Log in

PRINCIPLES OF PHARMACOKINETICS 1

HST-151 1 
PRINCIPLES OF PHARMACOKINETICS 
Learning Objectives: 
1. Describe the physicochemical and physiological factors that influence the 
absorption of drugs from enteral and parenteral routes of administration, their 
distribution within the body, and their routes and mechanisms of elimination. 
2. Explain how dose, bioavailability, rate of absorption, apparent volume of 
distribution, total clearance, and elimination half-life affect the plasma 
concentrations of a drug after administration of a single dose. 
3. Describe the factors which determine the time-course of systemic accumulation of 
a drug administered by infusion or multiple doses. 
I. Absorption of Drugs 
A. Transport Across Cell Membranes 
1. Passive diffusion 
a. Passage through lipid cell membrane by dissolution in membrane; rate 
dependent on concentration gradient and lipid:water partition coefficient of drug; 
rate markedly higher for unionized form of weak electrolyte because of its higher 
lipophilicity than the ionized form; obeys first-order kinetics (rate of transport is 
proportional to concentration gradient at transport site). 
b. Filtration through aqueous channels within membranes and between cells. 
2. Active transport 
a. Passage facilitated by an energy-dependent membrane carrier mechanism 
such that transport can occur against a concentration gradient; transporters 
include the family of ATP-dependent proteins, such as 
• the multidrug resistance p-glycoprotein (amphipathic cationic and 
neutral substrates, 170 kD, mdr gene product, verapamil sensitive) 
• the multidrug resistance-associated proteins (MRP1-6, organic anion 
substrates, 190 kD, probenecid sensitive). 
b. Exhibits structural selectivity, saturability, competition between structural 
analogues and genetic variants. 
Harvard-MIT Division of Health Sciences and Technology 
HST.151: Principles of Pharmocology 
Instructor: Prof. Carol WalshHST-151 2 
c. Sites for drugs in intestinal mucosa (cell to lumen), capillary endothelium 
of brain and testis (cell to blood), choroid plexus (CSF to blood), proximal renal 
tubular cell (blood to urine), hepatocyte (blood to bile), tumor cells (efflux pump). 
d. Obeys Michaelis-Menten kinetics: if drug concentration is high enough to 
saturate carrier mechanism, kinetics are zero-order (rate of transport is constant). 
3. Endocytosis 
a. Passage into cell within membrane invagination. 
b. Important mechanism for particulates and high molecule weight 
compounds, such as proteins. 
B. Routes of Drug Administration 
1. General determinants of absorption rate 
a. Dissolution into aqueous fluids at absorption site, lipid solubility, 
concentration gradient, blood flow at absorption site, surface area of absorption 
site. 
b. Importance of rate-limiting process 
2. Oral (p.o.) Ingestion 
a. Convenient route for administration of solid as well as liquid formulations. 
b. Additional variables which may influence rate and extent of absorption 
include disintegration and dissolution of solids, acidity of gastric contents, gastric 
emptying rate, intraluminal and mucosal biotransformation by host or bacterial 
enzymes, dietary contents, and presence of other drugs. 
c. First-pass effect: absorbed drug passes via portal circulation through liver 
which may clear substantial fraction and thus decrease bioavailability (percent of 
dose which reaches the systemic circulation). 
3. Parenteral Injection 
a. Subcutaneous (s.c.) and intramuscular (i.m.) administration: more 
extensive absorption of high molecular weight, polar molecules than by oral 
route, via lymphatic circulation; absorption rate can be manipulated by 
formulation, e.g. rapid from aqueous solution, slow from suspension or solid 
pellet. HST-151 3 
b. Intravenous (i.v.) injection: complete bioavailability; drugs only given in 
sterile solution; important when immediate effect required; increased risk of 
toxicity. 
