Page 201 - Color_Atlas_of_Physiology_5th_Ed._-_A._Despopoulos_2003

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Blood Vessels and Blood Flow power of the inner radius of the tube (r ).
Decreasing the radius by only about 16% will
In the systemic circulation, blood is ejected therefore suffice to double the resistance.
from the left ventricle to the aorta and returns The lesser arteries and arterioles account
to the right atrium via the venae cavae (! A). for nearly 50% of the TPR (resistance vessels;
As a result, the mean blood pressure (! p. 206) ! A1 and p. 187 A) since their small radii have
4
drops from around 100 mmHg in the aorta to a much stronger effect on total TPR (R ! 1/r )
2
2–4 mmHg in the venae cavae (! A2), result- than their large total CSA (R ! r ). Thus, the
ing in a pressure difference (∆P) of about blood pressure in these vessels drops signifi-
97 mmHg (pulmonary circulation; ! p. 122). cantly. Any change in the radius of the small ar-
According to Ohm’s Law, teries or arterioles therefore has a radical ef-
.
∆P ! Q ! R (mmHg) [8.1] fect on the TPR (! p. 212ff.). Their width and
.
– 1
where Q is the blood flow (L · min ) and R is that of the precapillary sphincter determines
Cardiovascular System at rest is about 18 mmHg · min · L . . radii (and thus much higher individual re-
the flow resistance (mmHg · min · L ). Equa-
the amount of blood distributed to the capil-
–1
lary beds (exchange area).
tion 8.1 can be used to calculate blood flow in a
Although the capillaries have even smaller
given organ (R = organ resistance) as well as in
the entire cardiovascular system, where Q is
sistances than the arterioles), their total con-
the cardiac output (CO; ! p. 186) and R is the
total peripheral flow resistance (TPR). The TPR
tribution to the TPR is only about 27% because
–1
their total CSA is so large (! A1 and p. 187 A).
The aorta and greater arteries distribute the
across the walls of capillaries and postcapillary
blood to the periphery. In doing so, they act as
8 a hydraulic filter because (due to their high The exchange of fluid and solutes takes place
venules. Both vessel types are particularly suit-
.
compliance, ∆V/∆P tm) they convert the inter- able for the task because (a) their V is very
mittent flow generated by the heart to a nearly small (0.02–0.1 cm/s; ! A3) (due to the large
steady flow through the capillaries. The high total CSA), (b) their total surface area is very
2
systolic pressures generated during the ejec- large (approx. 1000 m ), (3) and their walls can
tion phase cause the walls of these blood ves- be very thin as their inner radius (4.5µm) is
sels to stretch, and part of the ejected blood is extremely small (Laplace’s law, see below).
“stored” in the dilated lumen (windkessel). Transmural pressure P tm [N/m ], that is, the
2
Elastic recoil of the vessel walls after aortic pressure difference across the wall of a hollow
valve closure maintains blood flow during di- organ (= internal pressure minus external
astole. Arterial vessel compliance decreases pressure), causes the wall to stretch. Its mate-
with age. . . rials must therefore be able to withstand this
Flow velocity (V) and flow rate (Q) of the stretch. The resulting tangential mural tension
blood. Assuming an aortic cross-sectional area T [N/m] is a function of the inner radius r [m] of
2
2
(CSA) of 5.3 cm and a total CSA of 20 cm of all . the organ. According to Laplace’s law for cylin-
downstream arteries (! A5), the mean V drical (or spherical) hollow bodies,
(during systole and diastole) at rest can be cal- P tm ! T/r (or P tm ! 2 T/r, resp.) [8.3a/b]
culated from a resting CO of 5.6 L/min: It Here, T is the total mural tension, regardless how
equals 18 cm/s in the aorta and 5 cm/s in the thick the wall is. A thick wall can naturally withstand
arteries (! A3). As the aorta receives blood a given P tm more easily than a thin one. In order to
only during the ejection phase (! p. 90), the determine the tension exerted per unit CSA of the
.
.
maximum resting values for V and Q in the wall (i.e., the stress requirements of the wall material
2
aortic root are much higher during this phase in N/m ), the thickness of the wall (w) must be con-
.
.
(V = 95 cm/s, Q = 500 mL/s). sidered. Equation 8.3 a/b is therefore transformed to
In the Hagen–Poiseuille equation, P tm ! T ! w/r (or P tm ! 2 T ! w/r, resp.) [8.4a/b]
4
R ! 8 ! l ! η/(π ! r ) [8.2] The blood collects in the veins, which can ac-
the flow resistance (R) in a tube of known commodate large volumes of fluid (! A6).
length (l) is dependent on the viscosity (η) of These capacitance vessels serve as a blood res-
188 the fluid in the tube (! p. 92) and the fourth ervoir (! p. 186).
Despopoulos, Color Atlas of Physiology © 2003 Thieme
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