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Applied BioFluid Mechanics - Lee Waite and Jerry Fine

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62 Chapter Two

Figure 2.26 Aortic pressures as a function of heart rate. PS is the systolic pressure, and PD is the diastolic pressure. Picture 2, the middle picture, shows the fastest heart rate, and the picture on the right, picture 3, shows the slowest heart rate. (Modified from Selkurt, 1982, Figure 8.26.)

On the other hand, if heart rate and peripheral resistance are constant, but stroke volume changes, pressure and flow are also affected. Figure 2.27 shows the effect of stroke volume on pressure.An increase in stroke volume increases pressure because of the extra volume of blood that is pumped into the aorta during each heartbeat. However, a healthy human would not normally experience a case of constant heart rate and constant peripheral resistance with increasing stroke volume. As shown in the figure, under resting conditions, heart rate drops and peripheral resistance increases. The result is that a large stroke volume, as might be seen in well-trained athletes, increases systolic pressure or perhaps maintains it at a steady level, while the decreased heart rate allows more time between beats and the diastolic pressure decreases. A very small stroke volume, as might be seen in a patient with severe heart damage, would normally result in an increased heart rate as the cardiovascular system attempts to maintain cardiac output, although a very small amount of blood is ejected from the left ventricle during each heartbeat.

The third parameter that controls blood pressure and flow is peripheral resistance. This peripheral resistance comes chiefly from the resistance found in capillary beds, and the more capillaries that are open, the lower the resistance will be. If heart rate and stroke volume remain constant,

Figure 2.27 Effect of stroke volume on pressure. PS represents pressure at systole, and PD represents pressure at diastole. (Modified from Selkurt, 1982, Figure 8.26.)

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Figure 2.28 Aortic pressure as a function of peripheral resistance while heart rate and stroke volume are held constant. (Modified from Selkurt, 1982, Figure 8.26.)

as the need for oxygenated blood increases in peripheral tissues, more capillaries open to allow more blood to flow into the tissue; this corresponds to a decrease in peripheral resistance. Figure 2.28 shows that blood pressure increases with increasing peripheral resistance when heart rate and stroke volume are held constant.

Heart rate, stroke volume, and peripheral resistance are the primary factors that control the relationship between blood pressure and flow, or cardiac output, but there are other factors which contribute. For example, in the case of diseased heart valves, blood leakage backward through the valve into the heart can alter the relationship. This type of leakage through a valve is known as regurgitance. Regurgitance in heart valves has a similar effect to that of decrease in stroke volume. Blood which has been ejected into the aorta can flow backward into the left ventricle through a faulty aortic valve, resulting in a decreased effective stroke volume.

Arterial compliance, a characteristic which is related to vessel stiffness, can also affect the pressure flow relationship. Very stiff arteries increase the overall hydrodynamic resistance of the system. This increase in resistance causes a decrease in blood flow to the peripheral tissue. The complex control system in the cardiovascular system will result in a compensation that increases heart rate, and therefore increases blood pressure to compensate for the increased resistance.

2.10 Coronary Circulation

The blood supply to the heart is known as the coronary circulation. Because heart muscle requires a blood supply in order to be able to provide blood to the rest of the body, this system, which is relatively small by blood volume, provides a very important function. Approximately, onethird of people in the countries of the western world die as a result of coronary artery disease. Almost all elderly people have some impairment of the coronary circulation.

64 Chapter Two

The resting coronary blood flow in humans is around 225 mL/min, which is a bit less than 5 percent of cardiac output. During strenuous exercise, cardiac output in young healthy people increases fourto sevenfold. Because the heart also provides this increased flow at a higher arterial pressure, the work of the heart is increased six to nine times over the resting work output. The coronary blood flow increases only sixto ninefold to supply oxygen and nutrients needed by the cardiac muscle, during this increased workload.

The main coronary artery arises from the root of the aorta. It then branches into the left and right coronary arteries. Seventy-five percent of the coronary blood supply goes through the left coronary artery and 25 percent through the right coronary artery.

The left coronary artery supplies blood to the left lateral portion of the left ventricle and the anterior (front) portion of the ventricular septum. The ventricular septum is the wall between the left and right ventricles. The left coronary artery then branches into the anterior descending coronary artery and the circumflex coronary artery. Those two branches provide blood supply to the left ventricle.

The right coronary artery supplies the right ventricle and the posterior (back) portion of the ventricular septum. The right coronary artery also supplies blood to the specialized muscle fibers of the sinoatrial (SA) node, which is located at the top-rear-right of the right atrium and is the primary electrical pacemaking site of the heart.

