A Mathematical Model for the Morphology of the Pulmonary Acinus

1996 ◽  
Vol 118 (2) ◽  
pp. 210-215 ◽  
Author(s):  
E. Denny ◽  
R. C. Schroter

A computational method is proposed for the construction of a three-dimensional space-filling model of an acinar ventilatory unit. Its geometry consists of truncated octahedra arranged in a cuboidal block. The ducts and alveoli are formed by opening specific common faces between polyhedra. The branching structure is automatically computed using algorithms solely to maximise the number of alveoli and minimise the average path lengths; it is not formed with reference to published experimental data. Properties of the model such as the total alveolar and ductal volumes, the distribution of individual path lengths to the alveolar sacs, and the average number of ducts per generation are calculated. The predicted morphology of the model compares well with published data for rat lungs.

2021 ◽  
Vol 11 (3) ◽  
pp. 74-82
Author(s):  
N.I. Levonovich

This article discusses the development of a mathematical model for a device capable of tracking the movements of a human limb based on the readings of microelectromechanical sensors. For developing and selecting the most suitable model, experiments were conducted based on publicly available components. The result obtained is of practical importance since it can be used to create a device.


2009 ◽  
Vol 131 (3) ◽  
Author(s):  
Josué Sznitman ◽  
Thomas Heimsch ◽  
Johannes H. Wildhaber ◽  
Akira Tsuda ◽  
Thomas Rösgen

The inhalation of micron-sized aerosols into the lung’s acinar region may be recognized as a possible health risk or a therapeutic tool. In an effort to develop a deeper understanding of the mechanisms responsible for acinar deposition, we have numerically simulated the transport of nondiffusing fine inhaled particles (1 μm and 3 μm in diameter) in two acinar models of varying complexity: (i) a simple alveolated duct and (ii) a space-filling asymmetrical acinar branching tree following the description of lung structure by Fung (1988, “A Model of the Lung Structure and Its Validation,” J. Appl. Physiol., 64, pp. 2132–2141). Detailed particle trajectories and deposition efficiencies, as well as acinar flow structures, were investigated under different orientations of gravity, for tidal breathing motion in an average human adult. Trajectories and deposition efficiencies inside the alveolated duct are strongly related to gravity orientation. While the motion of larger particles (3 μm) is relatively insensitive to convective flows compared with the role of gravitational sedimentation, finer 1 μm aerosols may exhibit, in contrast, complex kinematics influenced by the coupling between (i) flow reversal due to oscillatory breathing, (ii) local alveolar flow structure, and (iii) streamline crossing due to gravity. These combined mechanisms may lead to twisting and undulating trajectories in the alveolus over multiple breathing cycles. The extension of our study to a space-filling acinar tree was well suited to investigate the influence of bulk kinematic interaction on aerosol transport between ductal and alveolar flows. We found the existence of intricate trajectories of fine 1 μm aerosols spanning over the entire acinar airway network, which cannot be captured by simple alveolar models. In contrast, heavier 3 μm aerosols yield trajectories characteristic of gravitational sedimentation, analogous to those observed in the simple alveolated duct. For both particle sizes, however, particle inhalation yields highly nonuniform deposition. While larger particles deposit within a single inhalation phase, finer 1 μm particles exhibit much longer residence times spanning multiple breathing cycles. With the ongoing development of more realistic models of the pulmonary acinus, we aim to capture some of the complex mechanisms leading to deposition of inhaled aerosols. Such models may lead to a better understanding toward the optimization of pulmonary drug delivery to target specific regions of the lung.


2018 ◽  
Vol 20 ◽  
pp. 02014
Author(s):  
Thanh-Phong Tran

In the context of investigating methods dedicated to identifying unknown parameters of the system described by partial differential equations, particularly in the field of heat transfer, it has been realized that the heat transfer process in particular three-dimensional features is really complex and takes longer to calculate. Therefore, an equivalent mathematical model which is simpler proposed to reduce the calculation time and the costs of experimental activities. We observe that the mathematical models of the diffusion equation can be minimized in three-dimensional space into a similar two-dimensional pattern within certain limits did not change the physical properties of heat transfer process. A mathematical model and the numerical results of simulation experiments in order to prove effectiveness the proposed method will be presented in detail in this article.


2008 ◽  
Vol 17 (01) ◽  
pp. 253-258 ◽  
Author(s):  
Z. ŁOJEWSKI ◽  
A. BARAN

Barriers and spontaneous fission half lives of superheavy isotopes of Z = 112 (N = 150–190) nucleus are calculated using state dependent δ-pairing and both BCS or Lipkin-Nogami (LN) approach. Four different models of macroscopic part of Strutinsky energy are probed. Results for different macroscopic models combined with δ+ LN approach give the half lives well compared to experimental data. The calculations are performed in three dimensional space of deformation parameters β = {β2, β4, β6}. The probability of spontaneous fission has been obtained by dynamical action minimization method.


2014 ◽  
Vol 541-542 ◽  
pp. 494-497
Author(s):  
Peng Xian Song ◽  
Ping Wang ◽  
Yao Hua Li

The three-phase four-leg converter can be obtained by adding a bridge into the traditional three-phase three-leg converter. The average mathematical model of three-phase four-leg converter is described in this paper. The three-dimensional space vector PWM (3D-SVPWM) is analyzed. For simplifying the modulation, a fast digital SVPWM algorithm which eliminates coordinate transformation and saves calculating time was proposed. The feasibility of the proposed modulation technique is verified by computer simulation. These results show that the proposed fast digital 3D-SVPWM technique can be easily implemented without conventional computational burden.


2012 ◽  
Vol 229-231 ◽  
pp. 2047-2051
Author(s):  
Yu Jian Li ◽  
Wen Chang Li ◽  
Yong Feng Yan

Lanping Pb-Zn mine is the biggest Pb-Zn mine of China. It is necessary for the mine to digital. On the basis of systematic analysis of and research on Jiayashan ore block in Lanping pb-zn mine, Mine Mathematical Model software, Surpac software and Micrmine software from abroad for digitization ware used to study this deposit. Finally, a three-dimensional space deposit model was established. As a result, the dynamic management of mine has been realized, the degree of automation and systematize have been increased for mining production, the scientific help have been presented for making use of resources sufficiently and reasonably.


2011 ◽  
Vol 19 (2) ◽  
pp. 81 ◽  
Author(s):  
Guoquan Liu ◽  
Haibo Yu

Serial sectioning technique provides plenty of quantitative geometric information of the microstructure analyzed, including those unavailable from stereology with one- and two-dimensional probes. This may be why it used to be and is being continuously served as one of the most common and invaluable methods to study the size and the size distribution, the topology and the distribution of topology parameters, and even the shape of three-dimensional space filling grains or cells. On the other hand, requiring tedious lab work, the method is also very time and energy consuming, most often only less than one hundred grains per sample were sampled and measured in almost all reported practice. Thus, a question is often asked: for typical microstructures in engineering materials, are so many grains or cells sampled adequate to obtain reliable results from this technique? To answer this question, experimental data of 1292 contiguous austenite grains in a low-carbon steel specimen obtained from the serial sectioning analysis are presented in this paper, which demonstrates the effect of sampling on the measurement of various parameters of grain size distribution and of the grain topology distribution. The result provides one of rules of thumb for grain stereology of similar microstructures.


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