scholarly journals Mathematical Modeling of Oxygen Transport in Retinal Layers

2019 ◽  
Vol 6 (6) ◽  
pp. 1-4
Author(s):  
Aadesh Kumar ◽  
◽  
Dr. Ram avtar ◽  
Dr. Deepti Seth ◽  
◽  
...  
Keyword(s):  
Mathematical Modeling ◽  
Differential Equation ◽  
Mathematical Model ◽  
Oxygen Consumption ◽  
Oxygen Transport ◽  
Oxygen Supply ◽  
Retinal Vasculature ◽  
Retinal Layer ◽  
Maximum Oxygen Consumption ◽  
Retinal Layers

The retina contains maximum oxygen ( consumption making it particular valuneric to vascular in fults, diminishing oxygen and circulation of nutrients. The goel of this paper to develop a mathematical model for quantitative analysis of transportation of oxygen and consumption in each retinal layer. Such models allows us to predict the effect of qualitatative change in retinal vasculature on oxygen supply in retinal layers. A differential equation , which used in this paper describing how the oxygen transport and cosumpt by the retinal layers.

Mathematical Modeling of the λ Switch

2010 ◽  
pp. 573-603
Author(s):  
Dmitriy Laschov ◽  
Michael Margaliot
Keyword(s):  
Mathematical Modeling ◽  
Differential Equation ◽  
Mathematical Model ◽  
Gene Regulation ◽  
Equilibrium Points ◽  
Domain Of Attraction ◽  
Verbal Description ◽  
Quantitative Understanding ◽  
Living Organisms ◽  
Scientific Challenge

Gene regulation plays a central role in the development and functioning of living organisms. Developing a deeper qualitative and quantitative understanding of gene regulation is an important scientific challenge. The Lambda switch is commonly used as a paradigm of gene regulation. Verbal descriptions of the structure and functioning of the Lambda switch have appeared in biological textbooks. We apply fuzzy modeling to transform one such verbal description into a well-defined mathematical model. The resulting model is a piecewise-quadratic, second-order differential equation. It demonstrates functional fidelity with known results while being simple enough to allow a rather detailed analysis. Properties such as the number, location, and domain of attraction of equilibrium points can be studied analytically. Furthermore, the model provides a rigorous explanation for the so-called stability puzzle of the Lambda switch.

Improved fatigue resistance not associated with maximum oxygen consumption in creatine-depleted rats

1997 ◽  
Vol 82 (6) ◽  
pp. 1911-1917 ◽  
Author(s):  
T. Tanaka ◽  
Y. Ohira ◽  
M. Danda ◽  
H. Hatta ◽  
I. Nishi
Keyword(s):  
Oxygen Consumption ◽  
Fatigue Resistance ◽  
Oxygen Transport ◽  
High Energy ◽  
Endurance Capacity ◽  
High Energy Phosphates ◽  
Transport Capacity ◽  
Maximum Oxygen Consumption ◽  
Oxygen Transport Capacity ◽  
Hindlimb Muscles

Tanaka, T., Y. Ohira, M. Danda, H. Hatta, and I. Nishi.Improved fatigue resistance not associated with maximum oxygen consumption in creatine-depleted rats. J. Appl. Physiol. 82 (6): 1911–1917, 1997.—Effects of feeding of either creatine or its analog β-guanidinopropionic acid (β-GPA) on endurance work capacity and oxygen consumption were studied in rats. Resting high-energy phosphate contents in hindlimb muscles were lower in the β-GPA group and higher in the creatine group than in controls. The glycogen contents in resting hindlimb muscles of rats fed β-GPA were significantly higher than those in controls. The endurance run and swimming times to exhaustion were significantly greater (32–70%) in the β-GPA group than in the control and creatine groups. However, there were no beneficial effects on the maximum oxygen consumption (V˙o 2 max) and oxygen transport capacity of blood by the feeding of β-GPA. None of these parameters were significantly influenced by creatine supply. Both maximum exercise time andV˙o 2 max in the β-GPA group were not changed by normalization of glycogen levels. The activities of mitochondrial enzymes in skeletal muscles were higher in the β-GPA group than in the controls. Thus endurance capacity is improved if the respiratory capacity of muscles is increased, even when the contents of high-energy phosphates in muscles are lower. Increased endurance capacity was not directly associated with the elevated levels of muscle glycogen, oxygen transport capacity of blood, orV˙o 2 max.

scholarly journals Different tamponade effects of intraocular silicone oil and sterilized air after single pars plana vitrectomy for rhegmatogenous retinal detachment

2020 ◽  
Author(s):  
Yifan Zhou ◽  
Siqi Zhang ◽  
Min Gao ◽  
Hao Zhou ◽  
Haiyun Liu ◽  
...  
Keyword(s):  
Retinal Detachment ◽  
Pars Plana Vitrectomy ◽  
Rhegmatogenous Retinal Detachment ◽  
Silicone Oil ◽  
Retinal Vasculature ◽  
Retinal Layer ◽  
Thickness Change ◽  
Gas Tamponade ◽  
Retinal Layers ◽  
Pars Plana

