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  • Intravenous Bolus Injection
    Exponential Decay:
    dC/dt œ C = -k.C = -(CL/V).C
    C(t) = C(0).e-kt
  • Intravenous Bolus Injection
    Logarithmic Transform:
    log C(t) = log C(0) - (kt/2.303)
    Elimination Half-Life:
    t1/2 = ln 2/k = 0.693.V/CL
  • Pharmacokinetics

    1. 1. Pharmacokinetics
    2. 2. Drug Effectiveness • Dose-response (DR) curve: Depicts the relation between drug dose and magnitude of drug effect • Drugs can have more than one effect • Drugs vary in effectiveness – Different sites of action – Different affinities for receptors • The effectiveness of a drug is considered relative to its safety (therapeutic index)
    3. 3. Dose-Effect Curves
    4. 4. Therapeutic Index This is a figure of two different This is a figure of two different dose response curves. You can dose response curves. You can obtain a different dose response obtain a different dose response curve for any system that the drug curve for any system that the drug effects. When you vary the drug, effects. When you vary the drug, this is the Independent variable, this is the Independent variable, what you are measuring is the % of what you are measuring is the % of individuals responding to the drug. individuals responding to the drug. Here we see the drugs effects on Here we see the drugs effects on hypnosis and death. Notice that the hypnosis and death. Notice that the effective dose for 50 % of the effective dose for 50 % of the people is 100 mg and if you double people is 100 mg and if you double the dose to 200 mg then 1 % of the dose to 200 mg then 1 % of your subjects die. Thus, if you your subjects die. Thus, if you want to use this drug to hypnotize want to use this drug to hypnotize 99 % of your subjects, in the 99 % of your subjects, in the process you will kill 2-3 % of your process you will kill 2-3 % of your subjects. subjects.
    5. 5. Drug Safety and Effectiveness • Not all people respond to a similar dose of a drug in the exact same manner, this variability is based upon individual differences and is associated with toxicity. This variability is thought to be caused by: – Pharmacokinetic factors contribute to differing concentrations of the drug at the target area. – Pharmacodynamic factors contribute to differing physiological responses to the same drug concentration. – Unusual, idiosyncratic, genetically determined or allergic, immunologically sensitized responses.
    6. 6. Pharmacokinetics • Drug molecules interact with target sites to effect the nervous system – The drug must be absorbed into the bloodstream and then carried to the target site(s) • Pharmacokinetics is the study of drug absorption, distribution within body, and drug elimination over time. – Absorption depends on the route of administration – Drug distribution depends on how soluble the drug molecule is in fat (to pass through membranes) and on the extent to which the drug binds to blood proteins (albumin) – Drug elimination is accomplished by excretion into urine and/or by inactivation by enzymes in the liver
    7. 7. Overview
    8. 8. Study of d[drug] over time
    9. 9. Pharmacokinetics
    10. 10. DISPOSITION OF DRUGS The disposition of chemicals entering the body (from C.D. Klaassen, Casarett and Doull’s Toxicology, 5th ed., New York: McGraw-Hill, 1996).
    11. 11. Routes of Administration • Routes of Administration:Orally: • Rectally: • Inhalation: Absorption through mucous membranes: • Topical: • Parenterally: – Intravenous: – Intramuscular: – Subcutaneous:
    12. 12. Routes of Administration
    13. 13. Drug Delivery Systems • • • • • • Tablets Injections (Syringe) Cigarettes Beverages Patches Suppositories • • • • • • Candy Gum Implants Gas Creams Others? – Stamps – Bandana
    14. 14. Membranes • Types of Membranes: • Cell Membranes: This barrier is permeable to many drug molecules but not to others, depending on their lipid solubility. Small pores, 8 angstroms, permit small molecules such as alcohol and water to pass through. • Walls of Capillaries: Pores between the cells are larger than most drug molecules, allowing them to pass freely, without lipid solubility being a factor. • Blood/Brain Barrier: This barrier provides a protective environment for the brain. Speed of transport across this barrier is limited by the lipid solubility of the psychoactive molecule. • Placental Barrier: This barrier separates two distinct human beings but is very permeable to lipid soluble drugs.
