scholarly journals Sensitivity analysis of solute kinetics in a four compartmental model for hemodialysis patients

2021 ◽  
Vol 48 (3) ◽  
Author(s):  
Mohammad Munir ◽  
◽  
Usman Saleem Khan Panni ◽  
Nasreen Kausar ◽  
Rukhshanda Anjum ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Sensitivity Analysis ◽  
Production Rate ◽  
Muscle Tissue ◽  
Clearance Rate ◽  
Compartmental Model ◽  
Hemodialysis Patients ◽  
Toxin Concentration ◽  
Extracellular Compartment ◽  
Sensitive Parameters

Sensitivity Analysis of the most advanced four compartmental mathematical model explaining solute kinetic in the hemodialysis patients was performed on the basis of the data collected from six patients with different Body Mass Indices (BMIs). The toxin concentration in all compartments increases with the decrease in the BMIs of the patients. The clearance rate, kclear, and the volume of extracellular compartment, VE, are the most sensitive while the volume of the muscle tissue compartment, VMT, and the clearance rate, kMT, are the least sensitive parameters during dialytic interval. The production rate, G, and the volume of the extracellular compartment, VE, are the most sensitive while kclear and kE, AT are the least sensitive parameters of all parameters during the interdialytic interval. The overall production rate, G, remains more sensitive than the clearance rate, kclear during one complete cycle.

SENSITIVITY ANALYSIS AND IDENTIFIABILITY OF A MATHEMATICAL MODEL OF A CHEMICAL REACTION

2021 ◽  
pp. 14-18
Author(s):  
Л.Ф. Сафиуллина
Keyword(s):  
Mathematical Model ◽  
Inverse Problem ◽  
Sensitivity Analysis ◽  
Chemical Reaction ◽  
Reaction Model ◽  
Numerical Calculations ◽  
Specific Reaction ◽  
Uniqueness Of The Solution ◽  
The Mathematical Model ◽  
Kinetics Of

В статье рассмотрен вопрос идентифицируемости математической модели кинетики химической реакции. В процессе решения обратной задачи по оценке параметров модели, характеризующих процесс, нередко возникает вопрос неединственности решения. На примере конкретной реакции продемонстрирована необходимость проводить анализ идентифицируемости модели перед проведением численных расчетов по определению параметров модели химической реакции. The identifiability of the mathematical model of the kinetics of a chemical reaction is investigated in the article. In the process of solving the inverse problem of estimating the parameters of the model, the question arises of the non-uniqueness of the solution. On the example of a specific reaction, the need to analyze the identifiability of the model before carrying out numerical calculations to determine the parameters of the reaction model was demonstrated.

scholarly journals Factors associating with oxygenation of lower-limb muscle tissue in hemodialysis patients

2016 ◽  
Vol 5 (6) ◽  
pp. 524 ◽  
Author(s):  
Haruhisa Miyazawa ◽  
Susumu Ookawara ◽  
Kiyonori Ito ◽  
Katsunori Yanai ◽  
Hiroki Ishii ◽  
...  
Keyword(s):  
Muscle Tissue ◽  
Lower Limb ◽  
Hemodialysis Patients ◽  
Lower Limb Muscle ◽  
Limb Muscle

scholarly journals Mathematical Analysis of Influenza A Dynamics in the Emergence of Drug Resistance

2018 ◽  
Vol 2018 ◽  
pp. 1-14 ◽  
Author(s):  
Caroline W. Kanyiri ◽  
Kimathi Mark ◽  
Livingstone Luboobi
Keyword(s):  
Mathematical Model ◽  
Sensitivity Analysis ◽  
Drug Resistance ◽  
Stability Analysis ◽  
Influenza A ◽  
Reproduction Number ◽  
Critical Value ◽  
Backward Bifurcation ◽  
Transmission Dynamics ◽  
High Morbidity