Blood flows through the capillaries of the heart and returns through the cardiac veins to the coronary sinus. The coronary sinus is the main drainage channel of venous blood from the heart muscle. It has the appearance of a groove on the back surface of the heart, between the left atrium and ventricle, and drains into the right atrium. Most of the coronary blood flow from the left ventricle returns to the coronary circulation through the coronary sinus. Most coronary blood flow to the right ventricle returns through the small anterior cardiac veins that flow directly into the right atrium.

2.10.1Control of the coronary circulation

Control of the coronary circulation is almost entirely local. The coronary arteries and arterioles vasodilate (increase in diameter) in response to the cardiac muscle’s need for oxygen. Whenever muscular activity of the heart increases, blood flow to the heart increases. Decreased activity also causes a decrease in coronary blood flow. After blood flows through the coronary arteries, about 70 percent of the oxygen in the arterial blood is removed as it passes through the heart muscle. This means that there is not much oxygen left in the coronary venous blood that could have been removed in more strenuous activity. Therefore, it is necessary that coronary flow increase as heart work increases.

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2.10.2Clinical features

When blockage of a coronary artery occurs gradually over months or years, collateral circulation can develop. This collateral circulation allows adequate blood supply to the heart muscle to develop through an alternative path. On the other hand, since atherosclerosis is typically a diffuse process, blockage of other vessels will also eventually occur. The end result is a devastating and sometimes lethal loss of heart function because the blood flow was dependent on a single collateral branch.

2.11 Microcirculation

Microcirculation is the flow of blood in the system of smaller vessels of the body whose diameters are 100 m or less. Virtually all cells in the body are spatially close to a microvessel. There are tens of thousands of microvessels per gram of tissue in the human body. These include arterioles, metarterioles, capillaries, and venules. The microcirculation is involved chiefly in the exchange of water, gases, hormones, nutrients, and metabolic waste products between blood and cells. A second major function of the microcirculation is regulation of vascular resistance.

Normally, all microvessels other than capillaries are partially constricted by contraction of smooth muscle cells. If that is so, then why are the capillaries not constricted in diameter? It is because capillaries do not have smooth muscle cells in the wall. Precapillary sphincters can close off some capillaries, but capillaries cannot change their diameters.

If all of your smooth muscle cells relaxed instantaneously, you would faint immediately. Such relaxation would allow a large increase in volume of blood in the cardiovascular system, dropping blood pressure precipitously. In skeletal muscle and other tissues, a large number of capillaries can remain closed for long periods due to the contraction of the precapillary sphincter. This mechanism is a part of the regulation of vascular resistance.

These capillaries provide a reserve flow capacity and can open quickly in response to local conditions, such as a fall in the partial pressure of oxygen, when additional flow is required.

2.11.1Capillary structure

Capillaries are thin tubular structures whose walls are one cell layer thick. They consist of highly permeable endothelial cells. Figure 2.29 shows the various layers of a capillary. In the peripheral circulation, there are about 10 billion capillaries with an average length of about 1 mm. The estimated surface area of all the capillaries in the entire system is about 500 m2, and the total volume of blood contained in those

66 Chapter Two

Figure 2.29 Structure of a human capillary. (From Tanner and Rhodes, 2003, p. 264.)

capillaries is about 500 mL. Capillaries are so plentiful that it is rare that any cell in the body is more than 20 m away from a capillary.

Consider the structure of blood vessels in terms of branching “generations.” If the aorta branches or bifurcates into two branches, those branches may be considered the second generation. Arteries branch six or eight times before they become small enough to be arterioles. Arterioles then branch another two to five times, for a total of eight to thirteen generations of branches within arteries and arterioles. Finally, the arterioles branch into metarterioles and capillaries that are 5 to 9 m in diameter.

In the last arteriole generation, blood flows from the arterioles into the metarterioles, which are sometimes called terminal arterioles. From there, the blood flows into the capillaries.

There are two types of capillaries. The first type is the relatively larger preferential channel; the second type is the relatively smaller true capillary. At the location where each true capillary begins from a metarteriole, there is smooth muscle fiber, known as the precapillary sphincter, surrounding the capillary. The precapillary sphincter can open and close the entrance to a true capillary, completely shutting off blood flow through this capillary.

After leaving the capillaries, most blood returns to venules and then eventually back into the veins. However, about 10 percent of the fluid leaving the capillaries enters the lymphatic capillaries and returns to the blood through the lymphatic system.

Arteriolar wall structure. Arterioles are tubes of endothelial cells surrounded by a basement membrane, a single or double layer of smooth muscle cells, and a thin outer layer of connective tissue. In most organs, arteriolar smooth muscle cells operate at about half their maximum length.

