scholarly journals Modelling Blood and Pulmonary Pressure for Solving a Performance Optimal Problem for Sportsmen

2012 ◽  
Vol 2012 ◽  
pp. 1-16
Author(s):  
Jean Marie Ntaganda
Keyword(s):  
Mathematical Model ◽  
Differential Equations ◽  
Comparative Study ◽  
Model Parameters ◽  
Stability Conditions ◽  
Nonlinear Ordinary Differential Equations ◽  
Respiratory Parameters ◽  
Blood Pressures ◽  
The Impact ◽  
Found Model

This paper aims at designing a three-compartmental mathematical model for determining the impact and response of blood pressures on cardiovascular and respiratory parameters. Three nonlinear ordinary differential equations are derived from three compartments. Stability conditions are established and inverse techniques are proposed for identifying model parameters. To test the efficiency of the found model, a validation is achieved based on an existing mathematical model through a comparative study.

scholarly journals Mathematical model of the system “manual vibration shock shaker – fruit branch”

2019 ◽  
pp. 210-223
Author(s):  
Krupych, R. ◽  
Nishchenko, I. ◽  
Shevchuk, R. ◽  
Krupych, S.
Keyword(s):  
Mathematical Model ◽  
Differential Equations ◽  
Operation Mode ◽  
Calculated Data ◽  
Oscillatory System ◽  
System Model ◽  
Movement Speed ◽  
Mathematical System ◽  
Shock Mechanism ◽  
The Impact

Purpose. Development of mathematical model of oscillating system “manual vibration shock shaker – fruit branch” for the purpose of theoretical substantiation of the parameters of the shaker. Methods. The basic positions of mathematics, theoretical mechanics, mathematical modeling, program development and numerical calculations on the PC using methods of constructing mathematical models of functioning of agricultural machines are used. Results. The paper proposes a mathematical system model “manual vibration shock shaker – fruit branch” of six differential equations describing the motion of five separate masses (the mass of branch and four masses of individual shaker strings) and differential equations of the transverse and rotational motion of the system as whole. The mathematical system model determines the regularity of the motion of all masses, as well as the reactions of the viscals of the oscillatory system to the impact and after the impact that is generated in the shock mechanism. The proposed nonlinear, complex system of differential equations solves the numerical Runge-Kutta method of the fourth order of accuracy. On the basis of the calculated data the theoretical regularities of change of movement, speed and acceleration of a branch in the place of capture are received, which confirm that in the case of interaction of the cups of the shock mechanism there is blow that is accompanied by an increase in the acceleration of the branch, which is 4–5 times greater than the acceleration of the vibration mode of operation. Conclusions 1. The mathematical model of oscillating system “manual vibration shock shaker – fruit branch” is proposed in the form of system of six differential equations that allows to theoretically substantiate the basic modes of work of the manual shaker in the vibration shock mode to provide the agrotechnical necessary extraction completeness. 2. The received theoretical regularities of change of displacement, speed and acceleration of branch at the place of capture confirm the effectiveness of the vibration shock mode of the shaker. Due to the vibration-shock mode, the acceleration of the branch at the point of transmission of disturbing forces is 4–5 times higher than the acceleration of the vibrational operation mode. Keywords: manual shakes, vibration shocking process, oscillation oscillators, mathematical model, fruit branch, harvesting.

scholarly journals Assessment of Social Distancing for Controlling COVID-19 in Korea: An Age-Structured Modeling Approach

2020 ◽  
Vol 17 (20) ◽  
pp. 7474
Author(s):  
Yongin Choi ◽  
James Slghee Kim ◽  
Heejin Choi ◽  
Hyojung Lee ◽  
Chang Hyeong Lee
Keyword(s):  
Mathematical Model ◽  
Age Groups ◽  
Epidemiological Data ◽  
The Elderly ◽  
Model Parameters ◽  
Social Distancing ◽  
First Case ◽  
Age Structured ◽  
Epidemiological Characteristics ◽  
The Impact

