Download Cardiopulmonary Physiology

Cardiopulmonary Physiology
Millersville University
Dr. Larry Reinking
Chapter 3 - Physical Properties of the Blood and Circulation
Pressure Units
In medical practice a variety of units are used for pressure, that is, force applied per area.
These units include mm Hg, torr, cm H2O, atmospheres, mbars, pascal, newton/m2, dynes/cm2
and kPa. In most physiological research journals, as well as in clinical practice in Europe, SI
(Système Internationale) units are used. In clinical practice in the U.S. however, mm Hg
remains in common use, especially for the expression of blood pressure. For this reason, mm Hg
will be the most used unit in this course. The following are conversion factors for these units:
Unit
atmospheres
mbars
cm H2O
dynes/cm2
newton/m2
kilopascal
torr (at 0°C)
mm Hg unit
mm Hg ÷ 760
mm Hg x 1.333
mm Hg x 1.36
mm Hg x 1333
mm Hg x 133.3
mm Hg x 0.133
same
unit  mm Hg
atm. x 760
mbars ÷ 1.333
cm H2O ÷ 1.36
dynes/cm2 ÷ 1333
N/m2 ÷ 133.3
kPa ÷ 0.133
same
Table 3.1
Pressure
Conversions
Pressure Differences
The term 'pressure' is often used very loosely (as will be the practice in this course).
Remember that pressure measurements are usually relative to some benchmark. When we say
that the average arterial blood pressure is 100 mm Hg, more correctly we mean that the average
arterial blood pressure is 100 mm Hg greater than atmospheric pressure. 'Pressure difference',
'pressure head' or ‘driving pressure’ are technically more precise terms.
Effect of Gravity (Hemostatics)
Pascal, in the 17th century, developed three laws applying to fluids at rest (hydrostatics).
One of these laws essentially states that in a column of fluid, at rest under the influence of
gravity, the pressure will increase with depth under the free surface. This pressure will depend
on the density of the fluid. You can envision this law by imagining a plastic garbage can full of
water. If you poke a hole in the side of the can near the bottom, water will spray out with more
force than if you poke a hole near the top.
In quantitative terms this relationship can be stated as follows:
P = gh
Equation 3.1
Where P is pressure,  (rho) is density (in kg/l), g is gravitational acceleration (9.8 m/sec2) and, h
is the depth (in m) below the free surface. Thus, the pressure at the base of a column of water,
one meter high is:
1.0 kg/l x 9.8 m/sec2 x 1 m = 9,800 N/m2 = 73.5 mm Hg
Chapter 3
1
If you check the math, recall that a liter of water is 0.001 m3 and that a newton is a
kg.m/sec2. N/m2 was converted to mm Hg using the factor in Table 3.1. In the above example,
73.5 mm Hg refers to the pressure encountered at the bottom of a column of mercury 73.5 mm
high.
When using the 'column of' type pressure unit (cm H2O, mm Hg, etc.) we can convert
from one measure to another by using a ratio of the densities. In the above situation the ratio of
1.0
densities is
(densityO = 1.0 kg/l; densityHg = 13.6 kg/l). Thus, the mm Hg pressure
13.6
at the base of one meter column of water is:
1.0
1 meter H2O  1,000 mm H2O x
= 73.5 mm Hg
13.6
If we changed the fluid to saline (density = 1.04 kg/l), the pressure would be
1.04
1,000 mm saline x
= 76.5 mm Hg
13.6
and if the column was filled with blood (density = 1.056 kg/l, see p.1, chapter 2), then
1.056
1,000 mm blood x
= 77.6 mm Hg.
13.6
The first measure of blood pressure was performed by inserting a long vertical tube into
the crural artery of a horse. This famous experiment was reported in 1733 by Reverend Stephen
Hales in his book Haemostaticks.
