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From Pressure-Volume Relationship to Volume-Energy Relationship: A Thermo-Statistical Model for Alveolar Micromechanics

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Applied Mathematics 2020年第11期11卷 1116-1131页

作者： kyongyob min Ueda-Shimotanabe Hospital Noborimachi Takatsuki Osaka Japan

The connective tissue fiber system and the surfactant system are essential and interdependent components of lung elasticity. Despite considerable efforts over the last decades, we are still far from understanding the quantitative roles of either the connective tissue fiber or the surfactant systems. Through thermo-statistic considerations of alveolar micromechanics, the author introduced a thermo-statistic state function “entropy” to analyze the elastic property of pulmonary parenchyma based on the origami model of alveolar polyhedron. By use of the entropy for alveolar micromechanics, from the logistic equation for the static pressure (P)-volume (V) curves including parameters a, b, c, and k (V - a = b/[1+ exp{-k (P - c)}]), a set of equations was obtained to define the internal energy of lungs (UL) and its corresponding lung volume (VL). Then, by use of parameters a, b, c, and k, an individual volume-internal energy (VL - UL) diagram was constructed from reported data in patients on mechanical ventilation. Each VL - UL diagram constructed was discussed that its minimal value Uo = c (a + b/2) and its shape parameter b/k represent quantitatively the energy of tissue force and the energy of surface force. Furthermore, by use of the VL - UL relationship, the hysteresis of lungs estimated by entropy production was discussed as dependent on the difference in the number of contributing pulmonary lobules. That is, entropy production might be a novel quantitative indicator to estimate the dynamics of the bronchial tree. These values obtained by combinations of parameters of the logistic P-

关键词： Thermo-Statistic Entropy Thermodynamic Temperature Sigmoid Pressure-Volume Curve Logistic Equation Volume-Energy Relationship

Entropy Change of Lungs: Determinant of the Static Properties of the Lungs

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Applied Mathematics 2015年第8期6卷 1200-1207页

作者： kyongyob min Respiratory Division Department of Internal Medicine Itami City Hospital Itami Japan

The static properties of the lungs have been explained by energy-change considerations on the elasticity, but this article explains the elasticity of the lungs by entropy-change considerations. Entropy of the individual lobule was defined by application of stochastic geometry on aggregated alveolar polyhedrons. Entropy of the lungs is the result of integrating a number of lobular entropies through the fractal bronchial tree. Entropy of the lungs was thus determined by the individual lobular entropy and the connectivity of the bronchial tree to the lobular bronchioles. Thermody-namic considerations on the static conditions of the pulmonary system composed of the lungs and the chest wall have provided a theoretical approach to understand the subdivisions of lung volume as the entropy-change of lungs. Entropy-change considerations on the elasticity of the lungs have shown that alveolar collapse and subsequent alveolar induration as the primary pathway for the loss of elasticity in the lungs is an acceptable hypothesis.

关键词： Energy Elasticity Entropy-Change Considerations Elastic Properties of Lungs Thermodynamics

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Applied Mathematics 2014年第12期5卷 1801-1809页

作者： kyongyob min Respiratory division Department of Internal Medicine Itami City Hospital Itami Japan

Pulmonary arterial hypertension (PAH) has become an important topic of basic and clinical research in recent years. Morphologic researches have shown that specific PAH-lesions are located in the lobular small muscular arteries and correlate with hemodynamic measurements. However, it still remains to be shown how pathological changes of the small arteries in the lobule develop to PAH. Based on both fractal properties of pulmonary arterial tree and asynchronous phasic contractions of lobular arterial muscles under the evenness of the pulmonary capillary pressure (PCP) in the lung, the author has constructed an integrated model of pulmonary circulation which has produced a mathematical relationship between the mean pulmonary arterial pressure (MPAP) and the cardiac output (CO). By use of the expression between MPAP and CO, it has been able to explain the pathogenesis of PAH in terms of statistical changes among regional and temporal perfusions in the lung. In order to detect clinically the early stage of PAH, the author has suggested that it is important to establish the pulmonary functional imaging of regional and temporal perfusions.

