MATHEMATICAL MODEL FOR SELECTING RESPIRATORY MODES FOR ARTIFICIAL VENTILATION OF THE LUNGS

2021 ◽  
Vol 3 ◽  
pp. 130-140
Author(s):  
Natalia Aralova ◽  
Keyword(s):  
Mathematical Model ◽  
Respiratory System ◽  
Artificial Ventilation ◽  
Exchange Process ◽  
Lung Ventilation ◽  
Viral Disease ◽  
Proposed Model ◽  
Ventilation Modes ◽  
Respiratory Gases ◽  
Ventilation Of The Lungs

COVID-19 mainly affects the lower respiratory tract, and in 20 % of people infected with the SARS-CoV-2 virus, it penetrates deep into the lungs. At the same time, the patient's condition quickly becomes critical, and the most severe patients must be urgently placed in the intensive care unit and connected to artificial lung ventilation (IVL) devices. Artificial ventilation is necessary when the lungs can no longer breathe in enough oxygen and breathe out the carbon dioxide that has been collected in them. In this case, ventilators take over the functions of the respiratory system. The methods of carrying out artificial ventilation of the lungs require not only experimental, but also theoretical justification. For the study, it is proposed to apply a mathematical model of the functional respiratory system, in which the breathing process is represented as a controlled dynamic system and which allows predicting the gas exchange process in the lung structures in the dynamics of the respiratory cycle under various disturbing influences. To expand the area of applicability, the process features characteristic of the conditions under consideration are taken into account. It is proposed to supplement the model with equations that take into account the elasticity and resistance of pulmonary structures. Since the possibility of obtaining quantitative and qualitative characteristics of the process of mass transfer of gases with various types of artificial ventilation of the lungs is essential, equations are proposed to describe different types of pulmonary respiration. Implementation of the proposed model will allow obtaining results on the study of the process of dynamics of respiratory gases during artificial ventilation of the lungs, contributing to the solution of practical problems on the optimization of the parameters of technical devices for artificial ventilation. The subsequent combination of the proposed model with the model of the development of a viral disease can, in the presence of an array of individual data, be of significant assistance in choosing mechanical ventilation modes in a complicated course of a viral disease.

scholarly journals Comparative effects of flow vs. volume-controlled one-lung ventilation on gas exchange and respiratory system mechanics in pigs

2020 ◽  
Vol 8 (S1) ◽  
Author(s):  
Jakob Wittenstein ◽  
Martin Scharffenberg ◽  
Xi Ran ◽  
Diana Keller ◽  
Pia Michler ◽  
...  
Keyword(s):  
Gas Exchange ◽  
Respiratory System ◽  
Lung Ventilation ◽  
Minute Volume ◽  
Mechanical Power ◽  
One Lung Ventilation ◽  
Impedance Tomography ◽  
Controlled Ventilation ◽  
Ventilation Modes ◽  
Volume Controlled

Abstract Background Flow-controlled ventilation (FCV) allows expiratory flow control, reducing the collapse of the airways during expiration. The performance of FCV during one-lung ventilation (OLV) under intravascular normo- and hypovolaemia is currently unknown. In this explorative study, we hypothesised that OLV with FCV improves PaO2 and reduces mechanical power compared to volume-controlled ventilation (VCV). Sixteen juvenile pigs were randomly assigned to one of two groups: (1) intravascular normovolaemia (n = 8) and (2) intravascular hypovolaemia (n = 8). To mimic inflammation due to major thoracic surgery, a thoracotomy was performed, and 0.5 μg/kg/h lipopolysaccharides from Escherichia coli continuously administered intravenously. Animals were randomly assigned to OLV with one of two sequences (60 min per mode): (1) VCV–FCV or (2) FCV–VCV. Variables of gas exchange, haemodynamics and respiratory signals were collected 20, 40 and 60 min after initiation of OLV with each mechanical ventilation mode. The distribution of ventilation was determined using electrical impedance tomography (EIT). Results Oxygenation did not differ significantly between modes (P = 0.881). In the normovolaemia group, the corrected expired minute volume (P = 0.022) and positive end-expiratory pressure (PEEP) were lower during FCV than VCV. The minute volume (P ≤ 0.001), respiratory rate (P ≤ 0.001), total PEEP (P ≤ 0.001), resistance of the respiratory system (P ≤ 0.001), mechanical power (P ≤ 0.001) and resistive mechanical power (P ≤ 0.001) were lower during FCV than VCV irrespective of the volaemia status. The distribution of ventilation did not differ between both ventilation modes (P = 0.103). Conclusions In a model of OLV in normo- and hypovolemic pigs, mechanical power was lower during FCV compared to VCV, without significant differences in oxygenation. Furthermore, the efficacy of ventilation was higher during FCV compared to VCV during normovolaemia.

