Relationship between blood flow, Relationship between blood flow, vascular resistance and blood vascular resistance and blood

pressurepressure

Kirk LevinsKirk Levins

Blood Flow 1Blood Flow 1

Blood flow is defined as the quantity blood Blood flow is defined as the quantity blood passing a given point in the circulation in a passing a given point in the circulation in a given period and is normally expressed in given period and is normally expressed in ml/minml/min

Overall blood flow in the total circulation of Overall blood flow in the total circulation of an adult is about 5000 ml/min….The cardiac an adult is about 5000 ml/min….The cardiac outputoutput

Equations of flowEquations of flow

Since flow is a measure of volume per unit time Since flow is a measure of volume per unit time => => Q=VAQ=VA, , where Q=Flow V=Velocity, A=Cross sectional areawhere Q=Flow V=Velocity, A=Cross sectional area

Since the vascular system obeys an adaptation of Since the vascular system obeys an adaptation of Ohms law, known as Darcy’s law Ohms law, known as Darcy’s law

=> => Q=Q=ΔΔP/RP/R, , where where ΔΔP is the pressure differential and R is the resistanceP is the pressure differential and R is the resistance

Cross-sectional areas and Blood flowCross-sectional areas and Blood flow

Because the same volume of blood must flow through each Because the same volume of blood must flow through each segment of the circulation each minute, the velocity of blood segment of the circulation each minute, the velocity of blood flow is inversely proportional to vascular cross-sectional area. flow is inversely proportional to vascular cross-sectional area. Thus, under resting conditions, the velocity averages about 33 Thus, under resting conditions, the velocity averages about 33 cm/sec in the aorta but only 1/1000 as rapidly in the cm/sec in the aorta but only 1/1000 as rapidly in the capillaries, about 0.3 mm/sec. capillaries, about 0.3 mm/sec.

VesselVessel Cross-Sectional Area (cmCross-Sectional Area (cm22))

AortaAorta 2.52.5

Small arteriesSmall arteries 2020

ArteriolesArterioles 4040

CapillariesCapillaries 25002500

VenulesVenules 250250

Small veinsSmall veins 8080

Venae cavaeVenae cavae 88

- If all the systemic vessels of each type were put side by side, their approximate total cross-sectional areas for the average human being would be as follows:

Modes of flow in vesslesModes of flow in vessles

Blood flow can either be laminar or turbulentBlood flow can either be laminar or turbulent

Laminar FlowLaminar Flow

When blood flows through a long smooth vessel it flows in When blood flows through a long smooth vessel it flows in straight lines, with each layer of blood remaining the same straight lines, with each layer of blood remaining the same distance from the walls of the vessel throughout its lengthdistance from the walls of the vessel throughout its length

When laminar flow occurs the different layers flow at different When laminar flow occurs the different layers flow at different rates creating a parabolic profilerates creating a parabolic profile

The parabolic profile arises because the fluid molecules touching The parabolic profile arises because the fluid molecules touching the walls barely move because of adherence to the vessel wall. the walls barely move because of adherence to the vessel wall. The next layer slips over these, the third layer slips over the The next layer slips over these, the third layer slips over the second and so on.second and so on.

Turbulent flowTurbulent flow

When When the rate of blood flow becomes too great, when it passes by 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 an obstruction in a vessel, when it makes a sharp turn, or when it passes over a rough surface, the flow may then become turbulentpasses over a rough surface, the flow may then become turbulent

Turbulent flow means that the blood flows crosswise in the vessel Turbulent flow means that the blood flows crosswise in the vessel as well as along the vessel, usually forming whorls in the blood as well as along the vessel, usually forming whorls in the blood called eddy currents. When eddy currents are present, the blood called eddy currents. When eddy currents are present, the blood flows with much greater resistance than when the flow is flows with much greater resistance than when the flow is streamline because eddies add tremendously to the overall friction streamline because eddies add tremendously to the overall friction of flow in the vessel. of flow in the vessel.