4. Pulmonary Inhalation 
a. Rapid absorption of drugs in gaseous, vaporized or aerosol form. 
b. Absorption of particulates/aerosols depends on particle/droplet size which 
influences depth of entry in pulmonary tree; 1-5 uM particles reach alveolus 
5. Topical Application 
a. Usually for local effect; patch formulations for systemic effect 
b. Absorption through mucous membrane may be rapid 
c. Absorption through skin generally slow; enhanced by increased 
lipophilicity, by damage to stratum corneum, and by increased blood flow. HST-151 4 
II. Distribution of Drugs 
A. Tissue differences in rates of uptake of drugs. 
1. Blood flow: distribution occurs most rapidly into tissues with high blood 
flow (lungs, kidneys, liver, brain) and least rapidly in tissues with low flow (fat). 
2. Capillary permeability: permeability of capillaries is tissue dependent; 
distribution rates relatively slower into CNS because of tight junction between 
capillary endothelial cells, insignificant aqueous membrane pores, juxtaposed 
glial cells around endothelium and efflux transporters in vascular endothelium 
("blood-brain barrier"); capillaries of liver and kidney more porous. 
B. Differences in tissue/blood ratios at equilibrium 
1. Dissolution of lipid-soluble drugs in adipose tissue 
2. Binding of drugs to intracellular sites 
3. Plasma protein binding; many drugs reversibly bind to albumin, α1-acid 
glycoprotein or other proteins in plasma; extent of binding dependent on affinity, 
number of binding sites, and drug concentrations; drug bound to albumin is not 
filtered by renal glomerulus but may be cleared by proximal renal tubule and 
liver; binding reduces free drug available for distribution into tissue; many drug 
interactions based on displacement from binding sites. 
C. Apparent Volume of Distribution (Vd) 
1. Fluid compartments of 70-kg subject in liters and as percent of body weight: 
plasma 3 l (4%), extracellular water 12 l (17%), total body water 41 l (58%). 
2. Estimation of Vd from extrapolated plasma concentration at "zero-time" (Co) 
after intravenous administration: 
Dose Vd =
C0 
3. Prediction of Vd from chemical characteristics of drug, e.g. high lipid 
solubility, high Vd 
4. The plasma half-life of a drug (the time to reduce the concentration by onehalf) is directly proportional to Vd, and inversely proportional to total clearance 
(ClT); for a given ClT, the higher the Vd, the longer the t1/2: HST-151 5 
2
1 =
ln2(Vd
ClT 
III.Elimination of Drugs 
A. Total Clearance (ClT) 
1. Volume of plasma completely cleared of drug per unit time by all routes and 
mechanisms. 
2. Summation of clearance values for each route, generally: 
Cl T =Cl renal +Cl hepatic 
3. If intrinsic capacity of an organ to clear drug is high and exceeds plasma flow 
to that organ, then the clearance equals plasma flow and is altered by changes in 
plasma flow. 
4. The plasma half-life of a drug is inversely proportional to total clearance, and 
directly proportional to Vd; for a given Vd, the higher the total clearance, the 
shorter the half-life. 
B. Biotransformation 
1. Elimination of drug by chemical modification of the molecule by spontaneous 
or (more usually) enzymatically catalyzed reaction. Drug may be biotransformed 
by reactions at several sites on the molecule. 
2. Product(s) may have greater, lesser or qualitatively different pharmacologic 
activity from parent compound. A prodrug is inactive and is biotransformed to a 
therapeutic agent. Highly reactive products such as quinones or epoxides may 
cause tissue necrosis or DNA damage. 
3. Reaction rate dependent on chemical structure and obeys Michaelis-Menten 
kinetics (usually first-order at therapeutic drug concentrations). 
4. Enzymatic activity generally highest in liver; enzymes in target organ may be 
responsible for conversion of drug to therapeutic or toxic metabolite; enzymes in 
intestinal bacteria may facilitate enterohepatic circulation of drug conjugates 
excreted in bile. 
5. Sources of individual variation in rates of biotransformation: 
chemical exposures (drugs, dietary constituents and supplements, smoke); 
genetics; age; disease HST-151 6 
6. Major pathways of hepatic biotransformation 
a. Phase I: often first step in biotransformation with formation of product 
susceptible to phase II conjugative reaction 
b. Phase II: Coupling of drug or its oxidized metabolite to endogenous 
conjugating agent derived form carbohydrate, protein or sulfur sources; generally 
products more water-soluble and more readily excreted in urine or bile. 
