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Hemodynamics 202
- 2. At the end of the lecture, the group should be able to: 1. describe and explain the interrelationships of different hemodynamic parameters and; 2. understand the physical laws governing blood flow in the vasculatures.
- 3. VASCULATUREBernoulli's principle Laplace law Ohm’s law Poiseuille’s law HEMODYNAMICS BIOPHYSICS OF CIRCULATORY PHYSIOLOGY
- 7. It is the quantity of blood that passes a given point in the circulation in a given period of time BLOOD FLOW(Q) Blood flow= Cardiac output= Stroke volume x Heart rate FACTORS AFFECTING BLOOD FLOW ΔP = pressure gradient R = resistance of blood vessels VOLUM EQ TIME ( L/min)
- 8. PRESSURE GRADIENT(ΔP) It is difference in pressure between the beginning and end of vessel and expressed in unit mm Hg. ΔP = P1 – P2 Blood flows from area of high pressure to an area of low pressure, down the pressure gradient.
- 9. RELATIONSHIP OF FLOW TO PRESSURE GRADIENT Δ𝑃 in vessel 2 = 2 times that of vessel 1 𝑄𝛼Δ𝑃 Flow is directly proportional to the pressure gradient Flow in vessel 2 = 2 times that of vessel 1
- 10. PERIPHERAL RESISTANCE (R) . Flow is inversely proportional to the resistance𝑄𝛼 1 𝑅 It occurs as a result of friction between the flowing blood and the intravascular endothelium all along the inside of the vessel.
- 12. Fluid Variable Electrical Variable Pressure, P Voltage, V Flow, Q Current, I Volume, V Charge, q Resistance, R = ∆P/Q Resistance, R = ∆V/I Capacitance, C = ∆V/∆P Capacitance, C = ∆q/∆V
- 13. Q = 𝚫𝐏 𝐑
- 15. It is characterized by smooth or in regular patterns of particles.
- 16. 𝑣 = 𝑑 𝑡
- 17. Laminar flow through vessels helps reduce energy losses in the flowing blood
- 18. It is characterized by irregular movement in axial, radial and circumferential directions.
- 19. REYNOLD’S NUMBER The Reynolds Number (Re) is a non-dimensional number that reflects the balance between viscous and inertial forces and hence relates to flow instability. Re = 𝑣 ⋅ 𝑑 ⋅ ρ η V = velocity ( cm/s) d = vessel diameter (cm) ρ = blood density (g/cm3) η= blood viscosity (poise)
- 20. Re = 𝑣 ⋅ 𝑑 ⋅ ρ η 𝑅𝑒 𝛼 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 𝑅𝑒 𝛼 𝑑𝑖𝑎𝑚𝑒𝑡𝑒𝑟 𝑅𝑒 𝛼 𝑑𝑒𝑛𝑠𝑖𝑡𝑦 𝑅𝑒 𝛼 1 η
- 21. Re = 30 Re = 40 Re = 47 Re = 55 Re = 67 Re = 100Re = 41 Tritton, D.J. Physical Fluid Dynamics, 2nd Ed. Oxford University Press, Oxford. 519 pp. 𝑹𝒆 𝐢𝐬 𝐠𝐫𝐞𝐚𝐭𝐞𝐫 𝐭𝐡𝐚𝐧 𝟑𝟎𝟎𝟎 𝐭𝐮𝐫𝐛𝐮𝐥𝐞𝐧𝐜𝐞 𝐰𝐢𝐥𝐥 𝐨𝐜𝐜𝐮𝐫
- 22. Component Peak Reynold’s number Turbulence Heart 5000 – 20, 000 PRESENT Arteries 5000 (ascending aorta) 500 ( small arteries) In ascending aorta Microcirculation 0.5 (largest arterioles) 0.0003( capillaries) ABSENT Veins 100 (smallest veins) ABSENT
- 23. Turbulence decreases blood flow required to drive a given perfusion pressure/pressure gradient.
