clinical pharmacokinetics slideahere final.pptx

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1. Clinical pharmacokinetics 5/6/2024 1

2. ELIMINATION RATE CONSTANT As stated in the previous section, the elimination rate constant ( K ) represents the fraction of drug removed per unit of time and has units of reciprocal time (e.g., minute -1 , hour -1 , and day -1 ). These units are evident from examination of the calculation of K . For example, C is the first plasma drug concentration, measured just after the dose is given, and C 1 is the second plasma drug concentration, measured at a later time (t 1 ). From our previous discussion, we know that the equation for this line ( y = mX + b ) is: ln C 1 = - Kt + ln C Furthermore, we know that the slope of the line equals - K, and we can calculate this slope: 5/6/2024 2

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4. HALF-LIFE Another important parameter that relates to the rate of drug elimination is half-life ( T1/2 ). The half-life is the time necessary for the concentration of drug in the plasma to decrease by half. A drug's half-life is often related to its duration of action and also may indicate when another dose should be given. One way to estimate the half-life is to visually examine the natural log of plasma drug concentration versus time plot and note the time required for the plasma concentration to decrease by half 5/6/2024 4

5. The half-life and the elimination rate constant express the same idea. They indicate how quickly a drug is removed from the plasma and, therefore, how often a dose has to be administered. If the half-life and peak plasma concentration of a drug are known, then the plasma drug concentration at any time can be estimated 5/6/2024 5

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7. The equation represents the important relationship between the half-life and the elimination rate constant shown by mathematical manipulation. We already know that:  ln C = ln C -Kt  By definition, the concentration ( C ) at the time ( t ) equal to the half-life ( T1/2 ) is half the original concentration ( C ). Therefore, at one half-life, the concentration is half of what it was initially. So we can say that at t = T1/2 , C = 1/2C . For simplicity, let's assume that C = 1. Therefore: ln 0.5 C = ln C - K ( T1/2 ) ln 0.5 = ln 1 - K ( T1/2 ) 5/6/2024 7

8. The AUC is determined by drug clearance and the dose given         When clearance remains constant, the AUC is directly proportional to the dose administered. If the dose doubled, the AUC would also double. Another way to think about this concept is that clearance is the parameter relating the AUC to the drug dose 5/6/2024 8

9. With a one-compartment model, first-order elimination, and intravenous drug administration, the AUC can be calculated easily: C has units of concentration, usually milligrams per liter ( ), and K is expressed as reciprocal time (usually hour -1 ), so the AUC is expressed as milligrams per liter times hours ( ). These units make sense graphically as well, because when we multiply length times width to measure area, the product of the axes (concentration, in milligrams per liter, and time, in hours) would be expressed as milligrams per liter times hours. 5/6/2024 9

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11. AUC can be calculated by computer modeling of the above AUC equation, or by applying the "trapezoidal rule". The trapezoidal rule method is rarely used, but provides visual means to understand AUC. If a line is drawn vertically to the x -axis from each measured concentration, Because we are using the determined concentrations rather than their natural logs, the plasma drug concentration versus time plot is curved 5/6/2024 11

12. Application of Pharmacokinetics to Clinical Situations: The success of drug therapy is highly dependent on the choice of the drug and drug product and on the design of the dosage regimen. The choice of the drug and drug product, eg , immediate release versus modified release, is based on the patient's characteristics and the known pharmacokinetics of the drug. 5/6/2024 12

13. A properly designed dosage regimen tries to achieve a specified concentration of the drug at a receptor site to produce an optimal therapeutic response with minimum adverse effects Individual variation in pharmacokinetics and pharmacodynamics makes the design of dosage regimens difficult. Therefore, the application of pharmacokinetics to dosage regimen design must be coordinated with proper clinical evaluation of the patient and monitoring. 5/6/2024 13

14. Pharmacokinetics After a drug is released from its dosage form, the drug is absorbed into the surrounding tissue, the body, or both. The distribution through and elimination of the drug in the body varies for each patient but can be characterized using mathematical models and statistics. Pharmacokinetics is the science of the kinetics of drug absorption, distribution, and elimination ( ie , excretion and metabolism). The description of drug distribution and elimination is often termed drug disposition. 5/6/2024 14

15. Characterization of drug disposition is an important prerequisite for determination or modification of dosing regimens for individuals and groups of patients. The study of pharmacokinetics involves both experimental and theoretical approaches. The experimental aspect of pharmacokinetics involves the development of biologic sampling techniques, analytical methods for the measurement of drugs and metabolites, and procedures that facilitate data collection and manipulation 5/6/2024 15

16. Pharmacokinetics and Pharmacodynamics Pharmacokinetics Pharmacodynamics Design of dosage regimen Where? How much? How often? How long? Plasma Concentration Effects Plasma refers to the clear supernatant fluid that results from blood after the cellular components have been removed 5/6/2024 16

17. During the drug development process, large numbers of patients are tested to determine optimum dosing regimens, which are then recommended by the manufacturer to produce the desired pharmacologic response in the majority of the anticipated patient population. However, intra- and interindividual variations will frequently result in either a subtherapeutic (drug concentration below the MEC) or toxic response (drug concentrations above the minimum toxic concentration, MTC), which may then require adjustment to the dosing regimen. 5/6/2024 17

18. Clinical pharmacokinetics is the application of pharmacokinetic methods to drug therapy. Clinical pharmacokinetics involves a multidisciplinary approach to individually optimized dosing strategies based on the patient's disease state and patient-specific considerations 5/6/2024 18

19. Pharmacogenetics Science of assessing genetically determined variations in patients and the resulting affect on drug pharmacokinetics and pharmacodynamics Useful to identify therapeutic failures and unanticipated toxicity 5/6/2024 19

20. Pharmacodynamics Pharmacodynamics refers to the relationship between the drug concentration at the site of action (receptor) and pharmacologic response, including biochemical and physiologic effects that influence the interaction of drug with the receptor. The interaction of a drug molecule with a receptor causes the initiation of a sequence of molecular events resulting in a pharmacologic or toxic response. 5/6/2024 20

21. Efficacy Degree to which a drug is able to produce the desired response Potency Amount of drug required to produce 50% of the maximal response the drug is capable of inducing Used to compare compounds within classes of drugs 5/6/2024 21

22. Effective Concentration 50% (ED 50 ) Concentration of the drug which induces a specified clinical effect in 50% of subjects Lethal Dose 50% (LD 50 ) Concentration of the drug which induces death in 50% of subjects 5/6/2024 22

23. Therapeutic Index Measure of the safety of a drug Calculation: LD 50 /ED 50 Margin of Safety Margin between the therapeutic and lethal doses of a drug 5/6/2024 23

24. . Pharmacokinetic- pharmacodynamic models are constructed to relate plasma drug level to drug concentration in the site of action and establish the intensity and time course of the drug. 5/6/2024 24

25. Pharmacodynamics and Pharmacokinetics As we have discussed the importance of using pharmacokinetics to develop dosing regimens that will result in plasma concentrations in the therapeutic window and yield the desired therapeutic or pharmacologic response. The interaction of a drug molecule with a receptor causes the initiation of a sequence of molecular events resulting in a pharmacodynamic or pharmacologic response . 5/6/2024 25

26. The term pharmacodynamics refers to the relationship between drug concentrations at the site of action (receptor) and pharmacologic response, including the biochemical and physiologic effects that influence the interaction of drug with the receptor. Early pharmacologic research demonstrated that the pharmacodynamic response produced by the drug depends on the chemical structure of the drug molecule. 5/6/2024 26

27. Pharmacokinetic models allow very complex processes to be simplified. The process of pharmacokinetic modeling continues until a model is found that describes the real process quantitatively. The understanding of drug response is greatly enhanced when pharmacokinetic modeling techniques are combined with clinical pharmacology, resulting in the development of pharmacokinetic– pharmacodynamic models 5/6/2024 27

28. Pharmacokinetic– pharmacodynamic models use data derived from the plasma drug concentration-versus-time profile and from the time course of the pharmacologic effect to predict the pharmacodynamics of the drug. Pharmacokinetic– pharmacodynamic models have been reported for antipsychotic medications, anticoagulants, neuromuscular blockers, antihypertensives , anesthetics, and many antiarrhythmic drugs (the pharmacologic responses of these drugs are well studied because of easy monitoring). 5/6/2024 28

29. Basic Pharmacokinetics and Pharmacokinetic Models Drugs are in a dynamic state within the body as they move between tissues and fluids, bind with plasma or cellular components, or are metabolized. The biologic nature of drug distribution and disposition is complex, and drug events often happen simultaneously. Yet such factors must be considered when designing drug therapy regimens. The inherent and infinite complexity of these events require the use of mathematical models and statistics to estimate drug dosing and to predict the time course of drug efficacy for a given dose. 5/6/2024 29

30. A model is a hypothesis using mathematical terms to describe quantitative relationships concisely. The predictive capability of a model lies in the proper selection and development of mathematical function(s) that parameterize the essential factors governing the kinetic process. The key parameters in a process are commonly estimated by fitting the model to the experimental data, known as variables . A pharmacokinetic parameter is a constant for the drug that is estimated from the experimental data. For example, estimated pharmacokinetic parameters such as k depend on the method of tissue sampling, the timing of the sample, drug analysis, and the predictive model selected. 5/6/2024 30

31. Such mathematical models can be devised to simulate the rate processes of drug absorption, distribution, and elimination to describe and predict drug concentrations in the body as a function of time. Pharmacokinetic models are used to: 1. Predict plasma, tissue, and urine drug levels with any dosage regimen 2. Calculate the optimum dosage regimen for each patient individually 5/6/2024 31

32. 3 . Estimate the possible accumulation of drugs and/or metabolites 4. Correlate drug concentrations with pharmacologic or toxicologic activity 5. Evaluate differences in the rate or extent of availability between formulations (bioequivalence) 6. Describe how changes in physiology or disease affect the absorption, distribution, or elimination of the drug 7. Explain drug interactions 5/6/2024 32

33. Simplifying assumptions are made in pharmacokinetic models to describe a complex biologic system concerning the movement of drugs within the body. For example, most pharmacokinetic models assume that the plasma drug concentration reflects drug concentrations globally within the body. A model may be empirically, physiologically, or compartmentally based. The model that simply interpolates the data and allows an empirical formula to estimate drug level over time is justified when limited information is available. 5/6/2024 33

34. Empirical models are practical but not very useful in explaining the mechanism of the actual process by which the drug is absorbed, distributed, and eliminated in the body 5/6/2024 34

35. Compartment Models If the tissue drug concentrations and binding are known, physiologic pharmacokinetic models, which are based on actual tissues and their respective blood flow, describe the data realistically. Physiologic pharmacokinetic models are frequently used in describing drug distribution in animals, because tissue samples are easily available for assay. On the other hand, tissue samples are often not available for human subjects, so most physiological models assume an average set of blood flow for individual subjects. 5/6/2024 35

36. In contrast, because of the vast complexity of the body, drug kinetics in the body are frequently simplified to be represented by one or more tanks, or compartments, that communicate reversibly with each other. A compartment is not a real physiologic or anatomic region but is considered as a tissue or group of tissues that have similar blood flow and drug affinity. Within each compartment, the drug is considered to be uniformly distributed. 5/6/2024 36

37. Mixing of the drug within a compartment is rapid and homogeneous and is considered to be "well stirred," so that the drug concentration represents an average concentration, and each drug molecule has an equal probability of leaving the compartment Rate constants are used to represent the overall rate processes of drug entry into and exit from the compartment. The model is an open system because drug can be eliminated from the system. Compartment models are based on linear assumptions using linear differential equation s 5/6/2024 37

38. Mammillary Model A compartmental model provides a simple way of grouping all the tissues into one or more compartments where drugs move to and from the central or plasma compartment. The mammillary model is the most common compartment model used in pharmacokinetics. The mammillary model is a strongly connected system, because one can estimate the amount of drug in any compartment of the system after drug is introduced into a given compartment. In the one-compartment model, drug is both added to and eliminated from a central compartment . 5/6/2024 38

39. The central compartment is assigned to represent plasma and highly perfused tissues that rapidly equilibrate with drug. When an intravenous dose of drug is given, the drug enters directly into the central compartment. Elimination of drug occurs from the central compartment because the organs involved in drug elimination, primarily kidney and liver, are well- perfused tissues 5/6/2024 39

40. In a two-compartment model, drug can move between the central or plasma compartment to and from the tissue compartment. Although the tissue compartment does not represent a specific tissue, the mass balance accounts for the drug present in all the tissues. In this model, the total amount of drug in the body is simply the sum of drug present in the central compartment plus the drug present in the tissue compartment. 5/6/2024 40

41. Knowing the parameters of either the one- or two-compartment model, one can estimate the amount of drug left in the body and the amount of drug eliminated from the body at any time. The compartmental models are particularly useful when little information is known about the tissues. 5/6/2024 41

42. Several types of compartment models are described in . The pharmacokinetic rate constants are represented by the letter k . Compartment 1 represents the plasma or central compartment, and compartment 2 represents the tissue compartment. The drawing of models has three functions. The model (1) enables the pharmacokineticist to write differential equations to describe drug concentration changes in each compartment, (2) gives a visual representation of the rate processes, and (3) shows how many pharmacokinetic constants are necessary to describe the process adequately 5/6/2024 42

43. Catenary Model In pharmacokinetics, the mammillary model must be distinguished from another type of compartmental model called the catenary model. The catenary model consists of compartments joined to one another like the compartments of a train. In contrast, the mammillary model consists of one or more compartments around a central compartment like satellites. Because the catenary model does not apply to the way most functional organs in the body are directly connected to the plasma, it is not used as often as the mammillary model. . 5/6/2024 43

44. Physiologic Pharmacokinetic Model (Flow Model ) Physiologic pharmacokinetic models , also known as blood flow or perfusion models, are pharmacokinetic models based on known anatomic and physiologic data. The models describe the data kinetically, with the consideration that blood flow is responsible for distributing drug to various parts of the body. Uptake of drug into organs is determined by the binding of drug in these tissues. In contrast to an estimated tissue volume of distribution, the actual tissue volume is used. Because there are many tissue organs in the body, each tissue volume must be obtained and its drug concentration described. 5/6/2024 44

45. The model would potentially predict realistic tissue drug concentrations, which the two-compartment model fails to do. Unfortunately, much of the information required for adequately describing a physiologic pharmacokinetic model are experimentally difficult to obtain. In spite of this limitation, the physiologic pharmacokinetic model does provide much better insight into how physiologic factors may change drug distribution from one animal species to another. Other major differences are described below 5/6/2024 45

46. The primary purpose of rigorous pharmacokinetic data analysis, compartmental or model-independent, is to determine the pharmacokinetic parameters useful in dosing drugs for patients. Consequently, multiple plasma drug concentrations are obtained at specific time points in healthy and diseased persons to assess a drug's population pharmacokinetic parameters. 5/6/2024 46

47. In clinical practice, it may be difficult to obtain multiple plasma samples after the first dose to determine a patient's pharmacokinetic parameters. Consequently, clinicians use population parameters from the literature to make individual patient dosage calculations. 5/6/2024 47

