Abstract:
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.

Abstract:
Respiratory variables, including tidal volume and respiratory rate, display significant variability. The probability density function (PDF) of respiratory variables has been shown to contain clinical information and can predict the risk for exacerbation in asthma. However, it is uncertain why this PDF plays a major role in predicting the dynamic conditions of the respiratory system. This paper introduces a stochastic optimal control model for noisy spontaneous breathing, and obtains a Shrödinger’swave equation as the motion equation that can produce a PDF as a solution. Based on the lobules-bronchial tree model of the lung system, the tidal volume variable was expressed by a polar coordinate, by use of which the Shrödinger’s wave equation of inter-breath intervals (IBIs) was obtained. Through the wave equation of IBIs, the respiratory rhythm generator was characterized by the potential function including the PDF and the parameter concerning the topographical distribution of regional pulmonary ventilations. The stochastic model in this study was assumed to have a common variance parameter in the state variables, which would originate from the variability in metabolic energy at the cell level. As a conclusion, the PDF of IBIs would become a marker of neuroplasticity in the respiratory rhythm generator through Shr?dinger’swave equation for IBIs.

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.

Abstract:
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.

Abstract:
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.

Abstract:
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 P_{Φ}=(1+tanh(βH))^{2}/4 along the tree, then the relation of dose βH to TVD was described by TVD=P_{Φ}[1-(1-P_{Φ})^{3}/P_{Φ}^{3}]-TVD_{0}. TVD_{0} 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.

Abstract:
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 (L_{j+1}/L_{j}=2^{λ}, where L_{j+1}, and L_{j} 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 r_{l}L_{l} = constant(c), where r_{l} and L_{l} denote the diameter and the length of a lobular bronchiole, respectively. API at the level of the lobu-lar bronchiole was described by log(r_{l}) = -(1+λ)/(1+5λ)log(h_{l}/c), where r_{l} and h_{l} 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.

Abstract:
This paper studies the route, steps and measures of the implementation of the emissions trading system in China. It combines desk research and case study. The desk research aims to explore the inherent discipline of emissions trading system, so as to disclose its nature and features while the case study involves the one-year field research conducted by the author, and provides the pilot emission systems in some provinces, together with the difficulties in its implementation. There are possibilities of comprehensive coverage of emission trading system, which can only be protected by a law relevant to environmental property protection (issued by the Standing Committee of National People’s Congress). And there is necessity for China to set up a quota system for different pollutions. After the initial allocation among provinces, the quota will be divided among enterprises, partial paid and partial for free, under the principle of “Giving priority to efficiency with due consideration to fairness”. It is useful to establish an efficient secondary market of emis-sion trading system.

Abstract:
A P2P approaches to extend the ability of Video on Demand systems to serve more users. In the proposed system users share with each other the media data obtained and the media server is no longer the only source to get data from, thereby, the load on the media server could be greatly alleviated and the overall system capacity increases and more users could be served. The P2P streaming system introduces efficient searching; data transfer dynamically monitoring and initial buffering to maintain a high quality of playback. Its provider selection policy helps to reduce the load of the underlying network by avoiding remote data transfer.

Abstract:
We present a family of formal expansions for the density function of a general one-dimensional asymptotic normal sequence X_{n}. Members of the family are indexed by a parameter τ with an interval domain which we refer to as the spectrum of the family. The spectrum provides a unified view of known expansions for the density of X_{n}. It also provides a means to explore for new expansions. We discuss such applications of the spectrum through that of a sample mean and a standardized mean. We also discuss a related expansion for the cumulative distribution function of X_{n}.