[A mathematical description of blood movement in a microvascular skeletal muscle unit]

Skeletal muscle is the most abundant type of muscle in the body. Tendons are the connective tissue that attaches skeletal muscle to bones. Skeletal muscles pull on tendons, which in turn pull on bones to carry out voluntary movements.

The human circulatory system consists of blood, blood vessels that carry blood away from the heart, around the body, and back to the heart, and the heart itself, which acts as a central pump. The systemic circuit supplies blood to the whole body, the coronary circuit supplies blood to the heart, and the pulmonary circuit supplies blood flow between the heart and lungs.

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.

Skeletal muscle cells, also called muscle fibers, are distinctly elongated, multi-nucleated, slender biological units. They are packed with specialized structures designed to facilitate their primary function, which is contraction.
The muscle sarcolemma is a plasma membrane enclosing each muscle cell that conducts electrical signals called action potentials. The sarcolemma extends into the cell to form T-tubules, ensuring the neural impulses are uniformly distributed across the entire muscle...

Excitation-contraction coupling is a series of events that occur between generating an action potential and initiating a muscle contraction. It occurs at the triad, a structure found in skeletal muscle fibers that comprise a T-tubule and terminal cisternae of the sarcoplasmic reticulum on each side. These triads are visible in longitudinally sectioned muscle fibers. They are typically located at the A-I junction — the junction between the A and I bands of the sarcomere.
When an action potential...

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...