The outbreak of the novel coronavirus disease 2019 (COVID-19) occurred all over the world between 2019 and 2020. The first case of COVID-19 was reported in December 2019 in Wuhan, China. Since then, there have been more than 21 million incidences and 761 thousand casualties worldwide as of 16 August 2020. One of the epidemiological characteristics of COVID-19 is that its symptoms and fatality rates vary with the ages of the infected individuals. This study aims at assessing the impact of social distancing on the reduction of COVID-19 infected cases by constructing a mathematical model and using epidemiological data of incidences in Korea. We developed an age-structured mathematical model for describing the age-dependent dynamics of the spread of COVID-19 in Korea. We estimated the model parameters and computed the reproduction number using the actual epidemiological data reported from 1 February to 15 June 2020. We then divided the data into seven distinct periods depending on the intensity of social distancing implemented by the Korean government. By using a contact matrix to describe the contact patterns between ages, we investigated the potential effect of social distancing under various scenarios. We discovered that when the intensity of social distancing is reduced, the number of COVID-19 cases increases; the number of incidences among the age groups of people 60 and above increases significantly more than that of the age groups below the age of 60. This significant increase among the elderly groups poses a severe threat to public health because the incidence of severe cases and fatality rates of the elderly group are much higher than those of the younger groups. Therefore, it is necessary to maintain strict social distancing rules to reduce infected cases.

Quasiperiodicity and Chaos in a Generalized Nosé–Hoover Oscillator

2016 ◽  
Vol 26 (10) ◽  
pp. 1650170 ◽  
Author(s):  
Paulo C. Rech
Keyword(s):  
Mathematical Model ◽  
Differential Equations ◽  
Harmonic Oscillator ◽  
Parameter Space ◽  
Nonlinear Ordinary Differential Equations ◽  
Two Dimensional ◽  
Dimensional Parameter ◽  
First Order ◽  
Chaotic Region ◽  
Quasiperiodic Structures

This paper reports on an investigation of the two-dimensional parameter-space of a generalized Nosé–Hoover oscillator. It is a mathematical model of a thermostated harmonic oscillator, which consists of a set of three autonomous first-order nonlinear ordinary differential equations. By using Lyapunov exponents to numerically characterize the dynamics of the model at each point of this parameter-space, it is shown that dissipative quasiperiodic structures are present, embedded in a chaotic region. The same parameter-space is also used to confirm the multistability phenomenon in the investigated mathematical model.

scholarly journals Mathematical Model Predicts that Acceleration of Diabetic Wound Healing is Dependent on Spatial Distribution of VEGF-A mRNA (AZD8601)

2021 ◽  
Author(s):  
S. Michaela Rikard ◽  
Paul J. Myers ◽  
Joachim Almquist ◽  
Peter Gennemark ◽  
Anthony C. Bruce ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Wound Healing ◽  
Spatial Distribution ◽  
Surrounding Tissue ◽  
Diabetic Patients ◽  
Model Parameters ◽  
Diabetic Wound ◽  
Diabetic Wound Healing ◽  
Diabetic Wounds ◽  
The Impact

Abstract Introduction Pharmacologic approaches for promoting angiogenesis have been utilized to accelerate healing of chronic wounds in diabetic patients with varying degrees of success. We hypothesize that the distribution of proangiogenic drugs in the wound area critically impacts the rate of closure of diabetic wounds. To evaluate this hypothesis, we developed a mathematical model that predicts how spatial distribution of VEGF-A produced by delivery of a modified mRNA (AZD8601) accelerates diabetic wound healing. Methods We modified a previously published model of cutaneous wound healing based on coupled partial differential equations that describe the density of sprouting capillary tips, chemoattractant concentration, and density of blood vessels in a circular wound. Key model parameters identified by a sensitivity analysis were fit to data obtained from an in vivo wound healing study performed in the dorsum of diabetic mice, and a pharmacokinetic model was used to simulate mRNA and VEGF-A distribution following injections with AZD8601. Due to the limited availability of data regarding the spatial distribution of AZD8601 in the wound bed, we performed simulations with perturbations to the location of injections and diffusion coefficient of mRNA to understand the impact of these spatial parameters on wound healing. Results When simulating injections delivered at the wound border, the model predicted that injections delivered on day 0 were more effective in accelerating wound healing than injections delivered at later time points. When the location of the injection was varied throughout the wound space, the model predicted that healing could be accelerated by delivering injections a distance of 1–2 mm inside the wound bed when compared to injections delivered on the same day at the wound border. Perturbations to the diffusivity of mRNA predicted that restricting diffusion of mRNA delayed wound healing by creating an accumulation of VEGF-A at the wound border. Alternatively, a high mRNA diffusivity had no effect on wound healing compared to a simulation with vehicle injection due to the rapid loss of mRNA at the wound border to surrounding tissue. Conclusions These findings highlight the critical need to consider the location of drug delivery and diffusivity of the drug, parameters not typically explored in pre-clinical experiments, when designing and testing drugs for treating diabetic wounds.

