## Contents

Review of Basic Fluid Mechanics Concepts 1 1.1 A Brief History of Biomedical Fluid Mechanics 1 1.2 Fluid Characteristics and Viscosity 6 1.2.1 Displacement and velocity 7 1.2.2 Shear stress and viscosity 8 1.2.3 Example problem shear stress 10 1.2.5 Clinical feature polycythemia 13 1.3 Fundamental Method for Measuring Viscosity 14 1.3.1 Example problem viscosity measurement 16 1.4 Introduction to Pipe Flow 16 1.4.2 Example problem Reynolds number 19 1.6 Conservation of Mass 24 1.7.1...

## Info

Courtesy of the National Library of Medicine Images from the History of Medicine, B029254. Figure 1.1 Hippocrates. Courtesy of the National Library of Medicine Images from the History of Medicine, B029254. Aristotle, a highly influential early scientist and philosopher, lived in Greece between 384 and 322 BC. He wrote that the heart was the focus of blood vessels, but did not make a distinction between arteries and veins. Praxagoras of Cos was a Greek physician and a...

## Cip cup

The problem with this approach is an acceptable determination of cu and cv. This process will be addressed later. For now, we want you to recognize that the Fry solution is very important since it is an analog with a simple electrical circuit, one having an inductor in series with a resistor and a voltage source. This allows very useful modeling analogies to be established. The solutions of these equations will now be addressed. Differential equations of the kind called for by Fry and...

## Alveolar Ventilation

Alveolar ventilation is the exchange of gas between the alveoli and the external environment. It can be measured as the volume of fresh air entering (and leaving) the alveoli each minute. Oxygen from the atmosphere enters the lungs through this ventilation and carbon dioxide from the venous blood returns to the atmosphere. Physicians and biomedical engineers often discuss alveolar ventilation in terms of standard lung volumes. These standard lung volumes are represented graphically in Fig. 3.2....

## Systemic Circulation

A 58-year-old German woman had undergone surgery in 1974 to fix a mitral stenosis.1 She later developed a restenosis, which caused the mitral valve to leak. She underwent surgery in November 1982 to replace her natural mitral valve with a Bj rk-Shiley convexo-concave mitral prosthesis.2 In July 1992, she suffered sudden and severe difficulty breathing and was admitted to the hospital in her hometown in Germany. She had fluid in her lungs, and the diagnosis was that she had a serious hemodynamic...

## Types of Arteries

Although arteries have the same general structure, they can be divided into groups by their specific functional characteristics. The three types of arteries discussed in this chapter are elastic arteries, muscular arteries, and arterioles. Elastic arteries have the largest diameter of the three groups of arteries. The aorta is a good example of an elastic artery. One of the chief characteristics of elastic arteries is their ability to stretch and hold additional volume, thus performing the...

## Mechanics of Arterial Walls

To understand the mechanics of arterial walls, begin by imagining a long tube of constant cross section and constant wall thickness. This imaginary tube is homogeneous and isotropic (the material properties are identical in all directions). The typical blood vessel is branched and Figure 5.3 An artery modeled as a homogeneous long, straight tube with constant cross section and constant wall thickness. tapered. It is also nonhomogeneous and nonisotropic. Although our assumptions do not fit the...

## S

Figure 2.8 A typical wave from a single heartbeat of an electrocardiogram. Figure 2.9 The component of M along lead I is na1. The unit vector along lead I is . Figure 2.9 The component of M along lead I is na1. The unit vector along lead I is . Einthoven's triangle, the triangle can be used to show the components along each lead. Conversely, if the components are known from an ECG, the direction of the dipole moment vector can be calculated. The mean electrical axis (MEA) defines the direction...

## Introduction

The three most important functions of the respiratory system are gas exchange, acid-base balance, and the production of sound. The most basic activity of the respiratory system is to supply oxygen for metabolic needs and to remove carbon dioxide. Carbon dioxide, which is carried in the hemoglobin of our red blood cells, is exchanged in the lungs for oxygen, which is also carried in the hemoglobin. Fresh air, which we continuously inspire into the lungs, is exchanged for air that has been...

