Quantitative Physiology

Amr A. Sharawi

Module (2)Cardiovascular System

Cardiovascular System – The Intended Function

• Blood flows through organs and tissues either to nourish and cleanse them or to be itself processed in some sense, e.g.;– oxygenated (pulmonary circulation)– stocked with nutrients (splanchnic or portal circulation)– filtered of used red blood cells (splenic circulation)– dialyzed (renal circulation)– cooled (cutaneous circulation)

Arrangement of the parallel routes by which the circulation passes from the aorta to the vena cava.

PATHWAYS OF CIRCULATION

• PULMONARY CIRCULATION– It begins at the right ventricle, continues through the

lungs, and terminates at the left atrium.• SYSTEMIC CIRCULATION– It begins at the left ventricle, continues through all other

body systems in parallel pathways, and terminates at the right atrium.

• HEPATIC PORTAL (SPALANCHNIC) CIRCULATION– This is a subdivision of systemic circulation in which

blood from the abdominal digestive organs and spleen circulates through the liver before returning to the heart.

Splanchnic Circulation

• The splanchnic circulation is composed of a parallel network of the following circulations: – gastric – small intestinal – colonic– pancreatic– hepatic – splenic

Simplified schematic of splanchnic vascular bed showing the parallel pathways of the circulationof the various gastrointestinal organs and their series arrangement with the portal circulation tothe liver, and the common venous drainage of all these organs.

The Vascular System - A Highway Network• Every cell in the human body is near enough to the

environment to easily exchange with it: – mass (including nutrients, oxygen, carbon dioxide, and

the waste products of metabolism)– energy (including heat)

• The human body is endowed with a major highway network — organized to make available thousands of miles of access tubing for the transport to and from a different neighborhood of any given cell whatever it needs to sustain life whatever it needs to sustain life.

The Vascular System - A Highway Network

• This highway network, called the cardiovascular system, cardiovascular system, includes:

• a pumping station, the heart; • a working fluid, blood; • a complex branching configuration of distributing

and collecting pipes and channels, blood vessels; • a sophisticated means for both intrinsic (inherent)

and extrinsic (autonomic and endocrine) control.

Path of blood flow through the entire cardiovascular system. All the structures within the colored box are located in the heart.

The Working Fluid: Blood

• Blood is a complex, heterogeneous suspension of formed elements, the blood cells, or hematocytes, suspended in a continuous fluid called plasma. It is further– Accounting for about 8 ± 1% of total body weight– Averaging in volume 5200 ml

• Nominally, the composite fluid has a mass density of 1.057 ± 0.007 g/cm3 and it is 3 to 6 times as viscous as water.

Measurement of the hematocrit by centrifugation. Due to the presence of a thin layer of leukocytes and platelets between the plasma and red cells, the value for plasma determined bycentrifugation is actually slightly less than 55 percent.

Hematocytes• Hematocytes are all derived in the active (“red”)

bone marrow of adults from undifferentiated stem cells called hemocytoblasts, and all reach ultimate maturity via a process called hematocytopoiesis.

• They include 3 basic types of cells:– red blood cells (erythrocytes, totaling nearly 95% of the

formed elements)– white blood cells (leukocytes, averaging <0.15% of all

hematocytes)– platelets (thrombocytes, on the order of 5% of all blood

cells)

Hematocytes• The primary function of erythrocytes is to aid in the

transport of blood gases.• The primary function of leukocytes is to provide the

human body with the ability to identify and dispose of foreign substances such as infectious organisms that do not belong there.

• The primary function of platelets is to participate in the blood clotting process.

• Removal of all hematocytes from blood by centrifugation or other separating techniques leaves behind the aqueous saline suspending medium called plasma.

Plasma• Plasma has an average mass density of 1.035 ± 0.005

g/cm3 and a viscosity 1½ to 2 times that of water and its almost 91% water by weight.

• Plasma contains plasma proteins, of which there are three major types:– Albumin– Globulins– fibrinogen

• Other plasma constituents are minerals, trace elements, and electrolytes, mostly cations: sodium, potassium, calcium, and magnesium; anions: chlorine, bicarbonate, phosphate, and sulfate

Plasma Proteins• Primary functions of albumin:

– help maintain the osmotic transmural pressure differential that ensures proper mass exchange between blood and interstitial fluid at the capillary level.