    15. 15. Drug Distribution • • • • Dependent upon its route of administration and target area, every drug has to be absorbed, by diffusion, through a variety of bodily tissue. Tissue is composed of cells which are encompassed within membranes, consisting of 3 layers, 2 layers of water-soluble complex lipid molecules (phospholipid) and a layer of liquid lipid, sandwiched within these layers. Suspended within the layers are large proteins, with some, such as receptors, transversing all 3 layers. The permeability of a cell membrane, for a specific drug, depends on a ratio of its water to lipid solubility. Within the body, drugs may exist as a mixture of two interchangeable forms, either water (ionized-charged) or lipid (non-ionized) soluble. The concentration of two forms depends on characteristics of the drug molecule (pKa, pH at which 50% of the drug is ionized) and the pH of fluid in which it is dissolved. In water soluble form, drugs cannot pass through lipid membranes, but to reach their target area, they must permeate a variety of types of membranes.
    16. 16. Pharmacokinetics vs Pharmacodynamics…concept • Fluoxetine increases plasma concentrations of amitriptyline. This is a pharmacokinetic drug interaction. • Fluoxetine inhibits the metabolism of amitriptyline and increases the plasma concentration of amitriptytline.
    17. 17. Pharmacokinetics vs Pharmacodynamics…concept • If fluoxetine is given with tramadol serotonin syndrom can result. This is a pharmacodynamic drug interaction. • Fluoxetine and tramadol both increase availability of serotonin leading to the possibility of “serotonin overload” This happens without a change in the concentration of either drug.
    18. 18. Basic Parameters • In the next few slides the basic concepts and paramaters will be described and explained. • In pharmacokinetics the body is represented as a single or multiple compartments in to which the drug is distributed. • Some of the parameters are therefore a little abstract as we know the body is much more complicated !
    19. 19. Volume of Distribution, Clearance and Elimination Rate Constant V Volume 100 L Clearance 10 L/hr
    20. 20. Volume of Distribution, Clearance and Elimination Rate Constant V V2 Cardiac and Skeletal Muscle Volume 100 L (Vi) Clearance 10 L/hr
    21. 21. V2 Cardiac and Skeletal Muscle V Volume 100 L (Vi) Clearance 10 L/hr Volume of Distribution = Dose_______ Plasma Concentration
    22. 22. V2 Cardiac and Skeletal Muscle V Volume 100 L (Vi) Clearance 10 L/hr Clearance = Volume of blood cleared of drug per unit time
    23. 23. V2 Cardiac and Skeletal Muscle V Volume 100 L (Vi) Clearance 10 L/hr Clearance = 10 L/hr Volume of Distribution = 100 L What is the Elimination Rate Constant (k) ?
    24. 24. CL = kV k = 10 Lhr -1 = 0.1 hr -1 100 L 10 % of the “Volume” is cleared (of drug) per hour k = Fraction of drug in the body removed per hour
    25. 25. CL = kV If V increases then k must decrease as CL is constant
    26. 26. Important Concepts • VD is a theoretical Volume and determines the loading dose. • Clearance is a constant and determines the maintenance dose. • CL = kVD. • CL and VD are independent variables. • k is a dependent variable.
    27. 27. Volume of Distribution (Vd) Apparent volume of distribution is the theoretical volume that would have to be available for drug to disperse in if the concentration everywhere in the body were the same as that in the plasma or serum, the place where drug concentration sampling generally occurs.
    28. 28. Volume of Distribution • An abstract concept • Gives information on HOW the drug is distributed in the body • Used to calculate a loading dose
    29. 29. Loading Dose Dose = Cp(Target) x Vdd Dose = Cp(Target) x V
    30. 30. Question • What is the loading dose required for drug A if; • Target concentration is 10 mg/L • Vd is 0.75 L/kg • Patients weight is 75 kg • Answer is on the next slide
    31. 31. Answer: Loading Dose of Drug A • Dose = Target Concentration x VD • Vd = 0.75 L/kg x 75 kg = 56.25 L • Target Conc. = 10 mg/L • Dose = 10 mg/L x 56.25 L • = 565 mg • This would probably be rounded to 560 or even 500 mg.
    32. 32. Clearance (CL) • Ability of organs of elimination (e.g. kidney, liver) to “clear” drug from the bloodstream. • Volume of fluid which is completely cleared of drug per unit time. • Units are in L/hr or L/hr/kg • Pharmacokinetic term used in determination of maintenance doses.
    33. 33. Clearance • Volume of blood in a defined region of the body that is cleared of a drug in a unit time. • Clearance is a more useful concept in reality than t 1/2 or kel since it takes into account blood flow rate. • Clearance varies with body weight. • Also varies with degree of protein binding.
