Fetal circulation is a unique system that facilitates the exchange of gases, nutrients, and waste products between the developing fetus and the mother. This intricate process takes place through a special organ called the placenta.
Two umbilical arteries transport blood from the fetus to the placenta. At the placenta, the blood absorbs oxygen and nutrients while simultaneously eliminating waste products. This oxygen-enriched and nutrient-rich blood then returns to the fetus through one...

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,...

The development of the vascular system in a fetus is a complex and intricate process that begins as early as 15 to 16 days post-conception. This process starts outside the embryo, specifically in the mesoderm of the yolk sac, chorion, and connecting stalk. Approximately two days later, the formation of blood vessels occurs within the embryo itself.
The initial formation of this system is facilitated by the small amount of yolk present in the ovum and yolk sac. Blood vessels originate from...

The development of lymphatic tissues and vessels in embryonic life begins around the fifth week. These structures originate from the mesoderm layer, with lymph sacs emerging from developing veins.
The first lymph sacs to form are the paired jugular lymph sacs located at the junction of the internal jugular and subclavian veins. From these sacs, lymphatic capillary plexuses extend to the thorax, upper limbs, neck, and head, eventually forming lymphatic vessels. Each jugular lymph sac maintains a...

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.