The Circulation

Dr. Adelina Vlad, MD PhD

The Cardiovascular System

Integrates three functional parts
The heart, a pump that circulates

a liquid, the blood,

through a set of containers, the vessels

The Vascular System

On the basis of its anatomy, can be divided into
Systemic circulation (greater circulation or peripheral

circulation) Pulmonary circulation

It is a closed network of tubes that start and end at the heart The arteries, a distribution system that transports blood under

high pressure from the heart to the tissues The microcirculation, a diffusion and filtration system The veins (and lymph vessels), a collection system that transports blood under low pressure from tissues to the heart

Physical Characteristics of the Vascular System

Aggregate Cross-Sectional Area (cm2)

Distribution of blood

Mean linear velocity of blood ow is inversely proportional to aggregate vascular cross-sectional area: - 21 cm/s in the aorta - 0.03 cm/s in the capillaries, under resting conditions - 14 cm/s in venae cavae

Pressures Along the Vascular System

High pressure zone: contracting LV systemic arterioles

Low pressure zone: systemic capillaries right heart

pulmonary circulation left atrium LV in relaxed state

Average pressure 17 mm Hg
Average pressure 7 mm Hg

LV

0 mm Hg

Pulsatile Mean value: 100 mmHg

Pulsatile Mean value: 16 mmHg

RV
Normal blood pressures in the different portions of the circulatory system when a person is lying in the horizontal position

HEMODYNAMICS
Is the study of the physical laws of blood circulation
Addresses the properties of The container blood vessels The content blood

Blood flow is driven by a pressure head across variable

resistances

Interrelationships Among Pressure, Flow, and Resistance

Blood ow F through a blood vessel is determined by two

factors: pressure difference DP of the blood between an upstream point and a downstream site = pressure gradient along the vessel, which is the driving force of the blood flow vascular resistance R between those two points, which is the impediment to blood ow through the vessel The analogous of Ohms law of electricity for direct current I = DV/R, is the Ohms low of hydrodynamics:

Blood Flow

Total Blood Flow in the Circulation

Blood flow is the quantity of blood (DV) that passes a given point

in the circulation in a given period of time ( Dt): F = DV/Dt The flow of blood delivered each minute by the heart, or the total mean flow in the circulation is the cardiac output CO = SV x HR = 5 liters/min at rest
F = P/R = cardiac output (l/min or ml/min) P = pressure difference between Ao and VC (mm Hg), or

between PA and PVs R = total peripheral resistance (TPR) (mmHg/ml/min) in systemic or pulmonary circulation

Flow Velocity Relationship

F, is the quantity of blood (DV) that passes a given point in the

circulation in a given period of time (Dt): F = DV/ Dt DV = A x Dx if A is the cross-section area of the blood vessel and Dx the distance the blood bolus advances in Dt with a mean velocity v; therefore:

Dx

Principle of Continuity
In any steady-state process, the rate at which the mass enters the

system must equal the rate at which mass leaves the system flow in = flow out
Hemodynamic applications
Two sets of vessels in series (systemic and pulmonary circulation)

have the same flow CO of the right and left heart must be equal
The aggregate flow at any level of vascular arborization must

be the same

The mean linear velocity of blood ow is inversely proportional to vascular cross-sectional area

The aggregate crosssectional area of each vascular teritory and the blood velocity through it are mirror images of one another

Vascular Parameters Vary with Arborization

PARAMETER Number of units AORTA 1

SMALL ARTERIES 8000 0.5 mm 7.9 10-3 cm2

63 cm2

ARTERIOLES 2 107

Internal radius Cross-sectional area

Aggregate crosssectional area

1.13 cm 4 cm2
4 cm2

15 m 7.1 10-7 cm2

141 cm2

CAPILLARIES 1 1010 open (4 1010 total) 3 m 2.8 10-7 cm2 2827 cm2

VENA CAVA 1

1.38 cm 6 cm2
6 cm2

Aggregate flow
Mean linear velocity

83 cm3/s (ml/s) 21 cm/s 83 cm3/s (ml/s)

83 cm3/s 1.3 cm/s 0.01 cm3/s

83 cm3/s 0.6 cm/s 4 10-6 cm3/s

83 cm3/s 0.03 cm/s 8 10-9 cm3/s

83 cm3/s 14 cm/s 83 cm3/s

Single-unit flow

Branching in a typical microcirculation (smooth muscle and submucosa of the intestine)

Poiseuilles Law
The flow can be predicted from the geometry of the vessel and

the properties of the fluid with the Poiseuille-Hagen equation:

