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Core Entrustables in Clinical : Pearls for Clinical Practice

The Journal of and 2016, 56(10) 1180–1195 C 2016, The American College of for Medical Students: A Proposed Clinical Pharmacology Course Outline DOI: 10.1002/jcph.732

David J. Greenblatt, MD,1 and Paul N. Abourjaily, PharmD2

Keywords pharmacokinetics, pharmacodynamics, interactions, medical

The discipline of pharmacokinetics (PK) applies math- Clinical Vignettes ematical models to describe and predict the time Case 1 course of drug and drug amounts in A 30-year-old man has been extensively evaluated for 1–3 body fluids. Pharmacodynamics (PD) applies sim- recurrent supraventricular tachycardia (SVT), which is ilar models to understand the time course of drug associated with palpitations and dizziness. No iden- actions on the body. Clinicians are most concerned with tifiable cardiac disease is evident, and other medical pharmacodynamics—they want to know how drug diseases have been excluded. dosage, , and frequency of ad- The treating physician elects to start therapy with ministration can be chosen to maximize the probability , 0.1 mg daily.One week later the patient is seen of therapeutic success while minimizing the likelihood again, and states that episodes of SVT are reduced in of unwanted drug effects. However the path to pharma- number. The plasma digitoxin level is 8 ng/mL (usual codynamics comes via pharmacokinetics. Because drug therapeutic range, 10–20 ng/mL). The is increased effects are related to drug concentrations, understand- to 0.2 mg/day. At a follow-up visit 7 days later, the ing and predicting the time course of concentrations patient claims that symptoms attributable to SVT have can be used to help optimize therapy. disappeared completely. The plasma digitoxin level is The link of drug dosage to drug effect involves 17.4 ng/mL. The patient continues on 0.2 mg/day of a sequence of events (Figure 1). Even when a drug digitoxin. is administered directly into the vascular system, the One month later the patient sees the physician on drug diffuses to both its pharmacologic target an urgent basis. He has diminished appetite and waves and to other peripheral distribution sites where it does not have the desired activity but may exert toxic ef- fects. Simultaneously, the drug undergoes by 1Program in Pharmacology and Experimental Therapeutics, Sackler and . After oral administration, School of Graduate Biomedical Sciences, Tufts University School of the situation is more complex, since the drug must , Boston, MA, USA undergo dissolution and absorption, then survive first- 2Departments of and Medicine, Tufts Medical Center, Boston, pass metabolism in the , before reaching the sys- MA, USA temic circulation. Pharmacokinetics provides a ratio- Submitted for publication 26 February 2016; accepted 3 March 2016. nal mathematical framework for understanding these Corresponding Author: concurrent processes, and facilitates achieving optimal David J. Greenblatt, MD, Tufts University School of Medicine, 136 clinical pharmacodynamic effects more efficiently than Harrison Avenue, Boston, MA 02111 trial and error alone. Email: [email protected] The following 3 clinical vignettes illustrate how This proposal was prepared under the guidance of the Special Com- familiarity with principles of pharmacokinetics and mittee for Medical School Curriculum of the American College of pharmacodynamics can facilitate optimal understand- Clinical Pharmacology. The proposal is intended as a resource for ing and prediction of drug effects in human subjects the Association of American Medical Colleges as it revises its Core Entrustable Professional Activities for Entering Residency, Curriculum and patients. Developer’s Guide. Greenblatt and Abourjaily 1181

