Vascular Pathologies
Atherosclerosis is a vascular pathology that has become a prominent disease in Western society. The term comes from the Greek words athero gruel or paste and sclerosis hardness , and the disorder is characterized by progressive narrowing and occlusion of blood vessels. When fatty substances, cholesterol, cellular waste products, calcium, and fibrin build up in the inner lining of an artery, this causes a narrowing of the lumen of the vessel and also an increase in the wall stiffness or a...
Review Problems Cax
1. 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...
Info Mvo
Pressure in the heart is related to volume in the heart and vice versa. How the two parameters are related depends on things like the geometry of the heart, the passive material properties of the heart, and the active participation of muscle tissue in changing the shape of the heart. Because of these useful but somewhat complex relationships, pressure-volume diagrams provide a wealth of information about heart function at a given set of circumstances. If the heart stopped beating completely,...
Info Ves
The problem asks for a Fry solution, giving the flow rate in the artery as a function of time. We will fit the Fry solution to a Womersley solution. 1. We organize the input data. From the previous example we know that a0 -796, a1 -1250 j, and a2 531. 2. We calculate the steady state flow term with Poiseuille's formula. - 796 3.1416 0.0025 4 b - 796 8 0.0035 b 3. We process each harmonic. We begin with some of the information generated in the previous example problem.
Info Ifx
provide a kind of filtering action to eliminate higher-frequency noise on the pressure waveform. If the system is undriven, this simply means that pressure may change, as with a step input, but that there is no oscillating pressure input. Imagine the pop test described in Sec. 8.3.7 and shown in Fig. 8.9. For the undriven system, we set the driving pressure equal to zero and Eq. 8.27 becomes Eq. 8.42 . Since the system is undriven, we might imagine that when there is a step change in pressure,...
Info Ezt
Figure 6.5 Cribier-Edwards Percutaneous Valve. From Edwards Lifesciences, Inc. AHA Circulation, Lippincott, Williams amp Wilkins. Figure 6.5 Cribier-Edwards Percutaneous Valve. From Edwards Lifesciences, Inc. AHA Circulation, Lippincott, Williams amp Wilkins. Andreas Vesalius 1514-1564 was the Belgian anatomist who was said to have suggested the picturesque term mitral to describe the left atrioventricular valve owing to its resemblance to a plan view of the bishop's mitre Ho, 2002 . The mitral...
Info Sgp
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...
Info Esu
EOA 5 5 5 5000 60 T 5 0.50 cm2 Finally, from Eq. 6.18 the energy loss coefficient is Energy loss coefficient 5 oaEOA 5 4 95- 4095 5 0.46 Chordae tendineae rupture and papillary muscle paralysis can be consequences of a heart attack. This can lead to bulging of the valve, excessive backward leakage into the atria regurgitation , and even valve prolapse. Valve prolapse is the condition under which the valve inverts backward into the atrium. Because of these valve problems, the ventricle does not...
I
Figure 2.15 Directions from each of the standard bipolar and augmented unipolar leads. Note that these leads, taken in combination with the negative of each lead, are spaced every 30 in the frontal plane. Modified from Webster, p. 240, Figure 6.5d. 2.6.5 Electrocardiogram interpretations Electrocardiograms are used to diagnose deviations of the MEA, heart arrhythmias, and heart blocks. A heart arrhythmia is a condition resulting in an abnormal heart rhythm. A sinus rhythm results from the...
L 1
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,...
Info Dde
Figure 6.1 Aortic valve. Reprinted with permission from Lingappa VR, Farey K. Physiological Medicine, McGraw-Hill, New York, 2000. Figure 6.1 Aortic valve. Reprinted with permission from Lingappa VR, Farey K. Physiological Medicine, McGraw-Hill, New York, 2000. fibrous ring that is embedded in the ventricular septum. The leaflets of the three cusps are lined with endothelial cells and have a dense collagenous core that is adjacent to the aortic side of the leaflets. A leaflet of an aortic valve...
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...