48. Model-independent pharmacokinetic data analysis provides the opportunity to obtain pharmacokinetic values that do not depend on a compartmental model. Total body clearance, mean residence time (MRT), volume of distribution at steady state, and formation clearance are four of the most frequently used model-independent parameters and are the focus of this section 5/6/2024 48

49. The use of model-independent data analysis techniques to generate model-independent parameters offers several advantages over traditional compartmental approaches. First, it is not necessary to assume a compartmental model. Many drugs possess complex distribution patterns requiring two, three, or more exponential terms to describe their elimination. 5/6/2024 49

50. As the number of exponential terms increases, a compartmental analysis requires more intensive blood sampling and rigorous data calculations. Second, several drugs (e.g., gentamicin) can be described by one, two, or more distribution compartments, depending on the characteristics of the patients evaluated or the aggressiveness of the blood sampling. 5/6/2024 50

51. Therefore, a compartmental approach would require that pharmacokinetic parameters be obtained for each distribution pattern, making it difficult to compare one data set to another. Third, calculations are generally easier with model-independent relationships and do not require a computer with sophisticated software. One drawback of using model-independent parameters is the inability to visualize or predict plasma concentration versus time profiles. This may result in the loss of specific information that provides important insight regarding drug disposition 5/6/2024 51

52. Mean Residence Time MRT is defined as the average time intact drug molecules transit or reside in the body. For a population of drug molecules, individual molecules spend different times within the body. Following the principles of statistical probability, specific drug molecules may be eliminated quickly whereas others may remain in the body much longer. Consequently, a distribution of transit times can be characterized by a mean value. In other words, elimination of a drug can be thought of as a random process. 5/6/2024 52

53. Residence time reflects how long a particular drug molecule remains or resides in the body. The MRT reflects the overall behavior of a large number of drug molecules. This parameter is not used frequently in clinical practice to monitor patients. However, it is useful when comparing the effect of disease, altered physiologic state, or drug-drug interaction on the pharmacokinetics of a specific drug. MRT can be calculated with the following equation 5/6/2024 53

54. 54 Nonlinear pharmacokinetics 5/6/2024

55. Nonlinear Pharmacokinetics: Introduction . These linear models assumed that the pharmacokinetic parameters for a drug would not change when different doses or multiple doses of a drug were given. With some drugs, increased doses or chronic medication can cause deviations from the linear pharmacokinetic profile previously observed with single low doses of the same drug. This nonlinear pharmacokinetic behavior is also termed dose-dependent pharmacokinetics. 5/6/2024 55

56. Many of the processes of drug absorption, distribution, biotransformation, and excretion involve enzymes or carrier-mediated systems. For some drugs given at therapeutic levels, one of these specialized processes may become saturated. Besides saturation of plasma protein-binding or carrier-mediated systems, drugs may demonstrate nonlinear pharmacokinetics due to a pathologic alteration in drug absorption, distribution, and elimination. 5/6/2024 56

57. Pharmacokinetic parameters, such as elimination half life (t1/2), the elimination rate constant (K), the apparent volume of distribution (V), and the systemic clearance ( Cl ) of most drugs are not expected to change when different doses are administered and/or when the drug is administered via different routes as a single dose or multiple doses The kinetics of these drugs is described as linear, or dose-independent, pharmacokinetics and is characterized by the first-order process 5/6/2024 57

58. The term linear simply means that plasma concentration at a given time at steady state and the area under the plasma concentration versus time curve (AUC) will both be directly proportional to the dose administered 5/6/2024 58

59. 59 Nonlinear For some drugs, however, the above situation may not apply For example, when the daily dose of phenytoin is increased by 50% in a patient from 300 mg to 450 mg, the average steady-state plasma concentration, (Cp) ss , may increase by as much as 10-fold This dramatic increase in the concentration (greater than directly proportional) is attributed to the nonlinear kinetics of phenytoin 5/6/2024

60. 60 Introduction: Nonlinear 5/6/2024

61. Saturable Enzymatic Elimination Processes: The elimination of drug by a saturable enzymatic process is described by Michaelis–Menten kinetics . If C p is the concentration of drug in the plasma, then where V max is the maximum elimination rate and K M is the Michaelis constant that reflects the capacity of the enzyme system. It is important to note that K M is not an elimination constant ,.. 5/6/2024 61

62. but is actually a hybrid rate constant in enzyme kinetics, representing both the forward and backward reaction rates and equal to the drug concentration or amount of drug in the body at 0.5 V max . The values for K M and V max are dependent on the nature of the drug and the enzymatic process involved 5/6/2024 62

63. Determination of K M and V max When an experiment is performed with solutions of various concentration of drug C, a series of reaction rates ( v ) may be measured for each concentration. Special plots may then be used to determine K M and V max . 5/6/2024 63

64. At steady state, the rate of drug metabolism ( v ) is assumed to be the same as the rate of drug input R (dose/day). However, steady state will not be reached if the drug input rate, R , is greater than the V max ; instead, drug accumulation will continue to occur without reaching a steady-state plateau. where R = dose/day or dosing rate; C ss = steady-state plasma drug concentration, V max = maximum metabolic rate constant in the body, and K M = Michaelis–Menten constant of the drug in the body 5/6/2024 64

65. Determination of K M and V max by Direct Method When steady-state concentrations of phenytoin are known at only two dose levels, there is no advantage in using the graphic method. K M and V max may be calculated by solving two simultaneous equations formed by substituting C SS and R with C 1 , R 1 , C 2 , and R 2 . The equations contain two unknowns, K M and V max , and may be solved easily. where C 1 is steady-state plasma drug concentration after dose 1, C 2 is steady-state plasma drug concentration after dose 2, R 1 is the first dosing rate, and R 2 is the second dosing rate. 5/6/2024 65

66. 66 Nonlinear Administration of different doses of drugs with nonlinear kinetics may not result in parallel plasma concentration versus time profiles expected for drugs with linear pharmacokinetics 5/6/2024

67. 67 Nonlinear kinetics Nonlinearity may arise at any one of the pharmacokinetic steps, such as absorption, distribution and/or elimination For example, the extent of absorption of amoxicillin decreases with an increase in dose For distribution, plasma protein binding of disopyramide is saturable at the therapeutic concentration, resulting in an increase in the volume of distribution with an increase in dose of the drug 5/6/2024

68. As for nonlinearity in renal excretion, it has been shown that the antibacterial agent dicloxacillin has saturable active secretion in the kidneys, resulting in a decrease in renal clearance as dose is increased Both phenytoin and ethanol have saturable metabolism, which means that an increase in dose results in a decrease in hepatic clearance and a more than proportional increase in AUC 68 5/6/2024

69. 69 Nonlinearity in metabolism Capacity-limited metabolism Capacity-limited metabolism is also called saturable metabolism, Michaelis–Menten kinetics Nonlinearity in metabolism, is one of the most common sources of nonlinearity 5/6/2024

70. 70 Nonlinearity in metabolism Capacity-limited metabolism The rate of metabolism, or the rate of elimination if metabolism is the only pathway of elimination, is defined by the Michaelis–Menten equation: where Vmax is the maximum rate (unit: amount/time) of metabolism; Km is the Michaelis–Menten constant (unit: same as the concentration [amount/volume]), and C is the drug concentration 5/6/2024

71. 71 Nonlinearity in metabolism Capacity-limited metabolism Two cases: Km>>C Km<<C 5/6/2024

72. 72 Nonlinearity in metabolism Capacity-limited metabolism 5/6/2024

73. 73 Estimation of Michaelis–Menten parameters from administration of a single dose 5/6/2024

74. 74 Estimation of Michaelis–Menten parameters from administration of a single dose Terminal line (C<< Km) Observed conc 5/6/2024

75. 75 Estimation of Michaelis–Menten parameters from administration of a single IV bolus dose Drug amount in the Body (X) IV bolus administration (dose = X ) Elimination process Based on the assumption of nonlinear elimination process: 5/6/2024

76. 76 Estimation of Michaelis–Menten parameters from administration of a single IV bolus dose Divide by Vd Assume that Rearrangement Derivation of observed concentration equation 5/6/2024

77. 77 Estimation of Michaelis–Menten parameters from administration of a single IV bolus dose Integration Previous equation represent the observed conc 5/6/2024

78. 78 Estimation of Michaelis–Menten parameters from administration of a single dose Terminal line (C<< Km) Observed conc 5/6/2024

79. 79 Estimation of Michaelis–Menten parameters from administration of a single IV bolus dose Divide by Vd Derivation of terminal concentration equation When C>>Km: Km+C ≈ C First order elimination This equation represent the terminal concentration equation 5/6/2024

80. 80 Estimation of Michaelis–Menten parameters from administration of a single dose Observed conc Terminal line (C<< Km) 5/6/2024

81. 81 Estimation of Michaelis–Menten parameters from administration of a single dose 5/6/2024

82. 82 Estimation of Michaelis–Menten parameters from administration of a single IV bolus dose Steps: Plot log(conc)-time profile Get the initial conc (C ) Extrapolate the terminal line to get an initial terminal conc (C * ) Calculate the slope of the terminal line using the log 5/6/2024

83. 83 Example 1 The following concentration time profile was constructed after administration of 300 mg dose of drug A to an adult patient. find Vm Km Vd The dose required to produce a steady-state conc of 20 mg/L in this patient. 5/6/2024

84. 84 5/6/2024

85. 85 Example 1 From the figure the following were calculated: C0=10 mg/L, C0*= 45 mg/L, and Slope (using the log) = -0.985 5/6/2024

86. 86 Example 1 The dose required to produce a steady-state concentration of 20 mg/L in this patient: 5/6/2024

87. 87 Estimation of Michaelis–Menten parameters from two steady-state drug concentrations arising from two dosing rates At steady state: Input rate = output rate Dosing rate = Elimination rate R is the input rate that is described as: 5/6/2024

88. 88 Estimation of Michaelis–Menten parameters from two steady-state drug concentrations arising from two dosing rates Two dosing rates resulted in the following steady state conc: Estimate Vmax and Km Dosing rate Css R1 Css1 R2 Css2 5/6/2024

89. 89 Estimation of Michaelis–Menten parameters from two steady-state drug concentrations arising from two dosing rates Two equations with two unknowns 5/6/2024

90. 90 Example 2 RM is a 32 year old, 80kg male who is being seen in the Neurology Clinic. Prior to his last visit he had been taking 300mg of Phenytoin daily; however, because his seizures were poorly controlled and because his plasma concentration was only 8mg/L, his dose was increased to 350mg daily. Now he complains of minor CNS side effects and his reported plasma Phenytoin concentration is 20mg/L. Renal and hepatic function are normal. Assume that both of the reported plasma concentrations represent steady state and that the patient has compiled with the prescribed dosing regimens. Calculate RM’s apparent Vm and Km and a new daily dose of Phenytoin that will result in a steady state level of about 15mg/L. 5/6/2024

91. 91 Example 2 Eqn (1)- Eqn(2): Eqn (1): 5/6/2024

92. 92 Example 2 Calculate RM’s a new daily dose of Phenytoin that will result in a steady state level of about 15mg/L 5/6/2024

93. Chronopharmacokinetics and Time-Dependent Pharmacokinetics Chronopharmacokinetics broadly refers to a temporal change in the rate process (such as absorption or elimination) of a drug. The temporal changes in drug absorption or elimination can be cyclical over a constant period (e.g., 24-hour interval), or they may be noncyclical, in which drug absorption or elimination changes over a longer period of time. Chronopharmacokinetics is an important consideration during drug therapy. 5/6/2024 93

94. Time-dependent pharmacokinetics generally refers to a noncyclical change in the drug absorption or drug elimination rate process over a period of time. Time-dependent pharmacokinetics leads to nonlinear pharmacokinetics. Unlike dose-dependent pharmacokinetics, which involves a change in the rate process when the dose is changed, time-dependent pharmacokinetics may be the result of alteration in the physiology or biochemistry in an organ or a region in the body that influences drug disposition . 5/6/2024 94

95. Drug distribution INTRODUCTION Once a drug begins to be absorbed, it undergoes various transport processes, which deliver it to body areas away from the absorption site. These transport processes are collectively referred to as drug distribution and are evidenced by the changing concentrations of drug in various body tissues and fluids. Information concerning the concentration of a drug in body tissues and fluids is limited to only a few instances in time (i.e., we know the precise plasma drug concentration only at the few times that blood samples are drawn ) 5/6/2024 95

96. Drug distribution means the reversible transfer of drug from one location to another within the body Once a drug has entered the vascular system it becomes distributed throughout the various tissues and body fluids in a pattern that reflects the physiochemical nature of the drug and the ease with which it penetrates different membranes 5/6/2024 96

97. Drug distribution patterns The drug may remain largely within the vascular system, ex: Plasma substitutes such as dextran and drugs which are strongly bound to plasma protein Some are uniformly distributed throughout the body water, ex: low molecular weight water soluble compounds (ethanol) and a few sulfonamides 5/6/2024 97

98. Distribution patterns (Contd.) A few drugs are concentrated specifically in one or more tissues that may or may not be the site of action, ex: Iodine (in the thyroid gland), chloroquine (in the liver even at conc 1000 times those present in plasma), tetracycline (irreversibly bound to bone and developing teeth) and highly lipid soluble compounds (distribute into fat tissue) 5/6/2024 98

99. Most drugs exhibit a non-uniform distribution in the body (largely determined by the ability to pass through membranes and their lipid/water solubility). The highest concentrations are often present in the kidney, liver, and intestine. Distribution patterns (Contd.) 5/6/2024 99

100. Table 1. Apparent Volumes of Distribution of Some Drugs Drug Liters/Kg Liter/70 Kg Chloroquine 94 - 250 94 - 250 Nortriptyline 211 500 Digoxin 7 500 Lidocaine 1.7 120 Theophylline 0.5 35 5/6/2024 100

101. Factors affecting drug distribution Rate of distribution - Membrane permeability Blood perfusion Extent of Distribution - Lipid Solubility pH - pKa Plasma protein binding Intracellular binding 5/6/2024 101

102. Factors Affecting Rate of distribution A. Membrane permeability The capillaries are typically lined with endothelium whose cells overlap, though to a lesser degree than epithelial cells. Also, the junctions between cells are discontinuous. Capillary walls are quite permeable . Lipid soluble drugs pass through very rapidly . Water soluble compounds penetrate more slowly at a rate more dependent on their size. Low molecular weight drugs pass through by simple diffusion. For compounds with molecular diameter above 100 Å transfer is slow. For drugs which can be ionized the drug's pKa and the pH of the blood will have a large effect on the transfer rate across the capillary membrane . 5/6/2024 102

103. Two deviations to the typical capillary structure which result in variation from normal drug tissue permeability : Permeability is greatly increased in the renal capillaries by pores in the membrane of the endothelial cells, and in specialized hepatic capillaries, known as sinusoids which may lack a complete lining. This results in more extension distribution of many drugs out of the capillary bed. On the other hand brain capillaries seem to have impermeable walls restricting the transfer of molecules from blood to brain tissue. Lipid soluble compounds can be readily transferred but the transfer of polar substances is severely restricted. This is the basis of the "blood- brain" barrier . 5/6/2024 103

