VASCULAR SYSTEM: THE HEMODYNAMICS Lecture 1. Dr. Ana-Maria Zagrean

Transcription

1 VASCULAR SYSTEM: THE HEMODYNAMICS Lecture 1 Dr. Ana-Maria Zagrean

2 Hemodynamics -is the study of the physical laws of blood circulation -studies the properties of both the content = blood and the container = blood vessels of the circulatory system The circulatory system is not a system of rigid tubes which carry substances all over the body, but consists in various segments of the vasculature that differ greatly from one to another, branching out finally into a network of billions of tiny capillaries. Its components are: -arteries - distribution system, -microcirculation - diffusion and filtration system -veins collection system.

3 Physical properties of vessels closely follow the level of branching in the circuit 1. Number of vessels at each level of arborization 2. Radius of a typical individual vessel 3. Aggregate cross-sectional area of all vessels at that level 4. Mean linear velocity of blood flow within an individual vessel 5. Flow (volume/second) through a single vessel 6. Relative blood volume (the fraction of the body s total blood volume present in all vessels of a given level) 7. Circulation (transit) time between two points of the circuit 8. Pressure profile along that portion of the circuit 9. Structure of the vascular walls 10. Elastic properties of the vascular walls

4 Physical properties of vessels closely follow the level of branching in the circuit Panel 1 shows branching of the cardiovascular system, from left side to right side of heart and back to left. Total circulation time (the time to go from left to right across panel 1) is ~1 minute. Circulation time across a single vascular bed (e.g., coronary circulation) may be as short as 10 seconds.

5 Components of the vasculature and their function 1. Arteries: highest blood pressure, thick-walled (elastic tissue, smooth mm) 2. Arteriols: highest resistance in the CV system, smooth mm innervated by ANS (skin, splanchnic circ.: a1-adren. rec., skeletal mm: b2-adren. rec.) 3. Metarteriols: -part of their wall surrounded by smooth mm -can by-pass capillaries going directly to the venous circulation if precapillary sphincters are constricted -allow WBC to circulate from arterioles to venous circulation 4. Capillaries: largest total cross-sectional and surface area, thin-walled (one layer of endothelial cells on a basal lamina), exchange area 5. Venules: smallest veins formed from merged capillaries 6. Veins: low pressure, thin-walled, capacitance vessels, contains the highest % of the blood in the CV system, the blood volume contained is called the unstressed volume (blood reservoir), innervated by ANS Microcirculation = network of arterioles, capillaries and venules

6 Morpho-functional diversity of blood vessels VESSEL TYPE FUNCTION Aorta Pulse dampening and distribution Aorta 25 mm Large Arteries Distribution Small Arteries Distribution and resistance Arterioles Resistance (pressure/flow regulation) Capillaries Exchange Venules Exchange, collection, and capacitance Veins Capacitance function (blood volume) Vena cava 35 mm Vena Cava Collection

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10 Physical properties of vessels closely follow the level of branching in the circuit -The number of vessels at a particular level of arborization increases enormously from a single aorta to ~10 4 small arteries, ~10 7 arterioles, and finally ~ capillaries. However, only about one fourth of all capillaries are normally open to flow at rest. Finally, all of the blood returns to a single vessel where the superior and inferior venae cavae join. -The radius of an individual vessel (ri) declines as a result of the arborization, decreasing from 1.1 cm in the aorta to a minimum of ~3 μm in the smallest capillaries.

11 Physical properties of vessels closely follow the level of branching in the circuit -The cross-sectional area of an individual vessel is proportional to the square of the radius (changes abruptly with change in radius). -The aggregate cross-sectional area at any level of branching is the sum of the single cross-sectional areas of all parallel vessels at that level of branching. At each branch point, the combined cross-sectional area of daughter vessels exceeds the cross-sectional area of the parent vessel. In this process of bifurcation, the steepest increase in total cross-sectional area occurs in the microcirculation.

12 The profile of the mean linear velocity of flow (v) along a vascular circuit is roughly a mirror image of the profile of the total cross-sectional area. According to the principle of continuity, which is an application of conservation of mass, total volume flow of blood (F - the aggregate flow for each level) must be the same at any level of arborization. v must be minimal in the postcapillary venules (~0.03 cm/s), where Atotal is maximal. conversely, v is maximal in the aorta (~20 to 50 cm/s). Thus, both Atotal and v values range ~1000-fold from the aorta to the capillaries but are inversely related to one another. The vena cava, with a cross-sectional area ~50% larger than that of the aorta, has a mean linear velocity that is about one third less

13 Panel 2 shows the variation of aggregate cross-sectional area of all vessels at any level of branching. Panel 3 shows how mean linear velocity of blood varies in typical vessels.