Let us now consider the gravitational effects, on pressure, in the cardiovascular system. If
we were to measure pressure (using Hales' technique), in a supine individual, at three different
levels, say the heart, head and feet, we would obtain the same average arterial value of 100 mm
Hg (which is equal to a 130 cm column of blood):
100 mm Hg
130 cm
100 mm Hg

pressure loss
to head
Figure 3.1
130 cm
pressure gain
to feet
Hydrostatic Columns

In an erect individual, however, the different gravitational effects will cause a drop in
pressure to the brain and an increase in pressure at the level of the feet. Suppose that we measure
pressure in an cerebral artery 40 cm (400 mm) above the heart. At the level of this artery,
1.056
pressure will be reduced by 400 mm blood x
= 31 mm Hg. In other words, the average
13.6
blood pressure at this level will only be 69 mm Hg (i.e., 100-31). If the feet are 130 cm below
the heart, the average pressure in an artery at this level will be increased by 1300 mm blood x
1.056
= 100 mm Hg, that is, the total pressure will be 200 mm Hg (i.e., 100 + 100).
13.6
Chapter 3
2
Gravity Effects and Aviation Physiology
The effects of gravity on static pressures are of prime interest in aviation physiology. As
an aircraft pulls out of a dive, the pilot is subjected to a centripetal force at the bottom of the
loop. This force may be several times gravity. Consider blood pressure to the head as a pilot
experiences a 3g pullout. The gravitational influence is three times as large so that in our
previous example the pressure to the head is reduced by 3 x 31 = 93 mm Hg. If the average
pressure generated by the heart remains at 100 mm Hg, it is obvious that the brain will receive
little blood. Blackout, caused by brain anoxia, occurs at around 3-4g in pilots. If the centripetal
force is in the opposite direction, the blood pressure in the brain increases above normal. In this
case, the retina becomes engorged with blood and a visual effect called red-out occurs.
Transducer Placement and Gravity Effects
The position of the measuring device has an effect on the apparent value of the arterial
blood pressure (or pulmonary pressure, venous pressure, etc.). If the transducer is not at the same
height as the heart (or other organ) a false high or low reading will be the result. This is
especially important with low pressure recordings (such as venous pressure) because a small
misplacement of the transducer can result in a large percent error.
Hemodynamics
Hemodynamics deals with the physical properties of flowing blood. This discipline
borrows heavily from hydrodynamics, which is the study of moving fluids. By definition, a fluid
cannot permanently resist a shearing force, that is, a force that causes layers within the fluid to
slide over one another. If we use a stack of papers to represent a fluid, a shearing force would
cause the papers to slide over one another and scatter across a table. Viscosity is a measure of a
fluid’s ability to temporarily resist a shearing force.
Principle of Bernoulli
The pressure in a tube can be measured in different ways. It can be measured from the
side of a tube (called side pressure, wall pressure or lateral pressure) or it can be measured from
the end (end pressure):
wall
pressure
difference due
to kinetic
energy
end
pressure
wall
pressure
X
Figure 3.2
end
pressure
End and Wall
Pressures
Note, in the above diagram, that end pressure is greater when the fluid is moving but
drops, and is equivalent to the wall pressure, when the flow is stopped. The end pressure is a
reflection of total energy and the difference between wall and end pressure, seen with flow, is
due to kinetic energy (i.e., energy associated with motion). This kinetic component of pressure
can be expressed as:
Equation 3.2
P kinetic = 12    v2
where is the density of the fluid and v is the velocity. Bernoulli’s principle states that the total
energy in a tube will remain constant with a given flow rate. Thus, if the velocity increases in a
Chapter 3
3
tube (and the total energy is constant), the wall pressure will drop (note that doubling the velocity
results in four times the kinetic pressure). In other words, more of the total energy will then be
represented as kinetic pressure and the difference between the two tubes will be greater. The
following diagram further illustrates this principle:
Figure 3.3
low
velocity
high
velocity
low
velocity
Wall Pressure and
Velocity of Flow
The dotted line represents the pressure drop that would occur in a tube due to normal
resistance to flow. At the constricted portion of the tube, velocity increases (principle of flow
continuity, p. 5, chapter 1) and the wall pressure drops significantly. This is because more energy
is converted to the kinetic component and since total energy is constant, the wall pressure must
drop. In essence, the higher the velocity, the lower the wall pressure.