scholarly journals Determining the loose medium movement parameters in a centrifugal continuous mixer using a discrete element method

2021 ◽  
Vol 3 (7 (111)) ◽  
pp. 59-67
Author(s):  
Volodymyr Statsenko ◽  
Oleksandr Burmistenkov ◽  
Tetiana Bila ◽  
Svitlana Demishonkova
Keyword(s):  
Mathematical Model ◽  
Differential Equations ◽  
Discrete Element Method ◽  
Pearson Correlation ◽  
Discrete Element ◽  
System Of Differential Equations ◽  
Continuous Action ◽  
Centrifugal Mixer ◽  
The Impact ◽  
Element Method

The processes to form the compositions of loose materials in centrifugal mixers of continuous action have been considered. Based on the method of discrete elements, a mathematical model of the movement of particles in the rotor of the centrifugal mixer was built, taking into consideration their geometric and physical-mechanical parameters. To assess the extent of influence of these parameters on the nature of particle movement, a well-known mathematical model in the form of a system of differential equations was used, which was built on the basis of classical laws of mechanics. The process of mixing particles of two loose materials under different initial conditions of movement was modeled. The trajectories of individual particles along the bottom and side wall of the rotor were calculated. The results of the research reported here have established that the model built on the basis of the discrete element method makes it possible to improve the accuracy of determining the parameters of the movement of loose materials in the mixing zone. Calculations that involved this method show that the length of the particle trajectory is 2.9, and the movement time is 9 times greater than those calculated by the system of differential equations. The built and known mathematical models demonstrated the same nature of the distribution of components in the mixer. The value of the Pearson correlation coefficient between the calculated values of the coefficients of variation is 0.758. The best homogeneity is achieved by separating the flows of the mixture components and reducing the distance between their centers. The experimental study was carried out using a centrifugal mixer of continuous action with a conical rotor. Particle trajectories were constructed; it was established that the shape of the trajectory built by a discrete element method is closer to the experimental one. The results reported in this paper make it possible to predict the impact of the structural and technological parameters of the mixers of continuous action on the uniformity of the mixture

A region-based mathematical model of the urine concentrating mechanism in the rat outer medulla. I. Formulation and base-case results

2005 ◽  
Vol 289 (6) ◽  
pp. F1346-F1366 ◽  
Author(s):  
Anita T. Layton ◽  
Harold E. Layton
Keyword(s):  
Mathematical Model ◽  
Rat Kidney ◽  
Tubuloglomerular Feedback ◽  
Transepithelial Transport ◽  
Base Case ◽  
Model Parameters ◽  
Outer Medulla ◽  
Concentrating Mechanism ◽  
The Impact ◽  
Urine Concentrating Mechanism