## Pulmonary Pathophysiology

Bronchitis is an inflammation of the airways resulting in excessive mucus production in the bronchial tree. Bronchitis occurs when the inner walls of the bronchi become inflamed. It often follows a cold or other respiratory infection and happens in virtually all people, just as the common cold. When the bronchitis does not go away quickly but persists, then it is termed chronic bronchitis. Emphysema is a chronic disease in which air spaces beyond bronchioles are increased. The stiffness of the...

## Respiration in Extreme Environments

Consider how you might feel if you drive your automobile to the top of Pikes Peak 14,109 ft above sea level, ASL or if you ride a cable car to the top of the Zugspitze, the highest point in Germany 9718 ft ASL . If you have had the opportunity to visit either of these locations, you probably experienced the shortness of breath associated with breathing in environments with low oxygen pressure. The percentage of oxygen does not vary much with the increase in altitude, but the partial pressure of...

## Plasma

Plasma is a transparent amber fluid and is 90 percent water by volume. The 10 percent that is not water adds some very important characteristics to the function of blood. Plasma contains inorganic substances like sodium ions, potassium ions, chloride ions, bicarbonate ions, calcium ions, and those chemicals make up about 1 percent of the plasma by volume. Plasma proteins make up about 7 percent of plasma by volume. Those proteins include albumins, globulins, and fibrinogens. In plasma there is...

## Review Problems

Whole blood assume m 0.004 Ns m2 is placed in a concentric cylinder viscometer. The gap width is 1 mm and the inner cylinder radius is 30 mm. Estimate the torque exerted on the 10-cm-long inner cylinder. Assume the angular velocity of the outer cylinder to be 30 rad min. 2. Whole blood is forced from a large reservoir through a small rigid tube diameter 2 mm length 500 mm and discharges into the atmosphere. If the gauge pressure in the reservoir is 4 x 104 N m2, estimate the discharge from...

## 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, one-third 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. Figure 2.28 Aortic pressure as a...

## Human Dissociation Curve Partial Pressure Oxygen

For oxygen flow, the resistance to diffusion offered by the membrane is approximately equal to the resistance associated with the oxygen-hemoglobin reaction. It is also interesting to note that carbon dioxide diffusion is approximately twenty times faster than oxygen diffusion. Therefore, it seems unlikely that CO2 elimination will be slowed by an increased resistance to diffusion. One gram of pure hemoglobin can combine with 1.34 mL of oxygen, and normal human blood has approximately 15 g of...

## L

The first step in the process is to choose three fundamental dimensions, which describe mechanical properties. One might choose from a list of fundamental dimensions like force, length, time, mass, temperature, charge, voltage, and the list would be extensive. In fact, it is pretty clear that charge, voltage, and temperature are not important in this problem, so we will choose force, length, and time. We will designate those dimensions by the characters F, L, and T representing force, length,...

## C3 O O

Figure 8.12 Doppler continuous wave probe elevated at an angle a with respect to the patient's skin. Consider now a probe at an angle a with respect to the patient's skin, as shown in Fig. 8.12. The signal can now be calculated as Some problems that occur with continuous wave Doppler ultrasound are as follows 1. The Doppler shifted frequency is actually not a single frequency, but a mixture of many frequencies. 2. The velocity profile of the flow field is not constant across the vessel cross...

## Erythrocytes

The word erythrocyte comes from the Greek erythros for red and kytos for hollow, which is commonly translated as cell. Erythrocytes are biconcave discs with a diameter of approximate 8 m. Figure 4.9 presents a drawing of a typical erythrocyte showing the basic geometry. Figure 4.10 is a photomicrograph of an erythrocyte. The volume of the typical erythrocyte is approximately 85 to 90 microns3. The shape of an erythrocyte gives a very large ratio of surface area to volume for the cell. In fact,...

## Modeling

Models are used widely in all types of engineering, and especially in fluid mechanics. The term model has many uses, but in the engineering context, it usually involves a representation of a physical system, a prototype, that may be used to predict the behavior of the system in some desired respect. These models can include physical models that appear physically similar to the prototype or mathematical models, which help to predict the behavior of the system, but do not have a similar physical...