Physiological Significance of the Bernoulli Principle
Some arteries start as 90°, lateral branches from larger arteries, a situation similar to the
wall pressure manometers depicted above. Coronary arteries, the nutritional source for the heart,
are one example; they arise laterally from the aortic sinuses (Sinus of Valsalva) at the root of the
aorta. Thus, the coronary circulation is fed by side pressure. Now consider the situation in aortic
valve stenosis. The narrowed valve surface results in an increased velocity of blood movement
(again, flow continuity) and, as a consequence, coronary artery pressure drops substantially.
Fluid Flow in a Tube (Poiseuille’s Law)
Suppose that we were able to inject a small amount of dye, at various points along the
cross section, into water flowing through a glass tube. We would see the following type of
results:
Figure 3.4
Laminar Flow
The velocity of water movement in the center, as shown by the dye movement, is greatest and
becomes progressively slower near the wall of the vessel. These findings suggest that the fluid
has a number of layers (or lamina), each moving at a different velocity. If we envision infinitely
thin layers, the layer closest to the wall is impeded by cohesive forces and has no velocity. The
next layer has a small velocity, the third’s velocity is a little larger, and so on, to the center of the
tube. This type of flow is characteristic of viscous fluids moving at low velocities and is referred
to as laminar flow or streamlined flow.
Chapter 3
4
Poiseuille-Hagen Formula
The following formula describes the rate of streamlined flow in a tube:
4
  1  r 
Flow Rate = PA - PB        
8     l 
or
Flow Rate =
P    r 4
8   l
Equation 3.3
P is pressure (dynes/cm2),  the viscosity (poise), r the radius (cm) and l (cm) is the length. If
the indicated units are used, the rate of flow will be in cm3/sec (i.e., ml/sec). Some of the terms
in this equation are common sense, others are quite surprising.
PA-PB is the driving pressure between point A and point B in the tube (also indicated as P).
The greater the driving pressure, the greater the rate of flow.
/8 is a geometrical term related to the circular cross section of the tube.
1/ indicates the inverse proportionality to the fluid viscosity. A more viscous fluid, such as
molasses, will flow slower than water given the same driving pressure.
r4/l - illustrates, first, that flow rate is decreased in long tubes, that is, resistance to flow
increases with tube length. If you have ever tried to run water through several connected
garden hoses, you have seen this principle at work. The relationship to r4 is a surprising and
profound part of this formula. The significance of r4 is expanded in the next section.
Flow Rate and Vessel Radius
The r4 relationship is a very powerful part of the Poiseuille formula and is quite important
to cardiovascular physiology. Local regulation of blood flow is regulated by vasoconstriction
and vasodilation and this formula indicates that only small changes in a vessel’s radius are
needed to bring about huge changes in blood flow. If a vessel were to double in diameter, the
flow rate would increase 16x (i.e., 2x2x2x2). A vessel changing from a diameter of 1 mm to 0.8
mm will have only 41% (0.84) of the original flow. Perhaps you have heard of someone with a
90% occlusion in a coronary artery. This means that the flow in that artery (and the nutrition to
that part of the heart) is only 0.01% (0.14) of normal!