14 Single-vessel flow Single-vessel flow, in contrast to total flow, varies by ~10 orders of magnitude. In the aorta, the flow is ~ 83 ml/s, the same as the cardiac output (~5 L/min). When about 25% of the capillaries are open, a typical capillary has a mean linear velocity of 0.03 cm/s and a flow of ml/s (8 pl/s) (10 orders of magnitude less than the flow in the aorta). Within the microcirculation, single-vessel flow has considerable range. At one extreme, a first-order arteriole (ri ~ 30 μm) may have a flow of ml/s. At the other, the capillaries that are closed at any given time have zero flow.

15 Blood distribution through the CV system 84 % systemic circulation 64 % - veins 13 % - arteris 7 % - arteriols & capillaris 9 % pulmonary system 7 % heart

16 Systemic Vessels of each type put side-by-side Cross-Sectional Area (cm2) Aorta 2.5 Small arteries 20 Arterioles 40 Capillaries 2500!!! Venules 250 Small veins 80 Venae cavae 8 velocity=flow/area Velocity of blood flow is inversely proportional to vascular crosssectional area, ~ 33 cm/sec in the aorta, but only ~0.3 mm/sec in the capillaries (capillaries length of ~0.3 1 mm blood remains in the capillaries for only 1 3 sec = time for diffusion )

17 Blood pressure in various portions of the circulation Left CO* Right CO* *Left CO = Right CO (mmhg)

18 Panel 4 shows ways of grouping blood volume in various compartments. Panel 5 shows profile of blood pressure, with superimposed oscillations that represent variations in time.

19 The intravascular pressures along the systemic circuit are higher than those along the pulmonary circuit

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21 Under normal conditions, the steepest pressure drop in the systemic circulation occurs in arterioles, the site of greatest vascular resistance Resistance of each vascular segment determines the profile of pressure fall between the upstream arterial & downstream venous ends of the circulation. The driving pressure difference, ΔP (pressure difference between two points along the axis of the vessel) depends on flow (F) and resistance (R): ΔP = F R According to Poiseuille s law, the resistance (Ri) of an individual, unbranched vascular segment is inversely proportional to the fourth power of the radius (r 4 ). Thus, the pressure drop between any two points along the circuit depends critically on the diameter of the vessels between these two points. However, the steepest pressure drop (ΔP/Δx) does not occur along the capillaries, where vessel diameters are smallest, but rather along the precapillary arterioles. The aggregate resistance contributed by vessels of a particular order of arborization depends not only on their average radius but also on the number of vessels in parallel. The more vessels in parallel, the smaller the aggregate resistance.

22 Although the resistance of a single capillary exceeds that of a single arteriole, capillaries far outnumber arterioles. The result is that the aggregate resistance is larger in the arterioles, and this is where the steepest ΔP occurs.

23 Main aspects of the circulatory function 1. Blood flow to most tissues is coupled to the tissue need: 20-30x blood flow local increase possible, but CO increases just 3-7x times need for local metabolic and nervous regulatory factors 2. Cardiac Output (CO) is the sum of all the local tissue flows: the heart receives pump as an automaton send - receive, etc; extra-control from the Autonomic Nervous System (ANS) 3. Arterial pressure regulation: fast by nervous reflexes, delayed by kidneys and humoral factors

24 Why does blood flow? In the systemic circulation the mean pressure decreases progressively (100 mmhg - aorta, 30 mmhg - end of arterioles, 4 mmhg - vena cava) with increase in resistance to blood flow. Largest decrease in pressure occurs across the arterioles.

25 Interrelationships of pressure, resistance and blood flow Ohms law for the blood flow (1) pressure difference (DP) of the blood - "pressure gradient" along the vessel, that pushes the blood through the vessel (2) vascular resistance (R)- impediment to blood flow through the vessel (result of friction between the flowing blood and the intravascular endothelium)

26 Blood flow: the Ohm s Low for the blood flow F = DP/R = blood flow = cardiac output (ml/min) The overall blood flow in the circulation at rest = CO= 5 L/min DP = pressure gradien that drives the blood flow = mean arterial pressure (mmhg) RA pressure (mm Hg) R = resistance = total peripheral resistance (TPR) (mmhg/ml/min)