关键词： Pulmonary Arterial Hypertension Weibel’s Number Fractal Arterial Tree Asynchronous Contractions of Arterioles PAP Decay Curve

A new geometrical and mechanical relation in the respiratory system with airflow limitation—From the perspective of analytical respiratory mechanics

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Open Journal of Molecular and Integrative Physiology 2013年第2期3卷 54-60页

作者： kyongyob min Respiratory Division Department of Internal Medicine Itami City Hospital Itami Japan

Classic respiratory mechanics is a branch of vectorial mechanics, which aims to recognize all forces acting on the respiratory system. Another branch of mechanics, analytical mechanics, has been used for analyzing the motions of complicated systems with constraints through equilibrium among scalar quantities such as kinetic energy and potential energy. However, until now, there have not been any studies concerning about analytical respiratory mechanics. In this paper, the author has obtained two types of motion equations (linear and nonlinear) for the airflow limitation from formulation of the analytical respiratory mechanics. Reconstructed flow-volume trajectories of the linear equation revealed a new relationship among the slope of the linear portion of trajectory, the coefficient of the dissipation function and the coefficient of the potential function. Reconstructed trajectories of the nonlinear equation suggested that a curved flow-volume trajectory would be caused by the emergence of regional hypoventilated clusters with airtrapped lobules. In conclusion, analytical respiratory mechanics will provide the basis for analyzing the mechanical properties of the respiratory system con cerning pulmonary functional images made by newly developed technologies.

关键词： Secondary Pulmonary Lobule Analytical Mechanics Airflow Limitation Flow-Volume Trajectory Regional Air-Trapping

Use of a mathematical model of autopoietic maintenance of pulmonary alveolar integrity to show a possible relationship between epithelial-mesenchymal transition and the genesis of emphysema and fibrosis

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Open Journal of Molecular and Integrative Physiology 2011年第2期1卷 23-28页

作者： kyongyob min Keita Hosoi Yoshinori Kinoshita Satoshi Hara Hiroyuki Degami Tetsuo Takada Takahiko Nakamura 不详

Rationale: There is accumulating evidence that a group of stem/progenitor cells (SPCs) maintain alveolar epithelial integrity. Pulmonary emphysema is characterized by the histological finding of the loss of alveolar epithelial integrity along with corresponding bronchiolar fibrosis. Objectives: Based on the concept of autopoiesis (the capacity to produce oneself), we proposed a mathematical model in the maintenance of alveolar epithelial integrity as related to the genesis of pulmonary emphysema and fibrosis. Methods: A tessellation automaton model was used to describe the autopoietic dynamics of the bronchiolo-alveolar epithelial surface. The alveolar septal volume en-closed by the epithelial surface is a distributed system of discrete elements, which move by random walk in the manner of Brownian motion. Assuming that the numbers of components and events in the automaton are large, an approximate theoretical treatment in terms of differential equations is possible, allowing a set of partial differential equations to be produced. Results: 1) Assuming the loss of progenitor cells through the epithelial-mesenchymal transition (EMT), a sharp bifurcation between two qualitatively distinct regions of the phase space (one that is repaired completely, and another that has disappeared entirely) clearly appeared. 2) Thus, from the system of discrete and spatial partial differential equations, we obtained a system of ordinary differential equations in equilibrium conditions that defined a close relationship between the degree of emphysema, the density of alveolar septal fibroblasts, and the mean concentration of SPCs. Conclusions: A mathematical model of the autopoietic maintenance of the alveolar epithelial surface suggested a close relationship between alveolar emphysema and fibrosis and EMT in lungs affected by chronic obstructive pulmonary disease.

关键词： Autopoiesis Pulmonary Emphysema Pulmonary Fibrosis Pulmonary Stem/Progenitor Cells

Use of fractal geometry to propose a new mechanism of airway-parenchymal interdependence

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Open Journal of Molecular and Integrative Physiology 2012年第1期2卷 14-20页

作者： kyongyob min Keita Hosoi Yoshinori Kinoshita Satoshi Hara Hiroyuki Degami Tetsuo Takada Takahiko Nakamura Respiratory Division Department of Internal Medicine Itami City Hospital Hyogo Japan

The topic of airway-parenchymal interdependence (API) is of great importance to those interested in identifying factors that influence airway patency. A carefully designed experiment has raised questions about the classical concept of API. This paper proposes a new mechanism of API. The pulmonary lobe is an aggregated body consisting of many Miller’s lobular polyhedrons and a fractal bronchial tree. The fractal cartilaginous bronchial tree was assumed to be characterized by both Horton’s ratio (Lj+1/Lj=2λ, where Lj+1, and Lj denote the mean lengths of branches at Horsfield’ order of j + 1 and j) and power laws between diameters and lengths of branches. Fluid dynamic parameters of fractal trees were assumed to be interrelated among powers and λ. A non-cartilaginous lobular bronchiole is adjoined to the edge of a lobular polyhedron, and is encircled by an inextensible basement membrane to reflect a reversible relationship of rlLl = constant(c), where rl and Ll denote the diameter and the length of a lobular bronchiole, respectively. API at the level of the lobu-lar bronchiole was described by log(rl) = -(1+λ)/(1+5λ)log(hl/c), where rl and hl denote the diameter of the lobular bronchiole and the parenchymal parameter relating the size of the lobular polyhedron, respectively. If the distribution in sizes of the lobular polyhedrons was described by a Weibull’s probability density function characterized by the shape parameter m as well as the fractal parameter λ = 0.5, the diameter R of a cartilaginous bronchial branch was determined by log(R) = F - 3/7log(h/c), where F(m) denotes a function of m, and h denotes the mean size of the polyhedrons in the lobe. As a conclusion, API can be described by a combination of both lobular API and corresponding adaptive changes in the degree of contraction of airway smooth muscles.

