Download Pharmacokinetics and Pharmacodynamics for Medical Students: A

Core Entrustables in Clinical Pharmacology: Pearls for Clinical Practice
Pharmacokinetics and Pharmacodynamics
for Medical Students: A Proposed
Course Outline
The Journal of Clinical Pharmacology
2016, 56(10) 1180–1195
C 2016, The American College of
Clinical Pharmacology
DOI: 10.1002/jcph.732
David J. Greenblatt, MD,1 and Paul N. Abourjaily, PharmD2
Keywords
pharmacokinetics, pharmacodynamics, drug interactions, medical
The discipline of pharmacokinetics (PK) applies mathematical models to describe and predict the time
course of drug concentrations and drug amounts in
body fluids.1–3 Pharmacodynamics (PD) applies similar models to understand the time course of drug
actions on the body. Clinicians are most concerned with
pharmacodynamics—they want to know how drug
dosage, route of administration, and frequency of administration can be chosen to maximize the probability
of therapeutic success while minimizing the likelihood
of unwanted drug effects. However the path to pharmacodynamics comes via pharmacokinetics. Because drug
effects are related to drug concentrations, understanding and predicting the time course of concentrations
can be used to help optimize therapy.
The link of drug dosage to drug effect involves
a sequence of events (Figure 1). Even when a drug
is administered directly into the vascular system, the
drug diffuses to both its pharmacologic target receptor
and to other peripheral distribution sites where it does
not have the desired activity but may exert toxic effects. Simultaneously, the drug undergoes clearance by
metabolism and excretion. After oral administration,
the situation is more complex, since the drug must
undergo dissolution and absorption, then survive firstpass metabolism in the liver, before reaching the systemic circulation. Pharmacokinetics provides a rational mathematical framework for understanding these
concurrent processes, and facilitates achieving optimal
clinical pharmacodynamic effects more efficiently than
trial and error alone.
The following 3 clinical vignettes illustrate how
familiarity with principles of pharmacokinetics and
pharmacodynamics can facilitate optimal understanding and prediction of drug effects in human subjects
and patients.
Clinical Vignettes
Case 1
A 30-year-old man has been extensively evaluated for
recurrent supraventricular tachycardia (SVT), which is
associated with palpitations and dizziness. No identifiable cardiac disease is evident, and other medical
diseases have been excluded.
The treating physician elects to start therapy with
digitoxin, 0.1 mg daily. One week later the patient is seen
again, and states that episodes of SVT are reduced in
number. The plasma digitoxin level is 8 ng/mL (usual
therapeutic range, 10–20 ng/mL). The dose is increased
to 0.2 mg/day. At a follow-up visit 7 days later, the
patient claims that symptoms attributable to SVT have
disappeared completely. The plasma digitoxin level is
17.4 ng/mL. The patient continues on 0.2 mg/day of
digitoxin.
One month later the patient sees the physician on
an urgent basis. He has diminished appetite and waves
1 Program
in Pharmacology and Experimental Therapeutics, Sackler
School of Graduate Biomedical Sciences, Tufts University School of
Medicine, Boston, MA, USA
2 Departments of Pharmacy and Medicine, Tufts Medical Center, Boston,
MA, USA
Submitted for publication 26 February 2016; accepted 3 March 2016.
Corresponding Author:
David J. Greenblatt, MD, Tufts University School of Medicine, 136
Harrison Avenue, Boston, MA 02111
Email: [email protected]
This proposal was prepared under the guidance of the Special Committee for Medical School Curriculum of the American College of
Clinical Pharmacology. The proposal is intended as a resource for
the Association of American Medical Colleges as it revises its Core
Entrustable Professional Activities for Entering Residency, Curriculum
Developer’s Guide.
Greenblatt and Abourjaily
Figure 1. Sequence of events between intravenous or oral administration 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
drug does to the body” (from reference 2, with permission).
of nausea. The electrocardiogram shows T-wave abnormalities, and the plasma digitoxin level is 31.3 ng/mL.
Discussion—Case 1
Digitoxin is seldom used in contemporary therapeutics,
but case 1 nonetheless illustrates 2 important principles:
dose proportionality, and attainment of steady-state.
