Introduction to Pharmacokinetics

Introduction to
Pharmacokinetics
David Karhu
AMWA 75th Annual Meeting, San Antonio, October 3, 2015
Introduction to Pharmacokinetics

Objectives

Define pharmacokinetics (PK)

Principles of ADME

Noncompartmental PK

Compartmental PK
2
Introduction to Pharmacokinetics
“I learned very early the difference between
knowing the name of something and knowing
something.”
- Richard Feynman
3
Introduction to Pharmacokinetics

What is pharmacokinetics?

“What the body does to the drug”

Assesses rate of movement of drugs in body;
ie, study of mathematical relationships
between administered dose of a drug and its
resulting concentrations

ADME: Absorption, Distribution, Metabolism,
Excretion
4
Introduction to Pharmacokinetics

Fundamental tenet: there is a relationship between blood
concentrations and pharmacological effect
Ref: Mehrotra, et al. Int J Impot Res 2007;19(3):253-64
5
ADME

Absorption

Process by which unchanged drug enters systemic
circulation following administration by an extravascular
route (eg, PO, SC, transdermal, inhalation)
Bioavailable fraction (f)

Bioavailability (F) is 100% following IV dosing
http://usmle1-general-pharmacology-2.html
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ADME

Factors affecting absorption
Physicochemical properties of drug (solubility,
permeability)
http://usmle1-general-pharmacology-2.html
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ADME

Factors affecting absorption
Extent of first-pass metabolism
http://usmle1-general-pharmacology-2.html
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ADME

Factors affecting absorption
Splanchnic blood flow
http://usmle1-general-pharmacology-2.html
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ADME

Factors affecting absorption
Gut motility
http://usmle1-general-pharmacology-2.html
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ADME

Factors affecting absorption
Transport back to intestinal lumen (eg, P-glycoprotein
efflux)
http://usmle1-general-pharmacology-2.html
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ADME

Factors affecting absorption
Fed versus fasting state (food slows rate of stomach
emptying; rate of splanchnic blood flow increases)
http://usmle1-general-pharmacology-2.html
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ADME

Distribution

Reversible process by which drug moves
between intravascular space (blood) and
extravascular space (other tissues)

Elimination
 Irreversible
loss of drug from site of
measurement (eg, blood)

Metabolism

Excretion
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ADME

Metabolism


Biochemical modification of drugs, usually through
specialized enzymatic systems (eg, cytochrome
P450 oxidases)
Most drugs are weak acids or weak bases (partially
ionized)




Lipophilic in un-ionized form; can readily diffuse
across membranes
Transformed (eg, hydroxylation, conjugation) to
more polar, water-soluble products to facilitate
renal excretion
Some metabolites are active (have pharmacological
effects); some are inactive
Metabolism is primarily hepatic, although most
tissues have some metabolic activity
14
ADME

Excretion

Removal of unchanged drug and metabolites from the
body

Major routes


renal (urine)

to a lesser extent, biliary (feces)
Minor routes

Sweat, tears, saliva, milk
15
ADME

Enterohepatic recycling
http://quizlet.com/10071850/pharm1-block3-general-flash-cards/
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17
Noncompartmental PK
 Common parameters
 Calculation
 Interpretation
18
Therapeutic range
In general, dosage regimen (ie, dose and dosing interval)
is adjusted so that both Cmax,ss and Cmin,ss are within
therapeutic range
Drug Concentration vs Time Plot
240
Drug Concentration (ng/mL)

Toxicity
200
Cmax,ss
160
Therapeutic range
120
Cmin,ss
80
Dose
40
0
Dose
0
Dose
Dose
Dose
Lack of efficacy
Dose
10
20
30
40
50
Time (h)
19
60
70
80
Area Under the Concentration vs Time Curve
(AUC)

Measure of extent of absorption (total systemic exposure)

AUC0-n, where n is any sampling time

AUC0-t, where t is time of last sample collection

AUC0-∞, extrapolation to infinity

AUC0-τ, where τ is a dosing interval at steady state
20
AUC0-t
The trapezoidal rule is used to calculate AUC0-t:
AUC0t
= C1
n
 C2
2
( t 2 - t1) + C2
 C3
2

( t3 - t 2)  …Cn1 C n ( t n - t n -1)
2
Drug Concentration vs Time Plot
C5
30
Drug Concentration (ng/mL)