We have developed a highly detailed mathematical model for the urine concentrating mechanism (UCM) of the rat kidney outer medulla (OM). The model simulates preferential interactions among tubules and vessels by representing four concentric regions that are centered on a vascular bundle; tubules and vessels, or fractions thereof, are assigned to anatomically appropriate regions. Model parameters, which are based on the experimental literature, include transepithelial transport properties of short descending limbs inferred from immunohistochemical localization studies. The model equations, which are based on conservation of solutes and water and on standard expressions for transmural transport, were solved to steady state. Model simulations predict significantly differing interstitial NaCl and urea concentrations in adjoining regions. Active NaCl transport from thick ascending limbs (TALs), at rates inferred from the physiological literature, resulted in model osmolality profiles along the OM that are consistent with tissue slice experiments. TAL luminal NaCl concentrations at the corticomedullary boundary are consistent with tubuloglomerular feedback function. The model exhibited solute exchange, cycling, and sequestration patterns (in tubules, vessels, and regions) that are generally consistent with predictions in the physiological literature, including significant urea addition from long ascending vasa recta to inner-stripe short descending limbs. In a companion study (Layton AT and Layton HE. Am J Physiol Renal Physiol 289: F1367–F1381, 2005), the impact of model assumptions, medullary anatomy, and tubular segmentation on the UCM was investigated by means of extensive parameter studies.

Mathematical modeling of adaptive immune response after transplantation

2020 ◽  
Vol 13 (08) ◽  
pp. 2050167
Author(s):  
Anka Markovska
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Immune Response ◽  
Differential Equations ◽  
Numerical Simulations ◽  
Ordinary Differential Equations ◽  
Cellular Immunity ◽  
Adaptive Immune Response ◽  
Nonlinear Ordinary Differential Equations ◽  
Adaptive Immune

A mathematical model of adaptive immune response after transplantation is formulated by five nonlinear ordinary differential equations. Theorems of existence, uniqueness and nonnegativity of solution are proven. Numerical simulations of immune response after transplantation without suppression of acquired cellular immunity and after suppression were performed.

scholarly journals A mathematical investigation into the uptake kinetics of nanoparticles in vitro

PLoS ONE ◽  
2021 ◽  
Vol 16 (7) ◽  
pp. e0254208
Author(s):  
Hannah West ◽  
Fiona Roberts ◽  
Paul Sweeney ◽  
Simon Walker-Samuel ◽  
Joseph Leedale ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Differential Equations ◽  
Mixed Culture ◽  
Uptake Kinetics ◽  
Multiphase System ◽  
Chemotherapy Drugs ◽  
Culture Model ◽  
The Impact ◽  
Kinetics Of

Nanoparticles have the potential to increase the efficacy of anticancer drugs whilst reducing off-target side effects. However, there remain uncertainties regarding the cellular uptake kinetics of nanoparticles which could have implications for nanoparticle design and delivery. Polymersomes are nanoparticle candidates for cancer therapy which encapsulate chemotherapy drugs. Here we develop a mathematical model to simulate the uptake of polymersomes via endocytosis, a process by which polymersomes bind to the cell surface before becoming internalised by the cell where they then break down, releasing their contents which could include chemotherapy drugs. We focus on two in vitro configurations relevant to the testing and development of cancer therapies: a well-mixed culture model and a tumour spheroid setup. Our mathematical model of the well-mixed culture model comprises a set of coupled ordinary differential equations for the unbound and bound polymersomes and associated binding dynamics. Using a singular perturbation analysis we identify an optimal number of ligands on the polymersome surface which maximises internalised polymersomes and thus intracellular chemotherapy drug concentration. In our mathematical model of the spheroid, a multiphase system of partial differential equations is developed to describe the spatial and temporal distribution of bound and unbound polymersomes via advection and diffusion, alongside oxygen, tumour growth, cell proliferation and viability. Consistent with experimental observations, the model predicts the evolution of oxygen gradients leading to a necrotic core. We investigate the impact of two different internalisation functions on spheroid growth, a constant and a bond dependent function. It was found that the constant function yields faster uptake and therefore chemotherapy delivery. We also show how various parameters, such as spheroid permeability, lead to travelling wave or steady-state solutions.

scholarly journals ВИКОРИСТАННЯ МОДЕЛІ НЕЛІНІЙНОЇ ДИНАМІКИ ДЛЯ АНАЛІЗУ ВПЛИВУ СИСТЕМИ УПРАВЛІННЯ ЗНАННЯМИ НА РЕАЛІЗАЦІЮ ВИСОКОТЕХНОЛОГІЧНИХ ПРОЕКТІВ