C. Excretion 
1. Elimination of drug by excretion unchanged in body fluid or breath. 
2. Routes of excretion 
a. Urine: quantitatively most important excretory route for nonvolatile drugs 
and their metabolites; excretion rate depends on rate of glomerular filtration (drug 
not bound to plasma proteins), proximal tubular active secretion, and passive 
reabsorption 
1) Determination of renal clearance (ClR), the volume of plasma completely 
cleared of drug per unit time (ml/min). 
excretion rate in urine Cl R =
plasma concentrat ion 
Measure the amount of drug excreted in the urine during a time interval t1
 to t2
Find the plasma concentration of the drug at the midpoint of the time interval, (t1 
+ t2
)/2, by interpolating on the ln Cp vs. t plot. 
amount excreted from t
1 to t
2 
(t 2 −t
1
) 
Cl R =
Cp at (t1 +t
2
2) Mechanism of renal excretion can be inferred by comparison of ClR
 to that of 
an indicator of glomerular filtration (creatinine), i.e., greater than 120 ml/min in 
70-kg subject indicates tubular secretion and less than that indicates net 
reabsorption (if no plasma binding); maximum renal clearance = renal plasma 
flow (e.g. para-aminohippuric acid, 650 ml/min in 70-kg subject). 
3) Factors modifying ClR
: extent of plasma protein binding (displacement 
enhances glomerular filtration), urinary pH (reabsorption of drugs with ionizable HST-151 7 
group is dependent on urinary pH; raising the pH promotes excretion of acids, 
impairs excretion of bases), renal disease (creatinine clearance or its estimate 
from serum creatinine provides a useful clinical indicator of impaired renal 
function and is approximately proportional to drug renal clearance; the effect of 
renal impairment on the total clearance of a drug can be estimated from the ClCR 
and the nonrenal clearance). 
b. Bile: quantitatively important excretory route for drugs and their 
metabolites which are actively transported by hepatocyte; once in small intestine, 
compounds with sufficient lipophilicity are reabsorbed and cleared again by liver 
(enterohepatic circulation), more polar substances may be biotransformed by 
bacteria (e.g. hydrolysis of drug conjugates) and products reabsorbed; unabsorbed 
drugs and metabolites are excreted in feces. 
c. Minor routes: sweat, tears, reproductive fluids, milk; generally pHdependent passive diffusion of lipophilic drugs; can be of toxicologic significance 
e.g. exposure of infants to drugs in milk. H
Pl ncen on
(
HST-151 8 
IV. Time Course of Plasma Concentrations 
A. Relationship between plasma concentration and drug effect: minimum effective 
concentration, latency, duration of effect, time and magnitude of peak effect 
B. Time-course of plasma concentrations for a single dose 
1. Case with Highly Rapid Absorption Relative to Elimination 
a. Single compartment model 
1) First -order elimination: drug assumed to rapidly equilibrate into volume of 
distribution; plasma concentrations decline according to first-order kinetics; 
elimination rate from plasma is proportional to plasma concentration, fraction 
eliminated per unit time is elimination rate constant (kel). 
dC p k = − el Cp dt 
C = C e 
−kel t 
p 0 
Plasma Concentration asma Co trati
(µg/ml) 
Hoours urs
Figure 1 
Determination of elimination rate constant and elimination half-life: 
lnC p = lnC 0 −kel t 
Plot of ln Cp
 vs. t is a straight line with slope of -kel. Plasma half-life (t1/2 = 
.693/kel) is constant and independent of dose.  
HST-151 9 
Determination of apparent volume of distribution: 
Extrapolation to time zero of the line of best fit for ln Cp vs t data; antilog of 
drug concentration at time 0 designated as C0
. Then, 
Total Dose Vd (in mls or liters) =
C0 
To express Vd as per cent of body weight, assume that 1 liter is equivalent to 
1 kg; divide the Vd in liters by body weight, and then multiply by 100. 