(C5 + C6)/2 = average C = height
25
C6
20
15
10
5
0
0
t6 – t5 = width
2
4
6
Time (h)
8
21
10
12
AUC0-∞
Semilog plot - concentrations in terminal phase decline
linearly
Drug Concentration vs Time Plot
100
Drug Concentration (ng/mL)

10
1
0
2
4
6
Time (h)
8
22
10
12
AUC0-∞

Slope of regression line = terminal elimination rate constant, or λz

To calculate AUC0-∞, extrapolate area from time = t to infinity and add to
AUC0-t

Ct/λz, where Ct is last observed nonzero conc (FDA)

Cz/λz where Cz is estimated conc from the regression line at time = t (Health
Canada)
Drug Concentration vs Time Plot
Drug Concentration (ng/mL)
100
slope = λz
10
Extrapolated area
1
0
2
4
6
Time (h)
8
23
10
12
AUC0-τ
Dose
Dose
Dose
Dose
Dose
Dose
 Note: If CL does not change with multiple dosing1,
AUC0-∞ (single dose) = AUC0-τ (at steady state)
1 Autoinduction
or autoinhibition may cause CL to change
24
Bioavailability (F)

Absolute bioavailability

Relative amount of extravascularly-administered drug
that reaches systemic circulation unchanged

For IV dose, F = 100%

Absolute bioavailability following PO dose:
F

Eg:
AUC
AUC
PO
IV

D
D
IV
PO
AUCPO = 75 ng·h/mL; AUCIV = 100 ng·h/mL;
DIV = DPO = 1 mg = 1 000 000 ng
F
75 ng  h/mL 1 000 000 ng

100  75%
100 ng  h/mL 1 000 000 ng
25
Bioavailability (F)

Relative bioavailability

Determined against reference standard (eg, oral solution,
innovator product, old formulation)

Relative bioavailability:
Frel 
AUC
AUC
Test
Reference
 DReference
D
Test
26
Maximum observed concentration (Cmax)

Read directly from concentration data

Estimate of maximum systemic exposure

Following IV dosing, Cmax typically occurs at end of injection or
infusion

Following extravascular dosing, Cmax occurs when rate of
absorption = rate of elimination
Am J Physiol Endocrinol Metab 2007;292:E1829–E1836
http://www.xenogesis.com/services-3/in-vivo/pharmacokinetics-pk/
27
Time of maximum observed concentration (tmax)

Read directly from data

Following extravascular dosing, maximum drug effects and
adverse events are likely to occur at or around tmax
28
Terminal elimination rate constant (λz)
Common abbreviations: k, kel, or λz
 Fraction of drug eliminated per unit time
 Depends on 2 parameters


volume of fluid cleared per unit time (ie, clearance)

volume to be cleared (ie, volume of distribution)
z 

V
d
Also related to half-life
z 

CL
ln 2
t
1/ 2
λz can also be determined from slope of regression line at
terminal phase of log concentration vs time curve
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Terminal elimination half-life (t1/2)

Time it takes for concentration in terminal elimination phase
(linear portion of a semi-log plot) to decrease by half
t1/ 2 
ln 2

z
Used to estimate dosing interval, time to steady state, or time
needed for drug concentration to return to safe level following
overdose
 A drug is considered essentially eliminated after 5 half-lives


1 half-life: 50%

2 half-lives: 75%

3 half-lives: 88%

4 half-lives: 94%

5 half-lives: 97%
30
Clearance (CL)

Most important PK parameter

Volume of fluid from which drug is completely removed in a given time period

Units: L/h or mL/min

Measure of the ability of the body to eliminate a drug
dX
Eliminatio n rate
dt
CL 

Concentration in blood
C


Integrating from 0∞,
CL 

0
dX
dt
dt

 Cdt
0

where

0
and
dX
dt
dt

 Cdt
= total amount eliminated (ie, Doseiv)
= AUC0-∞
0
Therefore
CL 
D
AUC
iv
0
31
Clearance (CL)

For extravascular dose,
CL 
CL / f 


f D
AUC
0
D
AUC
0
CL/f is the apparent clearance
CL is used to calculate dosing rate for long-term drug
administration:
Dosing rate = CL  Css
where Css is the desired steady-state concentration
32
Clearance

Calculated for organs responsible for clearing drug:
kidney (renal clearance, CLR), liver (hepatic clearance,
CLH), or other organs

