[A numerical study of the stability of some autowave solutions in a mathematical model of blood coagulation]

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...

Autoregulation mechanisms are characterized by their inherent capacity for self-regulation without necessitating specific nervous stimulation or endocrine control. These mechanisms facilitate the adjustment of blood flow and, therefore, perfusion specific to each tissue region. This self-regulation encompasses chemical signals and myogenic controls.
Chemical Signaling in Autoregulation
Chemical signaling operates at the precapillary sphincter level, inciting either contraction or relaxation.

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...

The coagulation phase is a critical part of the body's process to prevent blood loss following injury to blood vessels. It involves chemical reactions that form a clot to seal the injured area. The clotting process begins shortly after injury, within 15-20 seconds for severe damage and 1-2 minutes for minor injuries.
During the coagulation phase, clotting factors, or procoagulants, play a vital role in initiating and progressing the coagulation cascade. This cascade is a series of reactions...

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...

Fluid mechanics model studies often utilize scaled-down systems to predict fluid behavior in full-scale environments, such as river flows, dam spillways, and structures interacting with open surfaces. Maintaining Froude number similarity in river models is crucial, as it replicates surface flow features like wave patterns and velocities.