104. Factors Affecting Rate of distribution (Cont.) B. Blood perfusion rate : The rate at which blood perfuses to different organs varies widely 5/6/2024 104

105. Table 3. Blood Perfusion Rate Organ Perfusion Rate (ml/min/ml of tissue) % of cardiac output Bone 0.02 5 Brain 0.5 14 Fat 0.03 4 Heart 0.6 4 Kidneys 4.0 22 Liver 0.8 27 Muscle 0.025 15 Skin 0.024 6 5/6/2024 105

106. Total blood flow is greatest to brain, kidneys, liver, and muscle with highest perfusion rates to brain, kidney, liver, and heart. It would be expected that total drug concentration would rise most rapidly in these organs. Certain organs such as the adrenals (1.2/0.2%) and thyroid (2.4/1%) also have large perfusion rates. 5/6/2024 106

107. Factors affecting extent of distribution PROTEIN BINDING Another factor that influences the distribution of drugs is binding to tissues (nucleic acids, ligands, calcified tissues, and adenosine triphosphatase) or proteins (albumins, globulins, alpha-1-acid glycoprotein, and lipoproteins). It is the unbound or free portion of a drug that diffuses out of plasma. Protein binding in plasma can range from 0 to >99% of the total drug in the plasma and varies with different drugs. The extent of protein binding may depend on the presence of other protein-bound drugs and the concentrations of drug and proteins in the plasma. 5/6/2024 107

108. Theoretically, drugs bound to plasma proteins are usually not pharmacologically active. To exert an effect, the drug must dissociate from protein Although only unbound drug distributes freely, drug binding is rapidly reversible (with few exceptions), so some portion is always available as free drug for distribution. The association and dissociation process between the bound and unbound states is very rapid and, we assume, continuous 5/6/2024 108

109. Extensive plasma protein binding will cause more drug to stay in the central blood compartment. Therefore drugs which bind strongly to plasma protein tend to have lower volumes of distribution. Of these plasma proteins, albumin , which comprises 50 % of the total proteins binds the widest range of drugs . Acidic drugs commonly bind to albumin, while basic drugs often bind to alpha1-acid glycoproteins and lipoproteins. Many endogenous substances, steroids, vitamins, and metal ions are bound to globulins. 5/6/2024 109

110. Table 4. Proteins with Potential Binding Sites for Various Drugs Drugs Binding Sites for Acidic Agents Bilirubin, Bile acids, Fatty Acids,Vitamin C, Salicylates, Sulfonamides,Barbiturates, Phenylbutazone,Penicillins, Tetracyclines, Probenecid Albumins Binding Sites for Basic Agents Adenisine, Quinacrine, Quinine,Streptomycin, Chloramphenicol,Digitoxin, Ouabain, Coumarin Globulins, alpha1, alpha2, beta1, beta2, gamma 5/6/2024 110

111. Forces involved in protein binding electrostatic interactions between g roups on the protein molecules with drugs i.e. - the –NH 3 + of lysine and N- terminal amino acids, - the –NH 2 + - of histidine , - the - S - of cysteine - the - COO - of aspartic and glutamic acid residues. van der Waal's forces (dipole-dipole; dipole-induced dipole; induced dipole-induced dipole) hydrogen bonding . 5/6/2024 111

112. Agents which denature protein may cause the release of bound drug. Often there may be competition between drugs, in which agents that are bound very tightly, such as coumarin anticoagulants, are able to displace less tightly bound compounds from their binding sites. 5/6/2024 112

113. Slight changes in the binding of highly bound drugs can result in significant changes in clinical response or cause a toxic response. Since it is the free drug in plasma which equilibrates with the site of pharmacological or toxic response, a slight change in the extent of binding, such as 99 to 98 % bound, which can result in an almost 100 % change in free concentration, can cause very significant alteration in response . 5/6/2024 113

114. For a large number of drugs, including warfarin and phenytoin , drug response will be dependent on free drug concentration. Alteration of free concentration by drug interaction or disease state can alter the intensity of action of these drugs. Examples include phenylbutazone and salicylates displacing tolbutamide to give an increased effect, hypoglycemia. 5/6/2024 114

115. The degree of drug binding to plasma proteins is usually expressed as a percentage or as a fraction ( ) of the bound concentration ( C b ) to the total concentration (C t ), bound plus unbound (C u ) drug: = C b /( C u +C b )= C b /C t Drugs having an alpha value of greater than 0.9 are considered highly bound (90%); those drugs with an alpha value of less than 0.2 are considered to be little protein bound 5/6/2024 115

116. Bound drug is neither exposed to the body ’ s detoxication (metabolism) processes nor is it filtered through the renal glomeruli . Bound drug is therefore referred to as the inactive portion in the blood, and unbound drug, with its ability to penetrate cells, is termed the active blood portion 5/6/2024 116

117. The bound portion of drug serves as a drug reservoir or a depot, from which the drug is released as the free form when the level of free drug in the blood no longer is adequate to ensure protein saturation. For this reason a drug that is highly protein bound may remain in the body for longer periods of time and require less frequent dosage administration than another drug that may be only slightly protein bound and may remain in the body for only a short period of time. 5/6/2024 117

118. For most drugs, distribution throughout the body occurs mainly by blood flow through organs and tissues. However, many factors can affect distribution, including: · differing characteristics of body tissues, · disease states that alter physiology, · lipid solubility of the drug, · regional differences in physiologic pH (e.g., stomach and urine), and · extent of protein binding of the drug. 5/6/2024 118

119. BODY TISSUE CHARACTERISTICS To understand the distribution of a drug, the characteristics of different tissues must be considered. Certain organs, such as the heart, lungs, and kidneys, are highly perfused with blood; fat tissue and bone (not the marrow) are much less perfused. Skeletal muscle is intermediate in blood perfusion. The importance of these differences in perfusion is that for most drugs the rate of delivery from the circulation to a particular tissue depends greatly on the blood flow to that tissue. This is called perfusion-limited distributio n . . 5/6/2024 119

120. Perfusion rate limitations occur when the membranes present no barrier to distribution. The rate-limiting step is how quickly the drug gets to the tissue. If the blood flow rate increases, the distribution of the drug to the tissue increases. Therefore, drugs apparently distribute more rapidly to areas with higher blood flow 5/6/2024 120

121. Highly perfused organs rapidly attain drug concentrations approaching those in the plasma; less well-perfused tissues take more time to attain such concentrations. Furthermore, certain anatomic barriers inhibit distribution, a concept referred to as permeability-limited distribution . This situation occurs for polar drugs diffusing across tightly knit lipoidal membranes. It is also influenced by the oil/water partition coefficient and degree of ionization of a drug. 5/6/2024 121

122. DISEASE STATES AFFECTING DISTRIBUTION Another major factor affecting drug distribution is the effect of various disease states on body physiology. In several disease states, such as liver, heart, and renal failure, the cardiac output and/or perfusion of blood to various tissues are altered. 5/6/2024 122

123. A decrease in perfusion to the tissues results in a lower rate of distribution and, therefore, a lower drug concentration in the affected tissues relative to the plasma drug concentration. When the tissue that receives poor perfusion is the primary eliminating organ, a lower rate of drug elimination results, which then may cause drug accumulation in the body . 5/6/2024 123

124. LIPID SOLUBILITY OF THE DRUG The extent of drug distribution in tissues also depends on the physiochemical properties of the drug as well as the physiologic functions of the body. A drug that is highly lipid soluble easily penetrates most membrane barriers, which are mainly lipid based, and distributes extensively to fat tissues. 5/6/2024 124

125. Drugs that are very polar and therefore hydrophilic (e.g., aminoglycosides) do not distribute well into fat tissues. This difference becomes important when determining loading dosage requirements of drugs in overweight patients. If total body weight is used to estimate dosage requirements and the drug does not distribute to adipose tissue, the dose can be overestimated . 5/6/2024 125

126. REGIONAL DIFFERENCES IN PHYSIOLOGIC PH Another factor affecting drug distribution is the different physiologic pHs of various areas of the body. The difference in pH can lead to localization of drug in tissues and fluids. A drug that is predominantly in its ionized state at physiologic pH (7.4) does not readily cross membrane barriers and probably has a limited distribution. An example of this phenomenon is excretion of drugs in breast milk.. 5/6/2024 126

127. Only un-ionized drug can pass through lipid membrane barriers into breast milk. Alkaline drugs, which would be mostly un-ionized at pH 7.4, pass into breast tissue Once in breast tissue, the alkaline drugs ionize because breast tissue has an acidic pH; therefore, the drugs become trapped in this tissue. This same phenomenon can occur in the urine. Due to the nature of biologic membranes, drugs that are un-ionized (uncharged) and have lipophilic (fat-soluble) properties are more likely to cross most membrane barriers. 5/6/2024 127

128. DISTRIBUTION Storage (Concentration-Sequestration) of the Drugs in Tissues Stored drug molecules in tissues serve as drug reservoir. The duration of the drug effect may get longer. May cause a late start in the therapeutic effect or a decrease in the amount of the drug effect. Redistribution : Some drugs (especially general anesthetics) w hich are very lipophilic, following the injection, firstly (initially) distributes to the well-perfused organs like central nervous system . .. 5/6/2024 128

129. Later, the distribution occurs to less perfused organs like muscles. At last, distribution of these drugs shifts to the very low- perfused tissues like adipose (fat) tissue. Redistribution results with the running away of the drugs from their target tissue and last their effect 5/6/2024 129

130. DISTRIBUTION Passage of the drugs to CNS : A bl ood -brain barrier exists (except some areas in the brain) which limits the passage of substances . Non-ionized, highly lipophilic, small molecules can pass into the CNS and show their effects . S ome antibiotics like penicillin can pass through the inflamed blood-brain barrier while it can’t pass through the healthy one. 5/6/2024 130

131. Passage of the drugs to fetus : Placenta doesn’t form a limiting barrier for the drugs to pass to fetus. T he factors that play role in simple passive diffusion, effect the passage of drug molecules to the fetus. Placental blood flow Molecular size 5/6/2024 131

132. Drug solubility in lipids Fetal pH (ion trapping) : fetal plasma pH: 7.0 to 7.2; pH of maternal plasma: 7.4, so according to the ion trapping rules, weak basic drugs tend to accumulate in fetal plasma compared to maternal plasma 5/6/2024 132

133. Metabolism Drugs and toxins are seen as foreign to patients bodies Drugs can undergo metabolism in the lungs, blood, and liver Body works to convert drugs to less active forms and increase water solubility to enhance elimination 5/6/2024 133

134. . Drug metabolism Biotransformation is a term used to indicate the chemical changes that occur with drugs within the body as they are metabolized and altered by various biochemical mechanisms. The process of biotransformation is commonly referred to as the “ detoxification ” or “ inactivation ” process . 5/6/2024 134

135. BIOTRANSFORMATION Biotransformation processes are affected by many factors. The functioning of metabolic enzyme systems may be quite different at the extremes of age. Neonates are at risk of toxicity from chloramphenicol because they do not conjugate this drug efficiently. Also, the social habits of a patient may affect drug elimination. Alcohol use and smoking may increase hepatic clearance of some drugs by inducing metabolic enzymes.. 5/6/2024 135

136. The biotransformation of a drug results in its conversion to one or more compounds that are more water soluble, more ionized, less capable of being stored in fat tissue, less able to penetrate cell membranes, less active pharmacologically, less toxic and is more readily excreted 5/6/2024 136

137. There are four principal chemical reactions involved in the metabolism of drugs: oxidation reduction hydrolysis conjugation Other metabolic processes, including methylation , and acylation conjugation reactions, occur with certain drugs to foster elimination. 5/6/2024 137

138. Metabolism Liver - primary route of drug metabolism Liver may be used to convert pro-drugs (inactive) to an active state Types of reactions Phase I (Cytochrome P450 system) Phase II 5/6/2024 138

139. Phase I reactions Cytochrome P450 system Located within the endoplasmic reticulum of hepatocytes Through electron transport chain, a drug bound to the CYP450 system undergoes oxidation or reduction Enzyme induction Drug interactions 5/6/2024 139

140. Phase I reactions types Hydrolysis Oxidation Reduction Demethylation Methylation Alcohol dehydrogenase metabolism 5/6/2024 140

141. Drug metabolism or biotransformation refers to the biochemical conversion of a drug to another chemical form. The process of biotransformation is usually enzymatic but drugs may undergo non-enzymatic transformation e.g. ester hydrolysis. Metabolizing enzymes of the endoplasmic reticulum are called microsomal enzymes and are abundantly found in Liver. 5/6/2024 141

142. Phase I reactions are also called as Synthetic or Functionalization Reactions. Biotransformation usually results in the metabolites that are more polar and considerably less active than the parent compounds. Metabolites are excreted in the urine more rapidly than their precursors because often they are not subjected to tubular reabsorption . Hence the apparent volume of distribution of a metabolite is usually less than that of the parent drug. 5/6/2024 142

143. Hepatic microsomal enzymes (oxidation, conjugation) Extrahepatic microsomal enzymes (oxidation, conjugation) Hepatic non- microsomal enzymes ( acetylation , sulfation,GSH , alcohol/ aldehyde dehydrogenase , hydrolysis, ox/red) Drug Metabolism 5/6/2024 143

144. Enzyme Induction Enzyme Inhibition 5/6/2024 144

145. NADPH- cyp -c reductase substrate Oxidized substrate O 2 Mechanism of oxidation by cytochrome p-450 5/6/2024 145

146. Phase I reactions ( microsomal ) Oxidation reactions : Two types of oxidation reactions: Oxygen is incorporated into the drug molecule (e.g. hydroxylation) – Oxidation causes the loss of part of the drug molecule (e.g. oxidative deamination , dealkylation ) 5/6/2024 146

147. Aromatic hydroxylation : e.g. lignocaine → 3 – hydroxy lignocaine Aliphatic hydroxylation : Hydroxylation of aliphatic side chain of pentobarbitone . OH OH 5/6/2024 147

148. Epoxidation : e.g. carbamazepine dihydroxy – carbamazepine . N- Dealkylation 5/6/2024 148

149. O- Demethylation S- Demethylation 5/6/2024 149

150. N-Oxidation : e.g. N-Oxidation of 3-methylpyridine S-Oxidation : S-Oxidation of sulfides to sulfoxides is one of the most common metabolic transformations of sulfur-containing drugs. 5/6/2024 150

151. Non microsomal Oxidation : Alcohol dehydrogenase : e.g. 5/6/2024 151

152. Aldehyde oxidation : e.g. acetaldehyde to acetic acid OH Xanthine oxidase : 5/6/2024 152

153. Aromatases : cyclohexane benzoic acid to benzoic acid 5/6/2024 153

154. Reduction Dehalogenation : e.g. reductive defluorination of halothene . Nitro reduction 5/6/2024 154

155. Azo reduction : e.g. azo dyes used as colouring agents in pharmaceutical products and food are reduced to form amines both in the liver and the Intestine. Hydrolysis : ester hydrolysis : 5/6/2024 155

