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Hemodynamics

Hemodynamics. Michael G. Levitzky, Ph.D. Professor of Physiology LSUHSC mlevit@lsuhsc.edu (504)568-6184. P 1 - P 2. Dynes / cm 2. Dyn sec. R =. =. =. F. cm 3 / sec. cm 5. FLUID DYNAMICS. PRESSURE = FORCE / UNIT AREA = Dynes / cm 2.

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Hemodynamics

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  1. Hemodynamics Michael G. Levitzky, Ph.D. Professor of Physiology LSUHSC mlevit@lsuhsc.edu (504)568-6184

  2. P1 - P2 Dynes / cm 2 Dyn sec R = = = F cm3 / sec cm5 FLUID DYNAMICS PRESSURE = FORCE / UNIT AREA = Dynes / cm 2 FLOW = VOLUME / TIME = cm3 / sec RESISTANCE : POISEUILLE’S LAW P1 - P2 = F x R

  3. AIR FLOW : P1 - P2 = V x R . BLOOD FLOW : P1 - P2 = Q x R . POISEUILLE’S LAW

  4. 8L R =  r 4  = viscosity of fluid L = Length of the tube r = Radius of the tube RESISTANCE

  5. . (P1 – P2)r4 Poiseuille’s law: Q = 8L PL P1 P2 Constant flow

  6. POISEUILLE’S LAW - ASSUMPTIONS: 1. Newtonian or ideal fluid - viscosity of fluid is independent of force and velocity gradient 2. Laminar flow 3. Lamina in contact with wall doesn’t slip 4. Cylindrical vessels 5. Rigid vessels 6. Steady flow

  7. 1 1 1 1 = + + +... RT R1 R2 R3 RESISTANCES IN SERIES : RT = R1 + R2 + R3 + ... RESISTANCES IN PARALLEL :

  8. R1 R2 R3 RT = R1 + R2 + R3 R1 R2 1/RT = 1/R1 + 1/R2 + 1/R3 R3

  9. x Boundary layer edge

  10. TURBULENT FLOW P  Q2 x R . LAMINAR FLOW P  Q x R .

  11. 15 10 ml / sec 5 0 100 200 300 400 500 Pressure Gradient (cm water)

  12. TURBULENCE () (Ve) ( D) REYNOLD’S NUMBER =   = Density of the fluid Ve = Linear velocity of the fluid D = Diameter of the tube  = Viscosity of the fluid

  13. HYDRAULIC ENERGY ENERGY = FORCE x DISTANCE units = dyn cm ENERGY = PRESSURE x VOLUME ENERGY =(dyn / cm2 ) x cm3 = dyn cm

  14. HYDRAULIC ENERGY THREE KINDS OF ENERGY ASSOCIATED WITH LIQUID FLOW: 1. Pressure energy ( “lateral energy”) a. Gravitational pressure energy b. Pressure energy from conversion of kinetic energy c. Viscous flow pressure 2. Gravitational potential energy 3. Kinetic energy = 1/2 mv2 = 1/2 Vv2

  15. Laplace’s Law Po r Pi T T T T = Pr Transmural pressure = Pi - Po

  16. GRAVITATIONAL PRESSURE ENERGY PASCAL’S LAW The pressure at the bottom of a column of liquid is equal to the density of the liquid times gravity times the height of the column. P =  x g x h GRAVITATIONAL PRESSURE ENERGY =  x g x h x V

  17. IN A CLOSED SYSTEM OF A LIQUID AT CONSTANT TEMPERATURE THE TOTAL OF GRAVITATIONAL PRESSURE ENERGY AND GRAVITATIONAL POTENTIAL ENERGY IS CONSTANT.

  18. E1 Reference plane E2 Gravitational pressure E = 0 (atmospheric) Gravitational potential E = X + gh·V Thermal E = UV Total E1 = X + gh·V + UV h Gravitational pressure E = gh·V Gravitational potential at reference plane E = X Thermal E = UV Total E2 = X + gh·V + UV

  19. TOTAL HYDRAULIC ENERGY (E) E = ( P + gh + 1/2 v2 ) V Gravitational and Viscous Flow Pressures Gravitational Potential Kinetic Energy

  20. BERNOULLI’S LAW FOR A NONVISCOUS LIQUID IN STEADY LAMINAR FLOW, THE TOTAL ENERGY PER UNIT VOLUME IS CONSTANT. (P1 + gh1 + 1/2 v12) V = (P2 + gh2 + 1/2 v22) V

  21. Linear Velocity = Flow / Cross-sectional area cm/sec = (cm3 / sec) / cm2

  22. Bernoulli’s Law of Gases (or liquids in horizontal plane) [ P1 + ½v12 ] V = [ P2 + ½ v22 ] V lateral pressure kinetic energy

  23. The Bernoulli Principle PL PL PL Increased velocity Increased kinetic energy Decreased lateral pressure Constant flow (effects of resistance and viscosity omitted)

  24. LOSS OF ENERGY AS FRICTIONAL HEAT U x V

  25. TOTAL ENERGY TOTAL ENERGY PER UNIT VOLUME AT ANY POINT PRESSURE ENERGY GRAVITATIONAL POTENTIAL ENERGY KINETIC ENERGY THERMAL ENERGY E = (P•V) + (± gh •V) + ( 1/2v2•V) + (U •V) • (± gh) (Q•R) VISCOUS FLOW PRESSURE GRAVITATIONAL PRESSURE