    34. 34. Clearance • Rate of elimination = kel D, – Remembering that C = D/Vd – And therefore D= C Vd – Rate of elimination = kel C Vd • Rate of elimination for whole body = CLT C Combining the two, CLT C = kel C Vd and simplifying gives: CLT = kel Vd
    35. 35. Maintenance Dose Calculation • Maintenance Dose = CL x CpSSav • CpSSav is the target average steady state drug concentration • The units of CL are in L/hr or L/hr/kg • Maintenance dose will be in mg/hr so for total daily dose will need multiplying by 24
    36. 36. Question • What maintenance dose is required for drug A if; • Target average SS concentration is 10 mg/L • CL of drug A is 0.015 L/kg/hr • Patient weighs 75 kg • Answer on next slide.
    37. 37. Answer • Maintenance Dose = CL x CpSSav • CL = 0.015 L/hr/kg x 75 = 1.125 L/hr • Dose = 1.125 L/hr x 10 mg/L = 11.25 mg/hr • So will need 11.25 x 24 mg per day = 270 mg
    38. 38. Half-Life and k • Half-life is the time taken for the drug concentration to fall to half its original value • The elimination rate constant (k) is the fraction of drug in the body which is removed per unit time.
    39. 39. Drug Half-Life
    40. 40. Half-Life • C = Co e - kt • C/Co = 0.50 for half of the original amount • 0.50 = e – k t • ln 0.50 = -k t ½ • -0.693 = -k t ½ • t 1/2 = 0.693 / k
    41. 41. Drug Elimination ∆C = KC Δt dC = −KC dt −Kt C t = C 0e
    42. 42. Use of t ½ and kel data • If drug has short duration of action, design drug with larger t ½ and smaller kel • If drug too toxic, design drug with smaller t ½ and larger kel
    43. 43. Drug Concentration C1 Exponential decay C2 dC/dt ∝ C = -k.C Time
    44. 44. Log Concn. C0 C0/2 t1/2 t1/2 t1/2 Time Time to eliminate ~ 4 t1/2
    45. 45. Integrating: Cp2 = Cp1.e -kt Logarithmic transform: lnC2= lnC1 - kt logC2 = logC1 - kt/2.303 Elimination Half-Life: t1/2 = ln2/k t1/2 = 0.693/k
    46. 46. Steady-State • Steady-state occurs after a drug has been given for approximately five elimination half-lives. • At steady-state the rate of drug administration equals the rate of elimination and plasma concentration - time curves found after each dose should be approximately superimposable.
    47. 47. Accumulation to Steady State 100 mg given every half-life 175 187.5 194 … 200 150 100 87.5 94 75 50 97 … 100
    48. 48. C Cpav t Four half lives to reach steady state
    49. 49. What is Steady State (SS) ? Why is it important ? • Rate in = Rate Out • Reached in 4 – 5 half-lives (linear kinetics) • Important when interpreting drug concentrations in time-dependent manner or assessing clinical response
    50. 50. Therapeutic Drug Monitoring Some Principles
    51. 51. Therapeutic Index • Therapeutic index = toxic dose/effective dose • This is a measure of a drug’s safety – A large number = a wide margin of safety – A small number = a small margin of safety
    52. 52. Drug Concentrations may be Useful when there is: • An established relationship between concentration and response or toxicity • A sensitive and specific assay • An assay that is relatively easy to perform • A narrow therapeutic range • A need to enhance response/prevent toxicity
    53. 53. Why Measure Drug Concentrations? • • • • Lack of therapeutic response Toxic effects evident Potential for non-compliance Variability in relationship of dose and concentration • Therapeutic/toxic actions not easily quantified by clinical endpoints
    54. 54. Potential for Error when using TDM • Assuming patient is at steady-state • Assuming patient is actually taking the drug as prescribed • Assuming patient is receiving drug as prescribed • Not knowing when the [drug] was measured in relation to dose administration • Assuming the patient is static and that changes in condition don’t affect clearance • Not considering drug interactions
    55. 55. Acute vs Steady State
    56. 56. Elimination by the Kidney • Excretion - major 1) glomerular filtration glomerular structure, size constraints, protein binding 2) tubular reabsorption/secretion - acidification/alkalinization, - active transport, competitive/saturable, organic acids/bases protein binding • Metabolism - minor -
    57. 57. Elimination by the Liver • Metabolism - major 1) Phase I and II reactions 2) Function: change a lipid soluble to more water soluble molecule to excrete in kidney 3) Possibility of active metabolites with same or different properties as parent molecule • Biliary Secretion – active transport, 4 categories
    58. 58. The Enterohepatic Shunt Drug Liver Bile formation Bile duct Hydrolysis by beta glucuronidase Biotransformation; glucuronide produced gall bladder Portal circulation Gut