156. Amide hydrolysis : e.g. 5/6/2024 156

157. Summary Type of Reaction Drug undergoing metabolism Aromatic Hydroxylation Lignocaine Aliphatic Hydroxylation Pentobarbitone Epoxidation Carbamazepine N- Dealkylation Diazepam O- Demethylation Codeine S- Demethylation Methylthiopurine N-Oxidation Meyhylpyridine S-Oxidation Thioridazine Alcohol Dehydrogenase Ethanol Aldehyde Oxidation Aetaldehyde Xanthine Oxidase Theophylline Aromatases Cyclohexane benzoic acid 5/6/2024 157

158. Dehalogenation Halothene Azo -Reduction Azo -dyes Nitroreduction Ester hydrolysis Procaine Amide Hydrolysis Isoniazid 5/6/2024 158

159. Phase II reactions Polar group is conjugated to the drug Results in increased polarity of the drug Types of reactions Glycine conjugation Glucuronide conjugation Sulfate conjugation 5/6/2024 159

160. Several examples of biotransformations occuring within the body are as follows: Acetaminophen Acetaminophen glucuronide Amoxapine 8-hydroxy-amoxapine Procainamide p- Aminobenzoic acid Nitroglycerin 1-2and 1-3 dinitroglycerol 5/6/2024 160

161. It is important to mention that several factors influence drug metabolism. species differences age of the patient diet presence of disease states 5/6/2024 161

162. DRUG ELIMINATION The liver and kidneys are the two major organs responsible for eliminating drugs from the body. Although both organs share metabolic and excretory functions, the liver is principally responsible for metabolism and the kidneys for elimination. The importance of these organs cannot be overestimated in determining the magnitude and frequency of drug dosing. Additionally, an appreciation of the anatomy and physiology of these organs will provide insight into the impact of disease and altered physiologic states, as well as concomitant drug administration, on the clearance and dosing of drugs.. 5/6/2024 162

163. The physical and chemical properties of a drug are important in determining drug disposition. For example, lipophilic drugs (compared with hydrophilic drugs) tend to be: · bound to a greater extent to plasma proteins, · distributed to a greater extent throughout the body, and · metabolized to a greater extent in the liver 5/6/2024 163

164. Finally, concomitant drug use may affect drug metabolism. Certain drugs, such as phenobarbital, induce hepatic enzymes; others, such as cimetidine, may inhibit them. Even in healthy individuals, in the absence of hepatic enzyme inducers or inhibitors, the ability to metabolize drugs may vary considerably. For example, investigators have shown that two distinct subpopulations have varying capacities for drug acetylation (phase II reaction). 5/6/2024 164

165. These differences are the result of genetic variations. "Fast acetylators" have a greater rate of elimination for drugs such as isoniazid and hydralazine. For "slow acetylators," the usual doses of these agents may result in excessive plasma concentrations and, therefore, increased drug toxicities . 5/6/2024 165

166. RENAL ELIMINATION . The fraction of drug metabolized is different for various agents. The overall elimination rate is the sum of all metabolism and excretion processes and is referred to as total body elimination : total body elimination = drug excreted unchanged + drug metabolized  Excretion is the process that removes a drug from tissues and the circulation. A drug can be excreted through urine, bile, sweat, expired air, breast milk, or seminal fluid 5/6/2024 166

167. Excretion may occur for a biotransformed drug or for a drug that remains unchanged in the body. For example, penicillin G is primarily excreted unchanged in the urine. Elimination of this drug is thus dependent on renal function. Renal excretion is the net effect of three distinct mechanisms within the kidneys: · glomerular filtration, · tubular secretion, and · tubular reabsorption. 5/6/2024 167

168. RENAL EXCRETION 5/6/2024 168

169. RENAL EXCRETION Drugs and metabolites are excreted from the kidneys by 2 ways. a) Glomerular filtration b) Tubular secretion Tubular reabsorption is not an excretion way; however there is no doubt that it effects the excretion of drugs from the body by the kidney. a . 5/6/2024 169

170. ) Glomerular filtration : Simple passive diffusion play role in glomerular filtration. T he filtration rate is 110-130 ml/min. T hey are filtered from the glomerulus into proximal tubules except the bound fraction of drug molecules to the plasma proteins. Because albumin cannot be filtered from the glomerulus , the drugs cannot pass through into the proximal tubules 5/6/2024 170

171. RENAL EXCRETION b) Tubular secretion : There are 3 important points about the tubular secretion mechanism of the drugs : Tubular secretion occurs mainly in the proximal tubules . Active transport is the main mechanism for tubular secretion. The efficiency (performance) of the excretion by tubular secretion is higher than glomerular filtration route. Clearance maximum in glomerular filtration is approximately 120 ml/min, whereas the clearance maximum of tubular secretion is about 600 ml/min. 5/6/2024 171

172. RENAL EXCRETION Tubular reabsorption: This mechanism works in an opposite (counter) way by reducing the drug or metabolite excretion. Tubular reabsorption occurs mainly in distal tubules and partially in proximal tubules. It occurs by simple passive diffusion generally 5/6/2024 172

173. C hanging the pH value of the urine (making the urine acidic or basic) is going to change the ionization degree and the simple passive diffusion of the drug or the metabolite and lastly affect the excretion from the kidney. I f we make the urine acidic, the reabsorption of the weak acid drug from the renal tubules into the blood will increase, thus the excretion will decrease. In the opposite way, making the urine basic will cause an increase in the excretion of weak acid drugs 5/6/2024 173

174. These substances are generally secreted into the biliary ducts from the hepatocytes by active transport and finally they are drained into the intestines. Especially, highly ionized polar compounds (conjugation products) can be secreted into the bile in remarkable amounts. BILIARY EXCRETION 5/6/2024 174

175. After biotransformation, metabolites are drained into the small intestine by biliary duct. Drug metabolites in the small intestine are broken down again in the small intestine and reabsorbed back reaching the liver by portal vein again. This cycle between the liver and small intestine is called the enterohepatic cycle . ENTEROHEPATIC CYCLE 5/6/2024 175

176. Especially the drugs which are metabolized by the conjugation reactions go under enterohepatic cycle . This is important, because enterohepatic cycle prolongs the duration of stay of the drugs in our body which leads an increase in the duration of their effect . D rug examples that go under the enterohepatic cycle in remarkable amounts. Chlorpromazine Digitoxin 5/6/2024 176

177. ARTIFICIAL EXCRETION WAYS Hemodialysis is one of the options among the artificial excretion way for the drugs. 5/6/2024 177

178. ARTIFICIAL EXCRETION WAYS For the achievement of this system, there are some requirements : Plasma protein binding of the drug should be low (bound fraction should be low). Drug should not be stored in tissues (apparent volume of the drug should be low) The main elimination route of the drug should be from kidneys in unchanged (without biotransformation) form. 5/6/2024 178

179. CLEARANCE It can be described as the volume of plasma cleared from the drug per unit time (ml/min). Total Body Clearance : It is the plasma volume cleared from the drug per unit time via the elimination of the drug from all biotransformation and excretion mechanisms in the body. 5/6/2024 179

180. Renal Clearance : It can be described as the rate of the excretion of a drug from kidneys . So in other words, renal clearance is the volume of plasma cleared from the non-metabolized (unchanged) drug via the excretion by kidneys per minute. There are four important factors that affect the renal clearance of the drugs: Plasma protein binding of the drug. Tubular reabsorption ratio of the drug. Tubular secretion ratio of the drug. Glomerular filtration ratio of the drug. 5/6/2024 180

181. CL renal = [( Glomerular filtration rate + Tubular secretion rate) – Tubular reabsorption rate] / Cp If the renal clearance of the drug is higher than the physiological creatinine clearance (120-130 ml/min) , that time we can say that the tubular secretion helps and contributes the elimination of the drug additionally to filtration. In early newborns and newborns, glomerular filtration and tubular secretion mechanisms are immature and not sufficient. R enal Clearence (CL R ) = V x C U t x C P V = collected urine volume t = duration to collect the urine C P = plasma concentration of the drug C U = urine concentration of the drug 5/6/2024 181

182. From the Site of Delivery to Elimination… steps in drug delivery, absorption, distribution and elimination Distribution Drugs must reach the site of action Tissue Plasma Elimination Metabolism Liver, kidneys, cells Excretion Kidneys Feces Depends upon drug binding capabilities 5/6/2024 182

183. Oral Administration Intravenous Injection Intramuscular Injection Subcutaneous Injection Gastrointestinal Tract Circulatory System Tissues Metabolic Sites Excretion 5/6/2024 183

184. Mathematical Modeling of Drug Disposition Single compartment Single compartment with absorption Two compartments Two compartments with absorption Physiological Models 5/6/2024 184

185. Single Compartment Model Assumptions: Body as one compartment characterized by a volume of distribution ( V d ) Drug is confined to the plasma (small V) C, Vd absorption elimination k, C t C/C 5/6/2024 185

186. One-Compartment Model with Absorption Low absorption occurs Absorption is the rate-limiting step Slow absorption may represent drug entry through GI tract or leakage into circulation after SC injection Drugs require multiple doses to maintain drug concentration within therapeutic window t M/D t M/D 5/6/2024 186

187. The simplest pharmacokinetic model is the single compartment open-model system. This model depicts the body as one compartment characterized by a certain volume of distribution ( V d ) that remains constant . 5/6/2024 187

188. 5/6/2024 188

189. For drugs whose distribution follows first-order, one-compartment pharmacokinetics, a plot of the logarithm of the concentration of drug in the plasma (or blood) versus time will yield a straight line. 5/6/2024 189

190. The equation that describes the plasma decay curve is Cp=C0e-kelt where Kel is the first-order rate of elimination of the drug from the body, Cp is the concentration of the drug at time equal to t, C0 is the concentration of drug at time equal to zero. 5/6/2024 190

191. LogC p = LogC -K el /2.303(t) Most drugs administered orally can be adequately described using a one-compartment model. Drugs administered by rapid intravenous infusion are usually described by a two-compartment or three compartment model system . 5/6/2024 191

192. Half life The half-life (T 1/2 ) of a drug describes the time required for a drug ’ s blood or plasma concentration to decrease by one half. The biological half-life of a drug in the blood may be determined graphically off of a pharmacokinetic plot of a drug ’ s blood-concentration time plot, typically after intravenous administration to a sample population. 5/6/2024 192

193. The half-life can also be mathematically determined. K el t /2.303=log C - logC p =log C /C p If it assumed that C p is equal to one-half of C p , the equation will become: K el t /2.303= log C /0.5C =log2 Thus, t 1/2 =2.303log2/ K el =0.693/ K el K el =0.693/t 1/2 5/6/2024 193

194. Data on a drug ’ s biologic half-life are useful in determining the most appropriate dosage regimen to achieve and maintain the desired blood level of drug. Such determinations usually result in such recommended dosage schedules for a drug, as the drug to be taken every 4 hours, 6 hours, 8 hours, etc. 5/6/2024 194

195. Two-Compartment Model Drug rapidly injected Drug distributed instantaneously throughout one compartment and slowly throughout second compartment Describes drug concentration in plasma injected IV C 1 , V 1 C 2 , V 2 k 2 , C 2 k 12 k 21 k 1 , C 1 Compartment 1 Compartment 1 Compartment 2 Compartment 2 t t Concentration after ingestion Concentration with slow absorption C/C C/C 5/6/2024 195

196. In the two-compartment system, a drug enters into and is instantaneously distributed throughout the central compartment. Its subsequent distribution into the second or peripheral compartment is slower . 5/6/2024 196

197. The central compartment is usually considered to include the blood, the extracellular space, and organs with good blood perfusion, e.g., lungs, liver, kidneys, heart. 5/6/2024 197

198. Note the initial steep decline of the plasma drug concentration curve. This typifies the distribution of the drug from the central compartment to the peripheral compartment. 5/6/2024 198

199. A semi-logarithmic plot of the plasma concentration versus time after rapid intravenous injection of a drug which is best described by a two-compartment model system can often be resolved into two linear components. 5/6/2024 199

200. The slope of the feathered line (-a/2.303) and the extrapolated line (-b/2.303) and the intercepts, A and B, are determined. C p = Ae -at +Be -bt This is a bi-exponential equation which describes the two-compartment system. 5/6/2024 200

201. Intravenous Bolus Administration INTRODUCTION In clinical practice, most pharmacokinetic dosing is performed with one-compartment, intermittent infusion models at steady state. Using these models, we can obtain an elimination rate constant ( K ) and then calculate volume of distribution ( V ) and dosing interval (t) based on this K value. So far, our discussion has been limited to a single intravenous (IV) bolus dose of drug. Most clinical situations, however, require a therapeutic effect for time periods extending beyond the effect of one dose. In these situations, multiple doses of drug are given. The goal is to maintain a therapeutic effect by keeping the amount of drug in the body, as well as the concentration of drug in the plasma, within a fairly constant range (the therapeutic range ). 5/6/2024 201

202. INTRAVENOUS BOLUS DOSE MODEL Although not used often clinically, the simplest example of multiple dosing is the administration of rapid IV doses (IV boluses) of drug at constant time intervals, in which the drug is represented by a one-compartment model with first-order elimination. Clinical Correlate This lesson describes a one-compartment, first-order, IV bolus pharmacokinetic model. It is used only to illustrate certain math concepts that will be further explored with the more commonly used IV intermittent infusion 5/6/2024 202

203. The first dose produces a plasma drug concentration versus time curve like the one. C is now referred to as C max , meaning maximum concentration, to group it with the other peak concentrations that occur with multiple dosing. If a second bolus dose is administered before the first dose is completely eliminated, the maximum concentration after the second dose ( C max2 ) will be higher than that after the first dose ( C max1 ) The second part of the curve will be very similar to the first curve but will be higher (have a greater concentration. 5/6/2024 203

204. The time between administration of doses is the dosing interval . The dosing interval, symbolized by the Greek letter tau (t), is determined by a drug's half-life. Rapidly eliminated drugs (i.e., those having a short half-life) generally have to be given more frequently (shorter t), than drugs with a longer half-life 5/6/2024 204

205. If a drug follows first-order elimination (i.e., the fraction of drug eliminated per unit of time is constant), then plasma drug concentrations after multiple dosing can be predicted from concentrations after a single dose. This method uses the principle of superposition , a simple overlay technique. If the early doses of drug do not affect the pharmacokinetics (e.g., absorption and clearance) of subsequent doses, then plasma drug concentration versus time curves after each dose will look the same; they will be superimposable. The only difference is that the actual concentrations may be higher at later doses, because drug has accumulated 5/6/2024 205

206. A second IV bolus dose is administered after the dosing interval (t), but before the first dose is completely eliminated. Because C t = C e - Kt at any time ( t ) after the first dose, it follows that: C min1 = C max1 e - K t 5/6/2024 206

207. where C min1 is the concentration just before the next dose is given and t, the dosing interval, is the time from C max to C min . C max2 is the sum of C min1 and C max1 , as the same dose is given again: C max2 = C max1 + C min1 We showed that: C min1 = C max1 e - K t so: C max2 = C max1 + C max1 e - K t 5/6/2024 207