Similarly, if relative dose administered is known (i.e., the dose per kg or other 
unit of body weight) but not the total dose, 
Relative Dose Vd =
C0 
Determination of total clearance: 
According to definitions above, total clearance is the mass of drug 
(Cp Vd) eliminated per unit time divided by the plasma concentration; 
therefore, 
 
Cl T =
(k el )(Cp • Vd ) 
= (k el )(Vd
) =
0.693 
2
(Vd )
Cp 
t 
Determination of nonrenal clearance (ClNR): 
If total clearance and renal clearance are determined from plasma and urine 
samples as described above, then clearance by nonrenal routes (which 
includes biotransformation) can be estimated from 
Cl NR =Cl T −Cl R 
2.) Kinetics of zero-order elimination: elimination rate is constant, t1/2 is 
dose-dependent (example: ethanol). 
3.) 
Cp =C0 −k 0
t Hour
Plasma Concentration
(
HST-151 10 
b. Multicompartment model 
Non-instantaneous distribution from blood to tissue resulting in 
multiexponential plasma concentration curve, initial phase reflects distribution out of 
central compartment into total Vd, terminal phase reflects elimination. 
Cp = Ae −αt + Be −βt 
Where α and β are hybrid rate constants describing the 2 slopes. 
Plasma Concentration 
(µg/ml) 
Hourss 
Figure 2 
2. Case with Non-Instantaneous Absorption 
a. Kinetics of first-order absorption and elimination: determination of absorption 
and elimination half-lives 
ka
FD 
[e −k el t 
− e 
−k a
t
C ]
p =
Vd
(k a − kel ) 
Note that the terminal slope may be either the elimination rate constant, the 
absorption rate constant, or a hybrid 
See Katzung, Basic & Clinical Pharmacology, 2001, p. 42 Ho rs
Pl entr n
(
HST-151 11 
b. Peak plasma concentration is dependent on absorption and elimination 
half-lives, volume of distribution, dose (D), and fraction of dose absorbed (F) 
c. Area under plasma concentration vs. time curve (AUC) is dependent on 
dose (D), fraction of dose absorbed (F) and total clearance ClT 
F •D
AUC =
Cl T 
Fraction of dose absorbed into systemic circulation (F ) is the bioavailability of 
the drug product; determined experimentally by measuring AUC of dosage form 
of drug given by one route and comparing it to AUC of same dose of drug under 
conditions of complete absorption, i.e. given i.v. 
C. Effect of infusions or multiple dosing on time-course of plasma concentrations 
1. Infusion Kinetics 
One approach to maintaining a desired therapeutic level of a drug is to administer 
the agent by intravenous infusion. Drug delivery may be controlled by gravityregulated drip of the agent into i.v. tubing or by use of an infusion pump. 
a. When a drug is administered at a constant dosing rate (DR) and its 
elimination follows first-order kinetics, the concentration of drug in the plasma 
rises exponentially and reaches a steady-state or plateau level (Css). 
Cp
(t) = Css (1 − e 
−k el t
Plasma Concentration asma Conc atio
(µg/ml) 
Houurs
 Figure 4 
b. At steady-state the INPUT RATE = OUTPUT RATE. The input rate is 
DR, which may be expressed as the total dose (D) divided by the length of the HST-151 12 
infusion (T). The output rate in the case of first-order elimination is the total 
amount of drug in the body (Css Vd) times the elimination rate constant (kel). 
DR =Css •Vd •k el 
Therefore, the plasma concentration at steady-state can be predicted as follows: 
DR Css =
Vd
k el 
Remember that total clearance equals the elimination rate constant (kel) times the volume 
of distribution. Therefore, the plasma concentration at steady-state (Css) is directly 
proportional to the input rate (DR) of the drug and inversely proportional to its total 
plasma clearance (ClT). 
