Basic Pharmacokinetics: Principles of Drug Elimination

Introduction to Pharmacokinetics

Basic Pharmacokinetics
Malachi KellyIntroduction
What does pharmacokinetics mean?

• Time course of drug concentration in body
• Why do we need to know about it?
• Relationship between dose & unbound
  concentration at receptor
• Enable informed decisions regarding drug
  therapy to be made (e.g. how long will it take
  for a drug to take effect after administration)· Absorption
• First pass effect

Bioavailability and Drug Properties

• Bioavailability

◼
Salt factor
Proportion of dose
delivered systemically

• Protein binding
  = Distribution
• What it is
• Volume of distribution
• Loading doses / ILD
• Elimination

◼
Metabolism & excretion

• Clearance
• Elimination rate const
• Predicting decay of conc
• Half life
• Zero & 1st order kinetics
  = 1 & 2 compartment
  models
• Plasma conc profiles
• Maintenance doses
• TDM

Drug Absorption Process

Absorption
Process; movement of intact drug from
gut lumen to portal circulation

• Quantitative aspect; the extent to which
  this occurs (expressed as fraction fo)
  (Also used loosely to describe passage
  of drug from any route to bloodstream)

Absorption Pathway Diagram

Absorption
Dose
100 mg
Portal
vein
Liver
fH = 0.25
Systemic
circulationIntroduction to Pharmacokinetics

Basic Pharmacokinetics
Malachi KellyIntroduction
What does pharmacokinetics mean?

• Time course of drug concentration in body
• Why do we need to know about it?
• Relationship between dose & unbound
  concentration at receptor
• Enable informed decisions regarding drug
  therapy to be made (e.g. how long will it take
  for a drug to take effect after administration)· Absorption
• First pass effect

Bioavailability and Drug Properties

• Bioavailability

◼
Salt factor
Proportion of dose
delivered systemically

• Protein binding
  = Distribution
• What it is
• Volume of distribution
• Loading doses / ILD
• Elimination

◼
Metabolism & excretion

• Clearance
• Elimination rate const
• Predicting decay of conc
• Half life
• Zero & 1st order kinetics
  = 1 & 2 compartment
  models
• Plasma conc profiles
• Maintenance doses
• TDM

Drug Absorption Process

Absorption
Process; movement of intact drug from
gut lumen to portal circulation

• Quantitative aspect; the extent to which
  this occurs (expressed as fraction fo)
  (Also used loosely to describe passage
  of drug from any route to bloodstream)

Absorption Pathway Diagram

Absorption
Dose
100 mg
Portal
vein
Liver
fH = 0.25
Systemic
circulation
Small
intestine
fg = 0.8
80 mg
20 mg
EH = 0.75
60 mg
Not absorbed
20 mg

Determinants of Gut Absorption

Determinants of absorption
from gut.
Dissolution of drug
Gastric emptying rate
Intestinal motility
Drug interactions in gut lumen
Passage through gut wall

• DPS; further reading on above
• Textbooks
• Pharmacology/pharmaceutics teaching

Plasma Glycoprotein Interactions

Plasma glycoprotein
interactions

• P-gp is an ATP-dependent efflux pump with
  broad substrate specificity
  Present in; gut, kidney, liver, CNS etc
  Natural defence against toxins
• Reduces absorption & increases elimination
• Digoxin is substrate of this transporter
• Rifampicin - P-gp inducer ( | oral digoxin levels)
• Verapamil - P-gp inhibitor ( + oral digoxin levels)

First Pass Clearance

First pass clearance

◼
(first pass metabolism/extraction)
Process; removal of drug from plasma
during first passage through liver (via
portal circulation)

• Quantitative aspect; fraction of drug
  which escapes first pass clearance fh

First Pass Clearance Diagram

First pass clearance
Dose
100 mg
Portal
vein
Liver
fH = 0.25
Systemic
circulation
Small
intestine
fg = 0.8
80 mg
20 mg
EH = 0.75
60 mg
Not absorbed
20 mg

Bioavailability (F) Definition

Bioavailability (F)

◼
This is the proportion of an administered
dose which reaches systemic circulation as
intact drug.
Parenteral F =1, others F is variable
For oral administration bioavailability
depends on extent of absorption and first
pass effect.

• For oral administration F = fg x fn

Bioavailability Calculation Diagram

Bioavailability
Dose
100 mg
Portal
vein
Liver
fH = 0.25
Systemic
circulation
Small
intestine
fg = 0.8
80 mg
F = fa x fh
= 0.8 x 0.25 = 0.2
20 mg
EH = 0.75
60 mg
Not absorbed
20 mg

Measuring Bioavailability

Measuring bioavailability
Why measure it ??