208. 5/6/2024 208

209. Above equation , where n is the number of doses given. This equation can be simplified by mathematical procedures to a more useful form 5/6/2024 209

210. 5/6/2024 210

211. INTRAVENOUS BOLUS EQUATIONS AT STEADY STATE As successive doses of a drug are administered, the drug begins to accumulate in the body. With first-order elimination, the amount of drug eliminated per unit of time is proportional to the amount of drug in the body. Accumulation continues until the rate of elimination approaches the rate of administration:     rate of drug going in = rate of drug going out As the rate of drug elimination increases and then approaches that of drug administration, the maximum (peak) and minimum (trough) concentrations increase until an equilibrium is reached. After that point, there will be no additional accumulation; the maximum and minimum concentrations will remain constant with each subsequent dose of drug . 5/6/2024 211

212. When this equilibrium occurs, the maximum (and minimum) drug concentrations are the same for each additional dose given (assuming the same dose and dosing interval are used). When the maximum (and minimum) drug concentrations for successive doses are the same, the amount of drug eliminated over the dosing interval (rate out) equals the dose administered (rate in) and the condition of "steady state" is reached. Steady state will always be reached after repeated drug administration at the same dosing interval if the drug follows first-order elimination. However, the time required to reach steady state varies from drug to drug, depending on the elimination rate constant. With a higher elimination rate constant (a shorter half-life), steady state is reached sooner than with a lower one (a longer half-life) 5/6/2024 212

213. Steady state is the point at which the amount of drug administered over a dosing interval equals the amount of drug being eliminated over that same period and is totally dependent on the elimination rate constant . Therefore, when the elimination rate is higher, a greater amount of drug is eliminated over a given time interval; it then takes a shorter time for the amount of drug eliminated and the amount of drug administered to become equivalent (and, therefore, achieve steady state). If the half-life of a drug is known, the time to reach steady state can be determined. If repeated doses of drug are given at a fixed interval, then in one half-life the plasma concentrations will reach 50% of those at steady state. 5/6/2024 213

214. ACCUMULATION FACTOR Equations can describe the plasma concentrations and pharmacokinetics of a drug at steady state. Remember, steady state will be reached only after four or five half-lives. Recall that with an IV bolus injection of a drug fitting a one-compartment model and first-order elimination, the drug concentration at any time ( t ) after any number of doses ( n ), not necessarily at steady state , 5/6/2024 214

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216. To predict the plasma concentration of a drug at any time t after n number of doses, we therefore need to know four values: · drug dose ( X ), · volume of distribution ( V d ), · elimination rate constant ( K ), and · dosing interval (t). 5/6/2024 216

217. AVERAGE STEADY-STATE CONCENTRATION WITH INTRAVENOUS BOLUS DOSING We now have examined both the maximum and minimum concentrations that occur at steady state. Another useful parameter in multiple IV dosing situations is the average concentration of drug in the plasma at steady state. Because is independent of any pharmacokinetic model, it is helpful to the practicing clinician (model assumptions do not have to be made). is not an arithmetic or geometric mean. 5/6/2024 217

218. Several mathematical methods may be used to calculate the average drug concentration, but only one is presented here. A plasma drug concentration versus time curve, after steady state has been achieved with IV dosing By knowing the dose given ( X ) and the dosing interval (t), we can determine the average concentration if we also know the area under the plasma drug concentration versus time curve (AUC) over t. 5/6/2024 218

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220. Continuous Infusion As stated previously, repeated doses of a drug (i.e., intermittent infusions) result in fluctuations in the plasma concentration over time. For some drugs, maintenance of a consistent plasma concentration is advantageous because of a desire to achieve a consistent effect. To maintain consistent plasma drug concentrations, continuous IV infusions are often used. Continuous IV infusion can be thought of as the administration of small amounts of drug at infinitely small dosing intervals. If administration is begun and maintained at a constant rate, the plasma drug concentration versus time curve will result. The plasma concentrations resulting from the continuous IV infusion of drug are determined by the rate of drug input (rate of drug infusion, K ), volume of distribution ( V ), and drug clearance (Cl t ). The relationship among these parameters is: 5/6/2024 220

221. 5/6/2024 221

222. where t is the time since the beginning of the drug infusion. This equation shows that the plasma concentration is determined by the rate of drug infusion ( K ) and the clearance of drug from the body (remember, VK = Cl t ). The equation is used to find a concentration at a time before steady-state is reached. The term (1 - e -Kt ) gives the fraction of steady-state concentration achieved by time t after the infusion is begun. For example, when t is a very low number, just after an infusion is begun, K (1 - e -Kt ) is also very small. When t is very large, (1 - e -Kt ) approaches 1, so K (1 - e -Kt ) approaches K and plasma concentration approaches steady state 5/6/2024 222

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224. Loading Dose As stated previously, after a continuous IV infusion of drug is begun, five drug half-lives are needed to achieve steady state. If an immediate effect is desired, that may be too long to reach the therapeutic range. Sometimes a "loading dose" is administered at the initiation of the infusion so that the therapeutic range is maintained from the outset. This loading bolus IV dose is usually relatively large and may produce immediate therapeutic plasma concentrations. 5/6/2024 224

225. Note that a loading dose should not be used if substantial side effects occur with large doses of the drug. Also, sometimes clinicians desire for drugs to accumulate slowly rather than to achieve therapeutic concentrations immediately so that the patient may have adequate time to develop tolerance to the initial side effects (e.g., tricyclic antidepressants). 5/6/2024 225

226. The desired loading dose for many drugs can be derived from the definition of the volume of distribution. As shown previously, V = X / C for a drug described by a one-compartment model. Rearranging this equation, we see that the loading dose equals the desired concentration multiplied by the volume of distribution: X = C 0(desired) V Note that C in this case is equivalent to the desired steady-state concentration. 5/6/2024 226

227. Loading doses usually are given as short infusions (often 30 minutes). Taking this procedure into account, we can further modify the above equations to predict plasma concentrations. For the loading dose: 5/6/2024 227

228. 5/6/2024 228

229. where: X = dose; t = infusion period (e.g., 0.5 hour); K = elimination rate constant; and V = volume of distribution. 5/6/2024 229

230. 5/6/2024 230

231. Extravascular routes of drug administration Please note that a similar approach may be applied to determine pharmacokinetic parameters of drugs when any other extravascular route is used. The following assumptions are made: drug exhibits the characteristics of onecompartment model absorption and elimination of a drug follow the first-order process and passive diffusion is operative at all the time 5/6/2024 231

232. 5/6/2024 232

233. 5/6/2024 233

234. where dX / dt is the decrease in the amount of absorbable drug present at the site of administration per unit time. Ka is the firstorder absorption rate constant ( Xa )t is the mass or amount of absorbable drug at the site of administration (e.g. the gastrointestinal tract) at time t. 5/6/2024 234

235. Monitoring drug in the blood (plasma/serum) or site of measurement The differential equation that follows relates changes in drug concentration in the blood with time to the absorption and the elimination rates 5/6/2024 235

236. 5/6/2024 236

237. where dX / dt is the rate of change of amount of drug in the blood; X is the mass or amount of drug in the blood or body at time, t; Xa is the mass or amount of absorbable drug at the absorption site at time t; Ka and K are the firstorder absorption and elimination rate constants, respectively KaXa is the first-order rate of absorption and KX is the first-order rate of elimination 5/6/2024 237

238. Determination of elimination half life (t1/2) and elimination rate constant (K or Kel ) when written in concentration (Cp) terms, takes the following form: 5/6/2024 238

239. 5/6/2024 239

240. where KaFX0 VðKa KÞ is the intercept of plasma drug concentration versus time plot When time is large, because of the fact that KaK , eKat approaches zero, 5/6/2024 240

241. 5/6/2024 241

242. The apparent volume of distribution (V) For a drug administered by the oral, or any other extravascular , route of administration, the apparent volume of distribution cannot be calculated from plasma drug concentration data alone. The reason is that the value of F (the fraction of administered dose that reaches the general circulation) is not known. 5/6/2024 242

243. 5/6/2024 243

244. If we can reasonably assume, or if it has been reported in the scientific literature, that F¼1.0 (i.e. the entire administered dose has reached the general circulation), only then can we calculate the apparent volume of distribution Following the administration of a drug by the oral or any other extravascular route. In the absence of data for the fraction of administered dose that reaches the general circulation, the best one can do is to obtain the ratio of V/F: 5/6/2024 244

245. to obtain the peak plasma concentration There are three methods available for determining peak plasma concentration (Cp)max. Two are. Method 1. Peak plasma concentration obtained from the graph of plasma concentration versus time Method 2. Peak plasma concentration obtained by using an equation. shows that 5/6/2024 245

246. 5/6/2024 246

247. Flip-flop kinetics Flip-flop kinetics is an exception to the usual case in which the absorption rate constant is greater than the elimination rate constant (Ka>K). For a drug absorbed by a slow first-order process, such as certain types of sustainedrelease formulations, the situation may arise,where the elimination rate constant is greater than the absorption rate constant (K>Ka). 5/6/2024 247

248. Drug Dosage Regimen 5/6/2024 248

249. Goals Optimum therapeutic response with minimum adverse effects Individualization of drug dosage regimen, esp drugs with a narrow therapeutic window 5/6/2024 249

250. Drugs w/ narrow ther window Drug Disease/condition Therapeutic window Amikacin Carbamazepine Digoxin Gentamicin Lidocaine Lithium Phenytoin Procainamide Theophylline Tobramycin Valproic acid Vancomycin Gram-negative infection Epilepsy Cardiac dysfunction Gram-negative infection Ventricular arrhythmias Manic & recurrent depression Epilepsy Ventricular arrhythmias Asthma Gram-negative infection Epilepsy Penicillin-resistant infection 20-30 mcg/mL 4-12 mcg/mL 1-2 ng/mL 5-10 mcg/mL 1-5 mcg/mL 0.6-1.2 mEq/L 10-20 mcg/mL 4-10 mcg/mL 10-20 mcg/mL 5-10 mcg/mL 50-100 mcg/mL 20-40 mcg/mL 5/6/2024 250

251. Dosage regimen design Dosage Regimen Activity-toxicity -Therapeutic window -Side effects -Toxicity -conc-response rel Pharmacokinetics: ADME Clinical Factors -Patients (age, weight, patophysiologic cond -Management of ther (multiple drug ther, convenience of regimen, compliance of patient) Other factors: -Route of adm -Dosage form -Tolerance-dependence -Drug interaction -Cost 5/6/2024 251

252. Dosage regimen design The most accurate approach to dosage regimen design is to calculate the dose based on the pharmacokinetics of the drug in the individual patient (not for initial dose; only for readjustment of the dose). The initial dose was estimated using average population pharmacokinetic parameters obtained from literature. Clin pharm softwares for drugs with narrow ther window are available (Datakinetics etc) 5/6/2024 252

253. 3 methods 1. Dosage regimens based on population averages: (a) the fixed model (b) the adaptive model 2. Dosage regimens based on partial pharmacokinetic parameters 3. Empirical dosage regimens 5/6/2024 253

254. Dosage regimens based on population averages Obtained from clinical studies published in the drug literature (a) the fixed model, assumes that population average pharmacokinetic parameters may be used directly to calculate a dosage regimen for the patient without any alteration. 5/6/2024 254

255. Parameters such as : ka, F, VD apparent, and ke are assumed to remain constant; follow a one-compartment model. The practitioner may use the usual dosage suggested by the literature and/or make small adjustment based on the patient’s weight and/or age 5/6/2024 255

256. (b) the adaptive model dosage regimen was calculated by using patient variables such as: weight, age, sex, body surface area, and known patient patophysiology such as renal disease as well as the known population average pharmacokinetic parameters of the drug. This model assumes that drug clearance do not change from one dose to the next. 5/6/2024 256

257. Dosage regimens based on partial pharmacokinetic parameters For drugs with unknown or unavailable pharmacokinetic profile, the pharmacokineticist needs to make some assumptions to calculate the dosage regimen. Exp: to let F equal 1 or 100%. the risk of undermedicated or overmedicated. Assumptions will depend on the safety, efficacy and therapeutic range of the drug. 5/6/2024 257

258. Empirical dosage regimens Not based on pharmacokinetic variables, but on empirical clinical data, personal experience and clinical observations . 5/6/2024 258

259. Dosage regimens for continuous maintenance of therapeutic conc Half-lives < 30 minutes low TI drugs : must be infused ex: heparin high TI : may be given less frequently (than t1/2) but with higher MD ex: Penicillin, 4 – 6 hr interval (t1/2 = 30 min) 5/6/2024 259

260. Dosage regimens for continuous maintenance of therapeutic conc 30 min < t1/2 < 8 hr - low TI drugs: must be given every half- life or more frequently or by infusion ex: lidocain (90min) infusion, theophylline (3-6 doses/day) - high TI drugs: once every 1 – 3 t1/2 ex: cephalosporins (30min-3hr) 3 – 6 halflives 5/6/2024 260

261. Dosage regimens for continuous maintenance of therapeutic conc 8 < t1/2 < 24 hr - the most convenience - a dose is given every half life, LD must be twice MD to achieve Css immediately ex: sulfamethoxazole (high TI) and clonidine (low TI) 5/6/2024 261

262. Dosage regimens for continuous maintenance of therapeutic conc T1/2 > 24 hr administration once daily is convenient and promotes patient compliance Ex: Chloroquine (high TI), Digitoxin (low TI) 5/6/2024 262

263. When one considers the development of a dosage regimen, a number of factors that should be considered Inherent activity, i.e., pharmacodynamics , and toxicity, i.e., toxicology of the drug. The pharmcokinetics of the drug, which are influenced by the dosage form in which the drug is administered to the patient, e.g., biopharmaceutical considerations. 5/6/2024 263

264. 3) The patient to whom the drug will be given and encompasses the clinical state of the patient and how the patient will be managed. 4) A typical factors may influence the dosage regimen. 5/6/2024 264

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266. The dosage regimen of a drug may simply involve the administration of a drug once for its desired therapeutic effect, e.g. pinworm medication, or encompass the administration of drug for a specific time through multiple doses. The objective of pharmacokinetic dosing is to design a dosage regimen that will continually maintain a drug ’ s therapeutic serum or plasma concentration within the drug ’ s therapeutic index, i.e., above the minimum effective concentration but below the minimum toxic level. 5/6/2024 266

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268. MULTIPLE DOSE REGIMEN 5/6/2024 268

269. INTRODUCTION Drugs are rarely used in single doses to produce an acute effect But, drugs are administered in successive doses to produce a chronic or prolonged effect The goal in the design of dosage regimens is to achieve and maintain drug concentrations in plasma or at the site of action that are both safe and effective That is to maintain the drug concentration with in the therapeutic window (Below the minimum toxic concentration and above the minimum effective concentration) Toxicity would result if doses are administered too frequently, whereas, effectiveness would be lost if the dosage rate are too infrequent The two parameters important in dosage regimen are The size of the dose of the drug The frequency of drug administration (time interval between doses) 5/6/2024 269

