Blood coagulation dynamics: mathematical modeling and stability results.

Adélia Sequeira1, Rafael F Santos, Tomás Bodnár

  • 1Department of Mathematics and CEMAT/IST, Instituto Superior Tecnico, Technical University of Lisbon, Lisboa, Portugal. adelia.sequeira@math.ist.utl.pt

Summary

This study revisits a mathematical model of blood coagulation and fibrinolysis, integrating biochemical, physiologic, and rheological factors. Numerical simulations in a stenosed vessel provide insights into clot formation and stability.

Related Concept Videos

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...
Extrinsic and Intrinsic Pathways of Hemostasis01:20

Extrinsic and Intrinsic Pathways of Hemostasis

Blood clotting or coagulation involves extrinsic and intrinsic pathways, which ultimately merge into the common pathway, forming a fibrin clot.
The Extrinsic Pathway
The extrinsic pathway of coagulation is typically initiated by tissue damage that exposes blood to tissue factor (TF), a protein released by the damaged tissue cells outside the blood vessels—this interaction with TF triggers biochemical reactions involving specific clotting factors. The key player here is Factor VII, which forms a...
BIBO stability of continuous and discrete -time systems01:24

BIBO stability of continuous and discrete -time systems

System stability is a fundamental concept in signal processing, often assessed using convolution. For a system to be considered bounded-input bounded-output (BIBO) stable, any bounded input signal must produce a bounded output signal. A bounded input signal is one where the modulus does not exceed a certain constant at any point in time.
To determine the BIBO stability, the convolution integral is utilized when a bounded continuous-time input is applied to a Linear Time-Invariant (LTI) system.
Disorders of Hemostasis01:24

Disorders of Hemostasis

Hemostasis, the process that stops bleeding after a blood vessel injury, is crucial for maintaining the integrity of the circulatory system. However, disorders of hemostasis can disrupt this delicate balance, leading to either excessive clotting or bleeding. These disorders can be broadly classified into thromboembolic disorders and bleeding disorders.
Thromboembolic Disorders
Two factors primarily cause thromboembolic conditions.
Applications of Integration to Find Blood Flow01:27

Applications of Integration to Find Blood Flow

Blood flow through a cylindrical blood vessel can be mathematically described using the principles of laminar flow, a regime in which fluid moves smoothly in parallel layers. In this model, the velocity of the blood is not uniform across the cross-section of the vessel; rather, it varies with the radial distance from the center. The maximum velocity occurs along the central axis, decreasing progressively toward the vessel walls, where it reaches zero due to viscous drag.Approximating Blood...
Introduction to Hemostasis01:05

Introduction to Hemostasis

Hemostasis is a complex physiological process that prevents excessive bleeding when a blood vessel is injured. It's crucial for maintaining the integrity of the circulatory system, as it ensures that our blood remains fluid while still within the vascular network and yet clots to prevent blood loss upon vessel injury.
The three phases of hemostasis involve many clotting factors present in plasma and several substances released by platelets and injured tissue cells. It is a fast, localized, and...