Newtonian Fluids vs. Blood
A Newtonian fluid closely approximates the behavior predicted by Poiseuille’s law (Sir
Isaac Newton derived some of the first principles involved with streamlined flow). Water and
many other simple fluids have good Newtonian properties. On the other hand, blood is a nonNewtonian fluid. The presence of suspended cells and, perhaps, large protein molecules cause
significant deviations from ideal Newtonian behavior. In addition, the circulation is not
composed of rigid, straight tubes; rather they are elastic and branched. Quite unlike rigid tubes,
when the pressure drops below a certain pressure (the critical closing pressure) blood vessels will
collapse. Despite these problems, Poiseuille’s Law is a reasonable and useful approximation for
blood flow in the circulation under normal physiological conditions. The following section deals
with some of the non-Newtonian aspects of blood.
Viscosity of Blood
Chapter 3
5
Blood is a complex, colloidal solution with a viscosity about three times higher than
water (water has a viscosity of 1 centipoise at 37°C). The apparent viscosity of blood is greatly
affected by hematocrit, temperature and blood vessel diameter.
Hematocrit - As the packed cell volume increases, the viscosity of blood rises in an almost
exponential fashion:
14
12
Rela tive Viscosity
10
Figure 3.5
8
6
Hematocrit and
Blood Viscosity
4
2
0
0
20
40
60
80
10 0
Hem atocrit (%)
Above a hematocrit of 60%, viscosity rapidly rises (recall polycythemia vera, p. 3, chapter 2) and
the work of the heart becomes extreme.
Temperature - Like molasses, blood viscosity has a significant change with temperature. Blood
cooled from 37°C to ≈0°C will increase viscosity by about 2.5x. This temperature effect is an
important factor in frostbite and other cold injuries. As the affected tissue is cooled, perfusion is
reduced, compounding the situation.
Viscosity in Small Vessels (Fahraeus-Lindquist Effect) - A Newtonian fluid, such as water, has a
viscosity that is independent of tube size. The apparent viscosity of blood does not follow this
pattern and, surprisingly, greatly decreases in small (<0.05 mm diameter) tubes. This odd
behavior may be attributed to the colloidal properties of blood. Chemists have described a
similar phenomenon in colloidal solutions that is called the Sigma Effect. Recall that Poiseuille’s
law is based on the assumption that numerous, small layers slide over one another. In blood and
other colloids, the thickness of each layer is determined by the size of the colloid particle (i.e., an
erythrocyte for blood). Thus, in a very small tube only a limited number of layers would be able
to form and, therefore, a large deviation from expected behavior could occur.
Axial Streaming of Blood Cells
A final non-Newtonian property of blood is a of great interest; axial streaming. In a
blood vessel, the red blood cells tend to cluster along the axis, leaving a layer near the wall that is
primarily plasma:
Figure 3.6
Axial Streaming of
Red Blood Cells
Note the smaller vessel branching laterally from the wall. This smaller vessel will have blood
with a lower percent of red blood cells due to ‘plasma skimming’. Thus, the hematocrit in
Chapter 3
6
various parts of the circulation can be quite different (‘finger prick’ blood can yield a hematocrit
that is ≈25% lower than that in ‘large vessel’ blood from the same person). Also consider the
placement of a needle when a blood sample is taken. A needle that just penetrates a vessel wall
can produce a very different sample from one in which the needle extends into the axial stream of
cells.
Turbulent Flow
Poiseuille’s Law indicates that as the driving pressure increases there will be a proportion
increase in the rate of flow. Since the cross sectional area of the tube is constant, there will also
be a proportional increase in velocity of blood movement. However, beyond a critical velocity
this relationship will no longer hold true:
Figure 3.7
Critical Velocity for
Turbulent Flow
Above this critical point the fluid no longer flows as sliding layers, but rather forms a
series of chaotic swirls and eddies. Note that turbulent flow is much less efficient than laminar
flow; for a given increase in driving pressure, there is a rather small increase in the rate of flow
during turbulence. Reynolds first demonstrated that the critical velocity (Vc, cm/sec) depends on
the radius of the tube (r, cm), density of the fluid (, g/ml) and viscosity (, poise) in the
following fashion:
K 
Equation 3.4
Vc =
 r
K, the Reynold's number, is a constant that has a value of about 1000 for blood (and many
other fluids) when flowing in a long straight tube. K is much smaller (as will be Vc) for
branches, constrictions, bends and rough walls. In the normal circulatory system, turbulent flow
occurs only periodically in the heart (see problem #3 at the end of the chapter).