270. I NTRODUCTION … Effect of frequency of administration of a drug on plasma drug level Plasma Drug Concentration Time Minimum toxic concentration Minimum toxic concentration A B C Therapeutic Window A – Too frequent dosing B – Proper dosing C – Inadequate frequency 5/6/2024 270

271. DRUG ACCUMULATION When drugs are administered on multiple dose regimen, each dose (after first dose) is administered before the preceding doses are completely eliminated This results in a phenomenon known as ‘drug accumulation’, where the amount of the drug in the body (represented by plasma concentration) builds up as successive doses are administered But, after seven doses of the drug at an interval equal to the drug half-life, the maximum and minimum amounts in the body becomes fairly constant This is called ‘ Steady State Condition’ At this stage, the amount of the drug lost during dosing interval is equal to the administered dose 5/6/2024 271

272. DRUG ACCUMULATION … Drug Accumulation during Multiple Dose Regimen Dose =100 mg Dosing interval = t 1/2 of the drug No . of half lives (Frequency number) No. of doses 1 2 3 4 5 6 7 8 100 Max - 1 50 Min 150 2 75 175 3 87.5 187.5 4 93.8 193.8 5 96.88 196.88 6 98.44 198.44 7 99.22 199.22 Max 8 99.61 Min This prediction of the amount of the drug in the body following repeated doses of a drug in the above example is based on the assumption that its elimination half-life is constant throughout the dosage regimen 5/6/2024 272

273. PRINCIPLE OF SUPERPOSITION An accepted plasma concentration profile at the steady state can be devised with the aid of pharmacokinetic parameters derived from single dose experiments based on the ‘principle of superposition’ The principle of superposition assumes that early doses of a drug do not affect the pharmacokinetic of subsequent doses The basic assumptions are that the drug is eliminated by first order kinetics and that the pharmacokinetics of the drug after a single dose (first dose) are not altered for multiple doses Therefore, the blood level after the second, third, or n th dose will overlay or superimpose the blood level attained after n-1 th dose In addition, AUC (0 – α ) following the administration of a single dose equals the AUC (t1 – t2) during a dosing interval at steady state 5/6/2024 273

274. PRINCIPLE OF SUPERPOSITION … Simulated date showing blood level after administration of multiple doses and accumulation of blood level when equal doses are given at equal time intervals Plasma Drug Concentration Time (hours) AUC (t 1 – t 2 ) 5/6/2024 274

275. PRINCIPLE OF SUPERPOSITION … Thus, the drug levels in plasma versus time data obtained with a single dose is used to predict the drug levels in plasma after multiple doses As the superposition principle is an overly method , it may be used to predict drug concentrations after multiple doses given at equal and unequal dosage intervals The predicted plasma concentration would be the total drug concentration obtained by adding the residual drug concentration obtained after each previous dose The principle of superposition can not be used in certain situations, including, changing pathophysiology, saturation of the drug carrier system, saturated protein binding, saturated active secretion, enzyme induction and enzyme inhibition 5/6/2024 275

276. REPETITVE I.V. INJECTION – ONE COMPARTMENT OPEN MODEL Calculation of plasma drug concentrations following repetitive doses of a drug using superposition principle requires preparation of a list of plasma drug concentrations for each dose as shown in table Dose No. Time (hours) Plasma drug doses level (mg/ml) Total 1 2 3 4 5 1 1 2 3 21.0 22.3 19.8 21.0 22.3 19.8 2 4 5 6 7 16.9 14.3 12.0 10.1 21.0 22.3 19.8 16.9 35.3 34.3 29.9 3 8 9 10 11 8.5 7.15 6.01 5.06 16.9 14.3 12.0 10.1 21.0 22.3 19.8 25.4 42.5 40.3 35.0 4 12 13 14 15 4.25 3.58 3.01 2.53 8.5 7.15 6.01 5.06 16.9 14.3 12.0 10.1 21.0 22.3 19.8 29.7 46.0 43.3 37.5 5 16 17 18 19 20 2.13 1.79 1.51 1.27 1.07 4.25 3.58 3.01 2.53 2.13 8.5 7.15 6.01 5.06 4.25 16.9 14.3 12.0 10.1 8.5 21.0 22.3 19.8 16.9 31.8 47.8 44.8 38.8 32.9 5/6/2024 276

277. REPETITVE I.V. INJECTION – ONE COMPARTMENT OPEN MODEL…. Let us consider that a drug was repeatedly injected intravenously at a dose of X with a dosing interval of ‘t’ hours The maximum concentration of the drug in plasma following a rapid i.v . injection is equal to the dose divided by V d of the drug The concentration of the drug in plasma at any time t is given by Where K is the overall elimination rate constant The concentration of the drug in plasma at the end of the first dosing interval, , is given by 5/6/2024 277

278. REPETITVE I.V. INJECTION – ONE COMPARTMENT OPEN MODEL…. Where is the concentration of the drug in plasma at the end of the first dosing interval is zero time concentration for first dose The zero time concentration of the drug in plasma following the second dose will be But, Therefore, Let R = then, the above equation can be written as 5/6/2024 278

279. REPETITVE I.V. INJECTION – ONE COMPARTMENT OPEN MODEL…. The drug concentration in plasma at the end of the second dosing interval is given by Now, this procedure can be used for finding zero time concentration (maximum drug concentration in plasma) and drug concentration at the end of dosing interval (minimum drug concentration in plasma) for each dose of the drug 5/6/2024 279

280. REPETITVE I.V. INJECTION – ONE COMPARTMENT OPEN MODEL…. Since the plasma concentration at the beginning and end of the n th dosing interval are given by the following series Beginning = End = Since, R is always smaller than 1, R n becomes smaller as n increases Therefore, the high power terms in the above equations become negligible as ‘n’ increases and additional doses do not change the value of or significantly This explains why the plasma concentrations reach a plateau instead of continuing to rise as more doses are given 5/6/2024 280

281. REPETITVE I.V. INJECTION – ONE COMPARTMENT OPEN MODEL …. When n = ∞, the above equations become Hence, C max and C min are defined as the plasma concentration at the beginning and end, respectively, of the n th dosing interval after the plateau has been reached (i.e., n = ∞) Thus, the maximum and minimum plasma concentrations on the plateau of a repetitive i.v. dosing regimen can be calculated if the dosing interval ( ), the overall elimination rate constant (K), and the initial plasma concentration (C ) are known 5/6/2024 281

282. REPETITVE I.V. INJECTION – ONE COMPARTMENT OPEN MODEL…. An average steady state plateau drug concentration C ave , is obtained by dividing AUC for a doing period by the dosing interval it should be remembered that C ave is not the arithmetic mean of C max and C min because plasma drug concentrations decline exponentially The AUC (t 1 -t 2 ) is related to the dose X divided by the total body clearance (V d . K) Therefore, 5/6/2024 282

283. REPETITVE I.V. INJECTION – ONE COMPARTMENT OPEN MODEL …. Equations can also be expressed in terms of the amont of the drug in the body Where, X max , X min , and X avg are the maximum , minimum and average amount of the drug in the body at the steady-state It is sometimes desirable to know the plasma drug concentration at any time after the administration of ‘n’ doses of a drug The general expression for calculating this plasma drug concentration is 5/6/2024 283

284. REPETITVE I.V. INJECTION – ONE COMPARTMENT OPEN MODEL …. Where ‘n’ is the number of doses given and is the time after the n th dose At steady state approaches zero and equation reduces to Repetitive Extravascular Dosing – One Compartment Open Model Although the equations become considerably more complex than for the i.v . case, C max , C min , C ave can be calculated when the drug is administered by an extravascular route The basic assumptions made in developing the equations for the extravascular route are Drug absorption and eliminated processes follow first order kinetics The pharmacokinetic parameters such as K a , K, Vd , and the fraction of the dose absorbed (F) remain constant during multiple - dosing 5/6/2024 284

285. REPETITVE EXTRAVASCULAR DOSING– ONE COMPARTMENT OPEN MODEL…. The equation describing the plasma drug concentration – time profile following a single dose of extravascular administration of the drug is given by If n fixed doses of the drug (X ) are administered at fixed time intervals (t), the plasma drug concentrations following the n th dose are given below Whereas is the concentration of the drug at time t, after n th dosing When ‘n’ is large (i.e., when the plasma concentrations reach a plateau), the terms and becomes negligible 5/6/2024 285

286. REPETITVE EXTRAVASCULAR DOSING– ONE COMPARTMENT OPEN MODEL…. The above equation can be used to calculate the Cmax and Cmin values on the plasma concentration plateau by substituting values for t which correspond to the ‘peaks’ and ‘troughs’ in the C versus t curve Thus if t = t p (the time of peak concentration of drug in plasma), If t = 0 (the time at which another dose is to be given) the equation gives C min 5/6/2024 286

287. REPETITVE EXTRAVASCULAR DOSING– ONE COMPARTMENT OPEN MODEL …. The mean plasma level at steady state C ave is obtained by applying the similar method used for repeated i.v . injections or since Multiple Dose Regimen – Loading Dose The time required for the drug to accumulate to a steady state plasma level is dependent mainly on its elimination half-life The time need to reach 95% C ave is approximately 5 half-lives of the drug for a drug with a half-life of 5 hours, it would take approximately 25 hours to reach 95% of C ave 5/6/2024 287

288. REPETITVE EXTRAVASCULAR DOSING– ONE COMPARTMENT OPEN MODEL …. In order to initiate a immediate therapeutic effect, an ‘initial dose’ also called ‘loading dose’ or ‘primary dose’ is administered to achieve C ave i.v. injections: As we know Where X is i.v. dose, is dosing interval, Vd is the volume of distribution of the drug and k is the elimination rate constant Therefore we should administer a loading dose X* just before the administration of the maintenance dose X The amount present in the body is equal to X / The amount of the drug present in the body after t = following and an i.v dose of X* is X ave 5/6/2024 288

289. REPETITVE EXTRAVASCULAR DOSING– ONE COMPARTMENT OPEN MODEL …. The amount of the drug eliminated during this period must be supplied in the form of a maintenance dose X The amount of a the drug eliminated from a loading dose in time , is equal to the difference between the loading dose (X*) and the amount remained in the body after (X ave ) Amount of the drug eliminated The amount of the drug eliminated should be equal to the maintenance dose, X0, to maintain the steady-state level Therefore, Maintenance dose, 5/6/2024 289

290. REPETITVE EXTRAVASCULAR DOSING– ONE COMPARTMENT OPEN MODEL …. And loading dose, In practice, the C ave , value for a particular drug is known The elimination rate constant (K), Volume of distribution (Vd) and dosing interval are taken from the literature to calculate the loading dose (X*), using the following equation The ratio of loading to maintenance dose depends on the dosing interval and the half-life of the drug and is equal to the accumulation index, R ac 5/6/2024 290

291. REPETITVE EXTRAVASCULAR DOSING– ONE COMPARTMENT OPEN MODEL…. Extravascular Dosing In case of extravascular dosing, the fraction of the dose absorbed, F, should be taken into consideration while calculating the loading dose Loading Dose Maintenance Dose Multiple dose regimen – Two Compartment Open Model One compartment equations modified in minor ways apply to two compartment systems with reasonable accuracy, when the distribution phase after one dose is approximately complete before the next dose is administered 5/6/2024 291

292. REPETITVE EXTRAVASCULAR DOSING– ONE COMPARTMENT OPEN MODEL…. Under these conditions, β may be substituted for K and V d area for Vd , to adopt one compartment equations to two compartment systems for rough approximations of the two compartment parameters and plasma concentrations For i.v . injections: Loading Dose For extravascular dosing: Loading Dose The accumulation ratio of the drug R ac is the ratio of loading and maintenance doses 5/6/2024 292

293. DETERMINATION OF DOSE AND DOSING INTERVAL 5/6/2024 293

294. INTR O DUCTION  The d o se o f a d r ug i s t he a m o u nt a t t he t i m e o f a dm i n i str a t i on to obt a i n a d e s i r e d ther a p e utic r e sponse  Dosa g e r e g i m e n r e fe r s to the schedu l e o f dos i ng  Ge ne r a l l y, t he m a n u f ac tur e rs p r ov i d e s a r a nge o f d o s e s f or a g i ven drug  S i nc e , s e v e r a l f a cto r s aff e ct i ng t h e d o se o f a d r ug, t he e xact a m ount o f a drug to be ad mi nist e r e d i s d e c i d e d by t he h e a l th c a re p r of e ss i on al s  The dose o f a g i ven drug i s sp e c i f i c to the pat i e nt  Thu s , a f i xed dose o f a d r ug m i g ht be a n o ve r dose i n so m e p a t i e nt s , w he r e a s t h e s am e d o s e m i ght b e c o n s i d e r e d an u n d e r-dose i n another gr o up o f pat i e nts  The i nter a nd i ntra su bj e ct v a r i at i ons to t he e ff e c t s o f drugs can be av o i d e d by ta il o r i ng a dose (or a dos ag e r e g i m e n) to a g i ven pat i e nt through the use o f c li nic a l phar m ac o k i net i cs 5/6/2024 294

295. INTR O DUCTIO N …  S o me o f the facto r s affect i ng the dose o f a drug P h a r m a c e utic a l facto r s  Type o f dos a ge form  Route o f ad mi nist r at i on Pat i e nt r el at e d facto r s i nclude        Ind i v i dual pat i e nt ’ s to l e r a nce o f the drug G e net i c pr e d i spos i t i on Conc u r re n t ad mi nist r at i on o f other drugs Pat ie nt’s a ge , b o dy we i ght, g e nd e r L e ngth o f ill ness G e ne r al physic a l he a l th L i ver and k i dney f u ncti o n i n the pat i e nt P h a r m a cok i net i c facto r s  R a te and e xt e nt of     Abs o rpt i on D i str i buti o n Meta b o l i sm and E x cr e t i on o f drugs i n pat i e nts 5/6/2024 295

296. INTR O DUCTIO N …  For a n o p t i m a l ther a p e utic r e spo n s e , w e mu s t s e l e ct a sui t able drug and d e te r m i ne an app r op r i ate d o se wi t h t he av a i lable str e ngt h s and a conven i e nt dos i ng i nterv a l  To meet t h i s r e sp on s i bil i ty, t he s e r um or p l a sm a d r ug co n c e ntr a t i ons have to be a na l yzed, p har m a c ok i net i c pa r a m e te r s have to be ad j usted and the dos i ng e va l ua t e d, t he d r ug dose h a s t o be i nterv a l has to be d e te r m i ned P harm a cok i n e tic - Based Design and M odi f icat i on of D o sa g e R e gim e ns:  Tr a d i t i onally, d r ug i nf o r m at i on pr o v i d e d by phar m ac e utic a l co m pan i e s R e fe r e n c e ) (s u c h has as p ack a ge ins e rts a nd P hysic i a n s’ De s k the c onta i ned in for m a t i on ab ou t phar m ac o k i net i cs av a il ab l e )  Dep e nd i ng o n t his of drugs a nd the t he r a p e utic r a n ge ( i f in f o r m at i on, th e fo c us o f d e s i gn o f d os a ge r e g i m e ns has b ee n the use o f phar m ac o k i net i c data 5/6/2024 296