A model of mechanical interactions between heart and lungs

2009 ◽  
Vol 367 (1908) ◽  
pp. 4741-4757 ◽  
Author(s):  
Julie Fontecave Jallon ◽  
Enas Abdulhay ◽  
Pascale Calabrese ◽  
Pierre Baconnier ◽  
Pierre-Yves Gumery
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Respiratory System ◽  
Respiratory Muscles ◽  
Systemic Circulation ◽  
System Model ◽  
Link Type ◽  
Cardiovascular Model ◽  
Model Combining ◽  
Proposed Model

To study the mechanical interactions between heart, lungs and thorax, we propose a mathematical model combining a ventilatory neuromuscular model and a model of the cardiovascular system, as described by Smith et al. (Smith, Chase, Nokes, Shaw & Wake 2004 Med. Eng. Phys. 26 , 131–139. ( doi:10.1016/j.medengphy.2003.10.001 )). The respiratory model has been adapted from Thibault et al . (Thibault, Heyer, Benchetrit & Baconnier 2002 Acta Biotheor . 50 , 269–279. ( doi:10.1023/A:1022616701863 )); using a Liénard oscillator, it allows the activity of the respiratory centres, the respiratory muscles and rib cage internal mechanics to be simulated. The minimal haemodynamic system model of Smith includes the heart, as well as the pulmonary and systemic circulation systems. These two modules interact mechanically by means of the pleural pressure, calculated in the mechanical respiratory system, and the intrathoracic blood volume, calculated in the cardiovascular model. The simulation by the proposed model provides results, first, close to experimental data, second, in agreement with the literature results and, finally, highlighting the presence of mechanical cardiorespiratory interactions.

scholarly journals MATHEMATICAL MODEL FOR THE INVESTIGATION OF HYPOXIC STATES IN THE HEART MUSCLE AT VIRAL DAMAGE

2021 ◽  
Vol 14 (4) ◽  
pp. 38-52
Author(s):  
N. I. Aralova ◽  
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Viral Infection ◽  
Blood Vessels ◽  
Respiratory System ◽  
Mass Exchange ◽  
Partial Occlusion ◽  
Pharmacological Substance ◽  
Respiratory Gases ◽  
Hypoxic State

The main complications of organism damaged by SARS-CoV-2 virus are various cardiovascular system lesions. As a result, the secondary tissue hypoxia is developed and it is relevant to search the means for hypoxic state alleviation. Mathematical modeling of this process, followed by the imitation of hypoxic states development, and subsequent correction of hypoxia at this model may be one of the directions for investigations. Aim. The purpose of this study was to construct mathematical models of functional respiratory and blood circulatory systems to simulate the partial occlusion of blood vessels during viral infection lesions and pharmacological correction of resulting hypoxic state. Methods. Methods of mathematical modeling and dynamic programming were used. Transport and mass exchange of respiratory gases in organism, partial occlusion of blood vessels and influence of antihypoxant were described by the systems of ordinary nonlinear differential equations. Results. Mathematical model of functional respiratory system was developed to simulate pharmacological correction of hypoxic states caused by the complications in courses of viral infection lesions. The model was based on the theory of functional systems by P. K. Anokhin and the assumption about the main function of respiratory system. The interactions and interrelations of individual functional systems in organism were assumed. Constituent parts of our model were the models of transport and mass exchange of respiratory gases in organism, selforganization of respiratory and blood circulatory systems, partial occlusion of blood vessels and the transport of pharmacological substance. Conclusions. The series of computational experiments for averaged person organism demonstrated the possibility of tissue hypoxia compensation using pharmacological substance with vasodilating effect, and in the case of individual data array, it may be useful for the development of strategy and tactics for individual patient medical treatment.

