Page 40 - Libro 2

20
PART I — INTRODUCTION TO THE VASCULAR SYSTEM
r l
r
2l
2r
Q = 5 ml/s l
waste that occurs within the capillaries. The cross- sectional area of the vascular system then decreases from the capillary to the venules, then the veins, and lastly into the superior and inferior venae cavae. As the blood is returned to the heart via the venous sys- tem, the velocity increases.
POISEUILLE’S LAW
Poiseuille’s law describes the steady laminar flow of Newtonian fluids. Steady flow refers to a system where flow is nonpulsatile. Laminar flow describes flow that moves in a series of layers (this will be discussed in more detail later in the chapter). A Newtonian fluid is a homogeneous fluid such as air or water. Flow in the arterial system is pulsatile and thus not steady. Blood does tend to move in a laminar fashion, at least in some portions of the ar- terial system. Blood is definitely not homogeneous and thus is non-Newtonian. However, even with all these variations, Poiseuille’s law is used to define pressure/flow relationships in the vascular system.
The full definition of Poiseuille’s law states:
8􏰂l
RESISTANCE TO FLOW
Q􏰀
􏰃(P 􏰄P)r4 4
1 __
_
2 􏰃r
where Q is flow, r is the radius of the vessel, l is the length of the vessel, P1􏰅P2 is the pressure dif- ference, 􏰂 is the viscosity of the blood, and 􏰃/8 is the constant of proportionality. Examining the terms of Poiseuille’s law, a greater change in pressure will produce an increase in flow (providing the other components stay the same). If the viscosity of the blood increases, flow will decrease. If the radius of a vessel changes, this will have a significant impact on flow because it is the radius to the 4th power that is directly proportional to flow (Fig. 2-4).
Q = 10 ml/s
Figure 2-4 Effects of radius and length on flow.
Hemodynamic resistance is analogous to electrical resistance as described by Ohm’s law. Ohm’s law states that the current (flow) through two points is directly proportional to the potential difference or voltage across the two points and inversely pro- portional to the resistance between them. In other words:
I 􏰀 _V R
where I is the current, V is the voltage, and R is the resistance. If the terms are rearranged to solve for resistance, the expression becomes R 􏰀 V/I. In the vascular system, this is represented as resistance be- ing equal to the pressure drop divided by the flow:
R 􏰀 _􏰁 P Q
Looking back to the components of Poiseuille’s law, it can be determined that resistance can be expressed as:
In the circulatory system, the length of a given vessel is virtually constant and the blood viscosity does not vary. Thus, changes in resistance are virtually all due to variations in the radius. It is the smooth muscle cell layer within the media of the wall of a vessel that varies resistance by altering vessel radius.
In the vascular system, various types of vessels lie in series with one another. In addition, individual members of each category of vessels are arranged in parallel with each other. The notable exceptions to this are the renal and splanchnic vasculatures where capillary systems are arranged in a series.
8􏰂l R􏰀_
Q = 160 ml/s