    59. 59. Liver P450 systems • Liver enzymes inactivate some drug molecules – First pass effect (induces enzyme activity) • P450 activity is genetically determined: – Some persons lack such activity  leads to higher drug plasma levels (adverse actions) – Some persons have high levels  leads to lower plasma levels (and reduced drug action) • Other drugs can interact with the P450 systems – Either induce activity (apparent tolerance) – Inactivate an enzyme system
    60. 60. Drug Metabolism and pK
    61. 61. How are [drug] measured? • Invasive: blood, spinal fluid, biopsy • Noninvasive: urine, feces, breath, saliva • Most analytical methods designed for plasma analysis • C-14, H-3
    62. 62. Therapeutic Window • Useful range of concentration over which a drug is therapeutically beneficial. Therapeutic window may vary from patient to patient • Drugs with narrow therapeutic windows require smaller and more frequent doses or a different method of administration • Drugs with slow elimination rates may rapidly accumulate to toxic levels….can choose to give one large initial dose, following only with small doses
    63. 63. Shape different for IV injection
    64. 64. Distribution • Rate & Extent depend upon – – – – – Chemical structure of drug Rate of blood flow Ease of transport through membrane Binding of drug to proteins in blood Elimination processes
    65. 65. • Partition Coefficients: ratio of solubility of a drug in water or in an aqueous buffer to its solubility in a lipophilic, non-polar solvent • pH and ionization: Ion Trapping
    66. 66. The Compartment Model • We can generally think of the body as a series of interconnected well-stirred compartments within which the [drug] remains fairly constant. BUT movement BETWEEN compartments important in determining when and for how long a drug will be present in body.
    67. 67. Partitioning into body fat and other tissues ∀• A large, nonpolar compartment. Fat has low blood supply—less than 2% of cardiac output, so drugs are delivered to fat relatively slowly •For practical purposes: partition into body fat important following acute dosing only for a few highly lipid-soluble drugs and environmental contaminants which are poorly metabolized and remain in body for long period of time
    68. 68. IMPORTANT EFFECTS OF pH PARTITIONING: ∀• urinary acidification will accelerate the excretion of weak bases and retard that of weak acids; alkalination has the opposite effects ∀• increasing plasma pH (by addition of NaHCO3) will cause weakly acidic drugs to be extracted from the CNS into the plasma; reducing plasma pH (by administering a carbonic anhydrase inhibitor) will cause weakly acidic drugs to be concentrated in the CNS, increasing their toxicity
    69. 69. Renal Elimination • Glomerular filtration: molecules below 20 kDa pass into filtrate. Drug must be free, not protein bound. • Tubular secretion/reabsorption: Active transport. Followed by passive and active. DP=D + P. As D transported, shift in equilibrium to release more free D. Drugs with high lipid solubility are reabsorbed passively and therefore slowly excreted. Idea of ion trapping can be used to increase excretion rate---traps drug in filtrate.
    70. 70. Plasma Proteins that Bind Drugs • albumin: binds many acidic drugs and a few basic drugs ∀ β-globulin and an α1acid glycoprotein have also been found to bind certain basic drugs
    71. 71. A bound drug has no effect! • • • • Amount bound depends on: 1) free drug concentration 2) the protein concentration 3) affinity for binding sites % bound: __[bound drug]__________ x 100 [bound drug] + [free drug]
    72. 72. % Bound • Renal failure, inflammation, fasting, malnutrition can have effect on plasma protein binding. • Competition from other drugs can also affect % bound.
    73. 73. An Example • Warfarin (anticoagulant) protein bound ~98% • Therefore, for a 5 mg dose, only 0.1 mg of drug is free in the body to work! • If patient takes normal dose of aspirin at same time (normally occupies 50% of binding sites), the aspirin displaces warfarin so that 96% of the warfarin dose is protein-bound; thus, 0.2 mg warfarin free; thus, doubles the injested dose
    74. 74. Volume of Distribution • C = D/V Vd is the apparent volume of distribution C= [drug] in plasma at some time D= total [drug] in system Vd gives one as estimate of how well the drug is distributed. Vd < 0.071 L/kg indicate the drug is mainly in the circulatory system. Vd > 0.071 L/kg indicate the drug has entered specific tissues.
    75. 75. Conc. vs. time plots C = Co - kt ln C = ln Co - kt
    76. 76. Types of Kinetics Commonly Seen Zero Order Kinetics • Rate = k • C = Co - kt • Constant rate of elimination regardless of [D]plasma • C vs. t graph is LINEAR First Order Kinetics • Rate = k C • C = Co e-kt • Rate of elimination proportional to plasma concentration. Constant fraction of drug eliminated per unit time. • C vs. t graph is NOT linear, decaying exponential. Log C vs. t graph is linear.