DR Css =
Cl T HST-151 13 
c. The rate of achieving steady-state is dependent only on the elimination 
half-life of the drug. Half the Css level is achieved in one t1/2, and about 94% of 
Css in four t1/2. 
d. Because of the lag in achieving steady-state when a constant infusion rate 
is administered, a loading dose may be given to achieve the desired therapeutic 
effect more quickly. The loading dose may be chosen to produce the amount of 
drug in the body that would eventually be reached by the infusion alone. 
Loading dose =Css •Vd 
At least on a theoretical basis, the plasma concentration will instantaneously reach 
the therapeutic level and that level will be maintained. Note that the steady-state 
level achieved with a continuous infusion is determined by the infusion rate and is 
not affected by the size of the loading dose. 
2. Multiple Dosing Kinetics 
a. Commonly, drugs are administered repeatedly in order to maintain their 
therapeutic effects. In the simplest case, a maintenance dose (D) is given at a 
constant dosing interval (τ) – [note that this is not the same as the time constant, 
τ]. Since the route of administration may not be i.v., the amount of drug which 
reaches the systemic circulation may be some fraction (F) of the dose. If 
elimination is by first-order kinetics, a steady-state is eventually reached. The 
“average” Css at steady-state equals the fraction absorbed times dosing rate 
divided by total clearance, analogous to the Css from an infusion (see above). 
F •D 
 
Css "average" =
τ 
Cl T 
b. However, in the case of repetitive dosing, unlike an infusion, plasma 
concentrations of drug fluctuate during the dosing interval, depending on the 
kinetics of absorption and elimination. The degree of fluctuation in the plasma 
concentration during a dosing interval increases with increasing dose, dosing 
interval, clearance, and absorption rate. 
c. If a drug is administered i.v. (or where absorption is rapid and complete), the 
peak plasma concentration at steady-state (Cmaxss) relative to the peak after 
the first dose (C0) depends on the ratio of the elimination half-life and the 
dosing interval (t1/2/τ). Plasma Concentr
(
HST-151 14 
C =
C0 
max ss 1 − f
f is the fraction of drug remaining at the end of a dosing interval. 
0.693 
τ
−
•τ
f = e 
−k el •τ
= e 
t
1/2 
= 0.5 t 1/2 
Each time that the maintenance dose D is administered, the plasma concentration 
increases from Cmin to Cmax.. The decline from Cmax to Cmin is governed by the t1/2, 
just as in single dosing. These relationships are described mathematically as: 
D
C
min ss 
+
Vd 
=C
max ss
Vd 
=C0 
C
min ss 
+C0 = C
max ss 
0.693 
lnC min ss 
= lnC max ss 
− 
t
1/2 
τ
Plasma Concentration aon
(µg/ml) 
Hourourss
Figure 5 
d.  
HST-151 15 
d. Prediction of Cmax and Cmin at steady-state can be of great importance in 
cases where therapeutic efficacy is to be maintained while minimizing the risk of 
toxic side effects. (Note that the Css“average” described above lies between 
Cmaxss and Cminss, but it is not mathematically equivalent to their arithmetic or 
geometric mean.) The therapeutic window in a dosing regimen is the range of 
efficacious, non-toxic plasma concentrations lying between Cmaxss and Cminss. 
If these are known, then the dosing regimen is determined as follows: 
Maintenanc e Dose = (C max ss 
−C
min ss 
) •Vd 
 C max ss 
 t 
2
1 
Dosing Interval ( τ) = 
ln 
C
min ss 
0.693 
e. The rate of achieving steady-state is determined by the elimination half-life 
(as with an infusion). A loading dose may be used to rapidly achieve steady-state 
concentrations; especially important for drugs with long half-lives since 
attainment of steady-state is slow. 
Loading Dose =C
max ss 
•Vd t
t
t
HST-151 16 
V. Time-Course of Drug Effect 
Under certain conditions (first-order kinetics, reversible effect, single compartment 
kinetics, iv administration), the elimination half-life of a drug and its threshold dose 
for a particular effect can be estimated by monitoring the effect of the drug as a 
function of time after drug administration. Data obtained from several doses can then 
be evaluated by examining the duration of a given level of effect as a function of the 
logarithm of the dose, as illustrated below. The slope is directly proportional to the 
elimination half-life; the steeper the slope (i.e., increase in duration with an increase 
in dose), the longer the elimination half-life. The x-intercept indicates the log of the 
threshold dose; the smaller the x-intercept the greater the potency of the drug. 
