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Describing pulsatile fluid systems mathematically is very complex. Hemodynamics can be defined as the physical factors that influence blood flow which is based on fundamental laws of physics, namely Ohm's law: Voltage (Δ V) equals the product of current (I) and resistance (R), i.e.,


In relating Ohm's law to fluid flow, the voltage is the pressure difference between two points (δ P), the resistance is the resistance to flow (R), and the current is the blood flow (F):


Resistance to blood flow within a vascular network is determined by the length and diameter of individual vessels, the physical characteristics of the blood (viscosity, laminar flow versus turbulent flow), the series and parallel arrangements of vascular network, and extravascular mechanical forces acting upon the vasculature. This is expressed in Poiseuille's law:


Poiseuille's Law relates the rate at which blood flows through a small blood vessel (Q) with the difference in blood pressure at the two ends (Δ P), the radius (r) and the length (L) of the artery, and the viscosity (η) of the blood.

Of the above factors, changes in vessel diameter are most important quantitatively for regulating blood flow as well as arterial pressure within an organ. Changes in vessel diameter, either by constriction or dilatation, enable organs to adjust their own blood flow to meet the metabolic requirements of the tissue. Flow velocity increases as the pressure gradient increases and flow volumes are relatively preserved, only to a point though.

Osborne Reynolds determined how viscosity, vessel radius, and pressure/volume relations influenced the stability of flow through a vessel:


Density and viscosity are relatively constant, therefore the development of turbulence depends mainly on the velocity and size of the vessel. Density is defined as mass per unit volume and viscosity is defined as a measure of the resistance of a fluid to being deformed by either shear stress or extensional stress. A Reynolds number >2000 causes turbulence and vessel wall vibration producing a bruit. High velocities cause turbulence and hinder volumes flow, creating eddies.


Basics of Vascular Ultrasound

Ultrasonic waves entering human tissue are absorbed, reflected, and scattered to produce images of anatomic structures. The transmission properties of the sound waves depend on the density and elasticity of the tissues. Density and speed of propagation of ultrasound waves determine a tissue's acoustic impedance. The larger the differences in acoustic impedance between tissues, the more ultrasound waves are reflected. The reflection further depends on the angle of insonation. Strong reflective interfaces, such as air or bone, prevent imaging of weaker ...

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