– serve as a transport carrier molecule for several hormones and other small biochemical constituents (such as some metal ions).

• Primary functions of the globulins:– act as transport carrier molecules for large biochemical substances,

such as fats and certain carbohydrates and heavy metals.– work together with leukocytes in the body’s immune system.

• Primary function of fibrinogen:– work with thrombocytes in the formation of a blood clot—a process

also aided by one of the most abundant of the lesser proteins, prothrombin.

Serum• Removal from blood of all hematocytes and the

protein fibrinogen (by allowing the fluid to completely clot before centrifuging) leaves behind a clear fluid called serum, which has a density of about 1.018 ± 0.003 g/cm3 and a viscosity up to 1½ times that of water.

Laminar and Turbulent Flow of Blood in Vessels:

• When blood flows at a steady rate through a long, smooth blood vessel, it flows in streamlines, with each layer of blood remaining vessel, at the same distance from the vessel wall.

• Also, the central most portion of the blood stays in the center of the vessel.

• When laminar flow occurs, the velocity of flow in the center of the vessel is far greater than that toward the outer edges. This effect is called the “parabolic profile for velocity of blood flow”.

• In turbulent flow, blood is flowing in all directions in the vessel and continually mixing within the vessel.

Turbulent Flow• Some reasons for turbulent flow of blood are:

– when the rate of blood flow becomes too great– when it passes by an obstruction in a vessel– when it makes a sharp turn– when it passes over a rough surface

• In these cases the flow may then become turbulent, or disorderly, rather than streamline.

• Turbulent flow means that the blood flows crosswise in the vessel as well as along the vessel, usually forming whirls in the blood called eddy currents vessel.

• These are similar to the whirlpools that one frequently seen in a rapidly flowing river at a point of obstruction.

• 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.

Diagrammatic representation of normal laminar flow in comparison with turbulent flow

Example of normal laminar flow through aortic valve (top) and turbulent flow resulting from aortic stenosis (bottom)

Reynolds’ Number

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

• Re is Reynolds Re is Reynolds’’ number and is the measure of the tendency for turbulence to occur.

dvRe

Reynolds’ Number• When Reynolds’ number rises above 200 to 400, turbulent flow will occur at

some branches of vessels but will die out along the smooth portions of the vessels.

• However, when Reynolds’ number rises above approximately 2000, turbulence will usually occur even in a straight, smooth vessel.

• Reynolds’ number for flow in the vascular system even normally rises to 200 to 400 in large arteries; as a result there is almost always some turbulence of flow at the branches of these vessels.

• In the proximal portions of the aorta and pulmonary artery, Reynolds’ number can rise to several thousand during the rapid phase of ejection by the ventricles; this causes considerable turbulence in the proximal aorta and pulmonary artery where many conditions are appropriate for turbulence:– (1) high velocity of blood flow– (2) pulsatile nature of the flow– (3) sudden change in vessel diameter– (4) large vessel diameter

The Pumping Station: The Heart• Barely the size of the clenched fist of the individual in whom it

resides—an inverted, conically shaped, hollow muscular organ measuring 12 to 13 cm from base (top) to apex (bottom) and 7 to 8 cm at its widest point and weighing about 325 g, the human heart occupies a small region between the third and sixth ribs in the central portion of the thoracic cavity of the body.

• It rests on the diaphragm, between the lower part of the two lungs, its base-to-apex axis leaning mostly toward the left side of the body and slightly forward.

• The heart is divided by a tough muscular wall, the interatrial-interventricular septum, into a right side and a left side, each being one self-contained pumping station, but the two being connected in series.

Diagrammatic section of the heart. The arrows indicate the direction of blood flow.

Schematic diagram of the pumping system

The Two Sides of the Heart• The left side of the heart drives oxygen-rich blood through the aortic

semilunar outlet valve into the systemic circulation, which carries the fluid to within a differential neighborhood of each cell in the body—from which it returns to the right side of the heart low in oxygen and rich in carbon dioxide.

• The right side of the heart then drives this oxygen-poor blood through the pulmonary semilunar outlet valve into the pulmonary circulation, which carries the fluid to the lungs, where its oxygen supply is replenished and its carbon dioxide content is eliminated before it returns to the left side of the heart to begin the cycle all over again.