2.11.2Capillary wall structure

Acapillary is a tube of endothelial cells surrounded by a basement membrane. The wall of a capillary is one cell layer thick and consists of

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67

endothelial cells surrounded on the outside by a basement membrane. Pericytes (Rouget cells) are connective tissue and may be a primitive form of vascular smooth muscle cells, and add structural integrity to the capillary. Precapillary sphincters are small helical twists of smooth muscle around the smallest arterioles (metarterioles). These sphincters are very responsive to the local or intrinsic effects like the concentration of oxygen or carbon dioxide.

The wall thickness of a capillary is about 0.5 m. The inside diameter is approximately 4 to 9 m which is barely large enough for an erythrocyte, or red blood cell, to squeeze through. In fact, erythrocytes, which are approximately 8 m in diameter, must often fold in order to squeeze through the capillary.

Capillary walls have intercellular clefts, which are thin slits between adjacent endothelial cells. The width of these slits is only about 6 to 7 nm (6 to 7 10 9 m) on the average. Water molecules and most water-soluble ions diffuse easily through these pores.

The pores in capillaries are of different sizes for different organs. For example, intercellular clefts in the brain are known as “tight junctions.” These pores allow only extremely small molecules like water, oxygen, and carbon dioxide to pass through the capillary wall. In the liver, the opposite is true. The intercellular clefts in the liver are wide open and almost anything that is dissolved in the plasma also goes through these pores.

Because a single capillary has such a small diameter, each capillary taken alone has a very high hydraulic resistance. However, when you add together many capillaries in parallel, the capillaries account for only about 15 percent of the total resistance in each organ.

2.11.3 Pressure control in the microvasculature

Arterioles regulate vascular pressures and microvascular resistance. A constant “conflict” exists between preserving arterial pressure by increasing arteriolar resistance and allowing all regions to receive sufficient perfusion to provide oxygen to the tissue. By decreasing resistance in small vessels, more blood flows and oxygen perfusion increases. By decreasing resistance in arterioles and capillaries, however, system blood pressure falls.

The normal pressure in an arteriole is typically 30 to 70 mmHg, while the pressure in a venule is 10 to 16 mmHg. Large arteries are simply conduits to allow blood transfer between locations. These large vessels have very low resistance and do not play a significant role in pressure regulation. Small arteries (0.5 to 1 mm in diameter) control 30 to 40 percent of total vascular resistance, and arterioles ( 500 m in diameter) combined with those small arteries make up 70 to 80 percent of total vascular resistance. Nearly all of the rest of the resistance (20 to 30 percent) comes from capillaries and venules.

68 Chapter Two

Constriction of smooth muscle cells maintains the resistance in these resistance vessels. Release of norepinephrine from the sympathetic nervous system contributes to smooth muscle constriction. When fully relaxed, the diameter of the vessel surrounded by smooth muscle can nearly double. If the vessel diameter doubles, the resistance over a fixed length of vessel increases by 24 16 times.

Arterioles possess significant smooth muscle cells and can dilate 60 to 100 percent from their resting diameter. Arterioles can also constrict 40 to 50 percent from their resting diameter for long periods.

Only approximately 10 percent of muscle capillaries are open at rest. Therefore, muscle is capable of increasing its rate of bulk flow tenfold as the need for oxygen increases. Since humans are not capable of increasing their cardiac output tenfold (the human heart can achieve a maximal fivefold increase), shutting down other capillary beds is a necessary pressure control mechanism. That is, you can increase the blood flow to some muscle tenfold so long as not all muscles in the body try to do that simultaneously.

2.11.4Diffusion in capillaries

Lipid-soluble molecules like O2 and CO2 easily pass through the lipid components of endothelial cell membranes. Water-soluble molecules like glucose must diffuse through water-filled pathways in the capillary wall between adjacent endothelial cells. The water-filled pathways are known as pores. In humans, adjacent endothelial cells are held together by tight junctions, which have occasional gaps.

Capillaries of the brain and spinal cord allow only the smallest watersoluble molecules to pass through. Pores are partially filled with submicron fibers (fiber matrix) that act as a filter.

Most pores allow passage of 3- to 6-nm molecules. This pore size allows the passage of water, inorganic ions, glucose, and amino acids. Pores exclude passage of large molecules like serum albumin and globular proteins. A limited number of large pores exist. It is possible that these larger pores are actually defects in the cell wall. Large pores allow passage of virtually all large molecules. Because of these large pores and their associated leakage, nearly all serum albumin molecules leak out of the cardiovascular system each day.