Duration of Action = 
t 1/2 (Log Dose − Log Threshold Dose)
0.301 
200 
)
l 100 
mg/
n(
n
oi
ar 
n
e
c
n
o 10 
0 10 20 30 40 50 60 
Threshold 
Time (Min) 
40 
n
)
i 30 
M(
n
oi 20 
ar
u
D 10 
10 100 
Dose HST-151 17 
Note: Refer to PharmAid for simulations of single doses, multiple doses and infusions 
of specific drugs. Refer to Programmed Problems in Pharmacology at 
for a pharmacokinetic problem set in programmed text format. HST-151 18 
USE OF PHARMACOKINETIC PARAMETERS TO ESTIMATE DOSING 
REGIMENS 
You have decided to prescribe a new drug GOOD-4U
to your patient, Ms. H.S.T., who 
weighs 70 kg and has normal renal function. The population average pharmacokinetic 
parameters for GOOD-4U
are: Vd = 0.6 l/kg (about total body water), ClT = 60.6 
ml/min. Therapeutic efficacy generally occurs at Cp of 2.38 µg/ml; side effects begin to 
occur with Cp of 5.0 µg/ml. 
You decide to administer a single dose of 100 mg by iv injection. 
1. Assuming rapid distribution in the Vd, are you expecting to produce side effects 
(hint: what is the initial C0)? 
No, assuming a single compartment system, the 100 mg will distribute in 42 
liters to achieve an initial Cp of 2.38 µg/ml. See Fig. 1. 
2. How long before 94% of the dose is eliminated (hint: what is the half-life)? 
The half-life computed from the total clearance and Vd is 8 hours; 94% of the 
dose is eliminated in about 4 half-lives, 32 hours. 
3. A complete urine collection from the time of dosing until 16 hr later contains 37.5 
mg of the drug. To what extent is the renal function of Ms. H.S.T. of importance to 
the total clearance of this drug? 
Computation of the renal clearance indicates that it is about 50% of the total 
clearance. At 16 hr, which is 2 half-lives, 75 mg should have been eliminated 
by all clearance mechanisms. Half of that is appearing in the urine 
suggesting the renal clearance is 30 ml/min. The drug must be extensively 
bound to plasma proteins and/or is substantially reabsorbed after glomerular 
filtration. It is reasonable to predict that reduction of the patient’s creatinine 
clearance by 50% will reduce total clearance by at least 25%. 
One week later you decide to administer GOOD-4U
by constant iv infusion to achieve 
the therapeutic effect. 
4. What loading dose would you administer? 
The minimum loading dose would be (2.38.µg/ml)(42 liters) or 100 mg. 
5. What infusion rate would you prescribe? 
To achieve a Css of 2.38 µg/ml, given a total clearance of 60.6 ml/min, the 
infusion rate should be 144.2 µg/min. See Fig. 4. HST-151 19 
If instead you had administered 100 mg by iv injection every 8 hours: 
6. At steady-state what would be the Cmax? 
The drug is given repeatedly at a dosing interval which in this case equals the 
elimination half-life. The drug will accumulate to twice the initial C0, ie. 4.76 
µg/ml. You can prove that from the equation provided (cf. Figure 5). 
C
maxss 
=
1
0
7. At steady-state would the Cmin be sufficient to achieve continuous therapeutic 
efficacy throughout the regimen? 
Yes, since Cmin will be 2.38 µg/ml. At steady-state the input from each dose 
equals the output over the dosing interval. Since each dose adds 2.38 µg/ml, 
the Cmax,ss drops by 2.38 µg/ml to a Cmin of 2.38 µg/ml. Or approached 
another way, the dosing interval equals one half-life so Cmin will be 50% of 
Cmax! See Fig. 5.