Pharmacokinetics II: Basic Concepts and Drug Clearance

General Principles of Drug Therapy
Pharmacokinetics II
Applying Basic Principles to Clinical Medicine
Marc Imhotep Cray, M.D.
BMS / CK-CS Teacher
http://www.imhotepvirtualmedsch.com/
Integrated Scientific and
Clinical Pharmacology

Topics Outline
2
 Basic Concepts
 PK Compartment Models
 Desired Drug Level
 Drug Factors Affecting
 Pharmacokinetics
 Drug Clearance
 Patient-Specific Variables
 Determination of Loading Dose
 Determination of Maintenance Dose

Applying the PK Principles to
Clinical Medicine
3
This lecture will cover principles and equations
applied to determine dosing regimens for patients.

BASIC CONCEPTS
4

Drug Pathway
5

Course of a drug and its metabolites after oral
administration
6

Pharmacokinetics
7
PK describes changes in plasma drug concentration (Cp) over
time (T)
It is most ideal to determine amount of drug that reaches its
site of action as a function of time after administration
Usually impractical or not feasible
Therefore Cp is measured
Amount of drug in tissues is generally related to plasma
concentration

Clinical pharmacokinetics
8
Clinical pharmacokinetics is about all factors that
determine Cp and its time- course, i.e. it is about variability
These various factors are introduced through course of
the following sequence

Important PK abbreviations
9
t1/2 the half-life of elimination
Vd Volume of distribution
Cl Clearance
AUC Area under the curve
F Fractional oral availability
Fu fraction excreted unchanged
PB Protein Binding
Tmax Time to maximum concentration
Cmax Peak concentration
(Concentration maximum)
Abbreviation Definition

Important PK abbreviations (2)
10
ss Steady state
Cp Plasma concentration
Cpt Plasma concentration at time = t
Cpo Plasma concentration at time = o
Cpss Plasma concentration at steady state
Ab Amount in body
e The natural logarithm
(value = 2.7183)
ln log to the base e
k the rate constant of elimination
Abbreviation Definition

Therapeutic Considerations
When Selecting Drug Dosage
11
Dose
Bioavailability (F)
Route of administration
(PO, IV, etc.)
Drug interactions
Time interval between doses (τ)
Plasma level of drug initially (Co)
Plasma concentration of
drug reported by lab. (Cp)
Desired steady-state plasma
concentration of drug (Cpss)
Volume of distribution (Vd)
Clearance (Cl)
Half-life (t½)

Aim of drug therapy
12
Constant IV infusion
Main determinants of Cpss
dose
clearance (Cl)
Aim of drug therapy is to achieve
efficacy without toxicity
involves achieving a plasma
concentration (Cp) that is above
minimal effective concentration
(MEC), but
below minimal toxic
concentration (MTC)

Drug at site of action Cp
13
From a dosing point of view concentration of drug at site
of action (target) is most important
Practically difficult to measure
Under steady-state (ss) conditions plasma concentration
(Cp) is in equilibrium with concentration at sites of action
(assuming a one compartment-model)
In clinical practice Cp measured

Mammillary Pharmacokinetic Model
14
Most common pharmacokinetic model
An empirical model = does not explain actual mechanisms by
which drug is absorbed, distributed, and eliminated from body
It is a compartmental model= groups of tissues that have
similar blood flow and drug affinity are represented by a single
compartment
Thus, a compartment is not a real anatomic region within body

Mammillary Pharmacokinetic Model (2)
15
Uniform drug distribution is assumed within each compartment,
and first-order rate equations are used to describe transport of
drug into and out of the compartment
Since drug can enter and leave body, model is characterized as
an “open” model

Distribution and Elimination(1)
IV Bolus Dose
One-compartment model
16Before Drug
Administration
After Drug
Administration
In model body is considered
as a single container (one
compartment) where drug is
instantaneously and uniformly
distributed
Drug in
body
Input (dose)
Output
(elimination)

One-compartment model features…
17
Drug distribute instantaneously after IV
administration of a single dose
A semilog plot of Cp versus time will be
linear
Drug elimination is first order
( constant fraction of drug is eliminated per
unit time)
Slope of semilog plot is = -k, where k is rate
constant of elimination and has units of time
Intercept on y axis is CoAmount of drug in body Ab (mg)
Plasma drug concentration Cp (mg/L)
Vd =
Note: Co is used to calculate Vd for drugs
that obey a one-compartment model

One-compartment model features …cont.
18
The plasma drug concentration (Ct)
relative to t initial concentration (C0) at any
time (t) after administration is given by ln
Cpt = ln Cp0 – kt
The relationship of plasma
concentrations at any two points in time is
given by ln Cp2 = ln Cp1 - k (t2 - t1)

19
IV Bolus Dose
Two-compartment model
“A more common model for distribution and elimination of drugs”
Before Drug
Administration
After Drug
Distribution
Equilibrium
Immediately
After Drug
Administration
Central
compartment
(plasma)
Peripheral
compartment
Kin Kout

IV Bolus Dose Two-compartment model features…
Body is a central compartment with rapid mixing
and a peripheral compartment with slower
distribution
Central compartment is uniformly mixed very
shortly after drug administration, whereas it takes
some time for peripheral compartment to reach
“pseudo-equilibrium”
Cp decrease very rapidly b/c drug is being elim.
from body and also drug is exiting plasma space as it
distributes to other tissues and fluid compartments

IV Bolus Dose
Two-compartment model features …cont.
21
After distribution, a linear decrease in log drug
concentration is observed if elim. phase is first order
Curve is less steep in elim. phase because there is
no longer a net decrease in plasma levels of drug
due to distribution to tissues being completed
Co obtained by extrapolation of elim. phase is
used to calculate Vd, and elim. rate constant, k, is
obtained from the slope of elim. phase

