Ganong's Review of Medical Physiology, 23rd Edition

CHAPTER 32Blood as a Circulatory Fluid & the Dynamics of Blood & Lymph Flow 541

is the rate at which the axial velocity increases from the vessel
wall toward the lumen.

γ = η (dy/dr)
Change in shear stress and other physical variables, such as
cyclic strain and stretch, produce marked changes in the
expression of genes by endothelial cells. The genes that are
activated include those that produce growth factors, integrins,
and related molecules (Table 32–11).

AVERAGE VELOCITY

When considering flow in a system of tubes, it is important to
distinguish between velocity, which is displacement per unit
time (eg, cm/s), and flow, which is volume per unit time (eg,
cm^3 /s). Velocity (V) is proportional to flow (Q) divided by the
area of the conduit (A):

Therefore, Q = A × V, and if flow stays constant, velocity
increases in direct proportion to any decrease in A (Figure
32–22).
The average velocity of fluid movement at any point in a
system of tubes in parallel is inversely proportional to the total

cross-sectional area at that point. Therefore, the average

velocity of the blood is high in the aorta, declines steadily in

the smaller vessels, and is lowest in the capillaries, which have

1000 times the total cross-sectional area of the aorta (Table

32–9). The average velocity of blood flow increases again as

the blood enters the veins and is relatively high in the vena

cava, although not so high as in the aorta. Clinically, the

velocity of the circulation can be measured by injecting a bile

salt preparation into an arm vein and timing the first appear-

ance of the bitter taste it produces (Figure 32–23). The aver-

age normal arm-to-tongue circulation time is 15 s.

POISEUILLE–HAGEN FORMULA

The relationship between the flow in a long narrow tube, the

viscosity of the fluid, and the radius of the tube is expressed

mathematically in the Poiseuille–Hagen formula:

where

F = flow

PA – PB = pressure difference between two ends of the tube

η = viscosity

r = radius of tube

L = length of tube

Because flow is equal to pressure difference divided by

resistance (R),

Because flow varies directly and resistance inversely with

the fourth power of the radius, blood flow and resistance in

TABLE 32–11 Genes in human, bovine, and
rabbit endothelial cells that are affected by
shear stress, and transcription factors involved.a

Gene Transcription Factors

Endothelin-1 AP-1

VCAM-1 AP-1, NF-κB

ACE SSRE, AP-1, Egr-1

Tissue factor SP1, Egr-1

TM AP-1

PDGF-α SSRE, Egr-1

PDGF-β SSRE

ICAM-1 SSRE, AP-1, NF-κB

TGF-β SSRE, AP-1, NF-κB

Egr-1 SREs

c-fos SSRE

c-jun SSRE, AP-1

NOS 3 SSRE, AP-1, NF-κB

MCP-1 SSRE, AP-1, NF-κB

aAcronyms are expanded in the Appendix.

Modified from Braddock M et al: Fluid shear stress modulation of gene expression
in endothelial cells. News Physiol Sci 1998;13:241.

V Q

A

=----

FIGURE 32–23 Pathway traversed by the injected material

when the arm-to-tongue circulation time is measured.

Site of

injection

(antecubital vein)

Site of end point

(tongue)

FP( A PB) π

⎝⎠ 8 ---

⎛⎞^1

⎝⎠η---

⎛⎞ r^4

L

–= ××× ⎝⎠⎛⎞----

R^8 ηL

πr^4

=----------