Figure 1. Sequence of events between intravenous or oral adminis- tration of a drug and the drug’s interaction with the target receptor mediating pharmacologic action.This type of schematic diagram has been attributed to Dr. Leslie Z. Benet. The segment above the dashed line is the pharmacokinetic component—“what the body does to the drug.” Below the dashed line is the pharmacodynamic component—“what the Figure 2. Hypothetical mean plasma concentrations of digitoxin, cor- drug does to the body” (from reference 2, with permission). responding to case 1 in the text. Digitoxin is initially given at a dosage of 0.1 mg per day for 1 week, after which the plasma is 8 ng/mL (point a). The treating physician wants to increase the plasma concentration to a value within the usual therapeutic range of nausea. The electrocardiogram shows T-wave abnor- (10–20 ng/mL). If the physician stayed with the 0.1-mg-per-day dosage, malities, and the plasma digitoxin level is 31.3 ng/mL. the eventual steady-state concentration would have been 16 ng/mL (dashed line)—within the desired therapeutic range. Instead, the dosage Discussion—Case 1 is increased to 0.2 mg per day on day 7. The next measured plasma concentration is 17.4 ng/mL 1 week later (point b), but 1 month later Digitoxin is seldom used in contemporary therapeutics, it has reached 31.3 ng/mL (point c), close to the eventual steady-state but case 1 nonetheless illustrates 2 important principles: value of 32 ng/mL. This is well above the therapeutic range and may be dose proportionality, and attainment of steady-state. associated with . The rate of attainment of the steady-state condition after initiation of multiple-dose treatment is dependent on the half-life of the particular drug. In the case of motion. He contacts his physician. An x-ray is negative. digitoxin, the half-life is about 7 days, implying that 3–4 The physician prescribes rest, topical heat, and , weeks of continuous treatment (without a ) 650 mg 4 times daily. is necessary for steady-state to be reached.4 In the exam- At a return visit to the physician 2 days later, the ple given, the increase in dosage from 0.1 to 0.2 mg/day patient is greatly improved. The physician uses that is anticipated to proportionally increase the steady- opportunity to do a routine check of the plasma state concentration (Figure 2). At the daily dosage of level, which is reported as 5 μg/mL. There 0.1 mg (without a loading dose) and a half-life of 7 is no evidence of recurrent seizure activity, and the days, the plasma digitoxin concentration of 8 ng/mL patient insists that he is continuing to take phenytoin after 7 days of treatment represents 50% of the eventual as directed (300 mg/day). The physician increases the steady-state concentration of 16 ng/mL. If the physi- dose to 500 mg/day. cian had stayed with the 0.1 mg/day dosage, that steady- One week later the patient returns complaining of state concentration—attained after several weeks of difficulty with balance and with fixing his eyeson treatment (4 to 5 times the half-life)—would have been objects. The plasma phenytoin level is 14 μg/mL. in the therapeutic range. However the dosage was in- creased to 0.2 mg/day, yielding a corresponding steady- Discussion—Case 2 state concentration of 32 ng/mL, exceeding the thera- In case 2, of phenytoin is peutic range and producing adverse effects (Figure 2). reduced by coadministration of aspirin because of displacement of phenytoin from plasma-binding sites Case 2 by salicylate.5–7 This is evident as an increase in the free A 56-year-old man has a history of grand mal seizures, fraction (Table 1). However, the clearance of unbound which have been completely suppressed for the last 12 (free) drug, and the steady-state concentration of years by phenytoin, 300 mg daily. His plasma phenytoin unbound drug, are unchanged.8,9 As such, no change level consistently falls in the range of 12–16 μg/mL. The in clinical effect would be anticipated, and the correct patient is able to lead a normal life, and is an excellent clinical course would have been to leave the daily dosage tennis player. During a particularly competitive tennis at 300 mg/day. Because salicylate reduces plasma match, the patient injures his shoulder. That night he protein binding of phenytoin (higher free fraction in experiences severe pain, tenderness, and limitation of plasma), this has the effect of reducing total (free + 1182 The Journal of Clinical Pharmacology / Vol 56 No 10 2016

Ta bl e 1 . Total and Free (Unbound) Plasma Phenytoin Concentrations in Case 2

Phenytoin Daily Dosage, and Total Phenytoin Free Phenytoin Cotreatment (μg/mL) Fraction Free (μg/mL)

