A new drift-flux model for particle transport and deposition in human airways

Particle deposition and transport in human airways isfrequently modeled numerically by the Lagrangian approach. Current formulations of such models always require some ad hoc assumptions, and they are computationally expensive. A new drift-flux model is developed and incorporated into a commercial finite volume code. Because it is Eulerian in nature, the model is able to simulate particle deposition patterns, distribution and transport both spatially and temporally. Brownian diffusion, gravitational settling, and electrostatic force are three major particle deposition mechanisms in human airways. The model is validated against analytical results for three deposition mechanisms in a straight tube prior to applying the method to a single bifurcation G3-G4. Two laminar flows with Reynolds numbers 500 and 2000 are simulated. Particle concentration contour deposition pattern, and enhancement factor are evaluated. To demonstrate how the diffusion and settling influence the deposition and transport along the bifurcation, particle sizes from 1 nm to 10 microm are studied. Different deposition mechanisms can be combined into the mass conversation equation. Combined deposition efficiency for the three mechanisms simultaneously was evaluated and compared with two commonly used empirical expressions.     

Analysis of synapse density in cerebral cortex

The analytical method is proposed to estimate the synapse density of a large region of a brain. The data used in the theoretical estimation are only such ones that are obtained by simple electrophysiological experiment in terms of the frequency of spontaneous discharge and of the response by stimulus. In this analysis, the critical synaptic curves drawn analytically from the net equation are used. This method is applied to the motor area of the cerebral cortex of a monkey.     

A perturbation method for the analysis of impulse propagation in a mathematical neuron model

A perturbation method is presented for the calculation of signal propagation velocities in a mathematical neuron model. Impulse frequencies and waveforms are also determined. The method uses a non-linear conduction model containing a small parameter, such that analytical solutions are possible, yet the inherently non-linear physiological phenomena involved, can be explained. A simple two-variable membrane equation is used, but the method is generally applicable to various more complete systems.     

Mathematical modeling of heat and water transport in human respiratory tract

Excessive heat and water losses from the airways are stimuli to asthma. To study heat and water vapor transport in the human respiratory tract, a time-dependent model, based on a single differential equation with an analytical solution, was developed that could predict the intra-airway temperatures and water vapor contents. The key feature is the dependence of the temperature and water vapor along the respiratory tract as a function of the air residence time at each location. The model assumes disturbed laminar flow leading to enhanced transport mechanisms and wall temperature profiles modeled according to experimental data (E. R. McFadden, Jr., B. M. Pichurko, H. F. Bowman, E. Ingenito, S. Burns, N. Dowling, and J. Soloway. J. Appl. Physiol. 58: 564-570, 1985). It predicts that 1) the air equilibrates with the wall before it reaches body conditions (37 degrees C, 99.5% relative humidity); 2) conditioning of the inspired air involves several generations, with the number depending on the respiratory conditions; and 3) the walls of the upper airways are unsaturated, although it is difficult to judge at this state the depth of the respiratory tract affected.     

Numerical modelling and analysis of peripheral airway asymmetry and ventilation in the human adult lung

We present a new one-dimensional model of gas transport in the human adult lung. The model comprises asymmetrically branching airways, and heterogeneous interregional ventilation. Our model differs from previous models in that we consider the asymmetry in both the conducting and the acinar airways in detail. Another novelty of our model is that we use simple analytical relationships to produce physiologically realistic models of the conducting and acinar airway trees. With this new model, we investigate the effects of airway asymmetry and heterogeneous interregional ventilation on the phase III slope in multibreath washouts. The model predicts the experimental trend of the increase in the phase III slope with breath number in multibreath washout studies for nitrogen, SF(6) and helium. We confirm that asymmetrical branching in the acinus controls the magnitude of the first-breath phase III slope and find that heterogeneous interregional ventilation controls the way in which the slope changes with subsequent breaths. Asymmetry in the conducting airways appears to have little effect on the phase III slope. That the increase in slope appears to be largely controlled by interregional ventilation inhomogeneities should be of interest to those wishing to use multibreath washouts to detect the location of the structural abnormalities within the lung.     

Understanding airway pathophysiology with computed tomograpy.

Conventional pulmonary function tests are limited in the mechanistic insight that they can provide by the fact that they can only provide average measures of lung function. For example, a measurement of decreased expiratory flow assessed with conventional spirometry could result from narrowed large airways, narrowed small airways, closed airways, altered elasticity, or regional heterogeneities in parenchyma or airways. To examine specific mechanisms and pathology in the airways, a method is required that can actually look at specific individual airways. Over the past decade, several more direct methods of assessing specific mechanisms and structural alterations in normal airways and airway pathology in asthma have become available for such purposes. One such method is high-resolution computed tomography (HRCT), a method that allows the study of multiple individual airways during either contraction to closure or relaxation in real time, as well as changes in airway size with changes in lung volume. Although other imaging modalities have the potential to image airways in vivo, none presently has the convenience and the accessibility coupled with the resolution required to visualize the parenchymal airways in vivo. Although HRCT may never be widely utilized for routine measurements or screening, because of radiation exposure, cost issues, and a limited ability to follow changes over extended time periods, the method has distinct and unique advantages in quantifying the behavior of airways in vivo. In this mini-review, we focus on these capabilities of HRCT by briefly reviewing highlights of experimental results from several canine and human studies.     