Abstract Purpose: To investigate different fundus vasculature and structure changes after single pars plana vitrectomy (PPV) following silicone oil (SO) or sterilized air in macular-off rhegmatogenous retinal detachment (RRD) patients. Method: 39 eyes (39 patients) with macular-off RRD underwent standard three-port 23-gauge PPV and intraocular SO or gas tamponade. Optical Coherence Tomography (OCT) and angiography were used to evaluate fundus structure and vasculature including retinal layers thicknesses and vessel density (VD) changes throughout observation for 12 weeks. Retinal layers were segmented into: NFL, GCL+IPL, INL, OPL, ONL+IS, OS+RPE and BRM. Fundus vasculature was segmented into superficial and deep capillary plexus (SCP, DCP), and choriocapillaris plexus (CCP). Result: For fundus vasculature, SO tamponade led to significant decrease in both SCPVD and DCPVD, while only SCPVD was found significantly decreased in gas tamponade eyes. For specific retinal layer, SO led to significant decrease in NFL and INL thicknesses. OPL, ONL+IS and OS+RPE thicknesses had significant increase in both SO tamponade and gas tamponade eyes. Conclusion: Different intraocular tamponades could have various impacts on retinal vasculature and structure. Compared to sterilized air, silicone oil tamponade could have relatively more negative effects on retinal vasculature and specific retinal layer thickness change.

Peculiarities of the Dynamics of Indicators of Levels of Oxygen Transport System during Exercise in the Athletes of Different Sports

10.12737/5893 ◽  
2014 ◽  
Vol 21 (3) ◽  
pp. 35-39
Author(s):  
Виноградов ◽  
S. Vinogradov ◽  
Платонов ◽  
A. Platonov
Keyword(s):  
Oxygen Consumption ◽  
Transport System ◽  
Oxygen Transport ◽  
Load Capacity ◽  
Transportation System ◽  
The Body ◽  
Transport Systems ◽  
Regression Equations ◽  
Maximum Oxygen Consumption ◽  
Oxygen Transport System

The study of the dependence of the dynamics of change of indicators of the gas transportation system from the power of physical exercise in the athletes of different sports was carried out. It was identified non-linear character of changes at speed - increasing workload, strong and positive correlation with the load power and their relationship at various levels of maximal oxygen consumption. The regression equations derived in the form of polynomials of the third degree, describing the revealed features with a high degree of importance were presented. The coefficients of regression equations define the peculiarities of dynamics of parameters of separate links of the gas transportation system when increasing the load capacity. It was established that representatives of cyclic sports with a high level aerobic capacity for oxygen consumption, in conditions of step-increasing load to the level of maximum oxygen consumption equally optimally functioning links of the gas transportation system, which provides the delivery of oxygen and its disposal at the limiting physical activity at various stages of its implementation in comparison with the representatives of acyclic sports. The obtained results are consistent with survey data of reactive types of oxygen transport systems of the body at a maximum physical load. The authors suggest to using them in evaluating the functional possibilities of the oxygen transport system with subsequent identification of the factors limiting the maximum oxygen consumption at full load.

scholarly journals Generalized mathematical model of cancer heterogeneity

2020 ◽  
Author(s):  
Motohiko Naito
Keyword(s):  
Mathematical Modeling ◽  
Differential Equation ◽  
Mathematical Model ◽  
Stochastic Process ◽  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Stochastic Differential Equation ◽  
Cancer Growth ◽  
Cancer Heterogeneity ◽  
Growth Properties

AbstractThe number of reports on mathematical modeling related to oncology is increasing with advances in oncology. Even though the field of oncology has developed significantly over the years, oncology-related experiments remain limited in their ability to examine cancer. To overcome this limitation, in this study, a stochastic process was incorporated into conventional cancer growth properties to obtain a generalized mathematical model of cancer growth. Further, an expression for the violation of symmetry by cancer clones that leads to cancer heterogeneity was derived by solving a stochastic differential equation. Monte Carlo simulations of the solution to the derived equation validate the theories formulated in this study. These findings are expected to provide a deeper understanding of the mechanisms of cancer growth, with Monte Carlo simulation having the potential of being a useful tool for oncologists.

MATHEMATICAL MODEL FOR THE TRANSPORT OF OXYGEN IN THE LIVING TISSUE THROUGH CAPILLARY BED

2015 ◽  
Vol 15 (04) ◽  
pp. 1550055 ◽  
Author(s):  
M. A. KHANDAY ◽  
AIJAZ NAJAR
Keyword(s):  
Mathematical Model ◽  
Finite Element Method ◽  
Finite Element ◽  
Diffusion Equation ◽  
Oxygen Transport ◽  
Human Body ◽  
Oxygen Supply ◽  
Living Tissue ◽  
Capillary Bed ◽  
Living Tissues

Oxygen is essential for the survival of living tissues in the human body. The mechanism of oxygen transport in the human body is a subject of great concern. In the conditions like hypoxia and hypothermia, the amount of oxygen supply in the biological tissue loose homeostasis, thereby the concentration of O 2 and the liberation of CO 2 in the human body demands a special attention. The present study based on finite element method employed to the mass diffusion equation with suitable conditions has been established. The main objective of this work is to understand the behavior of O 2 through various compartments of the capillary bed. The concentration of O 2 at plasma and capillary layers has been estimated which in turn leads to understand the situation of oxygen transport during various situations.