300 mg/day (no 12–16 0.1 1.2–1.6 cotreatment) 300 mg/day + 50.31.5 aspirin 500 mg/day + 14 0.3 4.2 aspirin

bound) concentrations of phenytoin as well as the in- terpretation of these measured total concentrations.5–7 Increasing the daily dosage of phenytoin to 500 Figure 3. Hypothetical plasma concentrations of correspond- mg/day increases the free (unbound) concentration to ing to case 3 in the text. A 0.5 mg/kg intravenous dose of propofol is 4.2 μg/mL, which is associated with adverse effects initially given at time zero. The plasma propofol concentration declines despite the total concentration of 14 μg/mL. rapidly, falling below the hypothetical minimum effective concentration A second important point is the nonlinear kinetic (MEC) of 200 ng/mL at 0.75 hours, at which time the patient emerges 10 from the sedated condition. The rate of drug disappearance in the profile of phenytoin. At daily doses in a range postdistributive phase would be slower (dashed line), but an additional exceeding 300 mg/day, steady-state plasma concentra- 0.5 mg/kg dose of propofol is required at the 0.75-hour time to maintain tions increase disproportionately with an increase in plasma concentrations above the MEC and maintain the patient in a dosage. The free phenytoin concentration is 1.5 μg/mL sedated condition for the remainder of the procedure. at 300 mg/day, but increases to 4.2 μg/mL with an increase in dosage to 500 mg/day. This property of phenytoin makes it difficult to titrate dosage at this or elimination. The pharmacokinetics of propofol are higher dosage range. described by a 2- or 3-compartment model, in which the initial “distribution” phase represents rapid distri- Case 3 bution from systemic circulation to peripheral tissues, A fourth-year dental student is doing a clerkship in a followed by the terminal “elimination” phase which dental surgeon’s practice. A healthy 34-year-old woman mainly reflects clearance.11–14 Although the propofol is scheduled to undergo procedures estimated to last has not been eliminated from the body, its distribution approximately 2 hours. Following instillation of local from systemic circulation into peripheral results anesthesia and prior to the start of the procedure, in lower concentrations in plasma and , which is the surgeon notices that the patient still is extremely highly vascular and rapidly equilibrates with systemic agitated and fearful. The surgeon administers 0.5 mg/kg circulation (Figure 3). As such, the patient becomes of propofol intravenously over a 2-minute period. The more alert, and a second dose is required. patient becomes calm, relaxed, and falls into a light sleep from which she is easily roused. The surgical procedure is initiated and proceeds without incident for Components of Medical about 45 minutes. At this time, the patient becomes Education in Pharmacokinetics alert, and again is fearful and agitated. The surgeon ad- ministers another 0.5 mg/kg of propofol intravenously, and Pharmacodynamics the patient again becomes calm, and the surgical proce- An outline of key elements of content for the teaching dure proceeds to completion without incident. of clinical pharmacokinetics and pharmacodynamics The student is confused. He/she asks the surgeon, to first- or second-year medical students, along with “Why did the patient wake up after only 45 minutes? pertinent literature references,15–54 are presented in The half-life of propofol usually is at least 8 hours.” Table 2. The same or similar content can be applied to the teaching of graduate students at both the PhD and Discussion—Case 3 masters levels, or to postdoctoral education programs Case 3 is an example of how the pharmacodynamic for house staff or practicing physicians. The material effects of lipophilic psychotropic after single can be reasonably presented in 3 or 4 total lecture intravenous doses are dependent more on the rapid contact hours. The didactic presentations should be process of peripheral distribution than on clearance reinforced through problem sets and review sessions Greenblatt and Abourjaily 1183 aimed at supporting conceptual understanding, as well ceptual understanding. The outline in Table 2 has that as ensuring proficiency with pharmacokinetic calcula- objective. The need for memorization of formulas and tions and construction of graphics. equations is minimal. Individual instructors can adapt the outline and Table 3 lists biomedical journals that have a focus accompanying graphics as needed, to construct specific on clinical pharmacokinetics and pharmacodynamics. lecture content consistent with their own style and Students are encouraged to consult original research institutional needs. An ongoing point of discussion is sources when seeking information on pharmacoki- the extent to which formulas, equations, and mathemat- netic/pharmacodynamic properties or drug interactions ics are needed for the teaching of pharmacokinetics. involving specific drugs or drug classes. Review articles Student backgrounds in mathematics and their comfort and secondary sources do have a role in the educational with quantitative content vary widely. Some dislike process, in that large amounts of data are collated and and resist the mathematical content, whereas others summarized. However, secondary sources are inevitably welcome it. “Equation-free” pharmacokinetics is not “filtered” and interpreted by their authors. Students realistic, but the density of equations can be managed need to consider the benefits and drawbacks of available such that the mathematical framework enhances con- information sources. 1184 The Journal of Clinical Pharmacology / Vol 56 No 10 2016