In other words, the flow is:

Directly proportional to the axial pressure difference DP Increases with the fourth power of vessel radius r Inversely proportional to both the length of the vessel l and the

viscosity of the fluid h

The Ohms law applies to all vessels, whereas Poiseuilles

equation applies only to rigid, cylindrical tubes

Poiseuilles Law Requirements

The fluid must be incompressible
The tube must be strait, rigid, cylindrical, unbranched, with a

constant radius The velocity of the thin fluid layer at the wall must be zero (no slippage) The flow must be laminar
The viscosity of the fluid must be constant The flow must be steady (not pulsatile)

Laminar Versus Turbulent Flow

Laminar flow blood flows in streamlines, with each layer of

blood remaining the same distance from the vessel wall Turbulent ow - blood ows in all directions inside the vessel and mixes continuously
Occurs at high flow rates (beyond a

critical velocity), when blood passes by an obstruction in a vessel or when it makes a sharp turn A turbulent flow is not anymore proportional to DP, but to roughly the square root of DP because R increases turbulence causes kinetic energy losses Vortex formation during turbulence sets up murmurs

Reynolds Number
Is a parameter that determines when flow becomes turbulent

r tube radius, v velocity, r density, h - viscosity Turbulent blood flow occurs when vessel radius (r) is large (aorta) or blood velocity (v) is high (high cardiac output); also, when local decrease in vessel diameter causes an increase in v (arterial stenosis or external compression) viscosity (h) lowers (anemia); viscosity reflects the cohesive forces that tend to keep the layers well organized Re < 2000 laminar flow; Re > 3000 turbulent flow Murmurs occur in: vascular stenosis, shunts, cardiac valvular lesions

Raynolds Number
Re=2rvr/h
The Reynolds number gives a measure of the ratio of inertial forces to viscous forces:
at low Re, viscous forces (2r/h) are dominant laminar flow

characterized by smooth, constant fluid motion;

at high Re, inertial forces (vr) are dominant, which tend to

produce random eddies, vortices and other flow instabilities turbulent flow

Pressure Inside the Vessels

Pressure Inside the Vessels

Is the force exerted by the blood against any unit area of the

vessel wall, relative to the barometric pressure (PB) Standard units of pressure: mm Hg or cm H2O for clinicians (P = rgh) 1 mm Hg pressure = 1.36 cm H2O pressure Pascals, g/cm2, or dynes/cm2 for physicists

Pressure Differences in the Circulation

Driving pressure is the axial pressure difference and causes

blood to flow from x1 to x2; in the circulation, it is the P between the arterial and venous ends of the systemic (or pulmonary) circulation Transmural pressure, the P between r1 and r2, is the difference between the intravascular pressure and the tissue pressure Hydrostatic pressure, the P between point h1 and h2 along the height axis, it exists even in the absence of any blood flow

Factors that Generate Pressure in the Circulation

1.
2.

Compliance of the vessels

Gravity

3.
4.

Viscous resistance Velocity (Bernoulli effect)

1. Compliance of the Vessels

Is the volume of blood that can be stored in a given portion of the

circulation for each millimeter of mercury pressure rise:

Low compliance increases the transmural pressure when the

blood volume is increased (rigid vessels high blood pressure)

2. Gravity
Causes hydrostatic pressure when there is a difference in height:

DP = rgDh
In the cardiovascular system, the reference h level (zero height)

is the level of the heart; here the pressure is unaffected by changes of body posture
Horizontal position: relatively constant intravascular pressures

along the body

Upright position: intravascular pressure increases tremendously

in the foot, and decreases in the head

Arterial and Venous Pressures in the Horizontal and Upright Positions

The pressures are different between A and B, but the driving

pressures (P) between arteries and veins are the same (separation between red and blue lines, violet background)

3. Viscous Resistance
Blood viscosity, h, is the internal friction of blood layers
According to Poiseuilles law

DP = F x 8hl /pr4
an increase in blood viscosity generates a rise of blood pressure by increasing resistance

4.Pressure Velocity Relationship

The heart imparts its energy in a pulsatile manner, with each

heart beat velocity varies during a cardiac cycle

Changes in velocity lead to compensatory changes in

intravascular pressure: The fluid pressure (potential energy, p) must decrease when velocity (kinetic energy, v2) increases to satisfy conservation of energy or Bernoulli equation

p + v2 + g h = ct,
and for horizontal fluid flows: p + v2 = ct
Or: Total energy = potential energy + kinetic energy = constant

trade-off between velocity and pressure

Bernoulli Effect
Pressure decreases when the velocity of blood flow increases

F = A1 x v1 = A2 x v2 v2 > v1

P1 + v12 = P2 + v22 = ct

P2 < P1

 Considering all these sources of pressure, we can state that the

total pressure difference, instead of being given by Ohm's law of hydrodynamics (DP = F x R), is

