Fig. 17.23 ). Transmural pressure in a blood vessel in vivo is essentially equal to intraluminal pressure because extravascular pressure is generally negligible. To calculate wall tension, pressure in mm Hg is converted to dynes per square centimeter according to the equation P = hρg, where h is the height of an Hg column in centimeters, ρ is the density of Hg in g/cm3, and g is gravitational acceleration in cm/s2. For a capillary with a pressure of 25mmHg and a radius of 5 × 10−4 cm, the pressure (2.5 cm Hg × 13.6 g/cm3 × 980 cm/sec2) is 3.33 × 104 •Fig. 17.23 Diagram of a Small Blood Vessel to Illustrate the Law of Laplace. T=Pr,whereP=intraluminalpressure,r=radiusofthevessel,andT=walltensionastheforceperunitlengthtangentialtothevesselwall.Walltensionpreventsrupturealongatheoreticallongitudinalslitinthevessel.
dyne/cm2. Wall tension is then 16.7 dyne/cm. For an aorta with a pressure of 100 mm Hg and a radius of 1.5 cm, wall tension is 2 × 105 dyne/cm. Thus at the pressures normally found in the aorta and capillaries, the wall tension of the aorta is approximately 12,000 times greater than that of the capillaries. In a person standing quietly, capillary pressure in the feet may reach 100 mm Hg. Even under such conditions, capillary wall tension increases to a value that is still only one three-thousandth of the wall tension in the aorta at the same internal pressure.
The diameter of the resistance vessels (arterioles) is determined from the balance between the contractile force of the vascular smooth muscle and the distending force produced by intraluminal pressure. The greater the contractile activity of the vascular smooth muscle of an arteriole, the smaller its diameter. In small arterioles, contraction can continue to the point at which the vessel is completely occluded. Occlusion is caused by infolding of the endothelium and by trapping of blood cells in the vessel.
With a progressive reduction in intravascular pressure, vessel diameter decreases (as does vessel wall tension, according to the law of Laplace) and blood flow eventually ceases, although pressure within the arteriole is still greater than tissue pressure. The pressure that causes flow to cease has been called the critical closing pressure, and its mechanism is still unclear. The critical closing pressure is low when vasomotor activity is reduced by inhibition of sympathetic nerve activity in the vessel and is increased when vasomotor tone is enhanced by activation of the vascular sympathetic nerve fibers.
Iftheheartbecomesgreatlydistendedwithbloodduringdiastole,asmayoccurwithcardiacfailure,itfunctionslessefficiently.Toejectagivenvolumeofbloodperbeat,moreenergyisrequired(walltensionmustbegreater)forthedistendedheartthanforanormalundilatedheart.ThelessefficientpumpingofadistendedheartisanexampleofLaplace’slaw,accordingtowhichthetensioninthewallofavesselorchamber(inthiscase,theventricles)equalstransmuralpressure(pressureacrossthewall,ordistendingpressure)multipliedbytheradiusofthevesselorchamber.Laplace’srelationshipordinarilyappliestoinfinitelythin-walledvessels,butitcanbeappliedtothespherical,dilatedheartifcorrectionismadeforwallthickness.Undertheseconditions,theequationisσ=ΔPr/2w,whereσ= wallstress,ΔP= transmuralpressuredifference,r= radius,andw= wallthickness.
Vasoactive Role of the Capillary Endothelium