• R&D of drugs
  How do we measure it?
• Give dose
• Measure plasma concentrations
• Plot graph; conc vs time
• Measure area under curve

Absolute Bioavailability

Absolute bioavailability
Bioavailability of test dose compared to IV dose
F = AUCtest
AUC
'reference

• reference dose
  Cp
  -test dose
  Time

Relative Bioavailability

Relative bioavailability
Test bioavailability of new generic drug relative to
established preparation
F = AUCtest
AUC,
reference
-test dose
Cp
Reference
dose-
Time

Salt Factor (S)

Salt factor (S)
Proportion of drug given in salt or ester form
which is the active component.

• e.g. proportion of phenytoin in phenytoin sodium
• phenytoin (liquid) S = 1, phenytoin sodium (capsules) S = 0.9
• Salt factor more important where
• drug has relatively low molecular weight
• Drug has narrow therapeutic index

Salt Factor Calculation Example

Salt factor
Patient normally takes phenytoin
capsules, 300mg nocte, she is unable to
swallow capsules and must be given a
liquid, what is the equivalent liquid
dose?

• Equivalent dose (where only salt factor changes)
  = current dose x S
  S.
  original formulation
  new formulation

Phenytoin Salt Factor Calculation

Salt factor
Patient normally takes phenytoin
capsules, 300mg nocte, she is unable to
swallow capsules and must be given a
liquid, what is the equivalent liquid
dose?

• Equivalent dose (where only salt factor changes)
  = current dose x Soriginal formulation
  S
  new formulation
  - 300mg x 0.9
  1
  = 270mg

Ciclosporin Case Study

Pt with renal transplant,
admitted c CVA

• Normally ciclosporin 50mg OM & 75mg
  nocte
  NBM as unsafe swallow
• What happens if left w/o meds?
  What would you recommend doing?
• F of oral ciclosporin is ~0.33
  IV16.5mg mane & 25mg nocte

Drug Reaching Systemic Circulation

Amount & rate of drug
reaching systemic circulation

• Amount of drug reaching systemic
  circulation = S x F x D
  Rate of drug reaching systemic
  circulation
• Ra
  a
  =
  SxFxD
  dosage interval (t)

Drug-Protein Binding

Drug - protein binding
UNBOUND
DRUG
+
PROTEIN
DRUG-PROTEIN
COMPLEX
(BOUND DRUG
Dynamic equilibrium
Unbound drug is active

• PD active
• PK active
  Plasma conc monitoring measures total drug
  conc ie bound & unbound

Phenytoin Levels in Renal Failure

Phenytoin levels in renal
failure (low albumin)
Healthy Patient
Patient with renal failure
Total
phenytoin
conc (mg/L)
15
15
Fraction
unbound
(Fu)
0.1
0.2
Free
phenytoin
1.5
conc (mg/L)
3.0

Drug Distribution

Distribution

• On reaching the bloodstream, drugs
  equilibrate with other compartments;
  Organs, muscles, bones, cells,
  intracellular spaces, etc.
• Time dependent process
• Extent and nature of distribution depends
  on drug and physiological factors

Volume of Distribution (Vd)

Volume of distribution (Vd)
This is not a real volume but an
apparent volume reflecting distribution
to areas outside the plasma.
Vd = total amount of drug in the body
plasma concentration (Cp)
Vd = S x Fx D
Cp

Volume of Distribution Example

Volume of distribution (Vd)
1g drug added-
- measured conc 100mg/L
Container of liquid of
unknown volume
What is the volume of this container?

• This is an apparent volume

Calculating Actual Vd

Calculating actual Vd
Series of digoxin plasma concentrations measured
(following distribution) after a single 500mcg oral
(tablet) dose. Plasma conc extrapolated back to time
zero shows conc of 0.6mcg/L. Calculate Vd for
digoxin in this patient. (digoxin S=1, digoxin tabs
F=0.7)
Vd = Sx Fx D
Cp
Vd = 1 x 0.7 x 500 = 583L
0.6

Estimation of Vd from Population Data

Estimation of Vd from
population data
Less accurate than calculation, can be used
when calculation not possible

• Population Vd for digoxin is 7.3 L/Kg
• For 70 Kg patient this is 511 L
  = 511L (or 583L from calculation
  example) .... any comments on this?

Utility of Vd

What use is Vd ???