27 Fluids flow from a higher pressure to a lower pressure Flow ~ DP Fluid flow through a tube

28 1. Driving pressure. - the axial pressure difference (along the axis of the vessel), causes blood to flow 2. Transmural pressure. - the ΔP along the radial axis, between r1 and r2, the difference between the intravascular pressure and the tissue pressure. The reference pressure in human physiology is the atmospheric/barometric pressure - because blood vessels are distensible, transmural pressure governs vessel radius, which is in turn the major determinant of resistance. 3. Hydrostatic pressure. - pressure along the height axis, depends on the density of blood and gravitational forces, thus on hight difference (Δh), for vessels that do not lie in a horizontal plane - In CV physiology the reference level (h0) is the level of the heart.

29 Laminar vs. turbulent blood flow in the vessels Laminar flow - blood flows in streamlines, at a steady rate through a long, smooth blood vessel Each layer of blood remains at the same distance from the vessel wall. The central most portion of the blood stays in the center of the vessel. Cause for the parabolic profile for velocity of blood flow: the blood near the wall of the vessel flows extremely slowly, whereas that in the middle of the vessel flows extremely rapidly. Fluid 1 Fluid 2 before flow begins parabolic interface layers of slipping molecules 1 sec. after flow begins adherence to the vessel wall

30 The velocities increase from the wall to the center of the cylinder. The resulting velocity profile is a parabola with a maximum velocity, vmax, at the central axis. The lower the viscosity, the sharper the point of the bullet shaped velocity profile.

31 Turbulent flow when: -vessel radius is large (e.g. aorta) -the rate of blood flow becomes too great, velocity is large (high CO) -blood passes by an obstruction in a vessel (arterial stenosis) that causes a local increase in blood velocity -blood makes a sharp turn -changes in the blood density and low viscosity (e.g. anemia) Turbulent flow - the blood flows disorderly, both crosswise and along the vessel forming whorls in the blood called eddy/vortex currents increase the overall friction of flow in the vessel much greater resistance, that causes substantial kinetic energy losses; also, audible murmurs or mechanical vibrations (thrills) when the turbulence is very intense Turbulent flow - elements of the fluid moving in a disorderly pattern.

32 Reynolds' number (Re): measures the tendency for turbulence to occur Re ~ in large arteries ν - mean velocity of blood flow r - vessel radius ρ density (normal for blood ~1) η (eta) viscosity (normal for blood ~ 1/30 poise) The type of flow can be predicted by Reynold s number: if Re (> ) more turbulence; if Re less turbulence Reynold s number & turbulence are increased by: 1. blood viscosity (e.g., hematocrit, anemia) 2. blood velocity (e.g., during ejection, pulsatile flow, vessel narrowing) 3. blood making a sharp turn or passing over a rough surface 4. Sudden change into a larger vessel diameter. In small vessels Re is normally low and will not cause turbulence. But for Re>2000, turbulence can occur even in a straight, smooth vessel.

33 Blood flow is laminar when Re is <2000 and is mostly turbulent when Re exceeds ~3000.

34 Resistance opposes flow Blood flowing through vessels encounters friction from the walls of the vessels and from cells within the blood rubbing against each other as they flow. The tendency of the CV system to oppose blood flow is called its resistance (R) to flow. Blood flow will take the path of least resistance. Flow ~ 1/R

35 Resistance A. Resistances in series: each organ is supplied by a large artery, then smaller arteries, arterioles, capillaries, venules, that merge into veins, collectively arranged in series flow through each sector of vessels is continuous total resistance to blood flow (R total ) is equal to the sum of the resistances of each vessel: R total (TPR) =R artery +R arterioles(2/3) +R capillaries B. Resistance in parallel: in the systemic circulation each organ is supplied by an artery that branches off the aorta. This parallel arrangement enable tissue local blood flow regulation independently of flow to other tissues: 1/R total =1/R 1 +1/R /R n and F total =F 1 +F 2 + +F n F=flow or conductance (C)

36 A simplified model of CV system For multiple resistance elements (R1, R2, R3, ) arranged in series,

37 Resistance to Blood Flow Units of Resistance. If the pressure difference between two points is 1 mm Hg and the flow is 1 ml/sec, the resistance is 1 peripheral resistance unit (PRU). Total Peripheral Vascular Resistance (TPR): Resistance of the entire systemic circulation ~ DP/F ~ 100 mmhg/100 ml/sec ~1 PRU for a CO ~ 100 ml/sec Strong vasoconstriction TPR up to 4 PRU. Vasodilation TPR falls to 0.2 PRU Total Pulmonary Vascular Resistence Net pressure difference = mean pulmonary arterial press (16) - mean LA pressure (2) = 14 mmhg. Total pulmonary vascular resistance ~ DP/F ~ 14 mmhg /100ml/sec ~0.14 PRU (1/7 than the systemic one)