DPtotal = DPgravity + DPcompliance + DPviscous resistance + DPinertiance

Inertia is the resistance of any physical object to a change in its state of motion and reflects the trade-off between kinetic (velocity) and potential energy (pressure) inertiance refers to Bernoulli effect in vessels where velocity changes due to cardiac cycle or pathological events

Vascular Impedance
Both P and F through arteries are pulsatile during a cardiac

cycle an analogy with direct current circuits (DP = F x R) is not sufficient

It is more accurate an analogy with alternating currents:

DP = F

Z, where Z is mechanical impedance, that includes

Compliant impedance that opposes volume change (compliance of

the vessel) Viscous (or resistive) impedance that opposes flow (shearing forces in the liquid); this term is the "R" of Ohm's law of hydrodynamics: DP = F R that applies to steady P and F Inertial impedance that opposes a change of flow (kinetic energy of fluid and vessels)
Conclusion: When F and P oscillate, P/F = Z that depends not only on R, but on compliance and inertial properties of the vessels and blood as well

 Ohm's law for alternating currenst:

E=I

Z,

where Z is a complex quantity called the impedance;

Z depends on the
electrical resistance R - hydrodynamic analogy = viscous

resistance electrical capacitance C - hydrodynamic analogy = compliance electrical inductance L - hydrodynamic analogy = inertiance

Resistance to Blood Flow

Resistance to Blood Flow

Is the impediment to blood ow in a vessel
Can be expressed by rearranging the Ohms law of

hydrodynamics

R = DP/ F,
an approach independent of geometry, applicable to very complex circuits, such as the entire peripheral circulation
Units of resistance: PRUs (peripheral resistance unit): mm Hg/(ml/sec)

CGS (centimeters, grams, seconds) unit: dyne sec/cm 5

Conductance of Blood in a Vessel

Conductance is a measure of the blood ow through a vessel for

a given pressure difference

C = F/DP = 1/R
Unit measure: (ml/sec)/mm Hg

R Is Inversely Proportional to r4
R derived from Poiseuilles law is

R = 8hl /pr4
which states that for an individual unbranched, rigid vascular segment with a laminar blood flow the resistance increases tremendously with the decrease of the vessel radius

For a constant DP, a four fold decrease in vessel diameter decreases the flow (increases the R) as much as 256-fold

Total R is Higher in Arterioles than in Capillaries

In spite the smallest individual radius in the capillaries, total

resistance in arterioles exceeds total resistance in capillaries Why? Because the aggregate resistance of vessels of a particular order of arborization depends not only on r, but also on the number of vessels in parallel

PARAMETER Internal radius (ri) Individual resistance (Ri) (dyne s/cm5) Number of units
Total resistance (dyne s/cm5)

ARTERIOLES 15 m 15 1 107 107

15

CAPILLARIES 4 m 3000 1 107

1010
3

Vessels Connected in Parallel

Many parallel blood vessels make it easier for blood to ow

through the circuit because each parallel vessel provides another pathway for blood ow
or
The total resistance is far less than the resistance of any single

blood vessel
However, increasing the resistance of any of the blood vessels

increases the total vascular resistance

Vessels Connected in Series

When blood vessels are arranged in series,
flow through each vessel is the same the total resistance to blood ow (Rtotal) is equal to the sum of

the resistances of each vessel:

The overall resistance across a circulatory bed results from parallel and serial arrangements of branches

is governed by laws similar to those for the electrical

resistances of direct current circuits

Viscous Resistance
If the flow fulfills Poiseuilles requirements, R can be expressed

in terms of vessel dimensions (r, l) and viscous properties of the blood (h)

Viscosity measures the resistance to sliding when layers of

fluid are shearing against each other Unit of viscosity: poise (P) Whole blood viscosity = 3 cP

 For a laminar flow

The shearing laminae of the blood are concentric cylinders A very thin layer of blood close to the wall cannot move due to

cohesive forces between the blood and the inner surface of the vessel wall The velocities increase from the wall to the center of the cylinder the velocity profile is a parabola with a maximum velocity at the central axis

Whole Blood Viscosity

Depends on:
1) 2) 3)

Fibrinogen concentration Hematocrit Vessel radius Linear velocity

4) 5)