• Used in calculating loading dose
  LD
  what does LD mean?
• Rearranging previous equation
  LD
  =
  Vd x Cp
  SxF

Multiple Oral Doses and Steady State

Multiple oral doses leading to
steady state.
--- Cpss ave
Log Cp
dose
dose
dose
dose
dose
dose
Time

Loading Dose Example

Loading dose example
Patient (70kg
requires gentamicin, what IV
loading dose will give plasma conc. of 7mg/L?
(Population Vd = 0.25L/kg, S = 1)

• LD =
  Vd x Cp
  SxF
  LD = (0.25 x 70) x 7
  1×1
  =
  122.5mg

Loading Dose Practicability

Loading dose

• Is this a practicable dose?
• Available as 40mg/ml solution
• 122.5mg = 3.0625ml
• Round dose down to 120mg = 3ml
  Exercise: Calculate predicted plasma
  conc if 120mg dose given.
• Cp = SxFxD/Vd = 1 x 1 x 120/ (0.25 x
  70) = 6.86 mg/L

Drug Elimination Processes

Elimination
Elimination describes the processes through
which a drug is irreversibly removed from the
systemic circulation.
excretion and metabolism are elimination
processes.

• Excretion is the removal of unchanged drug into;
  urine, gut contents, expired air, sweat, etc.
• Metabolism of a drug usually renders it more
  suitable for eventual excretion.

Clearance (Cl)

Clearance (Cl)
Clearance describes the efficiency of
elimination.
Defined as volume of blood cleared of
drug per unit time,

• Units?
• volume/time (ml/min or L/hr)

Maintenance Doses and Steady State

Maintenance doses
--- Cpss ave
Log Cp
dose
dose
dose
dose
dose
dose
Time

Calculating Maintenance Doses

Maintenance doses
Multiple dosing eventually leads to
steady state (SS)
How do we calculate the maintenance
dose required to achieve target steady
state concentration
Cp
ave)?
ss ave

• At steady state Ra = Re
• For any Cp
  ss ave
  we can calculate rate of
  elimination using clearance.
• Re = CI x CPss ave

Maintenance Dose Equations

Maintenance doses
From earlier R = S x Fx D / t
These two equations can be combined

• S x Fx D / t = CI x Cpss ave
  And rearranged in terms of dosage rate
• D / t = CI x Cp.
  ss ave
  /SxF
  Or dose
• D = CI x Cpss ave X t / S x F

Lignocaine Maintenance Dose Example

Maintenance dose example

◼
Lignocaine infusion is to be given to a
patient. What maintenance dose is required
to give average steady state concentration of
5mg/L.
(Cl = 24L/hr, S = 1, F = 1 (as IV))

• D / t = CI x Cpss ave / S x F
  = D / t = 24 x 5 / 1 x 1 = 120mg / hr

Elimination Rate Constant (K)

Elimination rate constant (K)

• This constant relates change in
  concentration with time
• It is the proportion of remaining
  drug eliminated per unit time
  Related to CI and Vd as follows
• K = Cl/Vd
  Units?
  time-1 i.e.Hours-1 ,Mins-1 etc.

Carbamazepine K Calculation

Elimination rate constant (K)
Using population data for CI and Vd, calculate
the expected K for carbamazepine.
(Vd = 1.4 L/kg Cl = 0.064 L/kg/hr)

• K = CI/Vd = 0.064/1.4 = 0.046 hr-1

Determination of Elimination Rate Constant

Determination of elimination
rate constant

• K may be determined from a log Cp vs
  time graph, it is the gradient.
  Cpt = Cpo e-kt
• This equation can be used to calculate the
  concentration (Cpt) at any time (t), given
  Cp0 and k (providing no more drug given)

Concentration Decay Example

Decay of conc. example
Patient on lignocaine infusion, concentration
measured and infusion stopped (conc
5mg/L).
Calculate predicted concentration 4 hours
later. K = 0.085 hour-1
Cpt = Cpo e-kt
- Cp: = 5 x e-(0.085 x 4) = 3.6mg/L

Half-Life (T1/2)

Half-life (T1/2

• Half-life is the time taken for the
  concentration of a drug to drop by 50%
• What use is half life?
• Time to steady state during regular dosing:
  approximately 5 X | 1/2
• Time taken for drug to be eliminated after
  stopping: 5 x T1/2
  - Helps decide dosage interval

Half-Life Calculation

Half-life (1/2
It is related to K
T

◼
1/2
= 0.693/K
Calculate carbamazepine T
1/2
using K
from earlier (K = 0.046 hr-1)
T

◼
1/2
= 0.693/0.046 hr1 = 15.07 hours
- Approx. 15 hours

Zero and First-Order Kinetics

Zero and first-order kinetics

• Describes the relationship between
  concentration of drug and rate of
  change of concentration of drug.
  (We will illustrate in terms of
  elimination.)

Zero-Order Kinetics

Zero-order kinetics
A constant amount is removed per unit
time

◼
rate of change of concentration is
independent of concentration

• E.g. zero order decay of phenytoin
  concentration when metabolism
  becomes saturated

Zero-Order Kinetics Plot

Zero-order kinetics, plot
concentration vs time
Cp
Time

First Order Kinetics

First order kinetics

• A constant proportion of remaining drug
  is removed per unit time

◼
rate of change of concentration is
dependent on concentration

```