38 Blood Flow or conductance through individual blood vessels for a given pressure difference is determined by their resistance Flow ~ 1/Resistance

39 Slight changes in the blood vessels radius by vasodilation or vasoconstriction, can change the blood flow. A. Demonstration of the effect of vessel diameter on blood flow. B. Concentric rings of blood flowing at different velocities; the farther away from the vessel wall, the faster the flow.

40 Role of radius in determining resistance to flow Resistance ~ 1/radius 4 Flow ~ radius 4

41 Poiseuille s Law: Flow in an idealized vessel increases with the 4 th power of radius F~1/R and R~1/r 4 F~ r 4 F ~ DP F= flow, R = resistance (eta) = viscosity of blood flow l = length of blood vessel r 4 = radius of vessel to the 4 th power r ~ 4 25 mm in arterioles, changes up to 4 times in response to local or nervous control mechanisms Obs.:! High R with increased hematocrit (%RBC )! if radius (r) increases by a factor of 2, then resistance (R) decreases by a factor of 2 4 =16, and F increases by a factor of 16

42 Effect of Blood Hematocrit and Blood Viscosity on Vascular Resistance and Blood Flow Viscosity of normal blood ~ 3 x viscosity of water, mainly because of large numbers of suspended RBC increased friction against adjacent cells and vessel wall (three times as much pressure is required to force whole blood as to force water through the same blood vessel) Normal hematocrit (Ht=45%) blood viscosity ~ 3. Increased Ht to 60-70% (polycythemia) viscosity ~10 x blood flow greatly retarded. Viscosity secondary depends on plasma protein concentration and types of proteins in the plasma. Viscosity of blood plasma is about 1.5 x that of water.

43 Effect of hematocrit on blood viscosity. (Water viscosity = 1)

44 How is obtained the pressure gradient. Compressing a fluid raises its pressure LV systole the pressure created is transferred to the blood high-pressure blood displace lower-pressure blood already in the vessels = driving pressure Volume changes of the heart and blood vessels are major factors that influence blood pressure in the vascular system. Blood pressure is the force exerted by the blood against any unit area of the vessel wall, measured in mmhg, or cm H 2 O. 1 mmhg = 1.36 cm H 2 O as specific gravity of Hg is 13.6 x that of water

45 Pressure and flow oscillate with each heartbeat between maximum systolic and minimum diastolic values

46 Blood flow is pulsatile in both the systemic and pulmonary circulations The mean arterial pressure (MAP) is a single, time-averaged value, that in the large systemic arteries is ~95 mmhg. The blood pressure cycles between a maximal systolic arterial pressure (~120 mmhg) that corresponds to the contraction of the ventricle and a minimal diastolic arterial pressure (~80 mmhg) that corresponds to the relaxation of the ventricle.

47 Origins of pressure in the circulation: 1) gravity hydrostatic pressure 2) compliance of the vessels, 3) viscous resistance (R that opposes flow (shearing forces in the liquid)), 4) inertia (inertial impedance that opposes a change of flow (kinetic energy of fluid and vessels)). The total pressure difference at any point in time:

48 Gravity causes a hydrostatic pressure difference when there is a difference in height =53-(-32)=85 Below the heart level, the increased transmural pressure increases the diameter of distensible vessels

49 Vascular Distensibility Normally expressed as the % increase in volume /1mmHg rise in pressure: all blood vessels are distensible, but arteries on average are ~ 8 x less distensible than the veins arteries distensibility allows them to accommodate the pulsatile output of the heart and to average out the pressure pulsations smooth, continuous blood flow through the very small blood vessels. pulmonary circulation: - pulm veins distensibility similar to those of the systemic circulation. - pulmonary arteries normally operate under 6 x lower press. 6 x greater distensibility than the one in the systemic arteries.