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
digitoxin, the half-life is about 7 days, implying that 3–4
weeks of continuous treatment (without a loading dose)
is necessary for steady-state to be reached.4 In the example given, the increase in dosage from 0.1 to 0.2 mg/day
is anticipated to proportionally increase the steadystate concentration (Figure 2). At the daily dosage of
0.1 mg (without a loading dose) and a half-life of 7
days, the plasma digitoxin concentration of 8 ng/mL
after 7 days of treatment represents 50% of the eventual
steady-state concentration of 16 ng/mL. If the physician had stayed with the 0.1 mg/day dosage, that steadystate concentration—attained after several weeks of
treatment (4 to 5 times the half-life)—would have been
in the therapeutic range. However the dosage was increased to 0.2 mg/day, yielding a corresponding steadystate concentration of 32 ng/mL, exceeding the therapeutic range and producing adverse effects (Figure 2).
Case 2
A 56-year-old man has a history of grand mal seizures,
which have been completely suppressed for the last 12
years by phenytoin, 300 mg daily. His plasma phenytoin
level consistently falls in the range of 12–16 μg/mL. The
patient is able to lead a normal life, and is an excellent
tennis player. During a particularly competitive tennis
match, the patient injures his shoulder. That night he
experiences severe pain, tenderness, and limitation of
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Figure 2. Hypothetical mean plasma concentrations of digitoxin, corresponding 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 concentration
is 8 ng/mL (point a). The treating physician wants to increase the
plasma concentration to a value within the usual therapeutic range
(10–20 ng/mL). If the physician stayed with the 0.1-mg-per-day dosage,
the eventual steady-state concentration would have been 16 ng/mL
(dashed line)—within the desired therapeutic range. Instead, the dosage
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
it has reached 31.3 ng/mL (point c), close to the eventual steady-state
value of 32 ng/mL. This is well above the therapeutic range and may be
associated with toxicity.
motion. He contacts his physician. An x-ray is negative.
The physician prescribes rest, topical heat, and aspirin,
650 mg 4 times daily.
At a return visit to the physician 2 days later, the
patient is greatly improved. The physician uses that
opportunity to do a routine check of the plasma
phenytoin level, which is reported as 5 μg/mL. There
is no evidence of recurrent seizure activity, and the
patient insists that he is continuing to take phenytoin
as directed (300 mg/day). The physician increases the
dose to 500 mg/day.
One week later the patient returns complaining of
difficulty with balance and with fixing his eyes on
objects. The plasma phenytoin level is 14 μg/mL.
Discussion—Case 2
In case 2, plasma protein binding of phenytoin is
reduced by coadministration of aspirin because of
displacement of phenytoin from plasma-binding sites
by salicylate.5–7 This is evident as an increase in the free
fraction (Table 1). However, the clearance of unbound
(free) drug, and the steady-state concentration of
unbound drug, are unchanged.8,9 As such, no change
in clinical effect would be anticipated, and the correct
clinical course would have been to leave the daily dosage
at 300 mg/day. Because salicylate reduces plasma
protein binding of phenytoin (higher free fraction in
plasma), this has the effect of reducing total (free +
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Table 1. Total and Free (Unbound) Plasma Phenytoin Concentrations
in Case 2
Phenytoin Daily
Dosage, and
Cotreatment
300 mg/day (no
cotreatment)
300 mg/day +
aspirin
500 mg/day +
aspirin
Total Phenytoin
(μg/mL)
Fraction Free
Free Phenytoin
(μg/mL)
12–16
0.1
1.2–1.6
5
0.3
1.5
14
0.3
4.2
bound) concentrations of phenytoin as well as the interpretation of these measured total concentrations.5–7
Increasing the daily dosage of phenytoin to 500
mg/day increases the free (unbound) concentration to
4.2 μg/mL, which is associated with adverse effects
despite the total concentration of 14 μg/mL.
A second important point is the nonlinear kinetic
profile of phenytoin.10 At daily doses in a range
exceeding 300 mg/day, steady-state plasma concentrations increase disproportionately with an increase in
dosage. The free phenytoin concentration is 1.5 μg/mL
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
higher dosage range.