• Because of the anatomic proximity of the heart to the lungs, the right side of the heart does not have to work very hard to drive blood through the pulmonary circulation, so it functions as a low-pressure (P≤ 40 mmHg gauge) pump compared with the left side of the heart, which does most of its work at a high pressure (up to 140 mmHg gauge or more) to drive blood through the entire systemic circulation to the furthest extremes of body.

The Heart Chambers• Each cardiac pump is further divided into two chambers: a

small upper receiving chamber, or atrium, separated by a one-way valve from a lower discharging chamber, or ventricle, which is about twice the size of its corresponding atrium.

• Altogether, the heart chambers collectively have a capacity of some 325 to 350 ml, or about 6.5% of the total blood volume in a “typical” individual—but these values are not actual, since the organ alternately fills and expands, contracts, and then empties as it generates a cardiac output.

The Heart Chambers in Order of Size• The left atrium is the smallest chamber—holding about

45 ml of blood (at rest), operating at pressures on the order of 0 to 25 mmHg gauge, and having a wall thickness of about 3 mm.

• The right atrium is next (63 ml of blood, 0 to 10 mmHg gauge of pressure, 2-mm wall thickness).

• The left ventricle (100 ml of blood, up to 140 mmHg gauge of pressure, variable wall thickness up to 12 mm)

• The right ventricle (about 130 ml of blood, up to 40 mmHg gauge of pressure, and a wall thickness on the order of one-third that of the left ventricle, up to about 4 mm).

Phases of the Heart Cycle

• Filling phase (diastole)• Emptying phase (systole)

Diastole• It takes 480-ms or so of the average 750-ms cardiac cycle.

During this phase:• The inlet valves of the two ventricles are open. These are:– the 3.8-cm-diameter tricuspid valve from right atrium to right

ventricle– the 3.1-cm diameter bicuspid or mitral valve from left atrium to

left ventricle• The outlet valves are closed. These are:– the 2.4-cm diameter pulmonary valve– the 2.25-cm-diameter aortic semi-lunar valve

• The heart ultimately expands to its end-diastolic volume (EDV), which is on the order of 140 ml of blood for the left ventricle.

Systole• During the 270-ms emptying phase (systole) electrically

induced vigorous contraction of cardiac muscle drives the intraventricular pressure up, thus forcing:– the one-way inlet valves closed – the unidirectional outlet valves open

• The heart contracts to its end-systolic-volume (ESV), which is typically on the order of 70 ml of blood for the left ventricle.

• The ventricles normally empty about half their contained volume with each heart beat, the remainder being termed the cardiac reserve volume.

Summary of events in the left atrium, left ventricle, and aorta during the cardiac cycle.

Stroke Volume• The difference between the actual EDV and the

actual ESV, called the stroke volume (SV).• This is the volume of blood expelled from the heart

during each systolic interval• The ratio of SV to EDV is called the cardiac ejection

fraction, or ejection ratio:– 0.5 to 0.75 is normal,– 0.4 to 0.5 signifies mild cardiac damage,– 0.25 to 0.40 implies moderate heart damage, – less than0.25 warns of severe damage to the heart’s

pumping ability)

Cardiac Output• If the stroke volume is multiplied by the number of systolic intervals

per minute, or heart (HR), one obtains the total cardiac output (CO):CO = HR × (EDV – ESV)

• Dawson [1991] has suggested that the cardiac output (in milliliters per minute) is proportional to the Weight W (in kilograms) of an individual according to the equation CO = 224W3/4

• and that “normal” heart rate obeys very closely the relationHR = 229W(-1/4)

Example• For a “typical” 68.7-kg individual (blood volume = 5200

ml) the previous equations yield:– CO = 5345 ml/min,– HR = 80 beats/min– SV = CO/HR = 67.2 ml/beat, which are very reasonable values.

• Furthermore, assuming this individual lives about 75 years, his or her heart will have cycled over 3.1536 billion times, pumping a total of 210.7 million liters of blood (7692 liters per day)—all of it emptying into the circulatory pathways that constitute the vascular system.

The Piping Network: Blood Vessels

• The vascular system is divided by a microscopic capillary network into:– an upstream, high-pressure, arterial side consisting of

relatively thick-walled, viscoelastic tubes that carry blood away from the heart

– a downstream, low-pressure, venous side consisting of correspondingly thinner (but having a larger caliber) elastic conduits that return blood back to the heart.

