Analysis of unstable behavior in a mathematical model for erythropoiesis

Susana Serna1, Jasmine A Nirody, Miklós Z Rácz

  • 1Departament de Matematiques, Universitat Autonoma de Barcelona, Bellaterra, Barcelona, Spain. serna@mat.uab.es

Related Concept Videos

Factors Affecting Erythropoiesis01:24

Factors Affecting Erythropoiesis

The cardiovascular system regulates the number of erythrocytes in the bloodstream to ensure optimal oxygen transport. It also prevents over-proliferation of these cells, which helps to maintain blood viscosity and flow rate.
Several factors influence the erythrocyte production rate, with tissue oxygen level being among the most critical. Intense exercise or high altitudes can cause tissue hypoxia, which triggers the kidneys to release more erythropoietin (EPO) into the bloodstream.
EPO then...
Erythropoiesis01:14

Erythropoiesis

Red blood cells  (RBCs) transport oxygen to all body tissues. These cells survive only for 120 days and then need to be replenished. Erythropoiesis is the process of RBC production. In healthy individuals, erythropoiesis ensures all tissues are amply supplied with oxygen. In addition, blood loss due to injury leads to a drop in the physiological oxygen level that will cause erythropoiesis. Any defect in erythropoiesis leads to several physiological disorders, including thalassemia, anemia, and...
Erythropoiesis01:14

Erythropoiesis

Red blood cells  (RBCs) transport oxygen to all body tissues. These cells survive only for 120 days and then need to be replenished. Erythropoiesis is the process of RBC production. In healthy individuals, erythropoiesis ensures all tissues are amply supplied with oxygen. In addition, blood loss due to injury leads to a drop in the physiological oxygen level that will cause erythropoiesis. Any defect in erythropoiesis leads to several physiological disorders, including thalassemia, anemia, and...
Mechanistic Models: Compartment Models in Individual and Population Analysis01:23

Mechanistic Models: Compartment Models in Individual and Population Analysis

Mechanistic models are utilized in individual analysis using single-source data, but imperfections arise due to data collection errors, preventing perfect prediction of observed data. The mathematical equation involves known values (Xi), observed concentrations (Ci), measurement errors (εi), model parameters (ϕj), and the related function (ƒi) for i number of values. Different least-squares metrics quantify differences between predicted and observed values. The ordinary least squares (OLS)...
Modeling with Differential Equations01:25

Modeling with Differential Equations

Population dynamics can be described mathematically by considering the population size P(t) as a function of time. The rate of change of the population is then represented by the derivative of P(t). A simple assumption is that the rate of growth is proportional to the size of the population itself. This leads to an exponential growth model, where the population increases rapidly without bound. While this is a useful first approximation, it does not reflect realistic long-term...
Physiological Pharmacokinetic Models: Blood Flow-Limited Versus Diffusion-Limited Models00:57

Physiological Pharmacokinetic Models: Blood Flow-Limited Versus Diffusion-Limited Models

Physiological pharmacokinetic models, often called flow-limited or perfusion models, typically assume a swift drug distribution between tissue and venous blood, creating a rapid drug equilibrium. This premise is based on the idea that drug diffusion is extremely fast, and the cell membrane presents no barrier to drug permeation. In this scenario, where no drug binding occurs, the drug concentration in the tissue equals that of the venous blood leaving the tissue. This greatly simplifies the...