Hemodynamics in patent ductus arteriosus without a murmur

Blood is pumped by the heart into the aorta, the largest artery in the body, and then into increasingly smaller arteries, arterioles, and capillaries. The velocity of blood flow decreases with increased cross-sectional blood vessel area. As blood returns to the heart through venules and veins, its velocity increases. The movement of blood is encouraged by smooth muscle in the vessel walls, the movement of skeletal muscle surrounding the vessels, and one-way valves that prevent backflow.

The movement of blood in a human body, commonly referred to as blood flow, is determined by the volume of blood that traverses a certain section of the bodily system per unit time. It is the rhythmic contraction of the heart's ventricles that primarily instigates this movement. As the ventricles contract, blood is forced into the prominent arteries, which then flow from areas of greater pressure to lower pressure areas. This movement continues into smaller arteries and arterioles and...

The vascular system, an integral part of the circulatory system, comprises various blood vessels that play crucial roles in maintaining the body's homeostasis. These blood vessels form a complex and efficient circulatory network. The three primary categories of blood vessels are the arteries, veins, and capillaries.
Arteries
Arteries circulate oxygenated blood from the heart, except the pulmonary artery, which transports deoxygenated blood to the lungs. Large arteries, such as the aorta, have...

In steady, incompressible flow through a long, straight pipe with a uniform cross-section, the flow in the central region (far from the pipe walls) is irrotational. This irrotational nature means that fluid particles do not rotate around their axes, and a scalar function called the velocity potential, represented by ϕ, can be used to describe their movement. In irrotational flows, the velocity field V is defined as the gradient of the velocity potential:

Hagen-Poiseuille flow describes a viscous fluid's steady, incompressible flow through a cylindrical tube with a constant radius R. This flow profile is often applied to understand fluid transport in narrow channels, such as capillaries. It serves as a foundational example of laminar flow. In this model, cylindrical coordinates (r,θ,z) are used to describe the radial (r), angular (θ), and axial (z) dimensions within the tube. For Hagen-Poiseuille flow, the velocity profile is purely axial,...

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...