Theoretical study on two-dimensional aerodynamic characteristics of unsteady wings

A simple computing method based on a potential theory is developed for two-dimensional steady and unsteady deflected wings. This method of theoretical analysis is essentially related to thin and angular airfoils. Thus, the method is very simple but is effective to forecast aerodynamic forces for deflected or angular airfoils with a small camber operating in high Reynolds number flow, specifically in unsteady motion. The suction force acting on the leading edge of steady airfoils is theoretically obtained by using the Blasius formula. By Polhamus's leading edge suction analogy, the suction force is considered to be directed upward in partially separated flow for real thin airfoil with sharp leading edge. The theory can also be applied to obtain the aerodynamic characteristics of thin airfoils operating on low Reynolds number flow under some degree of approximation. This is very useful for the unsteady aerodynamic analysis because the Navier-Stokes equation can be solved by neither analytical nor numerical method for the thin and angular airfoils, which are common in the insect wing.     

Three-dimensional visualization and morphometry of small airways from microfocal X-ray computed tomography

Physiological morphometry is a critical factor in the flow dynamics in small airways. In this study, we visualized and analyzed the three-dimensional structure of the small airways without dehydration and fixation. We developed a two-step method to visualize small airways in detail by staining the lung tissue with a radiopaque solution and then visualizing the tissue with a cone-beam microfocal X-ray computed tomographic (CT) system. To verify the applicability of this staining and CT imaging (SCT) method, we used the method to visualize small airways in excised rat lungs. By using the SCT method to obtain continuous CT images, three-dimensional branching and merging bronchi ranging from 500 to 150 microm (the airway generation=8-16) were successfully reconstructed. The morphometry of the small airways (diameter, length, branching angle and gravity angle between the gravity direction and airway vector) was analyzed using the three-dimensional thinning algorithm. The diameter and length exponentially decreased with the airway generation. The asymmetry of the bifurcation decreased with generation and one branching angle decided the other pair branching angle. The SCT method is the first reported method that yields faithful high-resolution images of soft tissue geometry without fixation and the three-dimensional morphometry of small airways is useful for studying the biomechanical dynamics in small airways.     

通用选择指数的通径分析化模型

通过对各种选择指数的通径分析化模型进行系统化的研究,建立了通用选择指数的通径分析化模型,并给出了各种选择指数及其通径分析化的统一表示形式．用该模型可以充分利用各种信息来源,特别是在对各种信息来源需作各种约束时,为选种和评定优种提供了行之有效的计算方法和统一程序,避免了在实际应用中因计算体系不同而导致的混乱．     

Simultaneous determination of the carboxylate and lactone forms of 10-hydroxycamptothecin in human serum by restricted-access media high-performance liquid chromatography

A simple restricted-access media (RAM) HPLC method for simultaneous determination of the lactone and carboxylate forms of 10-hydroxycamptothecin (HCPT) in human serum was established. Using a RAM Hisep analytical column, serum samples were directly injected into the HPLC system. The eluted peaks of two forms of HCPT were monitored with a fluorescence detector. The separation was completed in 17 min. The linear range was 20-1000 ng/ml, intra-day and inter-day variations being less than 5%. The kinetic equation was introduced according to the analytical results. The equation shows that the course of the HCPT lactone form converting to carboxylate form in human serum at 4 degrees C is a first-order kinetic course. The concentration of each form at the moment of sampling was calculated by extrapolation.     

Simple constitutive model for a cortical bone

This short study presents a simple, one-dimensional constitutive model for the cortical bone with haversian structure. The model is developed within the general framework of the continuum damage theory. The kinetic equation is derived (rather than assumed a priori) through consideration of the irreversible changes of the mesostructure. As a consequence the analytical results closely approximate experimental measurements even though the theory does not introduce a single experimentally unidentifiable material parameter.     

Metabolic network simulation using logical loop algorithm and Jacobian matrix

A novel method to accomplish efficient numerical simulation of metabolic networks for flux analysis was developed. The only inputs required are the set of stoichiometric balances and the atom mapping matrices of all components of the reaction network. The latter are used to automatically calculate isotopomer mapping matrices. Using the symbolic toolbox of MATLAB the analytical solution of the stoichiometric balance equation system, isotopomer balances and the analytical Jacobian matrix of the total set of stoichiometric and isotopomer balances are created automatically. The number of variables in the isotopomer distribution equation system is significantly reduced applying modified isotopomer mapping matrices. These allow lumping of several consecutive isotopomer reactions into a single one. The solution of the complete system of equations is improved by implementing an iterative logical loop algorithm and using the analytical Jacobian matrix. This new method provided quick and robust convergence to the root of such equation systems in all cases tested. The method was applied to a network of lysine producing Corynebacterium glutamicum. The resulting equation system with the dimension of 546 x 546 was directly derived from 12 isotopomer balance equations. The results obtained yielded identical labeling patterns for metabolites as compared to the relaxation method.     