297. Pha r m a cokineti c -B a s e d Design and Modific a tion of Dosage Regi m ens… IV Bolus D o sin g : STEP – 1 : Es t imat i o n concentratio n ( C av e ∞ ) :  The fo ll owi n g e q uat i on of a ta r get a ve ra ge st e a d y state d e f i n e s C a v e ∞ the va lu e bas e d o n t he m i n i mum ( C m i n ∞ ) a n d m a x i mum ( C ma x ∞ ) s te a dy state c o nc e ntr a ti ons e qual to MEC and MTC, r e sp e ct i v e l y ∞ ∞ ∞ m in ∞ m ax ∞ m in C ave = C m ax - C / ln (C /C )  W e s h o u l d note t hat t he C ave ∞ i s s l i ght l y d i ffe r e nt fr o m an a l g e br a i c av e r a ge of C m i n ∞ and C max ∞ 5/6/2024 297

298. Pha r m a cokineti c -B a s e d Design and Modification of Dosage Regimens…  This o r d e r li ne a r i s b e c a use the p l as m a c o n c e n trat i ons o f drugs with fi rst e li m i n at i on d e c li ne e xpon e nti all y i nstead o f a si mple d e c l i ne (d o se/ τ ) S T EP – 2 : Esti m at i on o f t h e d o si n g rate C av e ∞ : necessary to achie v e  For this ca l c ul a t i on, o n e a l so ne ed s c l e a r ance ( Cl) o f syste m i c av a il ab i li ty (F) o f the drug and e x t e nt D o se / τ = Cl . C ave ∞ /F For I V ad mi nist r at i on, F i s e qual to 1. Ther e for e , D o se / τ = Cl . C ave ∞ 5/6/2024 298

299. Pha r m a cokineti c -B a s e d Design and Modification of Dosage Regimens… S T EP – 3 : Estimation o f the m a xim u m allo w a ble τ ( τ m a x ) ∞  The r a te o f d e c li ne i n t he p l as m a c onc e n trat i on from C max to or C m i n ∞ is gov e rn e d by the d r ug e li m i nat i on h a l f li fe (t ) 1 / 2 e li m i nat i on r a te constant (K)  The r e fo re , w e c a n e st i m ate h o w l ong i t w o u l d take f o r the p l as m a conc e n trat i on to d e c li ne f r o m a m a x i mum to a m i ni m um e - k τ max ∞ = ∞ C min C m a x The a b o v e equ a tion can b e re a rra n ged to sol v e f or m a x : τ τ ( C m a x ∞ /C min ∞ ma x = ln ) / K 5/6/2024 299

300. Pha r m a cokineti c -B a s e d Design and Modific a tion of Dosage Regi m ens… τ max  C h o o se a pr a ct i cal va l ue bas e d o n the ca l cul a ted τ max  The ca l cul a ted is t he l on g e st i nterv a l t hat m a y be s e l e cted for the pat i e nt τ m ax  B ut, t he d rug ad mi n i strat i on a t e ve r y h o ur is not pr a ct i cal  He nc e , a τ sh o u l d be s e l e ct e d fr o m one o f t h e fo l l ow i ng m o r e pr a ct i cal va l ues: v i z. , 4, 6, 8, 1 2, o r 2 4 hours  Obv i ous l y, w e will ch o ose a l ong e r τ if po s s i b l e (for pa t i e nt and staff conven i e nce)  H o wev e r, a s e l e cted p r act i cal τ τ max c a n not be m o re t h a n if the d e s i r e d o u t co m e is to ke e p the p l as m a co n c e ntr ati ons ∞ ∞ b e t w ee n C m i n and C max 5/6/2024 300

301. Pharmacokinetic-Ba s ed Design and Modification of Dosage Re g imens… S T EP – 4 : Estimation o f the d o s e :  K n o wing th e dos i ng r a t e (dos e / τ ) and dos a ge i nt e rv a l ( τ ) , we can s i m p l y e st i m a te the dose as D o se = D o sing R a te x D os a ge Interv a l  If not the dose i s n o t pr a c t i cal o r the av a il a b l e str e n g t h s w o uld a l l ow th e ad mi nist r at i on o f t he e x a ct dos e , w e m a y r o u nd i t to the ne a r e st pr a ct i cal n u m b er ∞ , ∞ ∞  Re - esti m a te C ave C m in , a n d C m ax b a s ed on the selected τ a n d d o se 5/6/2024 301

302. Pharmacokinetic-Ba s ed Design and Modification of Dosage Re g imens… C m i n ∞ C ma x ∞  To e st i m a te and va l ues with t he pr a c ti cal r e g i m e n, f i r s t , the C m a x a nd C m i n after t he f i rst dose ( C ma x 1 st and C 1 st m i n r e sp e ct i ve l y) ar e e st i m a ted C m ax 1st = D o se / V τ C m in 1st = C 1st . e - K m ax  Th e n, u s i ng t he a c c u m ul a t i on f a c t or ( R), va l ues ar e pr e d i cted a s shown b e l ow the C ma x ∞ and C m i n ∞ τ ) e - K R = 1 / ( 1 - C m ax ∞ = C 1st . R m ax ∞ 1st m in C m in = C . R 5/6/2024 302

303. Pha r m a cokineti c -B a s e d Design and Modification of Dosage Regimens… S T EP – 5 : Estimation o f the lo a ding d o se (if nee d ed ) :  In so m e c as es , ad mi nist r at i on of a l o a d i ng dose m a y be ne c e s s a ry, p a rt i cu l a rl y i f the ha l f li fe o f t h e d r ug i s l o n g and the i m m e d iate a c hi e ve m e nt of t he r a p e utic c onc e n trat i ons is i m p o r tant  I n t he se c a s e s , t he l o a d i ng dose ( D L )m a y e i ther o f the fo l l ow i ng two me thods D L = D M . R be e st i m a ted by D L = C m ax ∞ . V Whe re , D M = m ai ntenance dos e ; R = A ccumu l at i on facto r ; V = V ol u m e of d i str i but i on  A s m en t i o n e d e a r li e r, t he dose sh ou l d be ad j u s ted bas e d on the av a il ab l e str e ngt h s and/or sa l ts o f the drug 5/6/2024 303

304. Pha r m a cokineti c -B a s e d Design and Modification of Dosage Regimens… Co n st a nt IV Infusion:  This i s t h e s i m p l e st cas e , as one d e a l s w i th the i n f usi o n r a te constant (R ) on l y (no ne e d to e st i m a te τ )  The fo ll ow i ng proc e dure m a y be u s e d for this pr o c e ss: S T EP – 1: Estimation of infusi o n rate consta n t ( R ):  R c a n be ca l c ul a ted bas e d on t he d e s i r e d s te a dy s tate conc e ntra ti on ( C ss ) and the drug c l e a r ance R = Cl . C ss  The d e s i r e d C ss i s no r m a l l y a c o nc e n trat i on with i n t he M E C and MTC va l ues 5/6/2024 304

305. Pha r m a cokineti c -B a s e d Design and Modification of Dosage Regimens… S T EP – 2: Estimation of loa d ing d o se( D L ):  D L can be ca l cul a ted bas e d D L o n the C ss and V o f the drug = C ss . V  The d e s i r e d i s nor m a l ly a MTC va l ues co n c e n trat i on wit hi n t he M EC and  Ad mi nist r at i on of D L s h o uld pr o duce a co n c e ntr a t i on of C ss w h ic h i s m a i nta i ned by s i mu l tane ou s sta r t o f th e i nf u s i on a t a r a te o f R 5/6/2024 305

306. Pharmacokineti c -Based Design and Modificat i on of D o sage Re g im e ns… Intermittent IV Infusio n :  F e w d r ugs ( a mi no g l ycos i d e s and s o m e other ant i b i ot i cs s u c h a s v a n co m yc i n ) have to be us ua ll y adm i nist e r e d v i a mu l t i ple shorts ( 3 0- 6 0 m i n) I V i n f usi o ns a t r e gu l ar i nterv a l s  G e ne r a l l y, f or ant i b i ot i cs, t h e d e s i r e d C max i s a va l ue s e v e ral fo l d ab o ve the m i ni m um i n h i b i to r y c o nc e n tr a t i on o f t he drug for the r e spons i b l e o r gan i sm  H ow e v e r, C m i n i s u sua l l y s i gn i f i c a ntl y l ow e r th a n the m i n i mum i n h i b i tory conc e ntra ti on  For t he s e a ntib i ot i cs, i t i s d e s i r e d t o d e s i gn a dos a ge r e g i m e n C m i n ∞ C ma x ∞ to have a v a l ue a bove t he M IC o f t he d r ug a nd a va l ue a t o r b e l ow a conc e nt r at i on ass o c i at e d with tox i c i ty  The app r o a ch for s e l e c t i on o f a d o sage i nter v al i s, ther e f o re , s li ghtly d i ffer e nt from t hat u s e d e a r li e r for t he d e s i gn of dos a ge r e g i m e ns to pr o d u ce c o n c e n t r at i ons wi t hin a ther a p e utic r a nge (M E C and MT C ) 5/6/2024 306

307. Ph a rma c ok i neti c -B a s e d D e s i gn and Modifi c a t i o n of Dosage Regi m ens… Extr a v a scular A d ministratio n :  The e st i m a t i on o f do s e and d o s i ng r a te a f te r e xtrav a s cul a r dos i ng ( e . g . , ora l ad mi nist r at i on) i s m o re c o m p l i cat e d t h a n th a t a fter I V bo l us do s e s b e ca u se t he r a te a nd e x t e nt ( F) of e xtrav a sc ul a r av a il a b il i ty w o uld a l so be i m p o r ta n t fa c to r s in add i t i on to other k i net i c pa r a m e te r s  One e x tr e me case f or e xtr a v a s c ul a r dos i ng is w h e n t he abs o rpt i on i s so f a st th at i t c a n be as s um e d a s i n s t a nt an e ous for pr a ct i cal purpos e s  This c a se w ou l d be s i mi l ar to I V bo l us ad mi nist r at i on with F of 1  Be cause o f the co m p l e x i ty o f ca l c ul a t i ons i n v o l v i ng abs o rpt i on r a te c o nst a n t , i n p r a c ti c e , t he a b s o r p t i on o f m o s t i mm ed i ate r el e ase for m ul a t i ons i s assu me d to be i nstan t an e o u s  Ther e for e , t he e qu a t i o n s u s e d for I V bo l u s do s i ng c a n a l so be used for d e s i gn o f e xtrav a sc ul a r dos a ge r e g i m e ns wi t h r e as o nab l e accur a cy 5/6/2024 307

308. Ph a rma c ok i neti c -B a s e d D e s i gn and Modifi c a t i o n of Dosage Regi m ens…  In fact, the actu a l fluctuat i on in the p l as m a sam p l es aft e r extr a vasc u l ar d os i ng w o u l d b e l ess than that e s t i mated us i ng i nstant a neous a b sor p t i on or IV a d m i n i str a t i on  Th i s i s b e c a use i n r e a l i ty, a b sor p t i o n tak e s p l a c e over a certa i n p e r i od of t i me r e su l t i ng i n l ower from an i nstant a neous a b sor p t i on C m a x ∞ va l ues th a n those e s t i ma t e d  A l s o, the g ra d ual a b sor p t i on of t he d rug f r om the s i t e of a d m i n i str a t i o n ( e . g. , g a s tro i nte s t i nal tract) r e su l t s in h i g her C m i n ∞ va l ues aft e r extr a vasc u l ar d os i ng, co m p ar e d w i th I V a d m i n i str a t i on of the s a me d ose  G e ner a ll y, s l ower a b sor p t i on p rof il es wou l d r e su l t i n l e s s f l uctuat i on  In anoth e r extr e me, the p rof il es aft e r c ontrol l ed r e l e a se formulat i ons ( e . g . , zero-or d er a b sor p t i on) wou l d r e su l t i n al most const a nt co n c e ntrat i ons a t st e a d y state w i th m i nimal fluctuati o n, a s i tuat i on s i m il ar to const a nt IV i nfus i on  In these ca s e s, the const a nt i nfus i on e q uat i ons m a y b e us e d for the p r ed i ct i on of d osa g e r eg i mens of contro l l ed r e l e a se p ro d ucts 5/6/2024 308

309. E q uat i o n s to C ompute Indiv i dual i zed Dosa g e Reg i mens f o r Var i o u s R o u t es of Admi n ist r ati o n ∞ )/K ∞ )/ K ] + t′ i nfus io n ∞ )/ K ] + T c o ncentra t i on (any r o u t e D L = C ss . V / F ROUTE OF D OS AGE I N T E RVAL ( τ ), MAI N T E NA N CE A D MI N ISTRAT I ON D OS E (D or R ), AND L OA D I N G D OS E (D L ) EQUAT I ONS I n tr a v enous bo l us τ = l n ( C m a x ∞ / C m i n D = C ma x ∞ . V. (1 − e − K τ ) D L = C m a x ∞ . V C o n t i n u ous i n t rav e nous R = C s s . Cl = Css . K . V i nf u si o n D L = C s s . V I n termit t ent i n t rav e nous τ = [ l n ( C m a x ∞ / C m i n R = C ss . K . V [ (1 −e − K τ ) / (1 −e − K t ′ )] D L = R / (1− e −K τ ) Ex t ravascu l ar τ = [ l n ( C m a x ∞ / C m i n m a x D = [ ( C m a x ∞ . V) /F ] [ (1−e − K τ ) / e −K T m a x ] D L = C m a x ∞ . V /F A v e rage stead y -sta t e D = ( C ss . C l . τ ) / F = ( C ss . K . V . τ ) /F of ad m i nistra t i on) 5/6/2024 309

310. MU L T I COMPAR T MENT MODEL…   I m me d i at e ly a fter t he d o se i s g i v e n , d e c li ne r ap i d l y and t his po r t i on o f the d i str i buti o n phase s e r um c on c e nt r a t i ons c u r v e i s k no w n a s t he  D ur i ng t his ph a s e , d r ug is d i str i buting b e t we e n b l o o d and t i ssu e s a n d is r e mo v e d fr o m t he b o dy v i a he p at i c m e tab o li sm and r e nal e li m i nat i on  A f ter this phase o f t he c ur v e i s f i nish e d , d r u g d i str i buti o n is ne a r l y co m p l e te and a p s ued o e qu i l i b r i um is e stab li s h e d b e twe e n the b l o o d and t i ssu e s  Lat e r , s e r u m co n c e nt r at i ons d e c l i n e m o re s l ow l y dur i ng t he e l i m i nat i on phas e , i n w hich from the body d r ug i s pr i m a ri l y b e i ng r e m o v e d 5/6/2024 310