THE DEVELOPMENT OF THE MATHEMATICAL MODEL OF PREDICTING THE INDICATORS OF ACCREDITATION OF TECHNICAL UNIVERSITIES IN THE RUSSIAN FEDERATION

2017 ◽  
pp. 27-38
Author(s):  
Olga Mikhaylovna Tikhonova ◽  
Alexander Fedorovich Rezchikov ◽  
Vladimir Andreevich Ivashchenko ◽  
Vadim Alekseevich Kushnikov
Keyword(s):  
Mathematical Model ◽  
System Dynamics ◽  
Regression Model ◽  
Oriented Graph ◽  
Real Data ◽  
Educational Process ◽  
Proposed Model ◽  
Linear Differential ◽  
The University ◽  
The Mathematical Model

The paper presents the system of predicting the indicators of accreditation of technical universities based on J. Forrester mechanism of system dynamics. According to analysis of cause-and-effect relationships between selected variables of the system (indicators of accreditation of the university) there was built the oriented graph. The complex of mathematical models developed to control the quality of training engineers in Russian higher educational institutions is based on this graph. The article presents an algorithm for constructing a model using one of the simulated variables as an example. The model is a system of non-linear differential equations, the modelling characteristics of the educational process being determined according to the solution of this system. The proposed algorithm for calculating these indicators is based on the system dynamics model and the regression model. The mathematical model is constructed on the basis of the model of system dynamics, which is further tested for compliance with real data using the regression model. The regression model is built on the available statistical data accumulated during the period of the university's work. The proposed approach is aimed at solving complex problems of managing the educational process in universities. The structure of the proposed model repeats the structure of cause-effect relationships in the system, and also provides the person responsible for managing quality control with the ability to quickly and adequately assess the performance of the system.

A Mathematical Model for the Anaerobic Digestion Process Applied to a Mixture of Night Soil and Septic Tank Sludge

1986 ◽  
Vol 18 (7-8) ◽  
pp. 239-248 ◽  
Author(s):  
Sung Ryong Ha ◽  
Dwang Ho Lee ◽  
Sang Eun Lee
Keyword(s):  
Mathematical Model ◽  
Anaerobic Digestion ◽  
Biomass Concentration ◽  
Gas Production ◽  
Septic Tank ◽  
Volatile Acid ◽  
Hydraulic Residence Time ◽  
Anaerobic Digestion Process ◽  
Digestion Process ◽  
Proposed Model

Laboratory scale experiments were conducted to develop a mathematical model for the anaerobic digestion of a mixture of night soil and septic tank sludge. The optimum mixing ratio by volume between night soil and septic tank sludge was found to be 7:3. Due to the high solids content in the influent waste, mixed-liquor volatile suspended solids (MLVSS) was not considered to be a proper parameter for biomass concentration, therefore, the active biomass concentration was estimated based on deoxyribonucleic acid (DNA) concentration in the reactor. The weight ratio between acidogenic bacteria and methanogenic bacteria in the mixed culture of a well-operated anaerobic digester was approximately 3:2. The proposed model indicates that the amount of volatile acid produced and the gas production rate can be expressed as a function of hydraulic residence time (HRT). The kinetic constants of the two phases of the anaerobic digestion process were determined, and a computer was used to simulate results using the proposed model for the various operating parameters, such as BOD5 and volatile acid concentrations in effluent, biomass concentrations and gas production rates. These were consistent with the experimental data.

scholarly journals On the Dragging Trajectory of Anchors in Clay for Merchant Ships

2021 ◽  
Vol 9 (2) ◽  
pp. 118
Author(s):  
Xinqing Zhuang ◽  
Keliang Yan ◽  
Pan Gao ◽  
Yihua Liu
Keyword(s):  
Mathematical Model ◽  
Structural Integrity ◽  
Indirect Measurement ◽  
Test System ◽  
Flow Rule ◽  
Burial Depth ◽  
Proposed Model ◽  
Depth Increase ◽  
Two Parameters ◽  
The Mathematical Model