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

Vascular Wall• Except for their differences in thickness, the walls of

the largest arteries and veins consist of the same three distinct, well-defined, and well developed layers.

• the thinnest tunica intima• the thickest tunica media composed of:– numerous circularly arranged elastic fibers– a significant amount of smooth muscle cells arranged in

spiraling layers around the vessel wall– some interlacing collagenous connective tissue

• the medium-sized tunica adventitia

Vascular wall layers

Blood vessel structure is directly related to function:

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.

Poiseuille’s Law• The concentric rings inside the vessels indicate that the velocity of

flow in each ring is different from that in the adjacent rings because of laminar flow.

• Blood in the ring touching the wall of the vessel is barely flowing, because of its adherence to the vascular endothelium.

• The next ring of blood toward the center of the vessel slips past the first ring and, therefore, flows more rapidly.

• The third, … rings likewise flow at progressively increasing velocities.

• Thus, the blood that is near the wall of the vessel flows extremely slowly, whereas that in the middle of the vessel flows extremely rapidly.

• In the small vessel, essentially all the blood is near the wall, so that the so that the extremely rapidly flowing central stream of blood simply does not exist.

Poiseuille’s Law• Poiseuille’s law is given by:

• In the systemic circulation, the most resistance to blood flow is small arteriolar resistance.

• The internal diameters of the arterioles range from as little as 4mμm to as great as 25 μm.

• However, their strong vascular walls allow the internal diameters to change tremendously, often as much as fourfold.

• From the fourth power law that relates blood flow to diameter of the vessel, one can see that a fourfold increase in vessel diameter can increase the flow as much as 256-fold.

• Thus, this fourth power law makes it possible for the arterioles, responding with only small changes in diameter to nervous signals or local tissue chemical signals, either to turn off almost completely the blood flow to the tissue or at the other extreme to cause a vast increase in flow.

48rlP

Effect of tube radius (r) on resistance (R) and flow.

Vascular resistances: A, in series and B, in parallel.For A:

For B:

21 RRRtot

4321

11111RRRRRtot

Electrical Analogy of the Cardiovascular System

• In a global sense, one can think of the human cardiovascular system using an electrical analogy as:– a voltage source (the heart),– two capacitors (a large venous system and a smaller arterial system), and– a resistor (the microcirculation taken as a whole).

• The cardiovascular system is designed to bring blood to within a capillary size of each and every one of the more than 1014 cells of the body—but which cells receive blood at any given time, how much blood they get, the composition of the fluid coursing by them, and related physiologic considerations are all matters that are not left up to chance.

Cardiovascular Control

• Because of the body’s quest for homeostasis and stability, virtually nothing is left to chance, and every biochemical end can be arrived at through a number of alternative means.

• In a broader sense, as the organism strives to maintain life, it coordinates a wide variety of different functions.

• Central to its ability to do just that is the role played by the cardiovascular system in transporting mass, energy, and momentum.

Cardiovascular Function Parameters to be Controlled

• Blood flow• Cardiac output • Blood pressure• Blood volume • Blood composition

How a Vascular Network Receives Blood

• Any given vascular network normally receives blood according to:– the metabolic needs of the region it perfuses and/or– the function of that region as a blood treatment plant

and/or thermoregulatory pathway.• However, it is not feasible to expect that our

physiologic transport system can be “all things to all cells all of the time”, especially when resources are scarce and/or time is a factor.

Blood Perfusion Prioritization• The distribution of blood is further prioritized

according to three basic criteria:– how essential the perfused region is to the maintenance

of life itself– how essential the perfused region is in allowing the

organism to respond to a life-threatening situation– how well the perfused region can function and survive

on a decreased supply of blood

Relation of the perfused region to the maintenance of life itself:

• We can survive without an arm, a leg, a stomach, or even a large portion of our small intestine.

• But we cannot survive without a brain, a heart, and at least one functioning kidney and lung.

Response of the perfused region to a life-threatening situation:

• Digesting a meal is among the least of the body’s concerns in a “fight or flight” circumstance.

Functionality and survival of the perfused region on a decreased supply of blood:

• Some tissues like striated skeletal and smooth muscle have significant anaerobic capability.

• Others like several forms of connective tissue can function quite effectively at a significantly decreased metabolic rate when necessary.