- 25. Velocity, as relates to fluid movement, is the displacement that a particle of fluid travels with respect to time (cm/s) VELOCITY OF BLOOD STREAM 𝒗 = 𝒅 𝒕
- 27. Velocity(v)= Blood flow(Q) Cross−sectional area(A) v𝜶𝑸 v𝜶 𝟏 𝑨 v is directly proportional to the blood flow v is directly inversely proportional to the cross sectional area
- 29. Break the Ice : TRUE OR FALSE Object in motion possesses potential energy (PE) FALSE
- 30. Energetics of blood flow Blood flow possesses kinetic energy KE= 𝒎𝒂𝒔𝒔 𝒙 𝒗𝒆𝒍𝒐𝒄𝒊𝒕𝒚 𝟐 𝟐 KE 𝜶 v 𝟐
- 31. KE= ρ 𝒗 𝟐 𝟐 PRESSURE (force/area) PASCAL’ S PRINCIPLE PRESSURE IS EXERTED EQUALLY in all direction
- 32. KE PRESSURE(potential energy) KE + PE = TOTAL ENERGY OF THE BLOOD FLOW CONSERVATION OF ENERGY STATICDYNAMIC velocity 𝝆v2/2 + p + 𝝆gh = constant (neglecting viscosity)
- 34. BERNOULLI’S PRINCIPLE Blood flowing at higher velocities has a higher ratio of kinetic energy to potential (pressure) energy.
- 35. BLOOD FLOW SPEEDS UP IN THE NARROWED PORTION Pressure is lowered
- 36. Viscosity (η) measures the resistance of liquid to flow.
- 37. VOLUM EQ TIME = 𝜋 𝛥𝑃 𝑟4 8 𝜂 𝑙 POISEUILLE EQUATION
- 38. 𝐐 = 𝜋 𝛥𝑃 𝑟4 8 𝜂 𝑙 1. Pressure gradient is directly proportional to the length(constant Q, r, 𝜂) where r is internal radius and 𝜂 is viscosity of liquid 2. Pressure gradient is directly proportional to the blood flow Q (constant L, r, 𝜂) 3. Pressure gradient is directly proportional to viscosity(constant L, Q , r) POISEUILLE’S LAW 4. Pressure gradient is inversely proportional to FOURTH POWER OF RADIUS(constant L, Q )
- 39. i)The fluid is homogeneous and Newtonian. ii)The flow is steady and inertia-free. iii)The tube is rigid so that its diameter does not change with pressure.
- 40. POISEUILLE’S LAW 𝐐 = 𝜋 𝛥𝑃 𝑟4 8 𝜂 𝑙
- 41. Determinants of Resistance to Flow (Poiseuille's Equation) 𝐐 = 𝜋 𝛥𝑃 𝑟4 8 𝜂 𝑙 R= 8 𝜂𝑙 𝜋𝑟4R= 𝛥𝑃 𝑄
- 42. R= 8 𝜂𝑙 𝜋𝑟4 FACTORS AFFECTING RESISTANCE Resistance to blood flow depends on three factors: 1. Viscosity of blood 2. Blood vessel length 3. Radius of the blood vessel
- 43. 1.Viscosity of blood Hematocrit- proportion of blood that is RBC R 𝜶 𝑣𝑖𝑠𝑐𝑜𝑠𝑖𝑡𝑦
- 44. RHEOLOGICAL PROPERTIES OF BLOOD Viscosity: mechanical property of fluids that slows down their flow due to internal forces(unit POISE) . Newton’s definition: YU AF dydurateshear stressshear / / /
- 47. Fahraeus-Lindqvist effect The apparent viscosity of blood flowing through capillary tubes becomes lower as the tube diameter becomes smaller reaches a minimum value around 6 to 8 µm.
- 48. Greater the length of a vessel, more will be the resistance to flow. 2. Vessel length
- 49. 3.Radius of the vessel Increased CONDUCTANCE R𝜶 1 𝑟4
- 50. Vessel Diameter “Fourth Power Law” in Arteriolar Resistance
- 53. PARALLEL RESISTANCE The total resistance of a network of parallel vessels is less than the resistance of the vessel having the lowest resistance. When there are many parallel vessels, changing the resistance of a small number of these vessels will have little effect on total resistance for the segment.
