Hemodynamics Part I

1. Hemodynamics Part I

2. The heart pumps blood into the arteries raising the pressure within them. The high pressure in the arteries forces blood through the microcirculation into the veins where it returns to the heart

3. The left ventricle supplies the systemic circulation with oxygenated blood which returns to the right atrium.

4. The right ventricle forces de-oxygenated blood through the lungs that returns to the left atrium.

5. The bronchial circulation empties into the pulmonary veins making the aortic flow slightly higher than the pulmonary

6. Portal systems in the gut and the kidney place two capillary beds in series with each other.

7. Flow, Velocity and Pressure: These are not interchangeable terms

8. flow = Mass of a fluid moving past a point per unit time (units: volume per unit time). velocity = speed of the particles(units: distance/unit time) mean velocity = flow /cross sectional area

9. Pressure is a scalar quantity where the fluid exerts a force per unit area in all directions (units: force per unit area) ρ is the density of the fluid g is the acceleration of gravity h is the distance to the surface of the fluid

10. Hydrostatics Pressure changes as you moving up or down in the fluid. ΔP = ρ · g · Δh pressure

11. h = ρ·g·P P MercuryReservoir

12. Millimeters of mercury (mmHg) is the unit of pressure used in medicine. 100 mmHg is the pressure at the bottom of a 100mm high column of mercury. Mercury is 13.6 times denser than water. mmHg is not a true scientific unit.

13. 1 mmHg = 13.6 mm water = 1332 dynes/cm2 = 0.018 psi (pounds/inch2) Blood pressure averages about 100 mmHg or 1.8 psi, or 1,360 mm water 1 atmosphere is 760 mmHg or 14 psi or 32 feet of water). A car tire holds about 30 psi

14. 136 cm The shape of the container is not involved

15. Viscosity is the force with which a fluid resists shear. The force required to move one plate relative to the other increases with viscosity, speed, the surface area and the inverse of the distance between the plates F = η · A · Δv/Δx

16. The motion is distributed equally among many lamina so that each card moves just a little bit relative to its neighbor. The friction is distributed to all of the cards The more cards, the less motion for each If the top card is moved 1cm relative to the bottom card, then the relative motion between each card is 1/52 of a cm.

17. Shear stress F/A Shear rate Δv/Δx η = = Viscosity is the force with which a fluid resists shear. F = η · A · Δv/Δx

18. Fluid flowing through tubes assumes a parabolic velocity profile with an infinite # of concentric lamina. The outermost lamina next to the wall has zero velocity. As the concentric lamina slide past each other each layer travels slightly faster that the one surrounding it.

19. Fluid flowing at the center travels the fastest

20. V = Flow/Area Mean Velocity 0 2 4 6 8 10 Velocity Because of the geometry, velocity in the center is exactly twice the mean velocity

21. In perfect laminar flow all molecules move axially within their lamina and an insignificant portion of the molecules move transversely from one lamina to another.

22. Laminar flow minimizes (but does not eliminate) friction which occurs because viscosity still resists movement between lamina

23. How can we calculate flow through a tube? Poiseuille's equation !

24. F = η Poiseuille's equation High Viscosity You can suck Coke up a straw easier than a milk shake (viscosity term). Low Viscosity

25. F = r η Poiseuille's equation A milk shake is easier to drink with a large diameter straw than a small diameter straw (radius term)

26. F = r · ΔPη Poiseuille's equation The harder you suck the more Coke you get (pressure term)

27. F = r · ΔP L · η Poiseuille's equation The longer the straw the more difficult it is to drink (length term)

28. F = π · r · ΔP 8 · L · η Poiseuille's equation We need a 8 and a π just because we do

29. F = π · r4 · ΔP 8 · L · η Poiseuille's equation The radius is to 4th power (not squared like you might expect)

30. F = π · r4 · ΔP 8 · L · η Poiseuille's equation Doubling the radius increases flow 16 times (24 = 16). Small changes in a blood vessel’s radius have a big effect on flow.

31. We can use Ohm’s law to calculate blood flow F = ΔP / R Ohm’s law describes the relationship between volts (V), current (I) and resistance (R) in electrical circuits. I = ΔV / R

32. F = ΔP / R ΔP = R · F R = ΔP/F If we know any two of the terms we can calculate the third

33. Resistance = ΔP / F = R = 8 · L · η πr 4 ΔP 8 · L · η π · r 4·ΔP F = π ·r4 · ΔP 8 · L · η Ohm’s law is good for analyzing fluid flow through tubes Poiseuille's equation (inverted) Notice that resistance includes vascular dimensions and viscosity

34. Because the vascular system is composed of millions of tiny tubes calculating the resistance of each one is really not practical. Rather we usually measure the flow and ΔP across an organ and calculate the resistance. Resistances calculated by that method are usually reported in peripheral resistance units (PRU). 1 PRU is 1 mmHg/ml/sec.

35. In series circuits each drop of fluid must flow through all segments. The more segments the harder it is for the blood to get from one side to the other.

36. For series circuits simply add the resistances to get the total resistance: Rtotal = R1 + R2 + R3 .....

37. ΔP = F · Rtotal F · Rtotal must equal the total pressure drop across the entire circuit. If ΔP = 100 then flow = 100/130 = 0.77

38. ΔP = F · R1 The pressure drop across an individual resistor is the flow times its resistance. If flow = 0.77 then ΔPR1 = 0.77 · 5 = 3.85

39. R total = 130 130 > 100 > 25 > 5 The total resistance must be bigger than any individual resistance

40. Arteries, arterioles, capillaries, and veins are in series with each other.

41. For parallel circuits each parallel circuit that is added gives an alternative pathway and makes it easier for the blood to get from one side to the other.

42. For parallel circuits you must add reciprocals: 1 = 1 + 1 + 1 ...... Rtotal R1 R2 R3

43. R total = 4 100 > 25 > 5 > 4 The total resistance must be smaller than any single resistance. The answer is 4, not ¼ (Don’t forget to turn the answer over)

44. Each leg experiences the total pressure

45. One artery feeds many parallel capillaries.

46. Total peripheral resistance (TPR) gives the total resistance of the systemic circulation. TPR = AOP/CO Systemic TPR is about 5 times pulmonary TPR. That make Aortic pressure about 5 times higher than pulmonary pressure

47. Thevenin’s Theorem Any network or resistors can be reduced to a single resistor

48. Thevenin’s Theorem Any network or resistors can be reduced to a single resistor

49. Thevenin’s Theorem Any network or resistors can be reduced to a single resistor

50. Thevenin’s Theorem Any network or resistors can be reduced to a single resistor