2019 ◽  
pp. 76-82
Author(s):  
Василь Михайлович Вартанян ◽  
Дар'я Олександрівна Штейнбрехер
Keyword(s):  
Nonlinear Dynamics ◽  
Mathematical Model ◽  
Knowledge Management ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Management System ◽  
Knowledge Management System ◽  
Project Implementation ◽  
The Impact ◽  
The Mathematical Model

The article determines that at the present stage of the project management development in information-oriented society, the decision-making process on the efficiency of the knowledge management system assessment is complicated, due to the lack of approaches that determine the impact of the system on the project implementation. The article presents the main results of the analysis of the current state of the problem of modeling the knowledge management system of high-tech projects, which helped to establish that one of the factors of the introduction of an effective system of knowledge preservation is the ability to assess the impact of the system on the project environment.In order to solve the problem, the mathematical model of nonlinear dynamics for the analysis of the influence of knowledge management system on the project based on the Bulirsch–Stoer method was proposed, it is possible to evaluate the influence of elements of the knowledge management system on the projected stages of the project implementation and to calculate the duration of the project taking into account their influence. The mathematical model of nonlinear dynamics for the analysis of the influence of the knowledge management system on the Bulirsch–Stoer method is given to evaluate the influence of elements of the knowledge management system on the projected implementation stages and to calculate the duration of the project, taking into account their impact. Bulirsch–Stoer algorithm is a method for the numerical solution of ordinary differential equations which combines three powerful ideas: Richardson extrapolation, the use of rational function extrapolation in Richardson-type applications, and the modified midpoint method, to obtain numerical solutions to ordinary differential equations (ODEs) with high accuracy and comparatively little computational effort. The step-by-step tracking of the knowledge management system impact on the project development will allow the project manager to predict both its successful completion and the risks of deviation from the scheduled time due to the loss of critical knowledge, which largely stems from the successful implementation of the project.Further research will be aimed at developing a model that allows us to assess the profitability of the system in the design environment, based on the results of the proposed mathematical model.

scholarly journals Mathematical modeling of the transmission of SARS-CoV-2 ″ Evaluating the impact of isolation in São Paulo State (Brazil) and lockdown in Spain associated with protective measures on the epidemic of covid-19

2020 ◽  
Author(s):  
Hyun Mo Yang ◽  
Luis Pedro Lombardi ◽  
Fabio Fernandes Morato Castro ◽  
Ariana Campos Yang
Keyword(s):  
Mathematical Model ◽  
Sao Paulo ◽  
World Health ◽  
Model Parameters ◽  
São Paulo ◽  
Fatality Rate ◽  
Protective Measures ◽  
Paulo State ◽  
São Paulo State ◽  
The Impact

Coronavirus disease 2019 (covid-19), with the fatality rate in elder (60 years old or more) being much higher than young (60 years old or less) patients, was declared a pandemic by the World Health Organization on March 11, 2020. Taking into account this age-dependent fatality rate, a mathematical model considering young and elder subpopulations was formulated based on the natural history of covid-19 to study the transmission of the SARS-CoV-2. This model can be applied to study the epidemiological scenario resulting from the adoption of isolation or lockdown in many countries to control the rapid propagation of covid-19. We chose as examples the isolation adopted in São Paulo State (Brazil) in the early phase but not at the beginning of the epidemic, and the lockdown implemented in Spain when the number of severe covid-19 cases was increasing rapidly. Based on the data collected from Sa ̃o Paulo State and Spain, the model parameters were evaluated and we obtained higher estimation for the basic reproduction number R0 (9.24 for São Paulo State, and 8 for Spain) compared to the currently accepted estimation of R0 around 3. The model allowed to explain the flattening of the epidemic curves by isolation in São Paulo State and lockdown in Spain when associated with the protective measures (face mask and social distancing) adopted by the population. However, a simplified mathematical model providing lower estimation for R0 did not explain the flattening of the epidemic curves. The implementation of the isolation in Sa ̃o Paulo State before the rapidly increasing phase of the epidemic enlarged the period of the first wave of the epidemic and delayed its peak, which are the desirable results of isolation to avoid the overloading in the health care system.

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