Ta bl e 2 . Course Outline: Pharmacokinetics and Pharmacodynamics for a Medical School Curriculum

Section 1. Definition and scope A. Pharmacokinetics: concentration versus time B. Pharmacodynamics: effect versus time C. Kinetic-dynamic modeling: effect versus concentration Section 2. Value of pharmacokinetic principles in medical science15–19 A. Choice of loading and B. Choice of frequency and route of administration C. Predicting the rate and extent of drug accumulation D. Predicting the effect of dose changes E. Identifying and anticipating drug interactions F.Identifying patient and disease factors that could alter clinical response G. Interpreting drug concentrations in serum or plasma19 Section 3. Fundamental assumptions A. Proportionality cascade (Figure 4): –Intravascular free drug –Extracellular water –Receptor occupancy –Quantitative pharmacodynamic effect B. Concentration ranges –Subtherapeutic –Therapeutic –Potentially toxic Section 4. Body compartments and volumes of distribution15–17,20–22 A. Definition of a compartment B. Calculation of derived from definition of concentration: Amount Concentration = Volume

Amount of drug in body Volume of distribution V = d Concentration in reference compartment C. The value and ambiguity of compartment models (hydraulic analogues)

1. One-compartment model: Vd is unique 23 2. Two-compartment model: Vd is not unique D. Anatomic correlates of volume of distribution E. Physiochemical correlates of volume of distribution24 Section 5. Exponential behavior and the meaning of half-life A. First-order processes: 1. Rate is proportional to concentration dC =−kC dt 2. Rate is not constant, even though k is called a “rate constant” B. Calculation of half-life In 2 0.693 t1/ = = 2 k k

1 C. k and t/2 are independent of route of administration D. Logarithmic versus linear graphs (Figure 5) E. Interpretation and implications of half-life

1 Time elapsed (multiples of t/2 ) Fractional completion of process

1 0.5 2 0.75 3 0.875 4 >0.90

F.Implications of first-order behavior

1 –t/2,Vd, and clearance are fixed –After single doses, AUC (area under the curve from time = zero to “infinity”) is proportional to dose

–At steady state, Css (steady-state concentration) is proportional to infusion rate (or dosing rate) Greenblatt and Abourjaily 1185

Ta bl e 2 . Continued

Section 6. Clearance of drugs and mechanisms of elimination25 A. Model-independent definition (Figure 6): Dose Clearance = AUC B. Units of clearance: volume/time Clearance cannot exceed flow to clearing organ C. Routes of clearance 1. Hepatic clearance: chemical modification (biotransformation) 2. Renal clearance: excretion of intact drug 3. All other: pulmonary, biliary, fecal, intravascular (plasma )

1 D. Biologic dependence of t/2 on both Vd and clearance

0.693 x Vd t1/ = 2 clearance E. The meaning of “linear” or “dose proportional” kinetics (see also section 5F) Section 7. Rapid single-dose intravenous injection A. One-compartment model dC 1. =−kC dt

Boundary condition: at t = 0, C= C0 -kt C = C0 e satisfies differential equation and boundary condition C To t a l A U C = 0 k 2. If dose = D, then Dose Vd = C0

Note: For a 1-compartment model, Vd is unique. In practice, the best time to measure Vd is at t = 0. 3. Monoexponential decline (Figure 5) 0.693 1/ = t 2 k Dose k . Dose 4. Clearance = = k . Vd = AUC C0

1 5. Correct biologic relation among t/2 ,Vd, and clearance:

0.693 xVd t1/ = 2 Clearance 6. Graphical approach to problem solving B. Two-compartment model16,17(Figure 7) 1. Simultaneous differential equations with boundary condition:

