified In particular, we show that the simplest form of the proposed model, ie the hypo-elasticity model of grade zero, turns out to be integrable to deliver a linear isotropic relation between the Kirchhoff stress and the Eulerian logarithmic strain ln V, and moreover that this simplest model predicts the phenomenon of the known hypo-elastic yield at simple shear deformation
192 citations
TL;DR: It is demonstrated that the nature of the secondary vortical flows, which develop in such asymmetric airways, varies with the specific anatomical characteristics of the branching conduits.
152 citations
TL;DR: It was found that fully developed flow and uniform nanoparticle concentrations can be assumed beyond generation G12 and the deposition efficiencies at each individual bifurcation in the TB region can be well correlated as a function of an effective diffusion parameter.
Abstract: In order to achieve both manageable simulation and local accuracy of airflow and nanoparticle deposition in a representative human tracheobronchial (TB) region, the complex airway network was decomposed into adjustable triple-bifurcation units, spreading axially and laterally. Given Qin = 15 and 30 L/min and a realistic inlet velocity profile, the experimentally validated computer simulation model provided some interesting 3-D airflow patterns, i.e., for each TB-unit they depend on the upstream condition, local geometry and local Reynolds number. Directly coupled to the local airflow fields are the convective-diffusive transport and deposition of nanoparticles, i.e., 1 nm ≤ dp ≤ 100 nm. The CFD modeling predictions were compared to experimental observations as well as analytical modeling results. The CFD-simulated TB deposition values agree astonishingly well with analytical modeling results. However, measurable differences can be observed for bifurcation-by-bifurcation deposition fractions obtained with these two different approaches due to the effects of more realistic inlet conditions and geometric features incorporated in the CFD model. Specifically, while the difference between the total TB deposition fraction (DF) is less than 16%, it may be up to 70% for bifurcation-by-bifurcation DFs. In addition, it was found that fully developed flow and uniform nanoparticle concentrations can be assumed beyond generation G12. For nanoparticles with dp > 10 nm, the geometric effects, including daughter-branch rotation, are minor. Furthermore, the deposition efficiencies at each individual bifurcation in the TB region can be well correlated as a function of an effective diffusion parameter.
101 citations
TL;DR: Alveolar flow patterns under rhythmic wall motion contrast sharply with results obtained in a rigid alveolus, further confirming the importance of including inherent wall motion to understand realistic acinar flow phenomena.
Abstract: Low Reynolds number flows (Re < 1) in the human pulmonary acinus are often difficult to assess due to the submillimeter dimensions and accessibility of the region. In the present computational study, we simulated three-dimensional alveolar flows in an alveolated duct at each generation of the pulmonary acinar tree using recent morphometric data. Rhythmic lung expansion and contraction motion was modeled using moving wall boundary conditions to simulate realistic sedentary tidal breathing. The resulting alveolar flow patterns are largely time independent and governed by the ratio of the alveolar to ductal flow rates, Q a /Q d . This ratio depends uniquely on geometrical configuration such that alveolar flow patterns may be entirely determined by the location of the alveoli along the acinar tree. Although flows within alveoli travel very slowly relative to those in acinar ducts, 0.021 % ≤ U a /u d ≤9.1%, they may exhibit complex patterns linked to the three-dimensional nature of the flow and confirm findings from earlier three-dimensional simulations. Such patterns are largely determined by the interplay between recirculation in the cavity induced by ductal shear flow over the alveolar opening and radial flows induced by wall displacement. Furthermore, alveolar flow patterns under rhythmic wall motion contrast sharply with results obtained in a rigid alveolus, further confirming the importance of including inherent wall motion to understand realistic acinar flow phenomena. The present findings may give further insight into the role of convective alveolar flows in determining aerosol kinematics and deposition in the pulmonary acinus.
81 citations
TL;DR: The new methodology introduces the idea of a controlled air-particle stream which provides maximum, patient-specific drug-aerosol deposition based on optimal particle diameter and density, inhalation waveform, and particle-release position.
66 citations