Hemodynamics

1. Hemodynamics

2. Hemodynamics - the study of blood circulation and the forces and motion of blood flow Flow - the ability to move from one point to another when a force is applied

3. Matter is classified into 3 categories: Gas Liquid Solid

4. Fluid Substances that flow & assume the shape of their container Gases & liquids are fluids

5. Blood A liquid Supplies nutrients & oxygen to the cells Removes waste products Average human has 5 liters of blood

6. Blood Comprised of plasma, erythrocytes (red cells), leukocytes (white cells) & platelets Plasma - approx. 90% H2O; remainder is proteins Blood cells - 40% of blood�s volume; known as the hematocrit Erythrocytes - about 99% of all the blood cells Leukocytes - larger than erythrocytes & function to protect the body against disease organisms Platelets - smaller than erythrocytes & are important in blood clotting

7. Blood -is a fluid because it is a liquid - it follows the properties of a fluid

8. Fluid Fluids have 2 important characteristics: Density Viscosity

9. Density Mass per unit volume; grams/milliliter (g/mL) Mass - a measure of an object�s inertia (resistance to acceleration) The greater the mass - the greater the force must be to accelerate it Blood�s density (1.05 g/mL) > water�s (1 g/mL) because of the proteins & cells

10. Viscosity (?) fluid�s ability to resist a change in flow Unit - poise or kg/m-sOne poise is 1 g/cm-s Viscosity varies with flow speed

11. Viscosity Blood is a viscous fluid containing cells & plasma Blood viscosity - 0.035 poise at 370C - approx. 5X that of water Blood viscosity varies from 0.02 (anemia) to 0.10 (polycythemia) Since erythrocytes are the major cellular component of blood, if the number of RBCs increases, the viscosity of the blood increases (directly related) Anemia (low # of RBCs) has low viscosity Polycythemia (high # of RBCs) has high viscosity

13. Pressure force per unit area is equally distributed throughout a static fluid & exerts its force in all directions A pressure difference is required for flow to occur

16. Pressure Equal pressures applied at both ends of a liquid-filled tube results in no flow If the pressure is greater at one end, the liquid will flow from the higher-pressure end to the lower-pressure end This pressure difference can be generated by a pump or by the force of gravity The greater the pressure difference, the greater the flow rate will be

17. Pressure The difference in pressure (between the high pressure end & the low pressure end) is called a pressure gradient or energy gradient Pressure gradient is calculated by taking the pressure difference & dividing it by the distance between the 2 pressure locations

18. Pressure Gradient Pressure Gradient (?P) = P1-P2 Distance (length) between P1 and P2

19. Volume Flow Rate (Q) = volume of blood passing a point per unit time expressed in milliliters (mL)/minute or /second or cc/second (this is not a measurement of speed) Total adult blood flow rate (cardiac output) is about 5,000 mL/min (our total blood volume circulates in about 1 minute) Q in a long straight tube is determined by the pressure difference & the resistance to flow

20. Volume Flow Rate (Q) Volume flow rate (mL/s) = ?P (dyne/cm2) Flow resistance (g/cm4-s)

21. Flow Resistance Flow resistance (in a long, straight tube) depends on: Fluid�s viscosity Tube�s length & radius

22. Flow Resistance Flow Resistance = 8 X length x viscosity (?) ? X radius4

23. Poiseuille�s Equation Substituting the flow resistance equation into the flow-rate equation & using tube diameter rather than radius yields Poiseuille�s equation for volume flow rate

24. Poiseuille�s Equation Poiseuille�s equation predicts steady volume flow in long straight tubes Thus, it serves only as a rough approximation to the conditions in blood circulation

25. Flow Resistance = 8 X length X viscosity (?) ? X radius4 Volume flow rate (Q) = ?P Flow resistance

26. Q = ?P Flow resistance Q = ?P 8 X length x viscosity ? X radius4 Q = ?P X ? X radius4 8 X length X ?

27. Poiseuille�s Equation Q = ?P ? r4 8 ? L � Q = ?P ? d4 128 ? L

28. Extra Credit � 10 points Prove to me on paper why both of the equations given are equal. Due next class meeting

29. Using this formula, what relationships can be seen? Q = ?P ? r4 8 ? L � Q = ?P ? d4 128 ? L

30. Imagine you are drinking through a straw & you want to get more flow through the straw: ? pressure gradient (suck harder) ? radius of the vessel (use a bigger straw) ? viscosity of the fluid (dilute or heat it) ? length of the vessel (cut the straw in �)

31. Which factor affects flow, resistance & velocity the most? The one raised to the fourth power!!! A small change in vessel diameter will create a large difference. Resistance to flow depends on viscosity of blood, the radius of the blood vessel�s lumen & the length of the vessel.