Temperature

At a fibrinogen concentration of 260 mg/dl, a hematocrit of 40%

and a temperature of 37 C the whole blood viscosity is approx. 3.2 cP

1)

Fibrinogen Major plasma protein; key element in the coagulation cascade Induces erythrocyte aggregation, which is thought to be caused by a non-specific binding mechanism increased whole blood viscosity in the presence of fibrinogen

2)

Hematocrit It is the percentage of the blood that is cells (normal: 35 50%) Raising the hematocrit increases the interactions among RBCs increases viscosity At hematocrits above 60%, cell-cell interactions deform the RBCs, leading to a steeper increase in viscosity

3)

Vessel radius Viscosity decreases steeply at radii < 1 mm (FahraeusLindqvist phenomenon) due to: Axial accumulation of RBCs (plasma imparts a spin to peripheral RBCs) plasma layer close to the wall, where the shearing forces are the greatest Limited number of RBCs floating inside very small vessels (tank treading of RBCs, deformation of RBCs)

4) Velocity of flow The tendency for RBCs to move to the center of the stream requires a certain flow low velocities lead to increased viscosity
5) Temperature Low temperature increases viscosity (intense cooling of the extremities), due to an increase of the cohesive forces between molecules The presence of cryoglobulins (infections, autoimmune and lymphoproliferative disorders) that precipitate at less than 37 C can lead to vessel obstruction due to increased viscosity

Resistance and Vasomotion

Vascular resistance depends critically on the action of vascular

smooth muscle cells (VSMCs) that can change vessel r

The terminal small arteries and arterioles is the major site of

control of vascular resistance in the systemic circulation

Why? Because the VSMCs in their walls are well represented

(predominant) allowing up to four-fold variation in vessel diameter Lowering or increasing r by arteriolar VSMCs contraction/ relaxation under humoral or nervous influences can change R as much as 100-fold

Pressure-Flow-Resistance Relationship
Poiseuilles law predicts a linear pressure-flow relationship in

rigid tubes
In real vessels an increase in pressure not only imparts a

stronger impulse to the blood column (linear P - F relationship), but also distends the elastic arterial wall decrease of R which further increases F nonlinear pressure-flow relationship in elastic vascular beds
An increase in active tension (VSMCs contraction after

sympathetic stimulation) increases R and the stiffness of the walls, making the P-F relationship more linear and shifted to the right

20

40

60

80

100

Driving pressure (mm Hg)

 In conclusion, in elastic vascular beds

R decreases as P increases due to vascular distension Flow increases due to a lower R

P and F exhibit phasic oscillations that cannot be interrelated

only by viscous resistance, as in rigid tubes

a more complex term is needed for defining P/F = mechanical impedance, that depends on viscous resistance, as well as the compliance and inertial properties of vessels and blood

Vascular Distensibility and Functions of the Arterial and Venous Systems

Vascular Distensibility
Expresses the elastic properties of blood vessels
Is a property of great functional value because Influences the pressure-resistance-flow relationship

Smoothens the intravascular variation in pressure between

systole and diastole Influences the volume of blood that can be accommodate by a vessel

= (DV/V0)/DP

V0 the unstretched volume of the blood vessel

Vascular Distensibility
Depends on the structural particulars of each type of vessel

(elastic arteries, muscular arteries, veins):

- arteries are 8 times less distensible than the veins in systemic circulation
- pulmonary arteries are about 6 times more distensible than systemic arteries

Structure of Vascular Wall

The wall of blood vessels has three layers: intima, media,

adventitia; exception capillaries have only intima The vascular wall has four major components whose relative abundance varies along the vascular circuit: endothelial cells, elastic fibers, VSMCs and collagen fibers

Structure Function Relationship

(elastic fibers dominance)

(collagen fibers dominance)

Vascular Compliance or Capacitance

Is the total quantity of blood that can be

stored in a given portion of the circulation for each mm Hg pressure rise

= DV/DP

Elastic rich arteries have a grater compliance

than muscular arteries

Although the compliance of veins seems to be

high at a normal pressure range, their ability to accommodate large volumes of blood for each mm Hg is rather the result of a change in shape
Relative volume of 100% represents fully relaxed volume

Volume Pressure Curves

In the arterial system a slight increase in volume causes a steep

raise in pressure, proving that arteries have a moderate compliance, whereas veins can accommodate several hundreds ml of blood for an increase in pressure of only 3 5 mm Hg, acting as blood reservoirs Sympathetic stimulation decreases the arterial and venous capacitance by VSMCs contraction
It is an important response for redistribution of blood among

vascular territories increasing venous return which eventually increases cardiac output (Frank-Starling law) maintaining blood pressure during hemorrhage

