Relationship between blood flow,
vascular resistance and blood
pressure
Kirk Levins
Blood Flow 1
 Blood flow is defined as the quantity blood
passing a given point in the circulation in a
given period and is normally expressed in
ml/min
 Overall blood flow in the total circulation of
an adult is about 5000 ml/min….The cardiac
output
Equations of flow
 Since flow is a measure of volume per unit time
=> Q=VA, where Q=Flow V=Velocity, A=Cross sectional area
 Since the vascular system obeys an adaptation of
Ohms law, known as Darcy’s law
=> Q=ΔP/R, where ΔP is the pressure differential and R is the resistance
Cross-sectional areas and Blood flow
- If all the systemic vessels of each type were put side by side, their approximate total crosssectional areas for the average human being would be as follows:
Vessel
Cross-Sectional Area (cm2)
Aorta
2.5
Small arteries
20
Arterioles
40
Capillaries
2500
Venules
250
Small veins
80
Venae cavae
8
 Because the same volume of blood must flow through each
segment of the circulation each minute, the velocity of blood
flow is inversely proportional to vascular cross-sectional area.
Thus, under resting conditions, the velocity averages about 33
cm/sec in the aorta but only 1/1000 as rapidly in the
capillaries, about 0.3 mm/sec.
Modes of flow in vessles
 Blood flow can either be laminar or turbulent
Laminar Flow
 When blood flows through a long smooth vessel it flows in
straight lines, with each layer of blood remaining the same
distance from the walls of the vessel throughout its length
 When laminar flow occurs the different layers flow at different
rates creating a parabolic profile
 The parabolic profile arises because the fluid molecules touching
the walls barely move because of adherence to the vessel wall.
The next layer slips over these, the third layer slips over the
second and so on.
Turbulent flow
 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
 Turbulent flow means that the blood flows crosswise in the vessel
as well as along the vessel, usually forming whorls in the blood
called eddy currents. When eddy currents are present, the blood
flows with much greater resistance than when the flow is
streamline because eddies add tremendously to the overall friction
of flow in the vessel.
Turbulent flow
 The tendency for turbulent flow increases in direct
proportion to the velocity of blood flow, the diameter of
the blood vessel, and the density of the blood, and is
inversely proportional to the viscosity of the blood, in
accordance with the following equation:
Re=(v.d.ρ)/ η
where Re is Reynolds' number 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
density, and η is the viscosity (in poise)
 When Reynolds’ number increases above about 200
turbulent flow will result
Resistance
 Resistance is the impediment to blood flow in a vessel
 Resistance cannot be measured by any direct means, instead,
resistance must be calculated from measurements of blood flow and
pressure difference between two points in the vessel such that:
Q=(PA-PV)/R
Where Q= Flow, PA-PV=difference between mean arterial and venous pressures, R=resistance
 Resistance to blood flow within a vascular network is determined by
the length and diameter of individual vessels, the organization of the
vascular network , physical characteristics of the blood (viscosity,
laminar flow vs turbulent flow, and extravascular mechanical forces
acting upon the vasculature.
Regulation 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 pressure
Conductance
 Conductance is a measure of the blood flow
through a vessel for a given pressure difference
and is usually expressed in milliliters per second
per millimeter of mercury pressure
 Conductance is equal to the reciprocal of
resistance
Conductance and vessel diameter
 Slight changes in the diameter of a vessel cause
tremendous changes in the vessel's ability to conduct
blood when the blood flow is streamlined
 Although the diameters of these vessels increase only
fourfold, the respective flows are 1, 16, and 256
ml/mm, which is a 256-fold increase in flow. Thus, the
conductance of the vessel increases in proportion to the
fourth power of the diameter
Pouiseuille’s law
 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
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
multiplying them by the areas of the rings, one can derive the following
formula, known as Poiseuille's law:
Q = (π ΔPr4)/8 ηl
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.
Relationship between resistance and
vessel radius

Pressure
Blood pressure means the force exerted by the blood against any unit area of the vessel wall

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
high, averaging about 100 mm Hg

Heart pumping is pulsatile, the arterial pressure alternates between a systolic pressure level of
120 mm Hg and a diastolic pressure level of 80 mm Hg, as shown on the left

As the blood flows through the systemic circulation, its mean pressure falls progressively to
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.
Effect of pressure on vascular resistance
and blood flow
 Relationship between blood flow and pressure is
exponential
 Increase in arterial pressure not only increases the force that
pushes blood through the vessels but also distends the
vessels at the same time, which decreases vascular
resistance.
Relationship between blood flow,
vascular resistance and blood
pressure
 Blood flow through a blood vessel is determined by two
factors:
 (1) pressure difference of the blood between the two ends
of the vessel, also sometimes called "pressure gradient"
along the vessel, which is the force that pushes the blood
through the vessel, and
 (2) the impediment to blood flow through the vessel,
which is called vascular resistance
Q=ΔP/R
Questions???