311. MULTICO M PAR T ME N T MODEL…  S i m i l ar e q u at i ons f o r a t wo co m p a rt me nt m od e l ar e a v a i lable for i nt r a v e n ous (bo l us & in fu s i ons) a nd e x t r a v as c ul a r do s e s as that o f one co m pa r tm e nt m o d e l  In o r d e r to g e t a c c u r ate v a l u e s for the phar m ac o k in e t i c co n st a n t s i n t he e q uat i on, 3 − 5 s e r um co n c e n t r at i ons f o r e a c h phase o f t h e c u rv e ne e d to be ob t a i ned a f ter a dose i s g i v e n to a pat i e nt  Be cause o f the c o st a n d t i me i n v o l v e d to co l l e ct 6 –1 s e rum co n c e nt r a t i ons a f ter a dos e , mu l t i co m pa r t m e nt m o d e l s a r e r a re l y used i n pat i e nt ca r e s i tuati o ns  I f a d r ug f o l l ows mu l t i c o m pa r tm e nt p har m ac o k i net i cs, s e rum co n c e nt r a t i ons ar e u su al l y not d r a wn for c li n i cal u se u nt i l the d i str i buti o n phase i s o v e r and t he e l i m i nat i on phase h a s b ee n e stab li shed  I n t h e se c a s e s , i t i s poss i b l e to us e s i m p l e r one co m pa r t m e nt m o d e l e quat i ons to c o m p ute dos e s with a n a cc e ptab l e d e gr e e o f accu r acy 5/6/2024 311

312. Pharmac o dy nam i c - B a sed Dosage Regimen Design  R e c e ntly, v e ry sp e c i f i c phar m ac o d ynam i c in f o r m at i on s uc h as m a ximum e ff e ct ( E ma x ) a nd t he p l as m a c o nc e ntr a t i on pr o duc i ng ha l f of E max (EC 50 ) ar e b e g i n n i ng u s e d in d os a ge r e g i me n d e s i gn  Ther e for e , i t i s p o ss i b l e to d e s i gn dos a ge r e g i m e ns for th e se drugs to a c hi e ve c e r ta i n e ff e c t s r a t her t han c e r ta i n conc e ntra ti ons  For E max , e xa m p l e , t he so ca l l e d E max m o d e l e quat i o n , r el at i ng E C 5 , a nd t he p l as m a co n c e n trat i on ( C ) pr o d ucing a c e rta i n e f f e ct ( E) m a y be u s e d to tra n s l ate th e d e s i r e d u pp e r ( E U PP E R ) and l ow e r ( E L O WE R ) e ff e c t s (g o al o f th e r a py) to C ma x ∞ and C m i n ∞ va l ues 5/6/2024 312

313. Pharmac o dy nam i c - B a sed Dosage Design Regimen E = E max . C / E C 50 +C C = E C 5 . E / E max – E C ma x ∞ = E C 5 . E UPPER E max / – E UPPER E C m i n ∞ = EC . E / E – 50 LOWER max LOWER  The e s t i m a ted C m a x ∞ a n d C m i n ∞ v a l u e s t he n c an be u s e d for the d e s i gn o f mu l t i p l e dos i ng r e g i m e ns a s e xp l a i ned e a r li e r  S i m i l a r l y, for t he c o n st a nt I V inf usi o n, a tar g e t e f fe c t m a y be conv e rt e d to a C ss v a l ue a nd a c o n st a nt i nf u s i on r a t e be e st i m a ted a s e xp l a i ned e a r li e r 5/6/2024 313

314. A SIMPLER APPROACH TO PHARMACO K INETIC DOS A GE ADJUSTMENT C h ang i ng D o s e : The fo ll owi n g s i mple e quat i on do e s not r eq ui r e a ca l cul at o r , and c a n be done i n m o st cas e s wi t hin few s e c ond s , a s su m i ng s e rum conc e ntrat i ons were m e asur e d app r op r i at e l y  New Dose = Des i r e d Concentrat i on x Ol d Dose Me a sur e d Concentrat i on This e q uat i on i s bas e d o n t he f a ct t hat i ncr e a se o r d e cr e ase  in dos e s ( ke e p i ng c h a nges t he in i nt e rv a l t h e sa m e ) pr o duce pr o po r t i onal p e ak s , t r o u g h s , or s te a dy st ate s e rum c o nc e ntr a t i ons  In o t her w o r ds, if t he dose is d oub l e d, p e ak a nd tr o u g h conc e ntra ti ons ar e a l so doub l e d 5/6/2024 314

315. A SIM P LER APPROACH TO PHARMACOK I NETIC D O SAGE AD J USTMENT…  This pr o p o rt i onal do s e app r o a c h is p ha r m a cok i net i cal l y co r r e ct i f the fo ll ow i ng cond i t i ons ar e met  S e r um c o n c e n trat i o n s ar e m e a s u r e d a t ste a d y state and a r e c o r r e ct l y and a c cur a t e l y d r awn  The d r ug fo ll ows fi rst-o r d e r and o ne -c o m pa r tm e ntal phar m ac o k i net i cs  The dos i ng i nterv a l i s not changed  I n fu s i on t i m e s of t he pr e s e nt d os a ge a nd the t i m e s of co n c e ntr a t i ons m e as u r e d ar e t he s a m e for t he n e w dos ag e with i n r e as o n, say, p l us o r m i n u s 5- 1 0 m i n u tes  W i th t his m e thod one do e s not have to w o r r y ab o ut e xpon e nti a l f unct i o n s, i nfus i on r at e s , ha l f - l ives, vo l u m e of d i str i but i on, e li m i nat i on r a te c o nstan t s 5/6/2024 315

316. A SIM P LER APPROACH TO PHARMACOK I NETIC D O SAGE AD J USTMENT…  Ca l cul a te the d i ff e r e nce b e t we e n p e a k a nd t r o u g h conc e nt r a t i ons d e s i r e d i n that pat i e nt ( D d ) D m required is = ------- D d The new d o se x old d o se St e p 2: Det e r mi ne the New Dos i ng Inte r va l :  The d o s i ng i nterv a l the ha l f - li fe i s e st i m a ted u s i ng t he r o ugh e st i m a te of  The p e ak c onc e n trat i on dr o ps to trou g h c o nc e ntr a t i on o ver a p e r i od o f t 1 hou r s  F i nd t he nu m be r o f ha l f li ves tak e n for dr o p i n c o nc e n t r a t i on from p e ak to trough 5/6/2024 316

317. A SIM P LER APPROACH TO PHARMACOK I NETIC D O SAGE AD J USTMENT…  The d o s i ng i nterv a l i s e st i m a ted u s i ng t he r o ugh e st i m a te of the ha l f - li fe  The p e ak c onc e n trat i on dr o ps to trou g h c o nc e ntr a t i on o ver a p e r i od o f t 1 hours  F i nd t he nu m be r o f ha l f li ves tak e n for dr o p i n c o nc e n t r a t i on fr o m p e ak to tr o ugh  D i v i de t 1 by t he n umb e r o f ha l f li v e s ca l cul a t e d ab o ve to g e t app r ox i m a t e n umb e r o f ha l f li ves tak e n for d r op i n m e asur e d p e ak to trough conc e ntra ti on  S i m i l a r l y ca l cul a te th e app r ox i m a te n u m b e r of ha l f li ves r e qu i r e d for dr o p i n d e s i r e d p e ak to trough conc e ntrat i on 5/6/2024 317

318. A SIM P LER APPROACH TO PHARMACOK I NETIC D O SAGE AD J USTMENT…  M u l t i p l y the n umb e r o f ha l f li ves t ak e n for a c tual dr o p p e ak to trough with d e s i r e d one f r o m  The r e sult s h o uld be r o u nder o f f to the ne a r e s t pr a ct i cal i nterv a l for dos i ng t i m e Exercise: Consi d er a patient who is rece i ving 1 mg of a drug eve r y 8 hours a n d the m e a su r ed peak and trough mg/ L , trough steady s t ate c o nc e ntrations are 8 . 6 a n d 1 . 4 respect i ve l y . Ass um e the desired p eak a n d conc e ntra t ions are 3 a n d 1 m g/L. C a lcu l ate t h e d o se and d o sa g e interv a l to achie v e the desired concentratio ns . 5/6/2024 318

319. CALCULATING DOSAGE O r al Dr u g s :  Fr e qu e ntly, tab l e ts o r c apsu l e s for ora l ad mi n i strat i on ar e not av a il ab l e i n the e xact dose that has b ee n o r d e r e d I n t hese s it uat i o n s, w e mu s t ca l c ul ate the nu m be r o f t a b l e ts o r c a psu l e s that shou l d be g i v e n to m ake up the o r d e r e d d o se The e as i e st way to d e te r m i ne t his i s to s e t u p a r a t i o a nd pr o po r t i on e quat i on The r a t i o c o nta i ning t he t wo k n o wn e qu i va l e nt a m oun t s i s put    on o ne s i de of t he e quat i o n , a n d t he r a t i o c o nta i ning t he unk n own va l ue i s put o n the oth e r s i de The k no w n e qu i va l e nt i s t he a m o u nt o f d r ug av a i l a b l e i n o ne tab l e t o r c apsu l e ; t he u n k no w n i s t he n um b e r o f tab l e t s or  capsu l e s that ar e ne e d e d for the pr e scr i b e d dose am o unt of drug prescribed ----------------------- a m ount o f drug a v ail a ble ------------------------- - -- one ta b let o r ca p sule = number o f ta b lets o r ca p sules to gi v e 5/6/2024 319

320. CALCULATING DOSAGE O r al Dr u g s :  S o m e t i m e s the d e s i r e d dose wi l l be a fr a ct i on o f a tab l e t or capsu l e , 1/2 o r 1 / 4 S o me tab l e ts co m e wi t h s co r e m a r k i ngs t hat a l low t hem to be cut Pi l l cut t e r s ar e r e ad i l y av a i l a b l e i n m o st ph ar m a c i e s to help pat i e nts cut tab l e ts app r op r i at e l y One must use caut i on w h e n adv i s i ng a pat i e nt to cut a tab l e t Many tab l e ts tod a y c o me i n a m a tr i x syst e m that a l l ows for s l ow and st e a d y r el e a s e o f the a c t i ve d r ug These drugs cannot be cut, crushed, o r chewed A d r ug r e f e r en ce s hou l d a l ways be c o n sult e d b e fore c ut t i ng a tab l e t         Capsul e s can be I f t h e o n l y way ve r y d i fficu l t to d i v i de pr e c i s e l y to d el iver t he c o r r e ct d o se t o a p a t i e nt i s by c u tting one of t h e se pr e pa r at i ons, a d i ffe r e nt d r ug or a d i ffer e nt app r o a ch to tr e at i ng the pat i e nt shou l d be tr i e d 5/6/2024 320

321. CALCULATING DOSAGE – ORAL DOSA G E… O ther o r al d r ugs c o m e i n li qu i d p re p a r a t i ons Many o f t he d r ugs u s e d i n p e d i atr i cs and for a d ults w ho m i ght have d if f i c ul ty i n swa ll ow i ng a p i ll o r tab l e t a re pr e pa re d i n a li qu i d form   The sa m e pr i nci p l e u s e d to d e t e r m i ne t he n umb e r o f t ab l e ts  ne e d e d to a r r i ve at a pr e s c r i b e d dose can be us e d to to d e te r m i ne the vo l ume of li qu i d t h a t wi l l be r eq ui r e d ad mi nist e r the pr e scr i b e d dose a m ount o f drug prescribed ----------------------- v o lume to a d minister a m ount o f drug a v ail a ble ------------------------- - -- V o lume a v ail a ble =  E v e n i f you ar e work in g i n an ins t i tu t i on t h a t pr o v i d e s u ni t - dose m e d ic at i ons, p r a c t i ce y o ur c a l cul a t i on s kil l s occ a s i ona l ly to m ake s u re t hat y o u c a n f i gure out t he d o se o f a d r u g to g i ve P o wer c a n be l ost, c o m p uters c a n go d o w n, a nd t he abi l i ty to d e te r m i ne c onve r s i ons i s a sk i ll t h at a ny o ne w h o ad mi nist e r s drugs shou l d have i n r e s e rve  5/6/2024 321

322. CALCULATING DOSAGE Pare n teral Dr u g s :  A l l drugs a d m i n i ste re d pa r e nter a l ly m u st be ad mi n i ste r e d in li qu i d form  The p e r s o n a dm i n i st e r i ng t he d r ug ne e ds to c a l c u l ate t he the vo l ume o f the li qu i d that m u s t be g i ven to ad mi nist e r pr e scr i b e d dose  The sa m e f o r mu l a c a n be u s e d for this d e te r m i nat i on t hat us e d for d e t e r mi n i ng the d o se o f a n o r al li qu i d d r u g : a m ount o f drug was a m ount o f drug a v ail a ble ------------------------- - -- V o lume a v ail a ble prescribed ----------------------- v o lume to a d minister = 5/6/2024 322

323. CALCULATING DOSAGE I n trave n ous S o luti o n s :  In t r a ven o u s (IV) so l uti o ns are u s e d to d e li v e r a pr es c r i b e d a m ount of f l ui d , e l e c tro l ytes, v it a mi ns, n u t r i e nt s , or d rugs d i r e ct l y i nto the b l o o dstr e am A l th o ugh m o s t i n s t i tut i ons now u se d e l i ve r y sy s te m s, i t i s st i ll i m po r tant  e l e ctr o n i c a ll y m on i to r ed to be ab l e to d e t e r mi ne the a m o un t of an IV so l uti o n t hat s h o uld be g i ven using standa r d ca l cul a t i ons Most I V d e l ivery s y st e ms co m e with a st a nd a rd c o ntrol c al l e d  a m i c r o d r i p , by w h i ch e a c h m i l l ilit e r d eli v e r e d c o nta in s 60 dr o ps Macr o dr i p sy s te m s,  w hich d e li v e r 15 dr o ps/mL, are a l so av a i l a b l e; they ar e usu al l y used w h e n a l a r ge vo l ume must be d e li ve re d qu i ck l y I n g i v i ng I V dru g s, th e m i cr o dr i p sy s tem i s m o st co m m o nly e ncoun t e r e d C h e ck t he pack a g i ng o f t he I V tu b i ng i f you have a ny d oub t s o r ar e u n fa m ili ar with the pack a g i ng   5/6/2024 323

324. CALCULATING DOSAGE – IV SOLUT I ONS…  The r a t i o th at i s u s e d t o d e t e r mi ne how m a ny d r o p s o f f l u i d to ad mi nist e r p e r m i n u te i s the fo ll ow i ng dr o ps/minute = m L o f solution prescribed per hour x dr o ps deli v ered per mL ------------------------ - ----- 6 0 minutes / 1 hour  That i s, t he n u m be r will s e t by a djust i ng a m ount o f so l uti o n o f dr o ps p e r m i n u te, o r t he r a te t hat y o u t h e va l ve o n th e I V tubin g , i s e qual to t h e th a t has b ee n pr es cr i b e d p e r h o ur ti m e s the n umb e r o f dr o ps d e l i ve re d p e r m L d i v i d e d by 6 m i n u t e s i n a n hour Exercise: A n o r d e r h a s b ee n wr i t t e n f o r a pa t i e nt to r e c e i ve 40 mL o f 5 % d e xt r o se i n w at e r ov e r a p e r i od o f 4 h ours i n a s t anda r d m i cr o drip system ( i e , 6 dr o ps/mL). Ca lc ul a te the co r r e ct s e tting (dr o ps p e r m i n u te) 5/6/2024 324