2.11.5Venules

Venules are endothelial tubes that are usually surrounded by a monolayer of vascular smooth muscle cells. Smooth muscle cells in venules are much smaller in diameter, but longer than those of arterioles.

The smallest venules are more permeable than capillaries. A significant amount of the diffusion that occurs in the microcirculation, therefore, occurs in the venules.

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Tight junctions are more frequent and have bigger pores. Therefore, it is probable that much of the exchange of large water-soluble molecules occurs as blood passes through small venules.

The venous system acts like a huge blood reservoir, and at rest, approximately two-thirds of blood is located in the venous system. By changing venule diameter, volume of blood in tissue can change up to 20 mL/kg. For a 70-kg (154 lb) person, the volume of blood ready for circulation can change by nearly 1.5 L.

2.12 Lymphatic Circulation

Lymphatic vessels are endothelial tubes within the tissues. They carry fluid, serum proteins, lipids, and foreign substances from the interstitial spaces back to the circulatory system.

Lymphatic vessels begin as blind-ended lymphatic bulbs. The wall of a lymph capillary is constructed of endothelial cells that overlap one another. The pressure in the interstitial fluid surrounding the capillary pushes open the overlapping cells of the lymphatic bulbs. The movement of fluid from the surrounding tissue into the lymphatic vessel lumen is passive. That is, there are no active pumps in the lymphatic system. Once the interstitial fluid enters a lymph capillary, it is referred to as lymph.

A compression/relaxation cycle causes the lymphatic vessels to “suck up” lymph. Lymph valves in lymphatic vessels make this possible. A volume of fluid equal to the total plasma volume in a single human is filtered from the blood to the tissues each day. It is critical that this fluid is returned to the venous system by lymph flow each day. The lymphatic vasculature collects approximately 3 L/day of excess interstitial fluid and returns it to the blood. The lymph system is responsible for returning plasma proteins to the blood.

Lymphatic pressures are only a few mmHg in the bulbs and the smallest lymphatic vessels, but can be as high as 10 to 20 mmHg during the contraction of larger lymphatic vessels. Lymph valves make possible this apparent progression or flow from low pressure toward high pressure.

Review Problems

1.According to Poiseuille’s law, flow in a large artery is proportional to

(a)radius × viscosity

(b)radius4 × (pressure gradient)/viscosity

(c)radius4/(pressure gradient)

(d)radius2/viscosity

(e)viscosity/radius

70Chapter Two

2.According to the Reynolds number, turbulence is more likely with

(a)increasing viscosity

(b)decreasing tube diameter

(c)decreasing velocity

(d)increasing velocity

(e)increasing pressure

3.Decreased aortic compliance means

(a)decreased stiffness, resulting in increased resistance

(b)increased change in cross-sectional area for a given pressure increase

(c)increased stiffness, resulting in increased mean aortic pressure for the same cardiac output

(d)increased stiffness, resulting in a decrease in mean aortic pressure for same cardiac output

(e)decreased stiffness, resulting in a decrease in mean aortic pressure

4.Cardiac output is approximately proportional to

(a)aortic pressure divided by systemic vascular resistance

(b)systemic vascular resistance times aortic pressure

(c)systemic vascular resistance times right atrial pressure

(d)right ventricular pressure divided by systemic vascular resistance

(e)aortic pressure times stroke volume

5.If the heart were stopped, after due time, the pressure in the entire system circulation would come to equilibrium at some pressure greater than 0. This equilibrium pressure is known as

(a)mean aortic pressure

(b)diastolic pressure

(c)mean circulatory filling pressure

(d)vena cava pressure

(e)central venous pressure

6.For the following ECG, find the mean electrical axis.

5 mV

0

Lead aVF

0 3 mV

Lead II

Lead I

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7.The QRS complex of the ECG is associated with

(a)atrial depolarization

(b)atrial repolarization

(c)bundle branch block

(d)ventricular repolarization

(e)ventricular depolarization

8.Find the mean electrical axis for the following ECG:

7.1mV

0

Lead II

0 5.7mV

Lead I

Lead III

9.Excitation of the heart normally begins

(a)at the sinoatrial node

(b)at the atrioventricular node

(c)in the bundle of His

(e)in the left ventricular myocardium

(f)in the Purkinje system

10.The following ECG shows a patient with

(a)atrial flutter

(b)atrial tachycardia

(c)ventricular tachycardia

(d)right bundle branch block

(e)left bundle branch block

Modified from Selkurt, 1982, p. 287, Figure 8.13G.