Turbulent flowTurbulent flow

The tendency for turbulent flow increases in direct The tendency for turbulent flow increases in direct proportion to the velocity of blood flow, the diameter of proportion to the velocity of blood flow, the diameter of the blood vessel, and the density of the blood, and is the blood vessel, and the density of the blood, and is inversely proportional to the viscosity of the blood, in inversely proportional to the viscosity of the blood, in accordance with the following equation:accordance with the following equation:

Re=(v.d.Re=(v.d.ρρ)/)/ η η where Re is where Re is Reynolds' numberReynolds' number and is the measure of the tendency for turbulence to occur, ν is the and is the measure of the tendency for turbulence to occur, ν is the

mean velocity of blood flow (in centimeters/second), d is the vessel diameter (in centimeters), ρ is mean velocity of blood flow (in centimeters/second), d is the vessel diameter (in centimeters), ρ is density, and η is the viscosity (in poise) density, and η is the viscosity (in poise)

When Reynolds’ number increases above about 200 When Reynolds’ number increases above about 200 turbulent flow will resultturbulent flow will result

ResistanceResistance

Resistance is the impediment to blood flow in a vesselResistance is the impediment to blood flow in a vessel

Resistance cannot be measured by any direct means, instead, Resistance cannot be measured by any direct means, instead, resistance must be calculated from measurements of blood flow and resistance must be calculated from measurements of blood flow and pressure difference between two points in the vessel such that: pressure difference between two points in the vessel such that:

Q=(PQ=(PAA-P-PVV)/R)/RWhere Q= Flow, PWhere Q= Flow, PAA-P-PVV=difference between mean arterial and venous pressures, R=resistance=difference between mean arterial and venous pressures, R=resistance

Resistance to blood flow within a vascular network is determined by Resistance to blood flow within a vascular network is determined by the length and diameter of individual vessels, the organization of the the length and diameter of individual vessels, the organization of the vascular network , physical characteristics of the blood (viscosity, vascular network , physical characteristics of the blood (viscosity, laminar flow vs turbulent flow, and extravascular mechanical forces laminar flow vs turbulent flow, and extravascular mechanical forces acting upon the vasculature.acting upon the vasculature.

Regulation of blood pressureRegulation of blood pressure Regulation of blood pressure involves the exercise of a number of different functions in

different parts of the body. Their collective task is to maintain blood pressure value within a certain interval.

Blood pressure values are maintained within the relevant range by moment-to-moment regulation of cardiac output and of peripheral vascular resistance exerted primarily at the level of the arterioles, postcapillary venules and heart

The most important dimensions of this regulation are as follows:

– The heart contributes to the maintenance of blood pressure via cardiac output

– The kidney contributes by regulating the volume of the fluid present in the blood vessels.

– The internal cellular lining of the walls of the blood vessels regulates vascular resistance via local release of hormones such as endothlin-1 and nitric oxide.

– The baroreceptors are responsible for the rapid moment-to-moment adjustments in blood pressure affected by postural changes

Regulation of blood pressureRegulation of blood pressure

ConductanceConductance

Conductance is a measure of the blood flow Conductance is a measure of the blood flow through a vessel for a given pressure difference through a vessel for a given pressure difference and is usually expressed in milliliters per second and is usually expressed in milliliters per second per millimeter of mercury pressure per millimeter of mercury pressure

Conductance is equal to the reciprocal of Conductance is equal to the reciprocal of resistanceresistance

Conductance and vessel diameterConductance and vessel diameter

Slight changes in the diameter of a vessel cause Slight changes in the diameter of a vessel cause tremendous changes in the vessel's ability to conduct tremendous changes in the vessel's ability to conduct blood when the blood flow is streamlined blood when the blood flow is streamlined