C = C0 at t = 0 Solution: C = Ae-αt + Be-βt A, B, α, β are HYBRID

= A + B To t a l A U C α β 2. Volumes of distribution20–22 a. “Central” compartment Dose Dose V1 = = C0 A + B b. “Total” volume of distribution Dose Clearance V = = d β × AUC β 3. Half-lives a. Distribution half-life (cannot be derived from graph) 0.693 t1 / α = 2 α b. Elimination half-life (can be derived from graph) 0.693 t1 / β = 2 β

4. Clearance = dose/AUC = Vd · β 1186 The Journal of Clinical Pharmacology / Vol 56 No 10 2016

Ta bl e 2 . Continued

C. One-compartment approximation of the 2-compartment model Fundamental assumption: Aandα (and the corresponding component of AUC) are ignored Consequences:

B becomes C0 β becomes k

1 1 t/2 β becomes t/2

Quantity 2-Compartment 1-Compartment

-αt -βt −kt Equation for concentration versus time C = Ae + Be C = C0e (B analogous to C0, β analogous to k)   A B C B To t a l A U C + 0 analogous to α β k β   Dose Dose Dose To t a l V d analogous to β.AUC C0 B Dose Dose Clearance = V .β = V . k AUC d AUC d In 2 In 2 Elimination half-life dose β k

D. Graphical approach to problem-solving E. Distribution versus elimination as the determinant of duration of action (Figures 3 and 7)

Section 8. Multiple-dose kinetics: continuous intravenous infusion (without a loading dose) (Figure 8) A. Rate of attainment of steady state:

1 Depends almost entirely on t/2 (and k) as would occur with a single dose. Does not depend on infusion rate (abbreviation: Q). Inverted exponential function: -kt C = Css (1 − e ). This is the same k as after a single dose. B. Determinants of the extent of accumulation (absolute steady-state concentration) (Figures 8 and 9) Infusion rate C = ss Clearance C. Predictable consequences of changing infusion rate or stopping infusion (Figure 10) 1. Rate of attainment of new steady state 2. New steady-state concentration

Section 9. Drug absorption and (Figure 11) A. Rate of drug absorption 1. Lag time (due to dissolution, gastric emptying, etc.) 2. First-order absorption 3. Factors influencing absorption rate 4. Implications of absorption rate 5. Slow-release preparations B. Completeness of absorption (fractional absorption or absolute systemic availability) 1. Methods of assessment—intravenous data needed (Figure 12) AUC (P.O.) F = AUC (I.V.) AUC must be dose-normalized and extrapolated to infinity. 2. Mechanisms of incomplete bioavailability25–29 a. Incomplete absorption - Intrinsic properties of the chemical - Properties of the b. Efflux transport c. Presystemic extraction (first-pass metabolism) -Hepatic - Enteric (CYP3A) C. and the pharmacopolitics of generic substitution30,31 1. Competing political and economic influences 2. Fundamental premise: Bioequivalence implies therapeutic equivalence (not the reverse)

3. Methods of determining bioequivalence: statistical “equivalence” of Cmax,Tmax,andAUC Greenblatt and Abourjaily 1187

Ta bl e 2 . Continued

4. Areas of uncertainty a. Patients versus volunteers b. Limits of statistical tolerance c. Interpretation of anecdotes d. Voluntary versus forced generic substitution e. Sustained-release preparations 5. Special considerations for biologic therapies (biosimilars)32,33 Section 10. Multiple-dose kinetics: discrete doses (Figure 13) A. There is not a unique steady-state concentration, only a mean: AUCoverdoseintervel C = ss length of dose intervel B. Rate of attainment of steady-state: identical to section 8A C. Extent of accumulation: if each dose (D) is 100% available and given at fixed intervals (T), D/T C = ss Clearance D. Interdose fluctuation (Figure 14) 1. Estimating the degree of fluctuation

Cmax = maximum plasma concentration over the dosage interval Cmin = Minimum plasma concentration over the dosage interval Cmax/Cmin ratio is interdose fluctuation 2. Css stays the same as long as D/T is unchanged, but changing both D and T influences interdose fluctuation (Figure 15) 3. Clinical benefits of “slow-release” preparations