33. Types of Flow Profiles Flow is divided into 5 spatial categories: 1) plug 2) laminar 3) parabolic 4) disturbed 5) turbulent

34. Flow Profiles Velocity (speed & direction RBCs are traveling) is not constant or uniform across the vessel lumen Various flow profiles are seen in normal flow in: various vessels at different points in the cardiac cycle Velocity profile across a vessel depends on: curvature of a vessel branching to a smaller vessel obstruction in a vessel diverging cross section

35. Plug Flow - is constant flow velocity across the vessel It occurs in large vessels such as the aorta

36. Laminar Flow - is flow that occurs when straight, parallel layers of fluid slide over each other In a normal vessel, friction produces lowest velocities along the vessel wall & highest velocities occur in the center of the vessel Laminar flow is commonly seen; its absence often indicates abnormal flow conditions at a site where there is vascular or cardiac-valvular disease

37. Laminar Flow flow that occurs when straight, parallel layers of fluid slide over each other

38. Parabolic Flow - flow is steady laminar flow whose varying flow speeds across the tube are described by a parabola - ave. flow speed = � max. flow speed (at the center)

39. Parabolic Flow - not commonly seen in blood circulation because the vessels generally are not long & straight

40. Disturbed Flow - a form of laminar flow but the parallel streamlines are altered from their straight form Disturbed flow fluid flows  in a forward direction

41. Disturbed Flow This occurs in the region of stenosis or at a bifurcation (the point at which a vessel splits into two)

42. Turbulent Flow - (turbulence) is nonlaminar flow with random & chaotic speeds Turbulence with multiple velocity components is known as chaotic flow Eddies currents (flow particles moving in circles) occur creating regions of reverse flow As flow speed ?, turbulence will ultimately occur

43. Turbulent Flow

44. Turbulent Flow Flow speed for turbulent flow depends on the fluid�s density & viscosity and the vessel�s diameter Reynolds number predicts the onset of turbulent flow. If the Reynolds number (Re) exceeds about 2000 to 2500 (depending on tube geometry), flow becomes turbulent This is called the critical Reynolds number

45. Reynolds number = � Average flow speed x tube diameter X density Viscosity

46. If there is an increase in: Flow speed Diameter Density Reynolds number ? If viscosity ?, Reynolds number ?

47. With the exception of the heart and proximal aorta, turbulent flow does not typically occur in normal circulation Turbulent flow most commonly occurs beyond an obstruction, such as a stenosis, particularly in systole but will also occur in abnormal arterial geometry (kinked, bent, or tortuous vessels)

48. Steady Flow - is nonpulsatile hemodynamics that occurs in the venous system because the veins offer little resistance to flow and can accommodates a large change in volume with little change in pressure volume flow rate is simply related to pressure difference & flow resistance

49. Venous pressure & flow are affected by: Respiration Hydrostatic pressure (p)

50. Respiration Inspiration: diaphragm moves inferiorly, causing an increase in abdominal pressure, that slows down the flow of blood in the lower extremities. This causes a decrease in the thoracic pressure increasing the blood flow in the veins of the thorax & upper extremities The opposite happens on expiration This is called phasicity (waxes and wanes)

51. Hydrostatic Pressure (p) - the gravitational weight of a column of blood that extends from the heart to a level where blood pressure is determined The higher the column of blood in the body, the greater the pressure Hydrostatic pressure has greater effect on the venous system than on the arterial system

52. Hydrostatic Pressure (p) can be measured by taking a blood pressure, with measurement units of millimeters of mercury (mm Hg). Right atrium is considered the reference point & has zero hydrostatic pressure

53. Pulsatile Flow non-steady flow with variations of increasing & decreasing pressure and flow speed (cardiac cycle & arterial circulation The relationship between the varying  pressure & flow rate depends on the: flow impedance (resistance) inertia of the fluid as it accelerates & decelerates compliance (expansion & contraction) of the vessel walls

54. Major Characteristics of Pulsatile Flow are: windkessel effect flow reversal

55. Windkessel Effect - occurs when the pressure forces a fluid into a compliant vessel, (aorta) expanding & increasing the volume in it When the pressure is reduced, the vessel contracts producing extended flow later in the pressure cycle.

56. Windkessel Effect In the aorta, it results in continued flow in the forward direction, because aortic valve closure prevents flow back into the heart.