Anchor dragging is a major threat to the structural integrity of submarine pipelines. A mathematical model in which the mechanical model of chain and the bearing model of anchor were coupled together. Based on the associated flow rule, an incremental procedure was proposed to solve the spatial state of anchor until it reaches the ultimate embedding depth. With an indirect measurement method for the anchor trajectory, a model test system was established. The mathematical model was validated against some model tests, and the effects of two parameters were studied. It was found that both the ultimate embedding depth of a dragging anchor and the distance it takes to reach the ultimate depth increase with the shank-fluke pivot angle, but decrease as the undrained shear strength of clay increases. The proposed model is supposed to be useful for the embedding depth calculation and guiding the design of the pipeline burial depth.

scholarly journals Content Dependent Representation Selection Model for Systems Based on MPEG DASH

Electronics ◽  
2021 ◽  
Vol 10 (15) ◽  
pp. 1843
Author(s):  
Jelena Vlaović ◽  
Snježana Rimac-Drlje ◽  
Drago Žagar
Keyword(s):  
Mathematical Model ◽  
Spatial Information ◽  
Relevant Literature ◽  
Video Quality ◽  
Similarity Index ◽  
Video Encoding ◽  
Adaptation Algorithm ◽  
Subjective Testing ◽  
Proposed Model ◽  
The Mathematical Model

A standard called MPEG Dynamic Adaptive Streaming over HTTP (MPEG DASH) ensures the interoperability between different streaming services and the highest possible video quality in changing network conditions. The solutions described in the available literature that focus on video segmentation are mostly proprietary, use a high amount of computational power, lack the methodology, model notation, information needed for reproduction, or do not consider the spatial and temporal activity of video sequences. This paper presents a new model for selecting optimal parameters and number of representations for video encoding and segmentation, based on a measure of the spatial and temporal activity of the video content. The model was developed for the H.264 encoder, using Structural Similarity Index Measure (SSIM) objective metrics as well as Spatial Information (SI) and Temporal Information (TI) as measures of video spatial and temporal activity. The methodology that we used to develop the mathematical model is also presented in detail so that it can be applied to adapt the mathematical model to another type of an encoder or a set of encoding parameters. The efficiency of the segmentation made by the proposed model was tested using the Basic Adaptation algorithm (BAA) and Segment Aware Rate Adaptation (SARA) algorithm as well as two different network scenarios. In comparison to the segmentation available in the relevant literature, the segmentation based on the proposed model obtains better SSIM values in 92% of cases and subjective testing showed that it achieves better results in 83.3% of cases.

The Generation Principle and Mathematical Models of Double-Enveloping Internal Gear Pairs

2015 ◽  
Author(s):  
Xuan Li ◽  
Bingkui Chen ◽  
Yawen Wang ◽  
Guohua Sun ◽  
Teik C. Lim
Keyword(s):  
Mathematical Model ◽  
Load Capacity ◽  
Geometrical Shape ◽  
Gear Pair ◽  
Numerical Examples ◽  
Proposed Model ◽  
General Mathematical Model ◽  
Meshing Characteristics ◽  
Internal Gear ◽  
Tooth Pair

In this paper, the planar double-enveloping method is presented for the generation of tooth profiles of the internal gear pair for various applications, such as gerotors and gear reducers. The main characteristic of this method is the existence of double contact between one tooth pair such that the sealing property, the load capacity and the transmission precision can be significantly improved as compared to the conventional configuration by the single-enveloping theory. Firstly, the generation principle of the planar double-enveloping method is introduced. Based on the coordinate transformation and the envelope theory, the general mathematical model of the double-enveloping internal gear pair is presented. By using this model, users can directly design different geometrical shape profiles to obtain a double-enveloping internal gear pair with better meshing characteristics. Secondly, to validate the effectiveness of the proposed model, specific mathematical formulations of three double-enveloping internal gear pairs which apply circular, parabolic and elliptical curves as the generating curves are given. The equations of tooth profiles and meshing are derived and the composition of tooth profiles is analyzed. Finally, numerical examples are provided for an illustration.

Sign in / Sign up

Export Citation Format

Share Document