Delayed Compliance
A vessel exposed to increased volume at rst exhibits a large

increase in pressure (immediate elastic distention), but the pressure returns back toward normal over a period of minutes to hours = stress-relaxation the circulation can accommodate much extra blood when necessary Delayed compliance in the reverse direction: the circulation automatically adjusts itself (minutes hours) to diminished blood volume after a serious hemorrhage
Stress-relaxation and reverse stress-relaxation

are properties of smooth muscle they allow a hollow organ to maintain about the same amount

of pressure inside its lumen despite long-term, large changes in volume

Arterial Pressure Pulsations

With each beat of the heart a new surge of blood lls the arteries

pulsatile pressure variations during systole and diastole

The blood pressure cycles between a maximal systolic arterial

pressure that corresponds to the contraction of the ventricle and a minimal diastolic arterial pressure that corresponds to the relaxation of the ventricle

 The diastolic value is maintained at relatively high values despite

the absence of any pressure head

 Why?

During systole the pressure imparted by the heart to the blood column rises dilation of the arterial wall that stores a volume of fluid the flow rises gradually towards its maximal value During diastole the pressure generated by the ventricle falls to zero the expanded vessel comes to the initial size, delivering its stored volume downstream flow and an intravascular pressure that drops smoothly from the systolic value during diastole

Effect of pulsatile pressure on flow through a compliant vessel

P = F x R in the circulation P = CO x TPR

Pulse Pressure
Pulse pressure is the difference between the systolic and the

diastolic pressure Major factors affecting the pulse pressure: 1) the stroke volume output of the heart 2) the compliance of the arterial tree Pulse pressure is determined approximately by the ratio of stroke volume output to compliance of the arterial tree

Pressure pulsations at the root of the aorta

Pressure Pulse and Its Transmission

The spreading of the wave front of distention generated by

LV ejection along the arterial walls is called transmission of the pressure pulse in the arteries
Pressure pulse - a moving wave of pressure that involves little

forward total movement of blood volume The greater the compliance of each vascular segment, the slower the velocity, because some of the energy of the pressure pulse goes into dilating the vessel: 3 to 5 m/sec in the normal aorta 7 to 10 m/sec in the large arterial branches 15 to 35 m/sec in the small arteries

!!! The velocity of transmission of the pressure pulse is much higher than the velocity of blood ow

Damping of the Pressure Pulses

The intensity of pulsation becomes progressively less in the

smaller arteries, the arterioles, and, especially, the capillaries Damping of the pressure pulses is determined by: 1) resistance to blood movement in the vessels 2) compliance of the vessels (aggregate compliance increases in the periphery) The degree of damping is almost directly proportional to the product of resistance times compliance

Mean Arterial Pressure

Mean arterial pressure
is the average of the arterial pressures measured millisecond

by millisecond during one cardiac cycle is determined about 60 per cent by the diastolic pressure and 40 per cent by the systolic pressure mean arterial pressure < average of systolic and diastolic pressure MAP = DBP + 1/3(SBP - DBP)

Pressure Profiles Along Systemic and Pulmonary Circulations

LOCATION Systemic large arteries Systemic arterioles Systemic capillaries Systemic venules Systemic veins Pulmonary artery Pulmonary capillaries Pulmonary veins MEAN PRESSURE (mm Hg) 95 60 25 (range, 35-15) 15 15-3 15 10 5

Systemic circulation Systolic pressure 120 mm Hg Diastolic pressure 80 mm Hg Pulmonary circulation Systolic pressure 25 mm Hg Diastolic pressure 8 mm Hg

 Cardiac outputs of the left and right hearts are the same,

whereas the total resistance of the systemic circulation ( 1.1 PRU) is far higher than that of the pulmonary circulation ( 0.08 PRU) higher driving pressure in the systemic circulation
Pulmonary vessels are wider and shorter and have thinner and

less muscularly walls low resistance, high compliance

Systemic pressure falls steeply (arterioles), while the pulmonary

pressure drops rather uniformly (pulmonary arterioles are less muscularly and have a lower resistance)

Measuring Systemic Systolic and Diastolic Blood Pressures

An accurate and direct method is by means of a catheter

introduced in the vessel of interest - invasive, used only for special studies In clinics, the current approach for determining arterial systolic and diastolic pressure is the indirect, noninvasive auscultatory method; it usually gives values within 10% of those determined by direct catheter measurement

Auscultatory Method