A Mathematical Model of Neurohumoral Regulation of the Circulatory System

The cardiovascular system is modelled as a fluid flow system consisting of networks of pumps and piping systems. A mathematical model relating different cardiovascular parameters was developed. The change in cardiovascular parameters with individuals’ physical activity level, habits and environmental factors was established. The models used to predict how an individual can control the cardiovascular parameters to be healthy and diagnosing problems in the system.Keywords: Blood Pressure; Circulatory system modelling; Heart Rate.

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Mathematical model of the fetal cardiovascular system: the uncontrolled case

AJP Regulatory Integrative and Comparative Physiology ◽

10.1152/ajpregu.1980.239.3.r317 ◽

1980 ◽

Vol 239 (3) ◽

pp. R317-R325 ◽

Cited By ~ 1

Author(s):

F. Huikeshoven ◽

T. G. Coleman ◽

H. W. Jongsma

Keyword(s):

Mathematical Model ◽

Ductus Arteriosus ◽

Circulatory System ◽

Cardiovascular Physiology ◽

Control Mechanisms ◽

Foramen Ovale ◽

Fetal Circulation ◽

Upper Limits ◽

The Individual ◽

The Right

A mathematical model was developed to study and to interpret the results of different experiments undertaken in the field of fetal cardiovascular physiology. This model consists of a total of six peripheral blood compartments and a detailed description of the heart. The unique characteristics of the fetal circulation, particularly the ductus arteriosus, the foramen ovale, and the placenta are incorporated into this model. No control mechanisms are incorporated. The model was validated by simulating several previously described experiments. First, the performance of the individual ventricles was measured. The results indicate that, in the normal physiological situation, the right ventricle is working near the upper limits of its function while the left ventricle works below its limits. Second, the circulatory system was stressed by increasing the blood volume and the results show a shift from right to left in the relative contributions of each ventricle to the total cardiac output. Finally, effects of clamping the several blood vessels of the umbilical cord were studied.

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Evaluation of the efficiency of a new pulsatile flow‑generating circulatory-assist system in rotary blood pumps. Research on a mathematical model

Russian Journal of Transplantology and Artificial Organs ◽

10.15825/1995-1191-2021-4-73-78 ◽

2021 ◽

Vol 23 (4) ◽

pp. 73-78

Author(s):

G. P. Itkin ◽

A. I. Syrbu ◽

A. P. Kyleshov ◽

A. S. Buchnev ◽

A. A. Drobyshev

Keyword(s):

Mathematical Model ◽

Pulsatile Flow ◽

Circulatory System ◽

Left Ventricular ◽

Left Ventricular Cavity ◽

Pump Speed ◽

Diastolic Phase ◽

Flow Generation ◽

Blood Inflow ◽

Rotary Blood Pumps

Objective: to study the effect of a pulsatile flow-generation (PFG) device on the basic hemodynamic parameters of the circulatory system using a mathematical model.Results. Modelling and simulation showed that the use of PFG significantly (76%) increases aortic pulse pressure. The proposed mathematical model adequately describes the dynamics of the circulatory system and metabolism (oxygen debt) on physical activity in normal conditions and heart failure, and the use of non-pulsatile and pulsatile circulatory-assist systems. The mathematical model also shows that the use of PFG device blocks the development of rarefaction in the left ventricular cavity associated with a mismatch of blood inflow and outflow in diastolic phase when there is need to increase systemic blood flow by increasing the rotary pump speed.

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Dynamics of Epinephrine Distribution in the Dog

American Journal of Physiology-Legacy Content ◽

10.1152/ajplegacy.1958.193.2.365 ◽

1958 ◽

Vol 193 (2) ◽

pp. 365-370 ◽

Cited By ~ 3

Author(s):

Richard T. Jones ◽

William D. Blake

Keyword(s):

Mathematical Model ◽

Functional Relation ◽

Circulatory System ◽

Volume Of Distribution ◽

Order Reaction ◽

Sodium Pentobarbital ◽

Plasma Samples ◽

Fluorometric Method ◽

First Order ◽

Epinephrine Concentration

The dynamics of epinephrine distribution have been studied in dogs anesthetized with sodium pentobarbital. Epinephrine concentration in blood plasma samples from various sites of the circulatory system during and after constant intravenous infusions of epinephrine was estimated by a fluorometric method. The arterial epinephrine concentration was observed to reach a stable level after several minutes of infusion, the concentration varying directly with the rate of infusion. The disappearance of epinephrine was rapid and of a first order reaction variety. Various sites of epinephrine removal were detected and include the liver, kidney, gut and hindleg but not the lung. A mathematical model is formulated and proposed as a simple functional relation between the rate of infusion, epinephrine concentration, disappearance constant and the volume of distribution. From the data and this model, it was concluded that the epinephrine was not bound irreversibly to plasma constituents and that it was in ‘equilibrium’ with a volume of fluid greater than the intravascular space.

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