1 E. Termination of multiple dosage: the same value of k (and t/2 ) is applicable F. L o a d i n g d o s e s ( D L) 1. Determinants of when needed; benefits and disadvantages 2. Approximate calculations:

Given a desired Css and assuming Vd is known, DL should cause C0 for a single dose (see section 7A) to equal the target Css during continuous infusion (see section 8B) or Css during multiple discrete doses (see section 10C). 3. Complications with 2-compartment model: overshoot and undershoot G. Relative drug accumulation: depends on the interval between doses relative to the elimination half-life Section 11. Nonlinear (zero-order) kinetics10,35,37 (Figure 16) A. Linear (first-order) kinetics (as in section 5A): dC =−kC dt -kt Solution: C = Coe B. Nonlinear (zero-order) kinetics dC =−k dt

Solution: C = Co − kt C. For most affected drugs, first-order kinetic profile transitions to zero order as the concentration increases (Figure 17) D. Implications of transition to zero-order kinetics Section 12. Drug interactions involving altered drug clearance2,3,36–43 A. Epidemiology of drug interactions B. Mechanisms of inhibition versus induction C. Quantitative outcome of drug interactions (Figure 18) D. Clinical consequences of drug interactions: depends on the quantitative magnitude of the and the of the affected drug. Statistical significance does not imply clinical importance. E. prediction of clinical drug interactions: relation of inhibitor “exposure” to inhibitory “” Section 13. Drug therapy in vulnerable populations: the elderly44–48 A. Epidemiology of aging B. Mechanisms of altered drug response in the elderly 1. Kinetic 2. Dynamic C. Consequences of impaired clearance in the elderly. Section 14. Other vulnerable or special populations A. Renal insufficiency B. Hepatic insufficiency C. Obesity D. Children E. Pregnancy 1188 The Journal of Clinical Pharmacology / Vol 56 No 10 2016

Ta bl e 2 . Continued

Section 15. Pharmacodynamics3,51–53 A. Definition: time course of drug effect B. Approaches to measuring drug effect 1. Fully objective (blood pressure, QT interval, serum cholesterol, etc.) 2. Partially objective (memory tests, reaction times, pain threshold, etc.) 3. Subjective (psychiatric endpoints) C. Surrogate measures of drug effect (glycated hemoglobin, T-cell count, bone mineral density, intraocular pressure, etc.) D. Problems with pharmacodynamic measures 1. Effects of practice, adaptation, and time 2. Acute and chronic tolerance 3. Fatigue 4. Weak connection to clinical endpoints E. Kinetic-dynamic modeling49–54 (Figure 19)

1. Link between concentration and effect (linear, exponential, or sigmoid-Emax) 2. Sources of bias 3. Modification by effect-site entry delay 4. Interpretation of outcome

Ta bl e 3 . Medical and Scientific Journals Having a Focus on Clinical Pharmacokinetics, , and Drug Interactions

Biopharmaceutics and Drug Disposition British Journal of Clinical Pharmacology Clinical Pharmacokinetics Clinical Pharmacology and Therapeutics Clinical Pharmacology in Drug Metabolism and Disposition European Journal of Clinical Pharmacology International Journal of Clinical Pharmacology Journal of Clinical Pharmacology Journal of Clinical Journal of Pharmaceutical Sciences Journal of Pharmacology and Experimental Therapeutics Therapeutic Drug Monitoring Xenobiotica

Figure 4. Schematic relation between drug concentrations (green triangles) in circulating blood, concentrations in (ECF) surrounding the receptor site, the extent of occupancy of cellular receptor sites, and subsequent pharmacologic action. If receptor occupancy proportionally reflects blood and ECF concentrations, then blood concentration may serve as a surrogate measure of drug effect. Greenblatt and Abourjaily 1189

Figure 5. Plasma concentrations versus time after dosage of a drug given by rapid intravenous injection, assuming an underlying 1-compartment pharmacokinetic model. Each time an interval equal to the half-life elapses, the concentration falls to 50% of the value at the start of the interval. Left: linear concentration scale; right: logarithmic concentration scale. The same declining exponential function is applicable to both graphs (see Table 2, section 5A–E and section 7A1–3), but the logarithmic scale transforms the exponential curve into a straight line, which can be used for graphical calculations. Note that a logarithmic concentration scale never goes to zero.