    77. 77. Example of Zero Order Elimination: Pharmacokinetics of Ethanol • Ethanol is distributed in total body water. • Mild intoxication at 1 mg/ml in plasma. • How much should be ingested to reach it? Answer: 42 g or 56 ml of pure ethanol (VdxC) Or 120 ml of a strong alcoholic drink like whiskey • Ethanol has a constant elimination rate = 10 ml/h • To maintain mild intoxication, at what rate must ethanol be taken now? at 10 ml/h of pure ethanol, or 20 ml/h of drink.
    78. 78. First-Order Kinetics
    79. 79. To reiterate: Comparison • Zero Order Elimination • First Order Elimination – [drug] decreases linearly with time – Rate of elimination is constant – Rate of elimination is independent of [drug] – No true t 1/2 – [drug] decreases exponentially w/ time – Rate of elimination is proportional to [drug] – Plot of log [drug] or ln[drug] vs. time are linear – t 1/2 is constant regardless of [drug]
    80. 80. Route of Administration Determines Bioavailability (AUC)
    81. 81. AUC: An Indicator of Bioavailability • Dose is proportional to [drug] in tissues. • [drug], in turn, is proportional to the Area Under the Curve in a Concentration-decay curve. • Thus, we have k = dose/AUC • Because oral administration is full of barriers, the fraction, F, that is available by entering the general circulation, may not be significant. • Thus, FD = k(AUC) or k = FD/AUC
    82. 82. • Combining these 2 equations gives us: FDpo/AUCpo = Div/AUCiv • And thus, F = AUCpoDiv AUCivDpo • More generally, the relative bioavailability, F = AUCADoseB AUCBDoseA
    83. 83. AUC: IV Administration
    84. 84. AUC • For IV bolus, the AUC represents the total amount of drug that reaches the circulatory system in a given time. • Dose = CLT AUC
    85. 85. AUC: Oral Administration
    86. 86. Bioavailability • The fraction of the dose of a drug (F) that enters the general circulatory system, F= amt. of drug that enters systemic circul. Dose administered F = AUC/Dose
    87. 87. Bioavailability • A concept for oral administration • Useful to compare two different drugs or different dosage forms of same drug • Rate of absorption depends, in part, on rate of dissolution (which in turn is dependent on chemical structure, pH, partition coefficient, surface area of absorbing region, etc.) Also firstpass metabolism is a determining factor
    88. 88. The Effect of the Liver First Pass • F = 1-E, where E is fraction of the dose elim via the liver. • Cltot = D/AUC • Clhep = Cltot-Clren • Clhep = E × LBF, which is liver blood flow or E = Clhep/LBF • Combining the 1st eq with the last gives F = 1-E = 1-Clhep LBF
    89. 89. Rowland’s Equation • F = 1-E = 1-Clhep LBF This very useful equation calculates the magnitude of the effect of the liver’s 1 st pass of an oral dose and, more precisely, to predict it from and i.v. test. Thus, if E < 0.10, then, clearly, bioavailability F > 0.90.
    90. 90. P450 Interactions • Substrate: Is the drug metabolized via a specific hepatic isoenzyme? • Inhibitor: does a specific drug inhibit a specific hepatic isoenzyme? – Would expect this to interfere with drug inactivation • Inducer: does a specific drug enhance a specific hepatic isoenzyme? – Would expect this to speed up drug inactivation
    91. 91. Drug-CYP Interactions Enzyme (CYP) Substrate 1A2 Clozapine, haloperidol 2B6 Bupropion 2C19 Citalopram 2C9 Fluoxetine 2D6 Most ADs, APs 2E1 Gas anesthetics 3A4,5,7 Alprazolam Inhibitor Inducer Cimetidine Tobacco smoke Thiotepa Phenobarbital Fluoxetine Prednisone Paroxetine Secobarbital CPZ, ranitidine Dexamethasone Disulfiram Ethanol Grapefruit juice Glucocorticoid –
    92. 92. Drug Enantioners • A drug molecule may be organized in such a way that the same atoms are mirror images – Enantioners represent drug molecules that are structurally different (spatial configutation) • Different physical properties – Light rotation (levo = left; dextro = right) – Melting points • Different biological activities (typically: dextro > levo) – Fenfluramine = racemic mix of • dextro-fenfluramine • levo-fenfluramine • Enantiomers often have different affinity for receptors