- 54. SERIES RESISTANCE RT = RA + Ra + Rc + Rv + RV RA = 20, Ra = 50, Rc = 20, Rv = 6, RV = 4 RT = 20 + 50 +20 +6 + 4 = 100
- 57. The larger the vessel radius, the larger the wall tension required to withstand a given internal fluid pressure. La Place’s law
- 58. Vessel Diameter (mm) Aorta 22 Large arteries 6 Small arteries 3 Arterioles 0.02 Capillaries 0.01 Venules 0.04 Small veins 2 Large veins 10 Vena cavae 22
- 59. Why does wall tension increase with radius?
- 60. La Place’s law and Aneurysm
Editor's Notes
- When heart contracts, it gives pressure to the blood, which is main driving force for flow through a vessel. Due to resistance in the vessel, the pressure drops as blood flows.
- It is the measure of hindrance or opposition to blood flow through a vessel, caused by friction between the blood in the vessel Changes in resistance are the primary means by which blood flow is regulated within organs because control mechanisms in the body generally maintain arterial and venous blood pressures within a narrow range
- the central most portion of the blood stays in the center of the vessel
- the portion of fluid adjacent to the vessel wall has hardly moved, the portion slightly away from the wall has moved a small distance, and the portion in the center of the vessel has moved a long distance. The fluid molecules touching the wall move slowly because of adherence to the vessel wall. The next layer of molecules slips over these, the third layer over the second, the fourth layer over the third, and so forth. Therefore, the fluid in the middle of the vessel can move rapidly because many layers of slipping molecules exist between the middle of the vessel and the vessel wall; thus, each layer toward the center flows progressively more rapidly than the outer layers.
- Through minimizing viscous interactions between adjacent layers of blood and the wall of the blood vessel.
- When the rate of blood flow becomes too great, when it passes by an obstruction in a vessel, when it makes a sharp turn, or when it passes over a rough surface, the flow may then become turbulent, or disorderly, rather than streamlined When eddy currents are present, the blood flows with much greater resistance than when the flow is streamlined, because eddies add tremendously to the overall friction of flow in the vessel.
- Dominance of viscous force leads to laminar flow (low velocity, high viscosity, confined fluid) Dominance of inertial force leads to turbulent flow (high velocity, low viscosity, unconfined fluid)
- Turbulence is usually accomplished by audible vibration, can be detected using stethoscope. Turbulence in heart in murmur, if in vessel its bruit High velocity and low blood viscosity( as occurs in severe anemia due to reduced hematocrit resulting to high cardiac output) are more likely to cause turbulence
- Under ideal condition, the critical Re is relatively high. However, in branching vessels, or in vessels with atherosclerotic plaques protruding into the lumen, the critical Re is much lower so that there can be turbulence even at normal physiological flow velocities.
- fluid flow velocity is greatest in the section of the tube with the smallest cross-sectional area and slowest in the section of the tube with the greatest cross-sectional area.
- velocity decreases progressively as blood traverses the arterial system. At the capillaries, velocity decreases to a minimal value. As the blood then passes centrally through the venous system toward the heart, velocity progressively increases again. The relative velocities in the various components of the circulatory system are related only to the respective cross-sectional areas.
- This equation reveals that the kinetic energy of an object is directly proportional to the square of its speed. That means that for a twofold increase in speed, the kinetic energy will increase by a factor of four. For a threefold increase in speed, the kinetic energy will increase by a factor of nine. And for a fourfold increase in speed, the kinetic energy will increase by a factor of sixteen.
- In a narrow section, B, of a tube, the linear velocity, v, and hence the dynamic component of pressure, ρv2/2, are greater than in the wide sections, A and C, of the same tube. If the total energy is virtually constant throughout the tube (i.e., if the energy loss because of viscosity is negligible), the lateral pressure in the narrow section will be less than the lateral pressure in the wide sections of the tube.
- If the blood velocity is sufficiently high in the constricted region, the artery may collapse under external pressure, causing a momentary interruption in blood flow. At this point, there is no Bernoulli principle and the vessel, reopens under arterial pressure. As the blood rushes through the constricted artery, the internal pressure drops and again the artery closes. Such variations in blood flow can he heard with a stethoscope. If the plaque becomes dislodged and ends up in a smaller vessel that delivers blood to the heart, the person can suffer a heart attack.
