Erratum
1. p. 57, Example 2.1. Line 3. Change “compute the fluid acceleration” to “compute the x-component of the fluid acceleration”
2. p. 58, Change the phrase “For the steady flow of two velocity components, Equation (2.2.8) reduces to:” to “For steady flow, the x component of acceleration is, from equation (2.2.8):”
Change equation (2.2.10) to:
(2.2.10)
Change equation (2.2.11b) to:
(2.2.11b)
Change equation (2.2.12) to:
(2.2.12)
3. p. 82, Equations (2.5.22a,b) are:
(2.5.22a)
(2.5.22b)
4. p. 114. problem 2.9. The problem statement should be as follows.
Two parallel plates are separated by a thin gap of thickness H containing an unknown fluid. In order to determine some of the properties of the fluid, the following experiment is performed. A known force per unit area of 1 is applied to the upper plate and the steady-state velocity of the plate is V1. Next the force is (a) doubled and (b) increased by a factor of four and the velocity V determined. For each of the cases, determine whether the velocities describe a Newtonian fluid, a Bingham plastic, or a power law fluid. If the fluid is a Bingham plastic, determine the yield stress o in terms of 1. If the fluid is a power law fluid, determine the value of n.
1a) V = 2V1; b) V = 4V1
- a) V = 3V1; b) V = 7V1
- b) V = 4V1;b) V = 16V1
5.p. 114, problem 2.13. The units for the apparent viscosity are Pa s and not Pa.
6. p. 132. Equation (3.3.28b) is:
7. p. 132. Equation (3.3.28c) is:
6. p. 154. In equation (3.6.7b) is.
9. p. 161. Problem 3.4. The reference should be to equation (3.4.27) not equation (3.3.27).
10. p. 162. Problem 3.8. Note the following two typographical errors in the problem statement:
(1) (z) = 0 + z(since the reference position is denoted with a zero and the z-
direction is positive in the direction of gravity.)
(2)g’ = 2R
11. p. 195, Equation (4.7.1a) is .
12. p. 209, problem 4.13. The quantity replaces the term “y” in the equation.
13. p. 210, ref. 12, line 3. replace “V.C.M.a.W.C. Hayes,” with “V.C. Mow and W.C. Hayes,”.
14. p. 218, Legend to Figure 5.4, last two lines, Replace “normalized by A*” to “normalized by A*/” and “frequency if 1 Hz” to “frequency of 1 Hz”.
15. p. 249, In problem 5.3, the term “exp(i)” should be “exp(it)” in the second paragraph, and equation (5.11.1) should be: .
16. p. 250. Problem 5.4. Line 16, right hand side. The reference should be [74] and not [73]. In equation (5.11.10), the term “” should be “”. The term “” should be “”.
17. p. 251. line 2. “a < 1” should be “< 1”. “A = 10 mm Hg cm-1” should be “A = 0.02 mm Hg cm-1”
18. p. 310. The denominator of Equation (6.8.63) on p. 310 should be n and not [n]2.
19. p. 357. Note that there is a typographical error in equation (7.4.30b) and the minus signs were omitted from the exponential terms:
(7.4.30b)
20a. p. 358, equation (7.4.32). A minus sign is missing from the right hand side of the equation, it should read “Vm = [ … ”
21. p. 380, line 7. change the phrase “mass transfer resistance” to “mass transfer rate”.
22. p. 393, Line 6 in the last paragraph, it should read “… two liquid phases, such as oil and water. (See Section 6.3.2.).”
23. p. 412, insert the following sentences after “Section 8.5.” in Line 3. The original line 3 should be replaced by “…Section 8.5. One special case is that the normal forces on the cell membrane due to the elastic compression of the extracellular matrix are negligible compared with the pressure within the matrix if the interstitial space is highly compressible. In this case, the total force on the cell membrane is equal to the integration of the pressure, given in Equation (8.3.51), over the entire surface of the cell. (See Problem 8.14.) A general treatment of tissue-deformation-…”
24. p. 423, Problem 8.5.
(i) Replace the last sentence “and the interstitial gradient of fluid pressure is G.” with “and the Kozeny constant is G.”
(ii) Delete “(c) Find the interstitial fluid velocity.”
25. p. 424, Problem 8.7. in part (b),
(i) Replace “v/(kG/)” with “v/(kB/)”.
(ii) Replace “(p1 - p2)/L = G” with “(p1 - p2)/L = B”.
26. p. 424, Problem 8.10. The entire problem statement should be replaced by the following.
- 8.10. In the derivation of Equations (8.3.49), (8.3.51), and (8.3.52), we assume that the specific hydraulic permeability k is a constant. In general, k depends on local structures of tissues. Empirically,
,
where is the porosity, and n are empirical constants [36]. When tissue is deformed, changes. If both the solid and fluid phases are assumed to be incompressible, can be related to the volume dilatation e. (See Problem 8.4.) For one-dimensional deformation, shown in Figure 8.15,
.
We also assume that Vh = Vh0exp(-t), where = Vh0/(0h0) and t is the time. The baseline values of the constants of the model are = 0.003 nm2, n = 3.2, 0 = 0.98, h0 = 0.1 m, and R = 5 m.
(a) Determine the velocity vr as a function of z at r = R for t = 0, 0.1, 1, and 3.
(b) Determine the pressure p as a function of t at r = 0.
(c) Compare the pressure and velocity profiles you found in Parts (a) and (b) with those determined by Equations (8.3.51) and (8.3.51), respectively, with k = k0 = .
27. p. 424, Problem 8.11. The entire problem statement should be replaced by the following.