• Some organs like the liver are larger than they really need to be.

• Some anatomic structures like the eyes, ears, and limbs have duplicates, giving them a built-in redundancy.

Control of Cardiovascular Function and the Prioritization System

• Within this generalized prioritization scheme, control of cardiovascular function is accomplished by mechanisms that are based either on:– intrinsic control relying on the inherent physicochemical

aspects of the tissues and organs themselves.– extrinsic control relying on the responses that can be

attributed to the effects on cardiovascular tissues of other organ systems in the body, namely:• the autonomic nervous system• the endocrine system

Intrinsic Control of Blood Flow

• The accumulation of wastes and depletion of oxygen and nutrients that accompany the increased rate of metabolism in an active tissue both lead to:– an intrinsic relaxation of local precapillary sphincters– a consequent widening of corresponding capillary

entrances– reduction of the local resistance to flow thereby allowing

more blood to perfuse the active region

Local control of organ blood flow in response to (a) increases in metabolic activity, and (b) decreases in blood pressure. Decreases in metabolic activity or increases in blood pressure would produce changes opposite those shown here.

Extrinsic Control of Blood Flow

• The extrinsic innervation by the autonomic nervous system of smooth muscle tissues in the walls of arterioles allows the central nervous system to completely shut down the flow to entire vascular beds (such as the cutaneous circulation) when this becomes necessary (such as during exposure to extremely cold environments).

Physical model of the relationship between arterial pressure, arteriolar radius in different organs, and blood-flow distribution. In (a), blood flow is high through tube 2 and low through tube 3, whereas just the opposite is true for (b). This shift in blood flow was achieved by constricting tube 2 and dilating tube 3.

Major factors affecting arteriolar radius. Note that epinephrine can be a vasodilator or vasoconstrictor, depending on the tissue.

Cardiac Output Control• Remember: CO = HR × (EDV – ESV)• The cardiac output can be increased under the extrinsic

influence of the sympathetic nervous system and the adrenal glands by– increasing the heart rate (a chronotropic effect: changing HR). The

HR can triple to some 240 beats/min if necessary.– increasing the end-diastolic volume (allowing the heart to fill longer

by delaying the onset of systole). The EDV can increase by as much as 50% to around 200 ml or more of blood.

– decreasing the end-systolic volume (an inotropic effect: affecting the force or energy of muscular contractions). The ESV can decrease a comparable amount (the cardiac reserve) to about 30 to 35 ml or less.

• or doing all three things at once.

Major factors that influence heart rate. All effects are exerted upon the SA node. The figure shows how heart rate is increased; reversal of all the arrows in the boxes would illustrate how heart rate is decreased.

Major physiological controllers of stroke volume. The figure as drawn shows how stroke volume is increased. A reversal of all arrows in the boxes would illustrate how stroke volume is decreased. Remember that stroke volume SV is given by:

SV = EDV - ESV

Cardiac Output Control

• The combined result of all three effects can lead to over a sevenfold increase in cardiac output from the normal 5 to 5.5 liters/min to as much as 40 to 41 liters/min or more for very brief periods of strenuous exertion.

Major factors determining cardiac output

Blood Pressure Control• The control of blood pressure is accomplished mainly by adjusting the

downstream resistance to flow at the arteriolar level, an increased resistance leading to a rise in arterial backpressure, and vice versa.

• This effect is conveniently quantified by a fluid-dynamic analog to Ohm’s law:E = IR– voltage drop E being analogous to fluid pressure drop ∆P,– electric current I corresponding to flow cardiac output (CO)– electric resistance R corresponding to vascular “peripheral resistance” (PR)

• Thus one may write ∆P =(CO) (PR)• Normally, the total systemic peripheral resistance is 15 to 20

mmHg/(liter/min) of flow but can increase significantly under the influence of the vasomotor center located in the medulla of the brain, which controls arteriolar muscle tone.

Blood Volume Control

• The control of blood volume is accomplished mainly through the excretory function of the kidney. Example:– The antidiuretic hormone (ADH) secreted by the

pituitary gland acts to prevent renal fluid loss (excretion via urination) and thus increases plasma volume.

Blood Composition Control

• Blood composition is maintained primarily through the activity of endocrine hormones and enzymes that enhance or repress specific biochemical pathways.