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.5)where ± is the angle (ETG) = angle (EAB), because their sides are paral-lel, and is also equal to angle (EOP), because their sides are perpendicu-lar.Solving eq.(2.5) for T and replacing D, yields,T = D / 2sin(±) = PH / sin(±)(2.6) 28 Understanding the Human Machinebut inspection of Figure 2.5 easily shows that sin ± = H/R which, aftersubstitution in eq.(2.6), ends up inT = P × R (2.7)which describes in the plane the statement in italics given above.Nowwe face an arguable step:For one principal plane containing the principal radius R1, we haveT1 = P×R1 , which is eq.(2.7); for the other, perpendicular to the former,and following exactly the same rationale as developed above, we obtain,T2 = P×R2.Solving each for P and adding them up leads to,P = (T1 2) R1 + (T2 2) R2(2.8)because pressure, by Pascal s Law of hydrostatics, has to be the same.Moreover, if it is accepted that T1 = T2 = Tp and defining T = Tp/2, weend up withëø öø1 1ìø ÷øP = Tìø +(2.9)R1 R2 ÷øíø øøThe latter equation is fully coincident with eq.(2.2).The weakness in thelast part of the derivation is pointed out and, therefore, left to a more in-quisitive (and powerful) young mind as a possible little project .Ten-sors might supply a good tool for it.If the balloon is a sphere, the two radii are equal to R and eq.(2.9) re-duces to the well known T = PR/2.If now the concept of wall stress isintroduced in a balloon or hollow organ with wall thickness, h, as definedabove in (2.3), we get,Ws = k1 (P × R) h(2.10)always keeping in mind the existence of a proportionality constant.Itsnumerical value should be determined for each particular case withoutworrying about the come and go of a 2 in it.In the heart, intraventricularhypertension and ventricular dilatation increase wall stress (a riskycondition); with time, such hypertension produces hypertrophy, meaninga thickening (larger h) of the ventricular wall, obviously tending to reliefparietal tension.Hence, hypertrophy is a compensatory mechanism.Suggested exercise: Search in the published literature a possible value for left ventricularvolume in an adult healthy man.Thereafter, calculate the equivalent diameter (as if it werea sphere).Suggested exercise: Applying Laplace s Law, estimate the ratio of left ventricular wall thick-ness, hL, to right ventricular wall thickness, hR.Explain the result. Chapter 2.Source: Physiological Systems and Levels 292.2.1.6.Vessels: arteries and veinsBy definition, artery is a vessel carrying blood from the heart to the pe-riphery and vein is a vessel carrying it back to the heart, irrespective ofwhether it is or not well oxygenated.Figure 2.2 displays the arterial sec-tion on the right and the venous section on the left.Well embedded in thedifferent tissues is the microcirculation, which includes (i) the last andsmallest in diameter (the arterioles) portion of the arterial side; (ii) thecapillaries, as the only exchange section through their highly permeablethin walls; and (iii) the first and smallest in diameter (the venules) seg-ment of the venous side.The microcirculation constitutes a separatechapter of utmost importance in vascular physiology.One of the mostremarkable properties, especially in beds like the brain, heart or kidneys,is the ability to control the amount of blood reaching the network.This iscalled autoregulation, independent of mechanisms controlled by highercenters.Unlike any technological hydraulic system, all blood vessels are elastic,a property bestowing upon them a powerful regulatory tool, both as pas-sive mechanism and also as an active one via smooth muscles coveringthe external side of their walls.One way to evaluate passive elasticity isby application of the concept of compliance, C, defined as,C = dV dP(2.11)that is, the differential change in volume V per differential change inpressure P.Its units, as expected, are for example [cm3/mmHg].The in-verse of C is called elastance, E.One of the several reported values forthe latter in normal men puts it in about 1,500 dynes/cm5.The interestedstudent will find more details in the current literature, as for example,other definitions to describe the elastic properties that, interestinglyenough, have been kept essentially the same over the years(Valentinuzzi, Ghista & Nichols, 1979).Mostly, newer reports refer tothe action of drugs on these parameters or to the relative contributions ofelastin and collagen components (Armentano, Cabrera Fischer, Levensonet al., 1990; Armentano, Levenson, Barra et al., 1991; Cabrera Fischer,Levenson, Barra et al., 1993).A vessel with high compliance increases greatly its volume with a smallincrement in pressure.Veins are much more compliant than arteries and,as a consequence, most of the blood volume (about 8% of body weight)lodges dynamically within the venous system. 30 Understanding the Human MachineSuggested exercise: A person is placed horizontal in a centrifuge with his legs pointing tothe center and his head pointing outwardly.After rotation during a while, is he still alive? Ifnot, could you explain why? (It sounds weird and awful, but it is descriptive).Study subject: A reference is given above (Armentano, Cabrera Fischer, Levenson et al.,1990).In its title, it mentions the aortic elastic response to epinephrine .What is such re-sponse? Think in terms of an athlete who is getting ready to act.Do you remember Hooke's Law of elasticity? Try to correlate it with eq.(2.11) above.Another characteristic of the circulatory vessels is their smooth muscula-ture.These muscles are controlled by the autonomic nervous system andby hormonal secretions of different kind and origin.These muscles mod-ify the vessels caliber or lumen (see the suggested study subject above).Hence, the compliance of a vessel in active state is different than itscompliance when inactive
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