Figure 6. Plasma concentrations of the same dose of the same drug given to different individuals. The area under the plasma concentration curve (AUC) is shown as the shaded region. Since clearance can be calculated as administered dose divided by AUC, the subject in the left graph has lower clearance (higher AUC) than the subject in the right graph (proviso: in the calculation of clearance, the “dose” represents the systemically-available dose, and “AUC” represents the total area under the curve from time zero to “infinity”). 1190 The Journal of Clinical Pharmacology / Vol 56 No 10 2016

Figure 7. Left: Plasma concentrations of a drug, consistent with a 2-compartment model, after a single intravenous dose. Right: Corresponding drug behavior in the 2-compartment model schematic. Point I: Immediately after the dose, the entire dose is confined to the central compartment, and the plasma concentration is maximal (C0 = 60). Point II: During the initial distribution phase (the “alpha” phase), plasma concentrations fall rapidly and extensively,due mainly to drug distribution from central to peripheral compartments.Clearance (irreversible elimination) contributes minimally to this initial decline. If the concentration falls below the minimal effective concentration (MEC) during the distribution phase, the distribution process may limit the duration of clinical action.Point III:This is the point termed distribution equilibrium.The distribution process is complete,and the ratio of central to peripheral compartment concentrations from this time forward will remain approximately constant. Point IV: The decline in plasma concentrations during the elimination phase (the “beta” phase) is relatively slow, and is due mainly to clearance (irreversible elimination). (see Table 2, section 7B)

Figure 8. A continuous zero-order (fixed-rate) intravenous infusion of a drug obeying 1-compartment kinetics is started at time zero without Figure 9. Relation between zero-order infusion rate (Q, X axis) and a loading dose. The concentration rises in exponential fashion until the steady-state plasma concentration (Css, Y axis) for a drug having linear steady-state condition is reached (dashed lines). The actual steady-state (first-order) kinetic properties, as shown in Figuress 8.C has a direct linear relation to Q (see Table 2, sections 5F and 8B). The slope of the concentration (Css) at an infusion rate of Q is 3 units. If the infusion line is 1/clearance. rate were 2 × Q, Css would be 6 units. However the rate of attainment of steady state is the same in both cases, being dependent only on the half-life (from reference 2, with permission). Greenblatt and Abourjaily 1191

Figure 10. Left: A drug is given by continuous zero-order intravenous infusion (fixed rate of Q) starting at time zero. The plasma concentration ascends to Css (4 units) in exponential fashion, with attainment of steady state more than 90% complete after 4 × t1/2. This is similar to Figure 8. Right: After steady state is reached, the infusion rate is changed (arrow), and the time scale “resets” to zero. The rate is either increased to 2 × Q, decreased to 0.5 × Q, or stopped altogether.The new Css correspondingly changes to 8 units, 2 units, or 0, respectively. However,another 4 or more multiples of t1/2 are needed for the new steady state to be reached.

Figure 11. Plasma concentrations of a drug after oral dosage at Figure 12. Mean plasma concentrations of after single 29 time zero. After a lag time (Tlag), plasma concentrations begin to rise. intravenous and oral doses administered to healthy volunteers (*con- During this “absorption” phase, rates of drug entry into blood due to centrations were normalized to a 2-mg dose). Based on the relationship absorption exceed rates of elimination due to clearance. The maximum in section 9B1, in Table 2, the absolute bioavailability of oral midazolam concentration (Cmax = 7 units) is reached at time Tmax (1 hour after (F) was calculated as 0.29,indicating that only 29% of an oral dose actually dosage); at this point, instantaneous absorption and elimination rates are reaches the systemic circulation (from reference 2, with permission). equal. Concentrations then fall, indicating that elimination rates exceed absorption rates.The area under the plasma concentration curve (AUC) is used as a surrogate for the extent of absorption (from reference 2,with permission). 1192 The Journal of Clinical Pharmacology / Vol 56 No 10 2016

Figure 13. A drug is administered as discrete oral doses at intervals equal to the half-life. Six consecutive doses were given, after which the drug was discontinued. The dashed line is the hypothetical curve if the same dosing rate were administered by continuous zero-order intravenous infusion. Note that the rate of attainment of steady state is the same in both cases.