Every year, influenza causes high morbidity and mortality especially among the immunocompromised persons worldwide. The emergence of drug resistance has been a major challenge in curbing the spread of influenza. In this paper, a mathematical model is formulated and used to analyze the transmission dynamics of influenza A virus having incorporated the aspect of drug resistance. The qualitative analysis of the model is given in terms of the control reproduction number,Rc. The model equilibria are computed and stability analysis carried out. The model is found to exhibit backward bifurcation prompting the need to lowerRcto a critical valueRc∗for effective disease control. Sensitivity analysis results reveal that vaccine efficacy is the parameter with the most control over the spread of influenza. Numerical simulations reveal that despite vaccination reducing the reproduction number below unity, influenza still persists in the population. Hence, it is essential, in addition to vaccination, to apply other strategies to curb the spread of influenza.

Production rate, metabolic clearance rate and blood concentration of progesterone in conscious and anaesthetized pregnant rats

1984 ◽  
Vol 102 (3) ◽  
pp. 357-363 ◽  
Author(s):  
B. J. Waddell ◽  
N. W. Bruce
Keyword(s):  
Production Rate ◽  
Clearance Rate ◽  
Blood Concentration ◽  
Constant Infusion ◽  
Metabolic Clearance ◽  
Metabolic Clearance Rate ◽  
Short Term ◽  
Pregnant Rats ◽  
Pregnant Rat ◽  
Anaesthetized Rats

ABSTRACT Both production rate and metabolic clearance rate (MCR) of progesterone may vary rapidly and so effect short-term changes in blood concentration of the hormone. Here, a constant infusion and sampling technique was used to estimate these three characteristics of progesterone metabolism in seven conscious and ten anaesthetized rats on day 16 of pregnancy. After steady state was achieved, four samples were collected during a 1-h period from each rat. Mean values for production rate and MCR of progesterone in conscious rats were 14·0 ±1·4 μmol/day and 63·2 ± 6·2 litres/day respectively. Both values were substantially reduced in anaesthetized rats (8.6 ±0·8 μmol/ day and 39·4± 3·4 litres/day respectively) and so blood concentration was unchanged. The production rate was positively related to the total mass of luteal tissue (common correlation coefficient, r = 0·61, P <0·05). There were no consistent changes in the three characteristics with time but variation within rats was high. The estimated coefficients of variation for production rate, MCR and blood concentration within rats were 26, 18 and 17% in conscious and 27, 20 and 23% in anaesthetized rats respectively. Short-term changes in production rate and MCR generally were in the same direction (P <0·05). This reduced variation in blood concentration which would otherwise have occurred if production rate and MCR were unrelated. The pregnant rat is clearly capable of rapid shifts in production rate, MCR and blood concentration of progesterone and the positive relationship between production rate and MCR has a homeostatic effect on blood concentration. J. Endocr. (1984) 102, 357–363

scholarly journals Fractional-Order Modelling and Optimal Control of Cholera Transmission

2021 ◽  
Vol 5 (4) ◽  
pp. 261
Author(s):  
Silvério Rosa ◽  
Delfim F. M. Torres
Keyword(s):  
Mathematical Model ◽  
Optimal Control ◽  
Sensitivity Analysis ◽  
Fractional Order ◽  
Control Measures ◽  
Time Interval ◽  
Variable Order ◽  
Effectiveness Analysis ◽  
The Cost ◽  
Derivative Order

A Caputo-type fractional-order mathematical model for “metapopulation cholera transmission” was recently proposed in [Chaos Solitons Fractals 117 (2018), 37–49]. A sensitivity analysis of that model is done here to show the accuracy relevance of parameter estimation. Then, a fractional optimal control (FOC) problem is formulated and numerically solved. A cost-effectiveness analysis is performed to assess the relevance of studied control measures. Moreover, such analysis allows us to assess the cost and effectiveness of the control measures during intervention. We conclude that the FOC system is more effective only in part of the time interval. For this reason, we propose a system where the derivative order varies along the time interval, being fractional or classical when more advantageous. Such variable-order fractional model, that we call a FractInt system, shows to be the most effective in the control of the disease.

