Changes in vascular resistance occur when the caliber of vessels changes. The most important factor that leads to a change in vessel caliber is contraction of the circular smooth muscle cells in the vessel wall. Changes in internal pressure also alter the caliber of blood vessels and therefore alter the resistance to blood flow through these vessels. Blood vessels are elastic tubes. Hence, the greater the transmural pressure (i.e., the difference between internal and external pressure) across the wall of a vessel, the greater the caliber of the vessel and the less its hydraulic resistance.
It is apparent from
Fig. 15.3 that the greatest drop in pressure occurs in the very small arteries and arterioles. However, capillaries, which have a mean diameter of approximately 7 µm, have the greatest resistance to blood flow. Nevertheless, of all the different varieties of blood vessels that lie in series with one another (as in
Fig. 15.3 ), the arterioles, not the capillaries, have the greatest resistance. This seeming paradox is related to the relative numbers of parallel capillaries and parallel arterioles: There are far more capillaries than arterioles in the systemic circulation, and total resistance across the many capillaries arranged in parallel is much less than total resistance across the fewer arterioles arranged in parallel. In addition, arterioles have a thick coat of circularly arranged smooth muscle fibers that can vary the lumen radius. Even small changes in radius alter resistance greatly, as can be seen from the hydraulic •Fig. 17.5 Forresistances(R1,R2,andR3)arrangedinseries,totalresistance(Rt)equalsthesumoftheindividualresistances.P,pressure;Q,flow.
Eq. 17.6 ), wherein R varies inversely with r4.
In the cardiovascular system, the various types of vessels listed along the horizontal axis in
Fig. 15.3 lie in series with one another. The individual members of each category of vessels are ordinarily arranged in parallel with one another (see
Fig. 15.1 ). Thus capillaries are in most instances parallel elements throughout the body, except in the renal vasculature (in which the peritubular capillaries are in series with the glomerular capillaries) and the splanchnic vasculature (in which the intestinal and hepatic capillaries are aligned in series with each other). The total hydraulic resistance of components arranged in series or in parallel can be derived in the same manner as those for analogous combinations of electrical resistance.
Resistance of Vessels in Series
In the system depicted in
Fig. 17.5 , three hydraulic resistances, R1, R2, and R3, are arranged in series. The pressure drop across the entire system (i.e., the difference between inflow pressure [Pi] and outflow pressure [Po]) consists of the sum of the pressure drops across each of the individual resistances (equation a in
Fig. 17.5 ). In the steady state, the flow (Q) through any given cross-section must equal the flow through any other cross-section. When each component in equation (a) is divided by Q (equation [b] in
Fig. 17.5 ), it is evident from the definition of resistance (
Eq. 17.5 ) that for resistances in series, the total resistance (Rt) of the entire system equals the sum of the individual resistances; that is,
Equation 17.7
Resistance of Vessels in Parallel
For resistances in parallel, as illustrated in
Fig. 17.6 , inflow and outflow pressure is the same for all tubes. In steady state, the total flow (Qt) through the system equals the sum of the flows through the individual parallel elements (equation [a] in
Fig. 17.5).
Because the pressure gradient (Pi − Po) is identical for all parallel elements, each term •Fig. 17.6 Forresistances(R1,R2,andR3)arrangedinparallel,thereciprocalofthetotalresistance(Rt)equalsthesumofthereciprocalsoftheindividualresistances.P,pressure;Q,flow.
in equation (a) may be divided by that pressure gradient to yield equation (b). From the definition of resistance, equation (c) in