Case 3
A fourth-year dental student is doing a clerkship in a
dental surgeon’s practice. A healthy 34-year-old woman
is scheduled to undergo procedures estimated to last
approximately 2 hours. Following instillation of local
anesthesia and prior to the start of the procedure,
the surgeon notices that the patient still is extremely
agitated and fearful. The surgeon administers 0.5 mg/kg
of propofol intravenously over a 2-minute period. The
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
about 45 minutes. At this time, the patient becomes
alert, and again is fearful and agitated. The surgeon administers another 0.5 mg/kg of propofol intravenously,
the patient again becomes calm, and the surgical procedure proceeds to completion without incident.
The student is confused. He/she asks the surgeon,
“Why did the patient wake up after only 45 minutes?
The half-life of propofol usually is at least 8 hours.”
Discussion—Case 3
Case 3 is an example of how the pharmacodynamic
effects of lipophilic psychotropic drugs after single
intravenous doses are dependent more on the rapid
process of peripheral distribution than on clearance
Figure 3. Hypothetical plasma concentrations of propofol corresponding to case 3 in the text. A 0.5 mg/kg intravenous dose of propofol is
initially given at time zero. The plasma propofol concentration declines
rapidly, falling below the hypothetical minimum effective concentration
(MEC) of 200 ng/mL at 0.75 hours, at which time the patient emerges
from the sedated condition. The rate of drug disappearance in the
postdistributive phase would be slower (dashed line), but an additional
0.5 mg/kg dose of propofol is required at the 0.75-hour time to maintain
plasma concentrations above the MEC and maintain the patient in a
sedated condition for the remainder of the procedure.
or elimination. The pharmacokinetics of propofol are
described by a 2- or 3-compartment model, in which
the initial “distribution” phase represents rapid distribution from systemic circulation to peripheral tissues,
followed by the terminal “elimination” phase which
mainly reflects clearance.11–14 Although the propofol
has not been eliminated from the body, its distribution
from systemic circulation into peripheral tissue results
in lower concentrations in plasma and brain, which is
highly vascular and rapidly equilibrates with systemic
circulation (Figure 3). As such, the patient becomes
more alert, and a second dose is required.
Components of Medical
Education in Pharmacokinetics
and Pharmacodynamics
An outline of key elements of content for the teaching
of clinical pharmacokinetics and pharmacodynamics
to first- or second-year medical students, along with
pertinent literature references,15–54 are presented in
Table 2. The same or similar content can be applied to
the teaching of graduate students at both the PhD and
masters levels, or to postdoctoral education programs
for house staff or practicing physicians. The material
can be reasonably presented in 3 or 4 total lecture
contact hours. The didactic presentations should be
reinforced through problem sets and review sessions
Greenblatt and Abourjaily
aimed at supporting conceptual understanding, as well
as ensuring proficiency with pharmacokinetic calculations and construction of graphics.
Individual instructors can adapt the outline and
accompanying graphics as needed, to construct specific
lecture content consistent with their own style and
institutional needs. An ongoing point of discussion is
the extent to which formulas, equations, and mathematics are needed for the teaching of pharmacokinetics.
Student backgrounds in mathematics and their comfort
with quantitative content vary widely. Some dislike
and resist the mathematical content, whereas others
welcome it. “Equation-free” pharmacokinetics is not
realistic, but the density of equations can be managed
such that the mathematical framework enhances con-
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ceptual understanding. The outline in Table 2 has that
objective. The need for memorization of formulas and
equations is minimal.
Table 3 lists biomedical journals that have a focus
on clinical pharmacokinetics and pharmacodynamics.
Students are encouraged to consult original research
sources when seeking information on pharmacokinetic/pharmacodynamic properties or drug interactions
involving specific drugs or drug classes. Review articles
and secondary sources do have a role in the educational
process, in that large amounts of data are collated and
summarized. However, secondary sources are inevitably
“filtered” and interpreted by their authors. Students
need to consider the benefits and drawbacks of available
information sources.