57. Flow Reversal - is the reversal of flow in diastole as the pressure decreases & the distended vessels contract in the distal circulation where there are no valves to prevent the back flow

58. Flow Reversal in the distal circulation reversal of flow in diastole

59. Continuity Rule - states that the volume flow rate is equal to the average flow speed across the vessel multiplied by the cross-sectional area of vessel A stenosis (narrowing of the lumen of a vessel) produces disturbed & possibly turbulent flow The average flow speed in the stenosis must be ? flow speed proximal & distal to it, so that the volume flow rate is constant throughout the vessel

60. Continuity Rule Volume flow rate must be constantfor the 3 regions of the stenosis: proximal to at distal to But� Flow speed increases at a stenosis & turbulence can occur distal to it

61. Poiseuille�s law converted to average flow speed, rather than volume flow rate, is: �Average Flow Speed = Pressure difference X diameter2 32 X length X viscosity

62. Poiseuille�s Equation states: Volume Flow Rate (Q) = ?P X ? X radius4 8 X length X ? Continuity Rule states: Average Flow Speed = ?P X diameter2 32 X length X ?

63. Continuity Rule If a stenosis has an area measuring � that of the proximal & distal vessel, the average flow speed in the stenosis is 2X that proximal & distal to it.

64. Continuity Rule - E.C. If a stenosis has a diameter that is � that adjacent to it, the area at the stenosis is � that adjacent to it, so the average flow speed in the stenosis must quadruple.

65. Poiseuille�s law states that flow speed ? with smaller diameters and the continuity rule states that flow speed ? with smaller diameters Recall that Poiseuille�s law deals with a long straight vessel (no stenosis), the diameter refers to that of the entire vessel. If the diameter of the entire vessel is reduced (as in vasoconstriction), flow speed is reduced.

66. Bernoulli's Principle As the speed of a moving fluid increases, the pressure within the fluid decreases As fluid passes through a tube that narrows or widens, the velocity and pressure of the fluid vary. If the tube narrows - fluid flows more quickly Surprisingly, Bernoulli's Principle tells us that as the fluid flows more quickly through the narrow sections, the pressure actually decreases rather than increases!

67. http://home.earthlink.net/~mmc1919/venturi.html#animation http://library.thinkquest.org/27948/bernoulli.html

68. In the continuity rule, the diameter is referred to is for a short portion of a vessel (the stenosis). If the diameter of only a short segment of a vessel is reduced (stenosis), the flow speed in the vessel is only affected at the stenosis, where it is increased. The stenosis has little effect on the flow resistance of the entire vessel if the stenosis length is small compared to the vessel length.  Therefore, the two situations are different.

69. Bernoulli Effect Explains why there is a drop in pressure associated with high flow speed at a stenosis At a stenosis, the pressure is < the pressures proximal & distal to it. This allows the fluid to accelerate into the stenosis & decelerate out Energy balance is maintained because pressure energy is converted to flow energy upon entry, and then vice versa upon exit

71. pressure drop (?P) = � density x (flow speed)2 Bernoulli�s equation states that as flow energy ? , pressure energy ?. The magnitude of the decrease in pressure (from the increasing flow speed) at the stenosis can be found from a modified form of Bernoulli�s equation.

72. pressure drop = � density x (flow speed)2 In this modified equation, the flow speed proximal to the stenosis is assumed to be small enough, compared to the flow speed in the stenosis, to be ignored.

73. ?P = 4 (V2) Pressure drop from a stenotic heart valve can reduce cardiac output The following form of the equation is used in Doppler echocardiography for calculating pressure drop across a stenotic valve:

74. ?P = 4 (V2) V = flow speed (m/s) in the jet ?P (mm Hg) = pressure drop across the valve If the flow speed in the jet is 5 m/s, the pressure drop is 100 mm Hg Pressure drop can be calculated from a measurement of flow speed at the stenotic valve using Doppler ultrasound

75. The ? flow speed within a stenosis can cause turbulence distal to it. Sounds produced by turbulence are called bruits & can be heard with a stethoscope The ultimate stenosis is called an occlusion, (the vessel is blocked & there is no flow)

76. Doppler

77. Doppler Effect or Shift the change in frequency (& wavelength) due to motion of a sound source, receiver, or reflector the difference between the received & transmitted frequencies measured in Hz used to determine the velocity of the moving reflectors (Note: velocity is speed & direction)

78. If the source is moving toward the receiver, or the receiver is moving toward the source, or the reflector is moving toward the source and receiver, the received wave has a higher frequency than would be experienced without the motion. Doppler Effect or Shift

79. A moving source (red blood cells) approaching a stationary receiver (transducer), the cycles are compressed in front of the source as it moves into its own wave.