  26. UV = Frictional heat ( internal energy) ½ v2·V = Kinetic energy PV = Viscous flow pressure energy E = Total energy E1 E2 E3 h KE +UV Reference plane P1 P2 P3

  27. E1 E2 E3 Reference plane KE + UV P1 P2 P3

  28. E4 E3 E2 E1 P4 viscous flow P P1 gravitational energy Reference plane P3 P2

  29. a gh b

  30. E1 E2 E3 E4 E5 KE + UV Reference plane P1 P2 P3 P4 P5

  31. Pressure equivalent of KE

  32. P’ (mm Hg) h (cm) 15 0 4 4 4 10 8 5 0 12 12 12 12 12 Arteries Capillaries Veins

  33. P’ (mm Hg) h (cm) Q = 1.0 15 0 (9) (3) 1 -5 4 10 8 5 Q = 1.0 0 12 3 0 9 12 (9) (3) (0) (12) Arteries Capillaries Veins

  34. P’ (mm Hg) h (cm) Q = 0.43 15 0 (10.7) (8.1) -6.7 2.7 4 10 0.1 8 5 Q = 1.43 0 12 3 0 9 12 (9) (3) (0) (12) Q = 1.0

  35. P’ (mm Hg) h (cm) 15 0 4 10 8 5 12 0 16 -5 20 -10 Q 4 12 10 -6 c a b -8 d

  36. 20 15 10 5 0 (Pa – Pv) (mmHg) 100 Flow (ml/min) 0 -5 0 5 10 15 Pv (mmHg)

  37. S  = dv dv dv dx dx dx VISCOSITY Internal friction between lamina of a fluid STRESS (S) = FORCE / UNIT AREA S =  Is called the rate of shear; units are sec -1 The viscosity of most fluids increases as temperature decreases

  38. v1 v2 A dx ===

  39. VISCOSITY OF BLOOD 1. Viscosity increases with hematocrit. 2. Viscosity of blood is relatively constant at high shear rates in vessels > 1mm diameter (APPARENT VISCOSITY) 3. At low shear rates apparent viscosity increases (ANOMALOUS VISCOSITY) because erythrocytes tend to form rouleaux at low velocities and because of their deformability. 4. Viscosity decreases at high shear rates in vessels < 1mm diameter (FAHRAEUS-LINDQUIST EFFECT). This is because of “plasma skimming” of blood from outer lamina.

  40. Non-Newtonian behavior of normal human blood 0.3 0.2 Apparent Viscosity  (poise) 0.1 0 100 200 Rate of Shear (sec-1)

  41. 8 6 4 2 0 0.2 0.4 0.6 0.8 Effects of Hematocrit on Human Blood Viscosity 52 / sec Relative Viscosity 212 / sec Hematocrit

  42. PULSATILE FLOW 1. The less distensible the vessel wall, the greater the pressure and flow wave velocities, and the smaller the differential pressure. 2. The smaller the differential pressure in a given vessel, the smaller the flow pulsations. 3. Larger arteries are generally more distensible than smaller ones. A. More distal vessels are less distensible. B. Pulse wave velocity increases as waves move more distally. 4. As pulse waves move through the cardiovascular system they are modified by viscous energy losses and reflected waves. 5. Most reflections occur at branch points and at arterioles.

  43. Definitions (Mostly from Milnor) Elasticity: Can be elongated or deformed by stress and completely recovers original dimensions when stress is removed. Strain: Degree of deformation. Change in length/Original length. ΔL/Lo Extensibility: ΔL/Stress (≈ Compliance = ΔV/ΔP) Viscoelastic: Strain changes with time. Elasticity: Expressed by Young’s Modulus. E = ΔF/A = Stress ΔL/Lo Strain Elastance: Inverse of compliance. Distensibility: Virtually synonymous with compliance, but used more broadly. Stiffness: Virtually synonymous with elastance. ΔF/ΔL

  44. Progressive increase in wave front velocity of the pressure wave with increasing distance from the heart. Mean pressures were 97 – 120 mmHg. Inguinal ligament 15 Arch Diaphragm Bifid Knee Thoracic Aorta Carotid Illiac Tibial Ascending Aorta Abdominal Aorta 10 Femoral m / sec 5 2.5 20 10 0 10 20 30 40 50 60 70 80 Distance from the Arch (Average of 3 dogs)

  45. 100 P (mmHg) 80 60 Aorta Ascending Thoracic Abdominal Femoral Saphenous 140 100 V (cm/sec) 60 20 -20

  46. 1. Ascending aorta 2. Aortic arch Pressure waves recorded at various points in the aorta and arteries of the dog, showing the change in shape and time delay as the wave is propagated. 3. Descending thoracic aorta 4. Abdominal aorta 5. Abdominal aorta 6. Femoral Artery 7. Saphenous artery

  47. 65 100 Pressure (mmHg) 90 Flow (ml / sec) Pressure 0 Flow 70 Experimental records of pressure and flow in the canine ascending aorta, scaled so that the heights of the curves are approximately the same. If no reflected waves are present, the pressure wave would follow the contour of the flow wave, as indicated by the dotted line. Sustained pressure during ejection and diastole are presumably due to reflected waves returning from the periphery. Sloping dashed line is an estimate of flow out of the ascending aorta during the same period of time.

  48. Pulmonary Artery Pressure kPa / mmHg Pulmonary Artery flow 100 mls-1 2.5 kPa 20mmHg Aortic Pressure kPa / mmHg Aortic flow 5 kPa 40mmHg 100 mls-1

  49.  V Ca =  P CAPACITANCE (COMPLIANCE)

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