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Table 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 maintenance dose
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 volume of distribution derived from definition of concentration:
Concentration =
Amount
Volume
Volume of distribution Vd =
Amount of drug in body
Concentration in reference compartment
C. The value and ambiguity of compartment models (hydraulic analogues)
1. One-compartment model: Vd is unique
2. Two-compartment model: Vd is not unique23
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
0.693
In 2
=
k
k
C. k and t1/2 are independent of route of administration
D. Logarithmic versus linear graphs (Figure 5)
E. Interpretation and implications of half-life
t1/2 =
Time elapsed (multiples of t1/2 )
Fractional completion of process
1
2
3
4
0.5
0.75
0.875
>0.90
F. Implications of first-order behavior
–t1/2, 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
Table 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 blood 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 enzymes)
D. Biologic dependence of t1/2 on both Vd and clearance
0.693 x Vd
clearance
E. The meaning of “linear” or “dose proportional” kinetics (see also section 5F)
t1/2 =
Section 7. Rapid single-dose intravenous injection
A. One-compartment model
1.
dC
= −kC
dt
Boundary condition: at t = 0, C= C0
C = C0 e-kt satisfies differential equation and boundary condition
C0
k
2. If dose = D, then
Total AUC =
Vd =
Dose
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)
t1/2 = 0.693
k
4. Clearance =
Dose
k . Dose
= k . Vd =
AUC
C0
5. Correct biologic relation among t1/2 , Vd , and clearance:
0.693 x V d
C l ear ance
6. Graphical approach to problem solving
t1/2 =
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
Total AUC =
B
A
+
α
β
2. Volumes of distribution20–22
a. “Central” compartment
V1 =
Dose
Dose
=
C0
A+B
b. “Total” volume of distribution
Vd =
Dose
Clearance
=
β × AUC
β
3. Half-lives
a. Distribution half-life (cannot be derived from graph)
0.693
α
b. Elimination half-life (can be derived from graph)
t1 /2 α =
t1 /2 β =
0.693
β
4. Clearance = dose/AUC = Vd · β
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Table 2. Continued
C. One-compartment approximation of the 2-compartment model
Fundamental assumption:
A and α (and the corresponding component of AUC) are ignored
Consequences:
B becomes C0
β becomes k
t1/2 β becomes t1/2
Quantity
2-Compartment
1-Compartment
Equation for concentration versus time
C = Ae-αt + Be-βt
Total AUC
B
A
+
α
β
Total V d
Dose
β . AUC
C = C0 e−kt
(B analogous to C0 ,
β analogous to k)
C0
B
analogous to
k
β
Dose
Dose
analogous to
C0
B
Dose
= Vd . β
AUC
In 2
β
Dose
= Vd . k
AUC
In 2
k
Clearance
Elimination half-life dose
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:
Depends almost entirely on t1/2 (and k) as would occur with a single dose.
Does not depend on infusion rate (abbreviation: Q).
Inverted exponential function:
C = Css (1 − e-kt ). 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
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
Css =
Section 9. Drug absorption and bioavailability (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 dosage form
b. Efflux transport
c. Presystemic extraction (first-pass metabolism)
- Hepatic
- Enteric (CYP3A)
C. Bioequivalence 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 , and AUC
Greenblatt and Abourjaily
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Table 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:
Css =
AUC over dose intervel
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
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
E. Termination of multiple dosage: the same value of k (and t1/2 ) is applicable
F. Loading doses (DL )
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
Css =
Section 11. Nonlinear (zero-order) kinetics10,35,37 (Figure 16)
A. Linear (first-order) kinetics (as in section 5A):
dC
= −kC
dt
Solution: C = Co e-kt
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 drug interaction and the therapeutic index of the affected drug.
Statistical significance does not imply clinical importance.
E. In vitro prediction of clinical drug interactions: relation of inhibitor “exposure” to inhibitory “potency”
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
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Table 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
Table 3. Medical and Scientific Journals Having a Focus on Clinical
Pharmacokinetics, Drug Metabolism, and Drug Interactions
Biopharmaceutics and Drug Disposition
British Journal of Clinical Pharmacology
Clinical Pharmacokinetics
Clinical Pharmacology and Therapeutics
Clinical Pharmacology in Drug Development
Drug Metabolism and Disposition
European Journal of Clinical Pharmacology
International Journal of Clinical Pharmacology
Journal of Clinical Pharmacology
Journal of Clinical Psychopharmacology
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 extracellular fluid
(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”).