Most important PK parameters
22
Most important PK parameters from a dosing point of view are:
clearance (Cl),
volume of distribution(Vd)
half-life of elimination (t1/2 )
 Cl determines maintenance dose (MD)
 Vd determines loading dose (LD)
 t1/2 determines dose interval (τ=tao)
Remember: Pharmacokinetics involves movement
of drug into, within and out the body

Achieving Cpss
23
Key points:
(1) a new dose is administered once every t½,
(2) 50% of preceding peak plasma concentration is eliminated each t½
(3) Cpss is attained after 4 to 5 t½, regardless of whether drug was
given by constant IV infusion or by repeated intermittent doses
Multiple dosing regimens attain steady-state plasma concentrations

Infusion rate
(k0) k0= Cl × Css
Loading dose (LD)
LD = (Vd × Cpss)/(F); for our
purposes, F is usually 1
Maintenance dose (MD)
MD=(Cl × Cpss × τ)/(F),
where τ (tao) is the dosing
interval
Essential PK equation
Clearance (Cl)
Cl = K × Vd, where K is the
elimination constant
Volume of distribution (Vd)
Vd = (LD)/(Css)
Half-life (t1/2)
t1/2 = (0.693)/(K) or (0.693 ×
Vd)/(Cl)

Loading dose
25
In order to achieve rapid effect
(e.g. treating status epilepticus with
phenytoin) it is important to get Cp
up to effect zone as soon as possible
achieved with a loading dose
Factor determining loading dose is
volume of distribution (Vd)
IV injection followed by a
constant infusion
Vd = Amount of drug in the body
C0

Oral dosing
26
Curve reflects accumulation and
elimination, and intermittent administration

Cp higher than desired
Cause/s: excessive dosage and(or) decreased Cl

Cp higher than desired (2)
28
Factors causing decreased Cl are:
normal variation
 saturable metabolism
 genetic enzyme deficiency
 renal failure
 liver failure
 old age
very young age (neonate)
enzyme inhibition

Cp lower than desired
29
Dose may be too low, or
Cl too high:
Factors causing
increased Cl:
poor absorption
 high first-pass metabolism
 genetic hypermetabolism
 enzyme induction
 non-compliance
 normal variation

Time to steady state
30
Determined by t1/2 of drug
It takes 4-5 × t1/2 to achieve >90% of steady state
plasma concentration (Cpss)

Time for drug elimination
31
Determined by t1/2 of drug
It takes 4-5 × t1/2 for concentrations to reduce to
<10% of the starting value

Components of the line of steady state
32
Line of steady state is effectively made up
of sum of line of assimilation and line of elimination
i.e. net effect of input and output

Drug Clearance (Cl)
33
 Drug clearance (from plasma) is defined
as: volume of plasma cleared of drug per
unit time;
or
 A constant relating rate of elimination to
plasma concentration (Cp)
 i.e. rate of elimination = Cl * Cp
 Units: vol/time (e.g. L/h)

Clearance (2)
34
Clearance (Cl) is the single most important pharmacokinetic
parameter
 Cl determines maintenance dose-rate, i.e. dose per unit time,
required to maintain a plasma concentration
Clearance does not apply to drugs with zero-order kinetics, but
only to those with first-order (exponential) kinetics This
applies to majority of drugs

Clearance (3)
35
Graph to right shows that rate of
elimination (RE) is different at
different concentration,
i.e. it is driven by concentration
rate of elimination Cp
∴rate of elimination (mg/h) = constant
(L/h) * Cp (mg/L)

Clearance (4)
36
This ‘constant’ is clearance (Cl) and by deduction has
units of volume/time (e.g. L/h) since units for rate of
elimination are mg/h, and for concentration mg/L
i.e. rate of elimination = Cl * Cp

Thus, Cl is A constant relating rate of elimination to plasma
concentration
and Volume of plasma cleared of drug per unit time
The equation can be rearranged as follows:
Clearance (5)

Achievement of a constant steady state
plasma drug concentration (CpSS)
 In order to maintain a target Cp, drug must be administered at a
rate equal to rate of elimination at that concentration, i.e.
rate of administration = rate of elimination
Since
 rate of elimination = Cl * Cp, then
 rate of administration = Cl * CpSS, or
Maintenance dose-rate = Cl * CpSS

Maintenance dose-rate = Cl * CpSS
39

Physiological relevance of drug clearance
40
 Main organs responsible for drug clearance are liver
(metabolism) and kidneys (removal of unchanged drug)
 Total body Cl is sum of all clearance processes, i.e.

Determination of Cl
41
 Plasma Cl is usually determined
from area under plasma
concentration vs time curve (AUC)
after IV administration
 AUC is determined using the
‘trapezoidal rule’
AUC = Area 1 + Area 2 + Area 3 + . . .
Area n, where each area is
approximated by a trapezium

Area under the curve (AUC)
42
The bigger the AUC, the smaller the Cl
After oral administration:
where F = oral availability

Principles of Drug Therapy
43
NEXT Lecture , Pharmacokinetics-III including:
• Volume of Distribution
• The Half-Life
• Oral Availability
• Protein Binding
• pH and Pharmacokinetics

Companion learning tools:
44
 Doing the Math: To further understand the clinical use and
application of PK access the Clinical Pharmacokinetics Case-based
learning
 For well illustrated video-summaries of the pharmacokinetic concepts
covered in this series access the PK Concepts video mini-lectures folder
 MedPharm Guidebook: UNIT 1 General Principles of Pharmacology
 eNotes: General Principles of Drug Action

Pharmacokinetics II: Basic Concepts and Drug Clearance

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