80. ? wavelength = ? frequency as observed by a stationary receiver in front of the approaching source

81. Conversely, if the source motion is away, the received wave has a lower frequency & ? wavelength

82. Only the moving reflector is of interest for diagnostic Doppler ultrasound The amount of ? or ? in the frequency depends on the: speed of motion angle between the wave propagation  direction & the motion direction frequency of the source�s wave

83. Doppler equation relates the detected Doppler shift (?F) to those factors that affect it ?F = 2 x F0 x V x COS ? C

84. ?F = 2 x F0 x V x COS ? C F0 is the central sound frequency (aka - transmitted, emitted, incident, or ongoing frequency) transmitted by the transducer. ?F and F0 are directly related; if F0 is doubled, then ?F is doubled

85. ?F = 2 x F0 x V x COS ? C V - the velocity of the moving reflector  (i.e. red blood cells) ?F and V are directly related; if V is doubled, then ?F is doubled

86. ?F = 2 x F0 x V x COS ? C COS ? is the cosine of the angle between the direction of blood flow & the axis of the beam (the Doppler angle). If the cosine is doubled,the Doppler shift doubles.

87. sin & cos (in brief) A is the starting point (in our case, the blood cell), the side opposite of angle A is called �a� C is the right angle; the hypotenuse (the side of the triangle opposite of angle C) is called �c� B is the remaining angle; the side of the triangle opposite angle B is called �b�

88. As ? A ?, side �a� also ?; eventually �a� will equal �c� As ? A approaches 90�, ratio a/c becomes closer to 1 When ? A equals 90�,  a/c = 1 ? sin A = 1 when ? A = 90�(sin 90� = 1)

89. ?F = 2 x F0 x V x COS ? C Cosine values range from 0 to 1 Is an inverse relationship. As the angle ?, the cosine ? Example cosine of 0� = 1 cosine of 90� = 0

90. ?F = 2 x F0 x V x COS ? C C - speed of sound in the medium The speed of sound is approximately 1540 m/s or 1.54 mm/?s If the speed of sound in the medium ?; the detected Doppler shift ? C is inversely related to ?F

91. Detection of Doppler Shift Doppler ultrasound units do not use the Doppler equation to calculate the Doppler shift The ultrasound unit compares the frequency of the received echo (fr) to the frequency of the transmitted pulse (ft)

92. Doppler Frequency (fd) =Reflected Frequency (fr) - Transmitted Frequency (ft) When: received frequency = transmitted frequency there is no Doppler shift received frequency > transmitted frequencyDoppler shift is positive received frequency ? transmitted frequencyDoppler shift is negative

93. Factors influencing the magnitude of the Doppler shift frequency Doppler shift frequency occurs in  the audible range Example: A probe emits 5.0 MHz ultrasound beam striking the red blood cells traveling toward the transducer. The unit detects the reflected frequency to be 5.007 MHz. The transmitted & received frequencies are in the ultrasonic range, but the Doppler shift frequency is .007 MHz (7,000 Hz) (audible range). Typical Doppler shifts range: �10 kHz to +10 kHz

94. Factors influencing Doppler shift frequency As the angle between the transducer & flow ? (COS ?), the Doppler shift ? If the RBCs are moving toward the transducer, the received frequency is higher than the transmitted frequency (shown as a positive Doppler shift) If the RBCs are moving away from the transducer, the received frequency is lower than the transmitted frequency (shown as a negative Doppler shift)

95. Factors influencing Doppler shift frequency If there is no motion of the RBCs, the reflected frequency = transmitted frequency and the Doppler shift is zero. The faster the flow velocity, the higher the Doppler shift. Flow speed & Doppler shift, ? with vessel diameter2. If there is a ? in concentration of RBCs or if you are performing the Doppler exam of the vessel off to one side, there may be a ? in intensity (hard to hear & see on spectral display)

96. Since the RBCs are much smaller than the wavelength of the sound beam, Rayleigh scattering occurs ? the transducer frequency will ? scattering & ? the Doppler shift Although higher frequencies produce more scatter, they are attenuated more rapidly Factors influencing Doppler shift frequency

97. Factors influencing Doppler shift frequency Since these reflectors are very weak in intensity, lower frequency transducers may be needed to obtain Doppler information at deeper depths Modern transducer technology takes advantage of the wide bandwidth emitted by the transducer by allowing imaging at high frequencies and then downshifting into lower frequencies to acquire the Doppler information