50 Vascular Compliance Compliance (C)= total quantity of blood stored in a given portion of the circulation per 1 mmhg pressure rise: C (ml/mm Hg) = DV/DP Compliance = distensibility x original volume C veins >>C arteries unstressed vol. (veins)>>stressed vol. (arteries) Changes with age: arteries become stiffer and less distensible ( C)

51 Velocity of blood flow v (velocity) = F/A (flow/cross-sectional area) v = velocity of flow (cm/sec) = a measure of how fast blood flows past a point F = blood flow (L or ml/min) or flow rate (blood volume that passes one point in the system /unit time. A = cross-sectional area (cm 2 ) at a certain level of the cardiovascular system Obs: v in aorta vs. capillaries

52 Bernoulli effect v in the aorta increases and reaches a maximum during systole and falls off during diastole these change lead to compensatory changes in intravascular pressure, to keep the fluid flow (v=f/a). Fluids flow from a higher to a lower pressure, but more accurate, from a higher to a lower total energy. Total energy = the pressure or potential energy and the kinetic energy, with their interconversions.

53 Elastic recoil Continuous driving pressure for blood flow High-resistance outlet for arterial blood flow and distribution to individual tissues Blood flow through all the systemic capillaries equal the cardiac output (5 l/min) A simplified model of CV system

54 Laplace s law describes how tension in the vessel wall increases with transmural pressure T = ΔP x r, in which P, intravascular pressure; r, vessel radius; T, wall tension as the force per unit length tangential to the vessel wall (a force that opposes to the distending force that tends to pull apart an imaginary longitudinal slit in the vessel). r of resistance vessels ~ contractile force of the vascular smooth muscle ~ distending force produced by the intraluminal pressure. Intravascular pressure diminished vessel diameter and tension in the vessel wall decreased (Laplace's law) terminal arteriole response: vasodilation When intravascular pressure is progressively reduced, a value of the transmural pressure = critical closing pressure is reached; at this pressure the vessel is occluded and blood flow ceases even though a positive pressure gradient from the afferent to the efferent end of the vessel may still exist. Also, small arterioles may be occluded because of infolding of the endothelium.

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56 Consequences of Laplace's law: T=p x r Even the capillaries are thin-walled, they can withstand high internal pressures without bursting because of their narrow lumens. At normal aortic (100 mm Hg) and capillary (25 mm Hg) pressures, the wall tension of the aorta is about 12,000 times greater than that of the capillary: 100 mmhg r of 1.5 cm for the aorta vs. 25 mmhg r of cm for the capillary In a person standing quietly, capillary pressure in the feet reach 100 mmhg. Under such conditions, capillary wall tension increases to a value that is only that of the wall tension in the aorta at the same internal pressure. According to Laplace's equation, wall tension increases as vessels dilate, even when internal pressure remains constant (T=p x r). In aneurysm (local widening) of the aorta, the wall tension may become high enough to rupture the vessel.

57 Arterial pressure Flow in the arterial side of the circulation is pulsatile, reflecting the changes in arterial pressure throughout a cardiac cycle; once past the arterioles, pulse waves disappear. Systolic pressure (SP): highest value during a cardiac cycle, highest in aorta ~ 120 mmhg Diastolic pressure (DP): lowest value during a cardiac cycle ~ 80 mmhg! As diastolic pressure in LV ~ 0 mm Hg, DP in large arteries remains relatively high because of their capacity to store energy in the elastic walls.

58 The pressure pulse wave = a moving wave of pressure that assists the continuous flow - determined by the ejection of blood in aorta - transmitted through the fluid-filled arteries x more fast than the blood - its velocity increases from aorta (3-5 m/sec) to large arteries (7-10 m/sec), small arteries (15-35 m/sec), along with the decrease in the vessels compliance

59 Pulse pressure Pulse pressure = P systolic P diastolic =120-80= 40 mmhg = f (stroke vol., low arterial compliance) In aging: compliance cause pulse pressure. Friction effect

60 Mean arterial pressure (MAP) MAP = average arterial pressure with respect to time - representative for the driving pressure = diastolic pressure + 1/3 pulse pressure

61 MAP = 80 mmhg + 1/3( mmhg)= 93 mmhg for HR = beats/min MAP value more close to the DP. Why? Diastole lasts twice as long as systole. What happens with MAP value if HR increases?

62 Arterial pressure is estimated by sphygmomanometry AP in brachial artery of the arm Sphygmomanometer: inflatable cuff, pressure gauge When the cuff is inflated so that it stops arterial blood flow, no sound can be heard through a stethoscope placed over the brachial artery distal to the cuff.

63 Korotkoff sounds are created by pulsatile blood flow through the compressed artery. Blood flow is silent when the artery is no longer compressed.

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