Turbulence and Circulatory Sounds
While laminar flow is silent, the eddies and swirls of turbulent flow create vibrations;
turbulent flow is noisy. The heart sounds are a result of turbulence caused by the opening and
closing of the heart valves. Abnormal sounds can be heard with valvular defects (heart murmurs)
or over atherosclerotic arteries (bruits). Turbulent sounds occur more often with anemia due to
lowered blood viscosity (consider this in terms of the Poiseuille equation, flow continuity and the
effect on Vc). The sounds used to determine indirect blood pressure (Karotkoff's sounds) are the
result of compressing vessels with the blood pressure cuff and creating a momentary turbulent
blood flow.
Chapter 3
7
Resistance to Blood Flow
Another way to look at the relationship between the rate of flow and pressure is by way of
an analogy to Ohm’s law of electricity. Recall that this law involves voltage (E), current (I) and
resistance (R) and states that I = E/R. In a similar fashion we can make a statement about the
circulation if we consider the concept of resistance to blood flow. Thus the analogous
relationship is:
.
P
P
and R = .
Equation 3.5
Q =
R
Q
A symbol topped by a dot implies a rate of flow (see Appendix I), Q. is used for blood flow, P is
the driving pressure and R the resistance to blood flow. Incorporating the above relation ship
with Poiseuille’s equation (Equation 3.3),
R =
P
combined with
.
Q
R =
P    l
  r4
.
Q=
8  r 4
8   l
gives an expression for vascular resistance:
Vascular Resistance
Equation 3.6
This value has units of dynessec/cm5 and is a commonly used measure in cardiovascular studies.
The units, however, are not very intuititive so, for our purposes, a simpler approach will be used.
The Peripheral Resistance Unit (PRU) is the vascular resistance when the mean arterial
pressure is 100 mm Hg and the rate of blood flow is 100 ml/sec (100 ml/sec = 6 liters/min):
R =
P
.
Q
=
100 mm Hg
= 1PRU
100 ml/sec
Peripheral Resistance Unit
Equation 3.7
Thus, an individual with an average arterial pressure of 93 mm Hg and a cardiac output of 110
ml/sec has a peripheral resistance of 0.845 PRU.
Series Resitance
In a fashion analogous to electrical resistance, vascular resistances, in series, simply add
to form a total resistance (RT):
Equation 3.8
R T = R1 + R2 + R3
Series Resistance
In the above situation, if R1 = 2 PRU, R2 = 1 PRU and R3 = 3 PRU then RT = 6 PRU.
Parallel Resistance
In a set of parallel resistances, the reciprocal of the total resistance is equal to the sum of
the reciprocals of the individual resistances:
Chapter 3
8
Equation 3.9
1
1
1
1
=
+
+
RT
R1
R2
R3
Parallel Resistance
Cardiac Output, Resistance and Arterial Blood Pressure
We can convert the above analogy to Ohm's law into terms that are more commonly used
in circulatory physiology. The rate of flow ( Q. ) is called the cardiac output (CO), the driving
pressure (P) is the difference between the arterial pressure and the venous pressure (Pa-Pv), and
resistance is referred to as total peripheral resistance (RT). Using these terms the equation will
now be:
P  Pv
Equation 3.10
CO = a
RT
or, when stated in terms of arterial pressure becomes:
Pa = (CO  RT ) + Pv
Equation 3.11
This last formula will be very valuable when we examine controls of arterial blood pressure and
mechanisms in hypertension.