Although the diameters of these vessels increase only Although the diameters of these vessels increase only fourfold, the respective flows are 1, 16, and 256 fourfold, the respective flows are 1, 16, and 256 ml/mm, which is a 256-fold increase in flow. Thus, the ml/mm, which is a 256-fold increase in flow. Thus, the conductance of the vessel increases in proportion to the conductance of the vessel increases in proportion to the fourth power of the diameterfourth power of the diameter

Pouiseuille’s lawPouiseuille’s law

The relationship between conductance and diameter can be explained by The relationship between conductance and diameter can be explained by considering the number of ‘layers’ of blood in a vessel. For a small vessel a considering the number of ‘layers’ of blood in a vessel. For a small vessel a large proportion of the blood is in contact with the wall of the vessel.large proportion of the blood is in contact with the wall of the vessel.

By integrating the velocities of all the concentric rings of flowing blood and By integrating the velocities of all the concentric rings of flowing blood and multiplying them by the areas of the rings, one can derive the following multiplying them by the areas of the rings, one can derive the following formula, known as Poiseuille's law:formula, known as Poiseuille's law: Q = ( Q = (π π ΔΔPrPr44)/8 )/8 ηlηl

where Q is the rate of blood flow, ΔP is the pressure difference between the ends of the vessel, r is the radius of where Q is the rate of blood flow, ΔP is the pressure difference between the ends of the vessel, r is the radius of

the vessel, l is length of the vessel, and η is viscosity of the blood.the vessel, l is length of the vessel, and η is viscosity of the blood.

Relationship between resistance and Relationship between resistance and vessel radiusvessel radius

PressurePressure Blood pressure means the Blood pressure means the force exerted by the blood against any unit area of the vessel wallforce exerted by the blood against any unit area of the vessel wall

Blood pressure almost always is measured in millimeters of mercury (mm Hg)Blood pressure almost always is measured in millimeters of mercury (mm Hg)

Because the heart pumps blood continually into the aorta, the mean pressure in the aorta is Because the heart pumps blood continually into the aorta, the mean pressure in the aorta is high, averaging about 100 mm Hg high, averaging about 100 mm Hg

Heart pumping is pulsatile, the arterial pressure alternates between a Heart pumping is pulsatile, the arterial pressure alternates between a systolic pressure levelsystolic pressure level of of 120 mm Hg and a 120 mm Hg and a diastolic pressure leveldiastolic pressure level of 80 mm Hg, as shown on the left of 80 mm Hg, as shown on the left

As the blood flows through the As the blood flows through the systemic circulation,systemic circulation, its mean pressure falls progressively to its mean pressure falls progressively to about 0 mm Hg by the time it reaches the termination of the venae cavae where they empty about 0 mm Hg by the time it reaches the termination of the venae cavae where they empty into the right atrium of the heart. into the right atrium of the heart.

Effect of pressure on vascular resistance Effect of pressure on vascular resistance and blood flowand blood flow

Relationship between blood flow and pressure is Relationship between blood flow and pressure is exponentialexponential

Increase Increase in arterial pressure not only increases the force that in arterial pressure not only increases the force that pushes blood through the vessels but also distends the pushes blood through the vessels but also distends the vessels at the same time, which decreases vascular vessels at the same time, which decreases vascular resistance.resistance.

Relationship between blood flow, Relationship between blood flow, vascular resistance and blood vascular resistance and blood

pressurepressure Blood flow through a blood vessel is determined by two Blood flow through a blood vessel is determined by two

factors: factors: (1) (1) pressure differencepressure difference of the blood between the two ends of the blood between the two ends

of the vessel, also sometimes called "pressure gradient" of the vessel, also sometimes called "pressure gradient" along the vessel, which is the force that pushes the blood along the vessel, which is the force that pushes the blood through the vessel, and through the vessel, and

(2) the impediment to blood flow through the vessel, (2) the impediment to blood flow through the vessel, which is called which is called vascular resistancevascular resistance

Q=Q=ΔΔP/RP/R

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