Application of the method of mathematical modeling for forecasting channel deformations at the underwater crossing of the main pipeline

2020 ◽  
Vol 10 (6) ◽  
pp. 599-609
Author(s):  
Valery А. Gruzdev ◽  
◽  
Georgy V. Mosolov ◽  
Ekaterina A. Sabayda ◽  
◽  
...  
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Roughness Coefficient ◽  
Computational Domain ◽  
Channel Deformations ◽  
Geological Surveys ◽  
Kuban River ◽  
The Stability ◽  
Protective Structures

In order to determine the possibility of using the method of mathematical modeling for making long-term forecasts of channel deformations of trunk line underwater crossing (TLUC) through water obstacles, a methodology for performing and analyzing the results of mathematical modeling of channel deformations in the TLUC zone across the Kuban River is considered. Within the framework of the work, the following tasks were solved: 1) the format and composition of the initial data necessary for mathematical modeling were determined; 2) the procedure for assigning the boundaries of the computational domain of the model was considered, the computational domain was broken down into the computational grid, the zoning of the computational domain was performed by the value of the roughness coefficient; 3) the analysis of the results of modeling the water flow was carried out without taking the bottom deformations into account, as well as modeling the bottom deformations, the specifics of the verification and calibration calculations were determined to build a reliable mathematical model; 4) considered the possibility of using the method of mathematical modeling to check the stability of the bottom in the area of TLUC in the presence of man-made dumping or protective structure. It has been established that modeling the flow hydraulics and structure of currents, making short-term forecasts of local high-altitude reshaping of the bottom, determining the tendencies of erosion and accumulation of sediments upstream and downstream of protective structures are applicable for predicting channel deformations in the zone of the TLUC. In all these cases, it is mandatory to have materials from engineering-hydro-meteorological and engineering-geological surveys in an amount sufficient to compile a reliable mathematical model.

CARDIORESPIRATORY SYSTEM UNDER BICYCLE ERGOMETER TEST IN SKIERS WITH DIFFERENT TRAINING STATUS (KOMI REPUBLIC)

2019 ◽  
pp. 76-84
Author(s):  
Yu.G. Solonin ◽  
T.P. Loginova ◽  
I.O. Garnov ◽  
A.L. Markov ◽  
A.A. Chernykh ◽  
...  
Keyword(s):  
Heart Rate ◽  
Oxygen Consumption ◽  
Komi Republic ◽  
Rate Pressure Product ◽  
Training Status ◽  
Maximum Oxygen Consumption ◽  
Bicycle Ergometry ◽  
Cardiorespiratory System ◽  
Unit Pulse ◽  
Ski Racers

The aim of the study is to examine the impact of training status on ski racers (Komi Republic) at rest and under bicycle ergometry evaluating their cardiorespiratory system parameters. Materials and Methods. The authors examined male ski racers with different training status: 22 first-rank sportsmen, 22 candidates for Master of Sports and 22 Masters of Sports. Athletes underwent bicycle ergometry loads up to refusal. Oxycon Pro system (Germany) was used. Then authors studied the complex of cardiorespiratory parameters, calculating maximum oxygen consumption and unit physiological cost. Results. At rest and under standard physical load (200 W) Masters of Sports demonstrate significantly increased training status among ski racers in such cardiorespiratory system parameters as heart rate, rate pressure product and oxygen pulse. Under standard physical load (200 W) statistically significant differences between first-rank sportsmen and candidates for Master of Sports are detected by heart rate, rate pressure product, respiration rate, respiratory minute volume and oxygen utilization coefficient. Such deviations indicate differences in training status. Under maximum load, the highest training status is found in Masters of Sports: bicycle ergometry load power and duration; unit pulse, pressor and cardiac cost, bulk and unit values of maximum oxygen consumption. Heart rate values, unit pulse and heart-vent cost indicate a high training status in candidates for Master of Sports under load up to refusal, if compared with first-rank sportsmen. Athletes’ organism under load up to refusal works more efficiently than under moderate load (200 W). The training status in ski racers (Komi Republic) is manifested in the saving cardiorespiratory system functions, both at rest and under standard bicycle ergometry, as well as in parameters of unit physiological cost under loads up to refusal and increased values of maximum oxygen consumption. Keywords: ski racers, Komi Republic, training status, bicycle ergometry loads, cardiorespiratory system, maximum oxygen consumption.

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