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Murray's law has been verified in chicks; dog intestines and lungs; cat mesentery; and human intestines and lung capillaries. [15] [16] Mice genetically engineered to lack the blood-vessel-wall protein elastin have smaller and thinner blood vessels, but still obey Murray's law. [17]
Therefore, the quantity (F/A) that is the force per unit area is called the stress. The shear stress at the wall that is associated with blood flow through an artery depends on the artery size and geometry and can range between 0.5 and 4 Pa. [29] =.
The force exerted by the blood flow on the vessel walls is, according to the Poiseuille equation, the wall shear stress. This wall shear stress is proportional to the pressure drop. The pressure drop is applied on the section surface of the vessel, and the wall shear stress is applied on the sides of the vessel. So the total force on the wall ...
The formula to calculate average shear stress τ or force per unit area is: [1] =, where F is the force applied and A is the cross-sectional area.. The area involved corresponds to the material face parallel to the applied force vector, i.e., with surface normal vector perpendicular to the force.
These endothelial products include nitric oxide and endothelin-1 that are released in response to either chemical stimuli, like histamine, or increased shear stress on the blood vessel (meaning the amount of stress exerted by blood on the blood vessel walls). While nitric oxide causes vasodilation, endothelin-1 causes vasoconstriction.
Blood viscosity is a measure of the resistance of blood to flow. It can also be described as the thickness and stickiness of blood. This biophysical property makes it a critical determinant of friction against the vessel walls, the rate of venous return, the work required for the heart to pump blood, and how much oxygen is transported to tissues and organs.
As the vessels decrease in size, they increase their surface-area-to-volume ratio. This allows surface properties to play a significant role in the function of the vessel. Diffusion occurs through the walls of the vessels due to a concentration gradient, allowing the necessary exchange of ions, molecules, or blood cells.
When the diameter of the blood vessel is just slightly larger than the diameter of the red blood cell the Fahraeus–Lindquist effect occurs and there is a decrease in wall shear stress. However, as the diameter of the blood vessel decreases further, the red blood cells have to squeeze through the vessel and often can only pass in a single file.