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Structure function relationships in arteries

E inc = k 1 ∆Pr/h.r/∆r. = k 3 PWV 2. E p = k 2 ∆P.r/∆r. Functional Stiffness (E). Geometry (h/r). Occlusive disease/hyp. Z c = k 3 (E p ) 1/2 ≈ ∆P/∆Q. Pulse wave reflection. Elastic reservoir (Impedance, Z). Pulsatile. Peripheral resistance, R. Smooth muscle tone. Steady.

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Structure function relationships in arteries

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  1. Einc = k1∆Pr/h.r/∆r = k3PWV2 Ep = k2∆P.r/∆r Functional Stiffness (E) Geometry (h/r) Occlusive disease/hyp. Zc = k3(Ep)1/2 ≈ ∆P/∆Q Pulse wave reflection Elastic reservoir (Impedance, Z) Pulsatile Peripheral resistance, R Smooth muscle tone Steady Structure function relationships in arteries Chemical composition Material Stiffness (Y) = Einc.h/R Structure Heart work

  2. Changes in pressure waveform shape with age Safar, ME and Struijker-Boudier, Hypertension, 46, 205-209 (2005)

  3. As it moves away from the heart,the pressure wave changes shape

  4. Pulse pressure amplification and age Safar, ME and Laurent, S. Am.\J. Physiol, 285, H1363-H1369, 2003

  5. Why does the mean pressure drop so much in the arterioles? • Poiseuille’s law: resistance, (W) = kL/R4 = DP/Q • Assume • aortic radius = 15mm & length = 500mm • arteriolar radius = 7.5µm & length = 1mm • Radius ratio = 15000/7.5 = 2000 • Length ratio = 500/1 = 500 • Resistance ratio = (2000)4/500 = 3.2x1010 (aorta:arterioles) BUT • There are about 300 million (3x108) arterioles • Therefore their total resistance is one 300 millionth of the resistance of a single arteriole • Actual resistance ratio = 3.2x1010/3x108 ≈ 100

  6. Q Q Q = = aorta arterioles P x Q D = W aorta aorta P x Q D = W arterioles arterioles P D W arterioles arterioles 100 = ≈ P D W aorta aorta Arteriolar pressure drop (2) • Poiseuille’s law: resistance, (W) = kL/R4 = DP/Q †

  7. Capillary pressure drop • Capillaries have approx. same diam. as arterioles (but remember the glycocalyx) • There are approx. 3x109 capillaries so their combined resistance is about 1/10th of the arterioles • Venules are bigger than their arterioles and their resistance is approx 1/20th of the arterioles [1]. Westerhof, N., Stergiopulos, N. and Noble, M.I.M., Snapshots of Haemodynamics. An aid for clinical research and graduate education. 2005, New York: Springer.

  8. Aorta Venules Arterioles Small arts Large arts Capillaries Large veins 100 Summary Pressure [mmHg] 0 150 50000 Cross section area [mm2] Velocity [mm/s] 1 1000

  9. Body weight and mean arterial pressure Wolinsky, H. and Glagov, S. A lamellar unit of aortic medial structure and function in mammals. Circ. Res.:20;99-111. (1967)

  10. Red blood cell diameters From Altman, P.L. & Ditmer, P.S., Blood and other body fluids. Federation of American Societies for Exp. Biol. Washington (1961) Cited by Schmid-Neilsen, K. Scaling. CUP, (1984)

  11. approximately Why do most mammals have the same mean BP? • Little interspecies variation in the size of the mammalian red blood cell • Affinity between haemoglobin and oxygen • Diffusion coefficient of oxygen • Greater variation in the diameter of capillaries (≈ x2), but still small compared to the variation in mass (≈ x107). • Need to allow red blood cells access to the capillary wall

  12. Why do most mammals have the same mean BP? (2) • Little variation in the number of capillaries per unit volume of tissue • Depends on tissue function • and on diffusion constant of oxygen in tissue • Therefore little variation in muscular resistance vessels per unit volume • Therefore little variation in resistance of tissue per unit volume

  13. Why do most mammals have the same mean BP? (3) • Little variation of resistance per unit tissue volume, therefore total resistance k1/ V • Cardiac output µ volume = k2x V • Pressure = Cardiac output x total resistance = k2 V x k1/V = Constant

  14. Body weight and aortic pulse pressure Hypertension37, 313-21. (2001) Physiology & Behavior30, 719-22. (1983) Circulation101, 2097-102. (2000) Pflugers Archiv - European Journal of Physiology372, 95-9. (1977) J Appl Physiol88, 1537-44. (2000) Data book on mechanical properties of living cells, tissues and organs. Tokyo: Springer (1996)

  15. Why do most animals have approximately the samepulse pressure?

  16. Body weight and aortic functional stiffness (Strongly dependent on anatomical site, mean pressure, age, vascular disease) Ep ≈ kE.h/R W.W. Nichols and M.F. O'Rourke, McDonald's Blood Flow in Arteries (1998) Abé, H., Hayashi, K. & Sato, Data book on mechanical properties of living cells, tissues and organs. (1996)

  17. Structure Geometry Pulse pressure proportional to aortic stiffness ∆P = k1Ep = k2√E.h/R • E is determined by: • the elastic properties of elastin and collagen (& smooth muscle) • their relative amounts (assuming they bear stress in parallel) • In adulthood, arteries from a given location have constant ratio of elastin to collagen

  18. Vascular structure has to withstand relatively constant loads. • The lamellar unit has evolved to do this • Found in mammals, birds, reptiles and amphibians. • To make a bigger artery just add more lamellar units.

  19. Wolinsky H, Glagov S. Circulation Research 1967; 20: 99-111

  20. Wolinsky H, Glagov S. Circulation Research 1967; 20: 99-111

  21. Vascular structure has to withstand relatively constant loads. • The lamellar unit has evolved to do this • Found in mammals, birds, reptiles and amphibians. • To make a bigger artery just add more lamellar units.

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