Vascular Compliance (also called Capacitance or Distensibility)
Compliance (C) refers to the pressure change (P) that occurs with a change in volume
(V):
C =
V
P
Equation 3.12
A vessel that can take on a large additional volume with a small change in pressure is said
to be highly compliant,while a vessel that has a large increase in pressure with a small volume
addition is said to be non-compliant. The following graph depicts short term vascular
compliance for an artery and vein:
Pressure
s ymp. s tim.
Figure 3.8
artery
Vascular Compliance
s ymp. s tim.
vein
Volume
In general, the venous system is much more compliant than the arterial system. As
indicated above, the vasoconstricting action of sympathetic stimulation decreases compliance.
Chapter 3
9
This graph also confirms a previous statement (p.5, chapter 1) that the volume contained within
the venous system is greater than that in the arterial system.
Delayed Compliance
The relationship depicted in the above graph is valid for only a short period of time. The
compliance of the vascular system will actually change, over time, following an addition or
removal of volume. The following graph depicts the pressure change that will occur in an
isolated vessel following the addition and removal of blood:
Pressure
remo ve
vo lume
Figure 3.9
Delayed Compliance
add
vo lume
Time
This phenomenon is called delayed compliance and is caused by a change in tone of the
smooth muscle in the vessel wall. Smooth muscle when stretched or relaxed readjusts its tension
(this is called stress-relaxation). A stretched vessel, as shown above, will readjust by becoming
more compliant while a relaxed vessel becomes less compliant. Delayed compliance occurs to a
greater degree in veins than in arteries.
Physiological Significance of Delayed Compliance
In clinical cases of over infusion of fluids or in cases of blood loss a number of
mechanisms either correct or moderate a change in arterial blood pressure. Delayed compliance
is one of these mechanisms; we will encounter several others in later chapters. Many organs
maintain a constant blood flow, even over a wide range of perfusion pressures (60-120 mm Hg).
This phenomenon is known as autoregulation and will still occur after the autonomic nerve
supply to the arterioles has been removed. Delayed compliance may play a role in organ
autoregulation of blood flow.
Chapter 3
10
Some Blood Flow Problems
1. The cardiac output = 5.6 l/min (= 93 ml/sec = 93 cm3/sec) and the radius of the aorta = 1 cm.
What is the velocity of blood flow in the aorta? (this problem deals with flow continuity,
Equation 1.2)
2. The total cross-sectional area of the systemic capillaries is 5000 cm2. Using the information
from the previous question, determine the velocity of blood flow in the systemic capillaries.
3. Does turbulent flow normally occur in the circulatory system? (this problem also deals with
flow continuity)
The most likely spot is in the aorta since this vessel has the highest blood velocity. Use the
following information to answer this question:
critical velocity for turbulence in the aorta = 40 cm/sec
radius of the aorta = 1 cm
cardiac output = 93 cm3/sec
4. Normal blood pressure is 120/80 mm Hg. What is the equivalent in kPa? in dynes/cm2?
5. Hold your hand at the level of your heart so that you can see the veins on the posterior
surface. Lift your hand until the veins collapse and measure the distance you have raised
your hand (in mm). This distance is a measure of venous pressure (i.e. a column of xx mm
of blood). Using the specific gravities of blood and mercury, convert this measurement to
mm Hg.
6.
Given a circulatory system with the following:
three parallel vascular beds (#1, #2, #3) where
R1 = 3 PRU
R2 = 3 PRU
R3 = 2 PRU
cardiac output = 100 ml/sec
What is the mean arterial pressure? (assume venous pressure = 0)
What is the rate of blood flow in each vascular bed?
What happens to the mean arterial pressure if vascular bed #1 vasoconstricts and the
resistance in this bed increases to 5 PRU? (assume that total blood flow stays the same)
(consult Equations 3.7 through 3.11 for this problem)
Chapter 3
11
7. A person is informed that they have a coronary artery that is 50% occluded. What effect has
this occlusion had on blood flow in this vessel? (consult Poiseuille Equation, Equation 3.1)
Chapter 3
12