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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
a loading dose. The concentration rises in exponential fashion until the
steady-state condition is reached (dashed lines). The actual steady-state
concentration (Css ) at an infusion rate of Q is 3 units. If the infusion
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).
Figure 9. Relation between zero-order infusion rate (Q, X axis) and
steady-state plasma concentration (Css , Y axis) for a drug having linear
(first-order) kinetic properties, as shown in Figure 8. Css has a direct
linear relation to Q (see Table 2, sections 5F and 8B). The slope of the
line is 1/clearance.
Greenblatt and Abourjaily
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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
time zero. After a lag time (Tlag ), plasma concentrations begin to rise.
During this “absorption” phase, rates of drug entry into blood due to
absorption exceed rates of elimination due to clearance. The maximum
concentration (Cmax = 7 units) is reached at time Tmax (1 hour after
dosage); at this point, instantaneous absorption and elimination rates are
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).
Figure 12. Mean plasma concentrations of midazolam after single
intravenous and oral doses administered to healthy volunteers29 (*concentrations were normalized to a 2-mg dose). Based on the relationship
in section 9B1, in Table 2, the absolute bioavailability of oral midazolam
(F) was calculated as 0.29,indicating that only 29% of an oral dose actually
reaches the systemic circulation (from reference 2, with permission).
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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 14. A dosage interval at steady state. The elimination half-life
is assumed to be 24 hours, and the dosage interval is also 24 hours
(as in Figure 13). The plasma concentration starts at Cmin , increases to
Cmax , then falls again to Cmin . The mean steady-state concentration (Css,
dashed line) is the area under the curve for 1 dose interval divided by
the length of the interval. The interdose fluctuation is calculated as the
Cmax /Cmin ratio. (see Table 2, section 10A–D).
Figure 15. Serum concentrations of a drug at steady state if the drug
is given using 3 different dosing schedules: either 500 mg every 24 hours,
250 mg every 12 hours, or 125 mg every 6 hours. In each case the mean
steady-state concentration (Css) is the same, since the [(dose)/(dose
interval)] ratio does not change. However, the interdose fluctuation
becomes smaller as the dose interval becomes smaller. With the oncedaily dosing schedule, the interdose fluctuation is large, and the plasma
concentration falls outside the therapeutic range just after and just
before each dose (in part from reference 16, with permission).
Greenblatt and Abourjaily
Figure 16. Plasma concentrations (1-compartment model) of one drug
with first-order elimination (solid line), and another drug with zeroorder elimination (dashed line). Note that the concentration axis is
linear.
1193
Figure 17. Schematic relation of daily phenytoin dosage (X axis) to
phenytoin steady-state plasma concentrations (Y axis). In the lower
dosage range, the relation is linear, and Css increases in proportion to dosage. As the daily dosage increases to higher ranges, the
kinetic pattern transitions toward zero-order, and Css increases disproportionately 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 state to be
reached. Note that the onset of action of the inducer is slower than that of the inhibitor.
1194
SERUM PROPRANOLOL
VELOCITY REDUCTION
SERUM PROPRANOLOL (ng/mL)
350
20
300
16
250
12
200
150
8
100
4
50
0
0
0
1
2
3
4
5
6
HOURS
POSTERIOR WALL VELOCITY REDUCTION
(change over baseline, cm/sec)
The Journal of Clinical Pharmacology / Vol 56 No 10 2016
20
16
12
8
4
0
0
50
100
150
200
250
300
350
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.
Acknowledgments
We are grateful for the collaboration and assistance of Mr.
Jerold S. Harmatz, Ms. Yanli Zhao, Ms. Smaro Panagiotidou,
and Dr. Tianmeng Chen. The authors thank the American
College of Clinical Pharmacology for the opportunity to
participate in this project.
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