Pharmacokinetics

Lectures 3 & 4

  1. One compartment model
  2. Simplest
  3. Works for most drugs
  4. Model: For IV Bolus
  5. A is the amount of drug in the compartment at any given time
  6. C is the concentration of drug in the circulation
  7. V is the volume of distribution
  8. A = CV
  1. Assumptions
  2. Distribution is instantaneous and the compartment is “well stirred”
  3. That is that the tissue and plasma concentrations are proportional and reach equilibrium quickly
  4. IV Bolus lasts less than 5 minutes and is directly into a vein.
  5. K for first order kinetics
  6. K = km + ke (urinary and biliary)
  7. First order process Equations
  8. Important equations
  9. Ln (C/C0) = -kt
  10. C/C0 = e-kt
  11. C = =C0e-kt
  12. Log C = log C0 – (k/2.303)t
  13. Graphical presentations of plasma profiles
  14. Linear or regular plot
  15. Gives a negative exponential curve
  16. Concentration on the y-axis
  17. Time on the x-axis
  18. Semi-logarithmic plot
  19. Straight line (but not with multiple compartments)
  20. Log C on the y-axis
  21. Time on the x-axis
  22. The point where the line reaches the y-axis is log C0
  23. C0 = the initial concentration at t0
  24. it is the highest concentration for IV bolus
  25. it is only a theoretical value
  26. units are micrograms/ml or mg/L
  27. k can be determined by the slope of the line
  28. K = 2.303 x slope
  29. units are time –1
  30. AUC
  31. Units are micrograms x time /volume
  32. AUC is the total bioavailability of a drug after a given dose
  33. Can be used to calculate clearance, determine bioavailability and determine bioequivalence
  34. Determining AUC
  35. Trapezoidal rule
  36. AUC = the sum of[(Cn-1 +Cn)(tn-tn-1)/2] + Ctn/k
  37. Where Ctn is C at infinity
  38. Below: piece of AUC
  1. Pharmacokinetic Parameters
  2. C0 (see above)
  3. The relationship between k and t1/2
  4. T1/2 = 0.693/k
  5. Volume of Distribution
  6. Also called the apparent Vd
  7. Vd = Dose/C0 (for IV bolus one compartment model only!!!)
  8. Vd = CL/k or Dose/(AUC x k)
  9. A 70kg person has about 3 liters of plasma and 42L of total body water
  10. Useful parameter and indicator for the relative amount of drug in vascular and extravascular tissues
  11. more drug in extra vascular tissues when the Vd is more than 42L
  12. Effected by pathophysiological conditions
  13. Edemia
  14. Increases the Vd and decreases C
  15. age
  16. Decreases Vd and increases C
  17. Less lean body mass
  18. If the Vd is less than or equal to 3 L then the drug shows strong plasma protein binding
  19. Clearance (CL)
  20. Units are volume/time
  21. Measure of drug elimination form body
  22. Most drugs are cleared by 1st order
  23. rate is proportional to concentration
  24. the only thing constant in 1st order
  25. CLT = CLR + CLH + CLB + …
  26. Proportionality factor
  27. if the CL goes down and the Vd goes up then t1/2 goes up too
  28. the change in t1/2 depends on the magnitude of the change in CL and Vd if they are both changing in the same direction
  29. CL = elimination rate/ Concentration
  30. CL = dose/AUC
  31. Renal clearance:
  32. CLR = renal excretion rate/C
  33. CLR = (dDu/dt)/C
  34. Du = drug in urine unchanged
  35. = total amount excreted unchanged in urine/ AUC
  36. Fraction of drug excreted unchanged in urine is Fe
  37. fe = CLR/CL
  38. =total amount excreted unchanged in urine/Dose
  39. =ke/k
  40. (1-fe)
  41. the fraction eliminated by non-renal routes
  42. Estimation of parameters from plasma data
  43. See example on page 15
  44. Equations
  45. slope = (log 2 – log 0.2)/1-10 = -0.111h-1
  46. k = -2.303k = 0.256 hr-1
  47. C=C0e-kt = 2.58 mg/L
  48. t1/2 = 0.983/k = 2.7 hr
  49. AUC = C0/k = 10.08 mg*hr/L
  50. CL = Dose/AUC = 5.16 L
  51. Vd=Cl/k = 20.2 L
  52. More Examples on page 17
  53. Equations
  54. C0 = Dose/V
  55. log A = log A0 –(k/2.303)t
  56. MIC (minimum inhibitory concentration)
  57. Equal to C
  58. C = C0e-kt
  59. Log C = log C0 – (k/2.303)t
  60. Estimation of parameters from urinary excretion data
  61. Non invasive sampling
  62. Collected fro an interval
  63. Less accurate than plasma
  64. To obtain valid data
  65. Need significant amount unchanged (high Fe)
  66. Need specific assay (be able to distinguish parent molecule and metabolite)
  67. Frequent sampling for good curve description
  68. To get a complete profile you must sample for up to 5-6 half lives
  69. Must take into consideration the variation s in pH and volume
  70. Requires complete bladder emptying
  71. See table on page 19
  72. Amount excreted in time interval (Du)= Concentration of unchanged drug in urine (C) x the volume of urine (V)
  73. Excretion rate = Du/t
  74. Cumulative amount excreted = Du1 + Du2
  75. ARE = amount remaining to be excreted
  76. Rate method:
  77. Use the excretion rate
  78. Do a semi-logarithmic plot of the rate or excretion against the midpoint time of urine collection
  79. K can then be calculated from the slope
  80. The amount of drug excreted unchanged in the urine accumulates asymptotically toward the limiting value
  81. see fig B-2
  82. Du(infinity)/Dose = Fe
  83. Du/t = excretion rate
  84. Log(dDu/dt) = log (ke*dose) –k/2.303t
  85. Y-intercept = ke * dose
  86. Pros
  87. not required to determine Du infinity
  88. can determine ke and k from one diagram and then calculate Fe
  89. Sigma-minus method
  90. Ln(Duinfinity – Du) = ln Du infinity –kt
  91. Where t is the actual time at the end of the collection interval (rather than the midpoint)
  92. Plot amount remaining to be excreted vs time
  93. slope still used to determine k
  94. Pros
  95. less sensitive to incomplete bladder emptying because Fe = Du infinity/ dose