A
Figure 1.9a Cross section of a rotating cylinder viscometer. Figure 1.9a Cross section of a rotating cylinder viscometer. From the shear stress and the shear rate, the viscosity and or the kinematic velocity may be obtained as
Info Ogs
In Sec. 1.2.2 we learned about a fluid property known as viscosity. Viscosity is defined by the slope of the curve on a shear stress versus shearing rate diagram. Viscosity of the blood is one of the characteristics of blood that affects the work required to cause the blood to flow through the arteries. The viscosity of blood is in the range of 3 to 6 cP, or 0.003 to 0.006 Ns m2. For comparison, the viscosity of water at room temperature is approximately 0.7 cP. Blood is a non-Newtonian fluid,...
Info Daz
leading to an equation which relates the torque, the angular velocity, and the geometric parameters of the device. 1.3.1 Example problem viscosity measurement Whole blood assume m 0.0035 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 wall shear stress in the fluid. Assume the angular velocity of the outer cylinder to be 60 rpm. We can begin by calculating the shear rate based on the angular velocity of the...
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...
Review Problems Tqk
1. The following values of arterial compliance are reported in the literature Simon et al., 1982 2.2 x 10210 m4 N Mergerman et al., 1986 0.05 to 0.20 percent diameter change mmHg Both studies reported values for 5-mm-diameter arteries. Compare these values by converting to m2 Pa. 2. For the data in Prob. 4, assume a wall thickness of 0.25 mm and estimate the incremental modulus of elasticity. 3. For the data in Prob. 4, assume a wall thickness of 0.25 mm and calculate a pressure strain modulus...
V 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...
Review Problems 1
1. Determine the total lung capacity of a patient with vital capacity of 4.6 L, functional residual capacity of 2.6 L, and residual volume of 1.3 L. 2. Determine the expiratory reserve capacity of a patient with functional residual capacity of 2.9 L and a residual volume of 1.3 L. 3. Find the vital capacity for a person with a total lung capacity of 7 L and a residual volume of 1.5 L. 4. Find the inspiratory reserve volume for a patient with a total lung capacity of 7 L, a functional residual...
Info Nwq
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...
Info Ali
4. Blood flowing through the descending aorta can become turbulent in some highly trained athletes. Does blood act as a Newtonian fluid in this case Why or why not 5. Using the Einstein equation to predict viscosity as a function of hematocrit and temperature, calculate the viscosity of blood at 37 C using a hematocrit of 42 percent and a plasma viscosity of 1.24 x 10-3 Ns m2. 6. Using the Einstein equation to predict viscosity as a function of hematocrit and temperature, calculate the...
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 1
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...
Info Krv
Figure 2.16 An electrocardiogram showing a case of the arrhythmia known as ventricular tachycardia. Modified from Selkurt, 1982, p. 287, Figure 8.13G. Figure 2.16 An electrocardiogram showing a case of the arrhythmia known as ventricular tachycardia. Modified from Selkurt, 1982, p. 287, Figure 8.13G. Ventricular tachycardia is a serious condition that usually occurs in persons with heart disease. In ventricular tachycardia, the ventricle races at near maximal speed. An ECG showing ventricular...
Pulse Wave Velocity and the MoensKorteweg 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...
Info Mhw
Figure 1.14 Cross section of a tube, showing a ring of fluid dr thick, at a radius of r. Figure 1.14 Cross section of a tube, showing a ring of fluid dr thick, at a radius of r. Finally, it is now possible to solve for the average velocity across the cross section and to check assumption 5, that is, the flow is laminar. The expression for the average velocity across the cross section is To verify assumption 5, use Vavg to calculate the Reynolds number and check, to be sure, it is less than...
Show That For Poiseuille Flow In A Tube Of Radius R The Wall Shearing Stress
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...
L
12. A saline solution density 1050 kg m3 is ejected from a 20-mm-diameter syringe, through a 2-mm-diameter needle, at a steady velocity of 0.5 m s. Estimate the pressure developed in the syringe. Neglect viscous effects. 13. Estimate the value of velocity at which the saline solution in problem 12 would be turbulent in the 2-mm-diameter needle. At that velocity, what is the pressure developed in the syringe 14. A schematic of a 100-cm-long catheter having an inside diameter of 0.4 mm connected...