Chapter 8

### FUNCTIONAL MECHANICS OF NORMAL AND ABNORMAL VASCULAR FLOW

Mathematically describing fluid systems is very complex. Hemodynamics can be defined as the physical factors that influence blood flow that are based on fundamental laws of physics, namely Ohm's law. voltage (ΔV) equals the product of current (I) and resistance (R).

ΔV = I × R

In relating Ohm's law to fluid flow, the voltage is the pressure difference between two points (ΔP), 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:

Q = (πΔPr4)/(8ηL)

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 (ΔP), 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. 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.

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

Reynolds = [2(Velocity)(Density)(Diameter)] ÷ Viscosity

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 above 2000 causes turbulence and vessel wall vibration, producing a bruit. High velocities cause turbulence and hinder volumes flow, creating eddies.

### ANATOMY OF THE VENOUS SYSTEM IN THE LOWER EXTREMITIES

#### Deep Veins

The anterior tibial veins drain blood from the dorsum of the foot (dorsalis pedis veins) and anterior compartment of calf. The anterior tibial veins originate near the tibia at the ankle, lying anterior to the interosseous membrane as they ascend the lower leg and move toward the fibula. The anterior tibial vein joins the posterior tibial vein to become the popliteal vein. The posterior tibial vein originates from the plantar (superficial and deep) veins of the foot. They run from the medial malleolus along the medial calf with the posterior tibial artery. The posterior tibial veins ...

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