scholarly journals Sensitivity analysis of the mathematical model of catalytic reforming of gasoline

2019 ◽  
Vol 3 (2) ◽  
pp. 43-53
Author(s):  
L. F. Safiullina ◽  
◽  
I. M. Gubaydullin ◽  
K. F. Koledina ◽  
R. Z. Zaynullin ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Sensitivity Analysis ◽  
Catalytic Reforming ◽  
The Mathematical Model

scholarly journals SIMULATION AND SENSITIVITY ANALYSIS ON THE PARAMETER OF NON-TARGETED IRRADIATION EFFECTS MODEL

2018 ◽  
Vol 81 (1) ◽  
Author(s):  
Muhamad Hanis Nasir ◽  
Fuaada Mohd Siam
Keyword(s):  
Mathematical Model ◽  
Sensitivity Analysis ◽  
Real Life ◽  
Double Strand Breaks ◽  
Signal Molecules ◽  
Danger Signal ◽  
Survival Fraction ◽  
Strand Breaks ◽  
Radiation Induced ◽  
The Mathematical Model

Real-life situations showed damage effects on non-targeted cells located in the vicinity of an irradiation region, due to danger signal molecules released by the targeted cells. This effect is widely known as radiation-induced bystander effects (RIBE). The purpose of this paper is to model the interaction of non-targeted cells towards bystander factors released by the irradiated cells by using a system of structured ordinary differential equations. The mathematical model and its simulations are presented in this paper. In the model, the cells are grouped based on the number of double-strand breaks (DSBs) and mis-repair DSBs because the DSBs are formed in non-targeted cells. After performing the model's simulations, the analysis continued with sensitivity analysis. Sensitivity analysis will determine which parameter in the model is the most sensitive to the survival fraction of non-targeted cells. The proposed mathematical model can explain the survival fraction of non-targeted cells affected by the bystander factors.

scholarly journals Mathematical Model of Muscle Wasting in Cancer Cachexia

2020 ◽  
Author(s):  
Suzan Farhang-Sardroodi ◽  
Kathleen P. Wilkie
Keyword(s):  
Mathematical Model ◽  
Satellite Cell ◽  
Muscle Tissue ◽  
Cancer Cachexia ◽  
Muscle Wasting ◽  
Tissue Growth ◽  
Colon 26 ◽  
Treatment Conditions ◽  
Risk Of Mortality ◽  
Pharmacological Blockade

Cancer cachexia is a debilitating condition characterized by an extreme loss of skeletal muscle mass which negatively impacts patient’s quality of life, reduces their ability to sustain anticancer therapies, and increases the risk of mortality. Recent discoveries have identified the myostatin/activin-ActRIIB pathway as critical to muscle wasting by inducing satellite cell quiescence and increasing muscle-specific ubiquitin ligases responsible for atrophy. Remarkably, pharmacological blockade of the ActRIIB pathway has shown to reverse muscle wasting and prolong the survival time of tumor-bearing animals. To explore the implications of this signaling pathway and potential therapeutic targets in cachexia, we construct a novel mathematical model of muscle tissue subjected to tumor-derived cachexic factors. The model formulation tracks the intercellular interactions between cancer, satellite cell, and muscle cell populations. The model is parameterized by fitting to colon-26 mouse model data, and analysis provides insight into tissue growth in healthy, cancerous, and post-treatment conditions. Model predictions suggest that cachexia fundamentally alters muscle tissue health, as measured by the stem cell ratio, and this is only partially recovered by anti-cachexia treatment. Our mathematical findings suggest that the activation and proliferation of satellite cells, after blocking the myostatin/activin B pathway, is required to partially recover cancer-induced muscle loss.

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