关键词： Self-Similarity of Bronchial Branching Power Laws Fractal Geometry Airways-Parenchymal Interdependence

Determinants of airway hyperresponsiveness—Balance of tonic and phasic contractility of airway smooth muscles of lobular bronchioles

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Open Journal of Molecular and Integrative Physiology 2012年第1期2卷 8-13页

Airway hyperresponsiveness (AHR) is a characteristic feature of asthma, and generally correlates with severity of asthma. Understanding the protection mechanism against excessive airway narrowing and how it breaks down is fundamental to solving the problem of asthma. In this paper we have proposed a stochastic modeling the airway smooth muscle bundle for reproducing AHR such as an increased sensitivity of the airways to an inhaled constrictor agonist, a steeper slope of the dose-response curve, and a greater maximal response to agonist. A large number N of contractile muscle cells was assumed to repeat themselves in between contraction and relaxation asynchronously. Dynamic equilibrium of statistic physics was applied to the system of ASM bundle. Thus, the relation of dose to response of a piece of ASM bundle was described by Φ=tanh(βH) , where β was Boltzman factor and H represented energy of contraction induced by constrictor agents. Each of adjacent pair contractile cells was assumed to have Ising-type of antimagnetic interactions of preference energy J (for the condition of contraction-relaxation) between them. A motion equation for a piece of ASM bundle was described by Φ=N(H-zJΦ , which explained existence of combined tonic and phasic contractions. Based on observations of Venegas et al. [4], airway responsiveness was assumed to be assessable by total volume of the ventilation defects (TVD) of 13NN PET-CT images. Interactions via propagation of Ca ion waves between ASM bundles would cause percolation probability by PΦ=(1+tanh(βH))2/4 along the tree, then the relation of dose βH to TVD was described by TVD=PΦ[1-(1-PΦ)3/PΦ3]-TVD0. TVD0 represented the protection mechanism against excessive airway narrowing, which was determined by the ratio of amplitudes between tonic and phasic contractions, thus the balance of amplitudes between tonic and phasic contractions of peripheral lobular smooth muscles would be the determinant of AHR.

关键词： Airway Hyperresponsiveness Stochastic Model of Airway Smooth Muscle Ising-Type of Antimagetic Interactions Percolation Process Phasic and Tonic Contractions

New Second-Level-Discrete Zeroing Neural Network for Solving Dynamic Linear System

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IEEE/CAA Journal of Automatica Sinica 2024年第6期11卷 1521-1523页

作者： min Yang School of Robotics Hunan UniversityChangsha 410082China

Dear Editor,This letter deals with a new second-level-discretization method with higher precision than the traditional first-level-discretization ***,the traditional discretization method utilizes the first-order time derivative information,and it is termed first-level-discretization *** contrast,the new discretization method not only utilizes the first-order time derivative information,but also makes use of the second-order derivative *** combining the new second-level-discretization method with zeroing neural network(ZNN),the second-level-discrete ZNN(SLDZNN)model is proposed to solve dynamic(i.e.,time-variant or time-dependent)linear *** experiments and application to angle-of-arrival(AoA)localization show the effectiveness and superiority of the SLDZNN model.

关键词： method derivative utilize

Study on viscosity mechanism of caffeine crystallization solutions Author links open overlay panel

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Particuology 2024年第8期91卷 341-350页

作者： Linjing Yu min Su School of Chemical Engineering Hebei University of TechnologyTianjin300130China

The solid-liquid viscous system formed by high viscosity crystallization solution impacts the flow and separation ***,it is very important to study the viscosity mechanism to improve viscosity and regulate crystallization,ensuring a seamless production ***,the viscosity of crystallization solution was taken as the measurement parameter of caffeine as a model *** investigated the viscosity mechanism of caffeine crystallization solutions by combining experiment and *** results indicated that the weak interactions between caffeine and water result in increased viscosity of the caffeine crystallization ***,caffeine crystals possess elongated needle-like shapes,featuring a substantial specific surface ***,there isπ-πstacking occurring between the(200)crystal face and(110)crystal face,effectively fostering coalescence of the crystals towards the radial side of the crystal along its elongated axis,resulting in a more viscous crystallization *** results contribute to comprehending the viscosity mechanism of crystal systems and provide theoretical foundation to enhance engineering efficiency in crystallization.

关键词： Crystallization Caffeine Viscosity mechanism Molecular simulation