## Gmj

Figure 9.3 Single dimensionless plot that also includes all of the information included in the four plots in Fig. 9.2. From Munson, BR, et al., Fundamentals of Fluid Mechanics, 1994 John Wiley amp Sons, New York. Reprinted with permission of John Wiley amp Sons, Inc. Now it is possible to write a set of three equations, one for each basic dimension, and to solve them simultaneously for three values. Since we have five unknowns and only three equations, it is necessary to assume the values of...

## Coronary Artery Bypass Grafting

Coronary arteries are the blood vessels that deliver blood to heart muscle tissue. When atherosclerotic plaque builds up on the wall of the coronary arteries, the result is coronary artery disease. Plaque accumulations can be accelerated by smoking, high blood pressure, elevated cholesterol, and diabetes. In some cases, patients with coronary artery disease can be treated with a minimally invasive procedure called an angioplasty. During an angioplasty, a stent is placed inside the vessel to...

## Wave On Left Ventricular Wave Form

10.2.3 Summary of the lumped parameter electrical analog model Many scientists have used similar models to mimic blood flow and pressure conditions in animal circulation as well as in the human circulatory system, with the goal of better understanding of the relationship between the two. For example, Bauernschmidt et al. 1999a simulated flow hemodynamics during pulsatile extracorporeal perfusion. Control of perfusion is achieved by surgeons, anesthesiologists, and perfusionists making real-time...

## P1

Figure 1.17 Fluid in a reservoir showing the depth of point P1. 1.7.1 Example problem fluid statics A liquid viscosity 0.002 Ns m2 density 1000 kg m3 is pumped through the circular tube, as shown in Fig. 1.18. A differential manometer is connected to the tube to measure the pressure drop along the tube. When the differential reading h is 6 mm, what is the pressure difference between the points 1 and 2 Figure 1.18 Pipeline using a differential manometer. Figure 1.18 Pipeline using a differential...

## F

A wire cross-sectional area in square meters, m2 We can now examine the small changes in resistance due to the changes in length and cross-sectional area by using the chain-rule to take the derivative of both sides of Eq. 8.1 . The result is shown in Eq. 8.2 . We can now divide Eq. 8.2 by pL A to get the more convenient form of the equation shown in Eq. 8.3 . If you stretch a wire using an axial load, the diameter of the wire will also change. As the wire becomes longer, the diameter of the...

## Anacrotic Limb

Figure 2.21 Aortic pressure waveform. Figure 2.22 shows a close-up view of a single pulse from an aortic pressure-time curve. Systolic pressure, diastolic pressure, and pulse pressure are shown graphically in the figure. It is possible to find the mean pressure of a beat by integrating to find the area under the pressure curve, P t , and then dividing by the time interval between t1 and t2. In the graph shown, the mean pressure Pmean can be found from Figure 2.22 shows a close-up view of a...

## Pulse Wave Velocity and the Moens Korteweg Equation

Some years before Otto Frank's attack on the Windkessel problem, the relation between wave velocity and elasticity in a tube of fluid was established theoretically by Korteweg in 1878. Dutch mathematician Diederik Korteweg studied at the Polytechnical School at Delft. He attended the University of Amsterdam, receiving a doctorate in 1878. He remained at Amsterdam and became professor there in 1881 until he retired in 1918. For larger arteries the Moens-Korteweg equation relates the material...

## Show That For Poiseuille Flow In A Tube Of Radius R The Wall Shearing Stress Can Be Obtained From The Relationship

From the results, one can see that transient forces become relatively more important than viscous forces as the animal size increases. 1. Show that for the Poiseuille flow in a tube of radius R, the wall shearing stress can be obtained from the relationship for a Newtonian fluid of viscosity m. The volume rate of flow is Q. 2. Determine the wall shearing stress for a fluid, having a viscosity of 3.5 cP, flowing with an average velocity of 9 cm s in a 3-mm-diameter tube. What is the...

## Leukocytes

Leukocytes, also known as white blood cells, can be broadly defined into two groups, arranged by function phagocytes and immunocytes. They can also be classified into two groups by appearance granulocytes and agranulocytes. Healthy whole blood normally contains approximately 4000 to 11,000 leukocytes in each cubic millimeter. By comparing that number to 5 million erythrocytes per cubic millimeter, we would expect to see around 500 erythrocytes for every leukocyte. Leukocytes are translucent. If...