- Viscosity refers to the friction, which is developed between the molecules of fluid as they slide over each other during flow of fluid.
- French physician named Jean Léonard Marie Poiseuille and a German named Hagen. With the use of glass capillary tubes (rigid) of uniform diameter and a homogeneous liquid (water) with streamline flow, Poiseuille found that the pressure gradient between two points (P1 2 P2) varies.
- A. Blood may be considered as a Newtonian fluid only if the radius of the vessel exceeds 0.5 mm, and if the shear rate exceeds 100 sec.-1. This condition, therefore excludes arterioles, venules, and capillaries, since they are generally considerably less than 1 mm in diameter. B. If the flow is pulsatile, the variable pressure gradient communicates kinetic energy to the fluid, and the flow is no longer inertia-free. This condition excludes the larger arteries. C. This condition is never met in the circulatory system. The veins in particular depart from this assumption.
- It occurs as a result of friction between the flowing blood and the intravascular endothelium all along the inside of the vessel.
- Greater the viscosity, Greater the resistance to flow. Blood viscosity is determined by number of circulating RBC, blood viscosity is increased in Polycythemia and decreased in Anaemia.
- the viscosity of normal blood is about three times as great as the viscosity of water. What makes the blood so viscous? It is mainly the large numbers of suspended red cells in the blood, each of which exerts frictional drag against adjacent cells and against the wall of the blood vessel.
- Deformation of the fluid occurs as a result of shear forces. Fluids with a larger viscosity will resist motions that enduce deformation more easily than those with a lower viscosity.
- blood is a shear-thinning fluid in which the viscosity decreases with increasing shear rate. the non-Newtonian behavior of blood is closely related to RBC deformability and RBC aggregation. RBC deformability and aggregation also affect blood flow in smaller blood vessels and in the microcirculation
- Greater the length of a vessel, more will be the resistance. How length of a vessel affects the resistance? When blood flows through a vessel, blood rubs against the vessel wall, greater the vessel surface area in contact with the blood , greater will be the resistance to the flow
- Therefore, doubling the radius, reduces the resistance to 1/16 its original value. [r4 = 2×2×2×2 = 16 or R α 1/16] and there is increased flow through a vessel 16 fold. On the other hand, when we decrease the radius to the half, blood flow will be decreased 16 times
- The fourth power law makes it possible for the arterioles, responding with only small changes in diameter to nervous signals or local tissue chemical signals, either to turn off almost completely the blood flow to the tissue or at the other extreme to cause a vast increase in flow. Arteriolar Resistance converts the pulsatile systolic to diastolic pressure swings in the arteries into the non-fluctuating pressure present in the capillaries
- Therefore, a parallel arrangement of vessels greatly reduces resistance to blood flow. That is why capillaries, which have the highest resistance of individual vessels because of their small diameter, constitute only a small portion of the total vascular resistance of an organ or microvascular network
- The implication of this law for the large arteries, which have comparable blood pressures, is that the larger arteries must have stronger walls since an artery of twice the radius must be able to withstand twice the wall tension. Arteries are reinforced by fibrous bands to strengthen them against the risks of an aneurysm. The tiny capillaries rely on their small size.
- The implication of this law for the large arteries, which have comparable blood pressures, is that the larger arteries must have stronger walls since an artery of twice the radius must be able to withstand twice the wall tension. Arteries are reinforced by fibrous bands to strengthen them against the risks of an aneurysm. The tiny capillaries rely on their small size.
- If the upward part of the fluid pressure remains the same, then the downward component of the wall tension must remain the same. But if the curvature is less, then the total tension must be greater in order to get that same downward component of tension. For equilibrium of a load hanging on a cable, you can explore the effects of having a smaller angle for the supporting cable tension.
- If an artery wall develops a weak spot and expands as a result, it might seem that the expansion would provide some relief, but in fact the opposite is true. In a classic "vicious cycle", the expansion subjects the weakened wall to even more tension. The weakened vessel may continue to expand in what is called an aneurysm.