Renal clearance,
CLR 
A
AUC
e ( 0 n )
0 n
where Ae(0-n) is amount of drug excreted unchanged over a
specified time interval
Ae(0-n) = Cu(0-n)  Vu(0-n)
where Cu(0-n) and Vu(0-n) are concentration and volume of urine,
respectively, over collection interval (0-n)
33
Clearance


Reasons CL can decrease

Renal or hepatic impairment

Enzyme inhibition

Age
Reasons CL can increase

Enzyme induction
34
Volume of distribution (Vd)

Proportionality constant linking amount of drug in body to
measured concentration

Vd does not represent a physiologic volume
35
Volume of distribution (Vd)
36
Volume of distribution (Vd)


Add known amount
of soluble substance
(eg, 1000 mg), mix
well, determine
concentration (eg,
10 mg/L)
Then,
Volume 
37
Amt 1000 mg

 100 L
Conc 10 mg / L
Volume of distribution (Vd)

Now, imagine that the
added substance binds to
rocks on bottom of pond so
that measured
concentration is 1 mg/L

Then,
Volume 

1000 mg
 1000 L
1 mg / L
Note: Volume has not
changed, but apparent
volume has
38
Volume of distribution (Vd)

Immediately after IV dose,
V
c

Dose
C
0
where Vc is the volume in central (sampling) compartment,
and C0 is maximal concentration

C0 corresponds to initial plasma concentration resulting
from total drug mixing in blood before any distribution or
elimination

Vc can be viewed as the apparent volume from which drug
elimination occurs, because kidney and liver are wellperfused tissues and belong to central compartment
39
Volume of distribution (Vd)

Immediately after an IV bolus, Vc = DoseIV/C0
Vd (L)
Vc
VC
Vp
Time postdose (h)
Vc is volume of central compartment
Vp is volume of peripheral compartment
40
Volume of distribution (Vd)

Soon thereafter, drug begins to be distributed and
eliminated
Vd (L)
Vc
Vp
Vc
Time postdose (h)
Vc is volume of central compartment
Vp is volume of peripheral compartment
41
Volume of distribution (Vd)

Vd increases to an asymptotic value (Varea) when
equilibrium of distribution is attained

Once equilibrium attained, net exchange between
plasma (central compartment) and tissues (peripheral
compartments) is null
Varea
Vc
Vd (L)
Vc
Time postdose (h)
Vc is volume of central compartment
Vp is volume of peripheral compartment
42
Vp
Volume of distribution (Vd)

After this, any decrease of plasma concentration is due to
irreversible drug elimination
V
area

Amt of drug in body during terminal phase
Plasma concentration during terminal phase


CL
λ
z

Dose
AUC
0
 λz
For extravascular dose, the amount of drug accessing systemic
circulation is unknown; thus
V
area


f  Dose
AUC0  λz
V
area
f

Dose
AUC
V/f is the apparent volume of distribution
Ref: J Vet Pharmacol Therap 2004;27:441-53
43
0
 λz
Volume of distribution (Vd)


Some drugs distribute primarily in plasma

Tightly bound to plasma proteins (eg, warfarin)

Highly hydrophilic (eg, gentamicin)

These drugs have low Vd (eg, ≤ 0.25 L/kg)
Other drugs bind extensively to tissues outside of blood, eg
adipose tissue, muscle

eg, chloroquine

These drugs have a high Vd (eg, > 200 L/kg)
44
Compartmental PK

Not always possible to use noncompartmental
PK
 Drug
not eliminated (eg, IV iron)
 Extensive
blood sampling not feasible (eg, infants,
cancer patients)

Use compartmental PK to construct model
based on differential equations to explain
change in drug concentrations over time
 Use
simplest model that explains data
45
Compartmental PK
One-compartment model
Monoexponential decay
Toxicol Appl Pharmacol. 2013;271(2):216-228
46
Compartmental PK
Two-compartment model
Biexponential decay
Toxicol Appl Pharmacol. 2013;271(2):216-228
47
Compartmental PK
48
Noncompartmental vs Compartmental


Noncompartmental PK

Based on algebraic equations

Sensitive to sampling frequency

Simple

Reproducible

Does not require specialized software
Compartmental PK

Based on linear or nonlinear differential equations

Useful when sampling is sparse

Fitting compartmental models can be complex and lengthy process

Requires specialized software
49
Questions?
50