A compact model to predict quantized sub-band energy levels and inversion layer centroids of MOSFETs with a parabolic potential well approximation

A compact model to predict sub-band energy levels and inversion charge centroids in the MOSFET surface inversion layer has been presented in this paper for parabolic potential well approximation. Based on a coupled solution of the Schrödinger equation and the Poisson equation following the WKB method, one transcendental equation of the sub-band energy level has been rigorously derived and then the approximate analytical solutions for the sub-band energy levels and the inversion charge centroids have been obtained. The analytical results are compared with the numerical data and a good agreement between the analytical and numerical is found.     

A simple game-theoretic model for upstream fish migration

A simple game-theoretic model for upstream fish migration, which is a key element in life history of diadromous fishes, is proposed. Foundation of the model is a minimization problem on the cost of migration with the swimming speed and school size as the variables to be simultaneously optimized. Finding the optimizer ultimately reduces to solving a self-consistency equation without explicit solutions. Mathematical analytical results lead to the sufficient condition that the self-consistency equation has a unique solution, which turns out to be identified with the condition where the unique optimizer exists. Behavior of the optimizer is analyzed both mathematically and numerically to show its biophysical and ecological consequences. The analytical results demonstrate reasonable agreement between the present mathematical model and the theoretical and experimental results of upstream migration of fish schools reported in the past research.     

Diffusion as a function of aggregation in colloidal media

With the assumption that adsorption is a simple function of surface area, an analytical treatment is given for the dependence of the diffusion coefficient of an adsorbable solute upon the degree of aggregation of the adsorbing colloid. A simple relation is deduced after introducing some approximations. Some implications of the final diffusion equation are given.     

Algebraic determination of the evolutionary stable germination fraction

In this article, we consider a bet-hedging model with density dependence for germination behavior of dormant seeds. We show how to compute accurate values of the evolutionary stable germination fraction using a method based on expansion around the average seed bank size. The expansion is made up to the fourth order and is expressed in terms of the first four moments of the distribution of the year-to-year variation in the average yield per adult plant. This method leads to a simple algebraic equation, which can be solved without recurring to simulations of the seed bank dynamics. We first show the analytical derivation under general assumptions about the effect of density dependence. We then test our results with a numerical analysis where an explicit form of the density dependence has been taken.     

The drift approximation solves the Poisson, Nernst-Planck, and continuum equations in the limit of large external voltages

Nearly linear current-voltage curves are frequently found in biological ion channels. Using the drift limit of the substantially non-linear Poisson-Nernst-Planck equations, we explain such behavior of diffusion-controlled charge transport systems. Starting from Gauss' law, drift, and continuity equations we derive a simple analytical current-voltage relation, which accounts for this deviation from linearity. As shown previously, the drift limit of the Nernst-Planck equation applies if the total electric current is dominated by the electric field, and integral contributions from concentration gradients are small. The simple analytical form of the drift current-voltage relations makes it an ideal tool to analyze experiment current-voltage curves. We also solved the complete Poisson-Nernst-Planck equations numerically, and determined current-voltage curves over a wide range of voltages, concentrations, and Debye lengths. The simulation fully supports the analytical estimate that the current-voltage curves of simple charge transport systems are dominated by the drift mechanism. Even those relations containing the most extensive approximations remained qualitatively within the correct order of magnitude. Received: 24 September 1998 / Revised version: 22 January 1999 / Accepted: 22 January 1999     

Development of a Quantitative Real-Time Nucleic Acid Sequence-Based Amplification Assay with an Internal Control Using Molecular Beacon Probes for Selective and Sensitive Detection of Human Rhinovirus Serotypes

Evidence demonstrating that human rhinovirus (HRV) disease is not exclusively limited to the upper airways and may cause lower respiratory complications, together with the frequency of HRV infections and the increasing number of immunocompromised patients underline the need for rapid and accurate diagnosis of HRV infections. In this study, we developed the first quantitative real-time nucleic acid sequence-based amplification assay with an internal control using molecular beacon probes for selective and sensitive detection of human rhinovirus serotypes. We described a simple method to accurately quantify RNA target by computing the time to positivity (TTP) values for HRV RNA. Quantification capacity was assessed by plotting these TTP values against the starting number of target molecules. By using this simple method, we have significantly increased the diagnostic accuracy, precision, and trueness of real-time NASBA assay. Specificity of the method was verified in both in silico and experimental studies. Moreover, for assessment of clinical reactivity of the assay, NASBA has been validated on bronchoalveolar lavage (BAL) specimens. Our quantitative NASBA assay was found to be very specific, accurate, and precise with high repeatability and reproducibility.