Figure 15. Serum concentrations of a drug at steady state if the drug Figure 14. A dosage interval at steady state. The elimination half-life is given using 3 different dosing schedules: either 500 mg every 24 hours, is assumed to be 24 hours, and the dosage interval is also 24 hours 250 mg every 12 hours, or 125 mg every 6 hours. In each case the mean (as in Figure 13). The plasma concentration starts at Cmin,increasesto steady-state concentration (Css) is the same, since the [(dose)/(dose Cmax, then falls again to Cmin. The mean steady-state concentration (Css, interval)] ratio does not change. However, the interdose fluctuation dashed line) is the area under the curve for 1 dose interval divided by becomes smaller as the dose interval becomes smaller. With the once- the length of the interval. The interdose fluctuation is calculated as the daily dosing schedule, the interdose fluctuation is large, and the plasma Cmax/Cmin ratio. (see Table 2, section 10A–D). concentration falls outside the therapeutic range just after and just before each dose (in part from reference 16, with permission). Greenblatt and Abourjaily 1193

Figure 16. Plasma concentrations (1-compartment model) of one drug Figure 17. Schematic relation of daily phenytoin dosage (X axis) to with first-order elimination (solid line), and another drug with zero- phenytoin steady-state plasma concentrations (Y axis). In the lower order elimination (dashed line). Note that the concentration axis is dosage range, the relation is linear, and Css increases in propor- linear. tion to dosage. As the daily dosage increases to higher ranges, the kinetic pattern transitions toward zero-order, and Css increases dispro- portionately with dosage (dashed line). At doses above 350 mg per day, Css falls above the therapeutic range of 10–20 μg/mL) (horizontal dotted lines).

Figure 18. Pharmacokinetic consequences of a drug–drug interaction that either decreases clearance or increases clearance of the substrate drug (inhibition or induction, respectively). Left: After single doses of the substrate (victim) drug, area under the plasma concentration curve (AUC) is increased by inhibition of clearance, or decreased by induction of clearance. Right: The substrate drug is given as a continuous regimen such that steady state is reached (interdose fluctuation not shown). At the arrow, an inhibiting or inducing drug is coadministered, causing a new steady statetobe reached. Note that the of the inducer is slower than that of the inhibitor. 1194 The Journal of Clinical Pharmacology / Vol 56 No 10 2016

SERUM VELOCITY REDUCTION 350 20 20

300 16 16

250

12 12 200

150 8 8

100

4 4

SERUM PROPRANOLOL (ng/mL) 50 POSTERIOR WALL VELOCITY REDUCTION (change over baseline, cm/sec) 0 0 0 0 1 2 3 4 5 6 0 50 100 150 200 250 300 350 HOURS SERUM PROPRANOLOL (ng/mL) Figure 19. Example of a kinetic-dynamic study. A single 80-mg oral dose of propranolol was administered to a series of healthy volunteers.54 Serum propranolol concentrations were measured at multiple points after the dose, and posterior ventricular wall velocity was determined by echocardiography as a measure of pharmacodynamic effect — higher numbers indicate greater decrements in wall velocity, consistent with reduced velocity of cardiac contraction.Left:Time-course of the 2 measures plotted on the same graph.Points represent the mean values at corresponding times. After the serum Cmax is reached, the contractility measure returns close to zero in advance of the serum concentration. This might be explained by acute tolerance. Right: A kinetic-dynamic plot, in which pharmacodynamic effect is shown in relation to serum concentration at corresponding times. Arrows indicate the direction of increasing time. The pattern is termed “clockwise hysteresis,” and can be observed as a consequence of acute tolerance.

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