8.11. Assume that the interstitial space between two cells can be modeled as a porous medium bounded by two parallel plates. (See Figure 8.13.) The effective hydraulic conductivity in the channel (Kchannel) can be determined by following the procedure described in Example 8.7 and using the results from Problem 8.10. If the interstitial space is deformed, determine how Kchannel changes with h.
28. p. 425, Problem 8.14. Replace the last sentence with “If the interstitial space is highly compressible, determine the total forces on the cell membranes.”
29. p. 460. Figure 10.6. The scale of the vertical axis is inversed. The top should be label 0 and the bottom should be labeled 1.0.
30. p. 460, Line 5 in the second paragraph, insert “(See Figure 10.7.)” after “sequences represented by that population.”
31. p. 461. Figure 10.7. The scale of the vertical axis is inversed. The top should be label 0 and the bottom should be labeled 1.0.
32. “Km” should be replaced by “KM” on the following pages: p. 469, lines 5, 8, 10; p. 470, legend to Figure 10.13; p.471, lines 1 and 3 in the last paragraph; p. 496, denominator of Da in equation (10.6.34); p. 498, caption of Figure 10.24.
33. p. 474, Equation (10.4.27b), “” in the numerator should be replaced by “”. Thus, the equation becomes
34. p. 504 Problem 10.3 (10.2.33) becomes (10.2.32) and (10.2.34) becomes (10.2.33).
35. p.504. Problem 10.7. Replace the phrase “to extract the carcinogen from tobacco leaves and then pass the solution” with “to separate blood cells from plasma and pass the blood plasma”.
36. p. 522. Equations (11.3.13a)and (11.3.13b): CL0 is replaced with C*L0.
Equation (11.3.13c): NL0 is replaced with CL0.
37. Page 533, the legend of Figure 11.20. Line 3, replace “k-1” with “k1”.
38. p. 555, line 6. “greater” should be “less”.
39. p. 564, problem 11.10, equation (11.9.4) replace with .
40. p. 565, problem 11.10, equation (11.9.6) Replace with .
41. p. 565, problem 11.10, part a. NRi = 1.8 x 105 receptors per cell should be replaced with NR = 0.5 x 105 receptors per cell.
42. p. 584, Equation (12.3.15b) should be
Equation (12.3.17) should be
43. p 585, line 1-2. “..the total force on all bonds is 4.66 x 10-5 dyne = 466 pN.”
44. p. 603, Problem 12.6. The statement for part (a) is “Using MATLAB, present simulations of Px as a function of dimensionless time, kxot for x0 = 6.”
45. p. 613, equation (13.2.3) The term “CHb” should be preceded by a “4”, i.e. “4CHb”
46. p. 614, line 1. Change “HP +” to “HP – “.
47. p. 614, line 4. Change “- 3.54” to “+ 2.90”.
48. p. 615, fifth line from the bottom. Replace “10” with “0”. The dissociation rate coefficients are from reference 2 and k-2, k-3, k-4 listed at the bottom of the page are 100 to 1000 times too small. They should be k-2 = 158 s-1, k-3 = 539 s-1, and k-4 = 50 s-1.
49. p. 616, line 4. Change “’ to “H” C50 = HP50.
50. p. 624, equation (13.5.7) The “+” on the left hand side of the equation should be replaced with “-“, so “Rc2 – R02 - 2R0 ln(Rc/R0)”
51. p. 635 Table 13.1 The NO production rate should be 5.5 x 10-12 mol cm-2 s-1.
52. p. 637, problem 13.4. CO2 (r=RC) = 0.14 mM.
53. p. 637, problem 13.5. On line 3, insert the phrase “in RBC” between the words “concentration” and “is”.
54. p. 637, problem 13.8. A “’” is missing from the expression “R’O2 = 0.5 x 10-7 mole cm-3 s-1”.
55. p. 637, problem 13.10. This problem was inadvertently replaced with problem 13.9. The correct problem is as follows.
Consider a spherical tumor of radius RT that contains capillaries which provide oxygen at a concentration Cpl. The capillaries have a permeability Pec and a surface to volume ratio S/V. Capillaries are present in the region from R1 to RT where R1 > 0. In the region 0 < r < R1, only oxygen uptake occurs. Oxygen uptake is uniform in the tumor at a rate RO2.
(a)For these conditions determine the oxygen concentration distribution as a function of position.
(b)Necrosis arises when the concentration of oxygen is zero. Determine a condition when necrosis occurs in the region without capillaries.
56. p. 666, replace “QL” with “QiL” in Equation (14.5.1) and “Qc ” with “Qic” in (14.5.3).
57.p. 667, Line 2, replace “where QL and Qc are the rates” with “where QiL and Qic are the rates”
58. p. 668, remove “” in Equation (14.5.7).
59. Page 702, 2nd paragraph, Line 6, insert “(See Problem 15.3.)” between “in Equations (15.3.23) and (15.3.24).” and “The result is”
60. Page 702, the expression for cn in Equation (15.3.26) should be changed as
61. Page 715, Problem 15.4, Line 4, insert “at r = 0” after “If the interstitial fluid pressure pi”
62. Page 715, Problem 15.7, Part (a), the values of 1 and 2 in the Table should be changed to 410-4 min-1 and 710-6 min-1, respectively.
63. Page 716, Problem 15.7, Part (c), Line 2, replace “at 48 hours” with “at 12 and 48 hours, respectively”.
64. Page 716, Problem 15.10, Part (a), Line 1, replace “Determine the1 drug distribution” with “Determine the drug distribution”.
65. Page 729, replace “1VM” with “VM”.
66. Page 732, Figure 16.6, the unit of the vertical axis should be “g/g”.
67. Page 786, Remove “47,” in the index for “Partition coefficient”.