A brief description of calculating pharmacokinetic parameters.

1. Calculation of Pharmacokinetic Parameters

2. Although drug discovery is primarily
designed to find compounds with desired
efficacy, the choice from among multiple
compounds potentially offering efficacy
often comes down to those with the most
favorable pharmacokinetics
(Welling and Tse, 1995).

3.  Pharmacokinetics is defined as the
quantitative analysis of the processes of drug
absorption, distribution, and elimination that
determine the time course of drug action.

4.  ADME Scheme
 Absorption, Distribution, Metabolism and
Excretion
 LADME
 Inclusion of new term Liberation
 Liberation is the process of release of drug from
the formulation

5.  Where is it measured?
 For in-vitro data
 In phase I studies for any new drug
 During therapeutics to adjust dose
 For toxicity studies and during poisoning

6.  What to measure?
 Dose
 Bio-availability
 Clearance
 Volume of distribution
 Half-life
 Area under curve
 Steady state concentration

7.  How to measure?
 Pharmacokinetic models
▪ Non compartmental
▪ Compartmental
▪ Physiological
▪ Bioanalytical methods
 Equipment used
▪ High pressure liquid chromatography
▪ Gas liquid chromatography
▪ Fluorescence polarizing immunoassay

8. 8

9.  CTissue indeterminable directly  Indirect analysis
using Cp vs Time data
 Several inter-connected compartments 
mathematical entities
 Each compartment has pharmaco-kinetically
similar tissues
 In graph, no. of models shown by lines with
different slopes
 Drug administered to & eliminated from central
compartment
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10.  Non-compartmental Models
 Offers little insight into the rate or processes
involved in drug distribution
 Mainly uses area under curve parameters
 Compartment Models
 Catenary and mammalian models
 Kinetic models to describe and predict the
concentration-time curve
 Simplest PK compartmental model one-
compartmental PK model with IV bolus
administration and first-order elimination

11. 11

12.  Body assumed to be one homogenous
compartment
 Instantaneous distribution
 Elimination starts simultaneously
 Only one straight line in ln(Cp) vs time
graph
ke = Slope
ln(C0) = y-intercept
C0 = exp(y-intercept)
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13.  Absorption + Elimination during upstroke
 Terminal straight line portion
Elimination)
13

14.  One Central (1) & One Peripheral (2)
compartment
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15.  Slower distribution
 Ct = A * e-αt + B * e-βt
 α = Distribution + Elimination
 β = Elimination
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17.  Consider absorption & distribution
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18.  One Central (1) + Two peripheral (2, 3)
Compartments
 Compartment 2 & 3 not interconnected
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19.  Achieved by mathematically transcribing
 anatomical,
 physiological,
 physical, and chemical descriptions
of the phenomena involved in the complex ADME
processes
 Used to extrapolate dose, metabolism and excretion of
drugs prior to human exposure

20.  For single-dose study of an immediate release product:
 For at least three elimination half-lives (cover >80% of AUC)
• Absorption phase : 3-4 points
• Around Tmax : 3-4 points
• During elimination : 4 points
 Intervals not longer than the half-life of the drug
 Truncated AUC undesirable except in entero-hepatic recycling
(elimination half life difficult to calculate)
 If urine tested, collect it for at least 7 half-lives

21.  Plasma, serum or blood?
 Collect after steady state of drug is achieved
(5-6 t½)
 Trough or Peak concentration?
 Immediate sampling in toxicity
 Other samples (Saliva)
19/11/2008 Dept.of Pharmacology Grant Medical College

22.  Most cases: Active drug substance
 Active / Inactive metabolite maybe measured in cases of:
 Concentration of drug too low
 Limitation of analytical method
 Unstable drug(s)
 Drug(s) with very short half life
 Pro-drugs
 Measurement of individual enantiomers is sometimes
recommended for safety / efficacy purposes

24.  Quantity of a drug or other agent administered
for therapeutic purposes
 Calculating drug dosages for humans based on
the doses used in animal studies
From
 weight (eg. mg/kg) initial
 surface area (eg. mg/m2) animal
 LD50 = Median lethal dose studies
 NOEL = No Observed Effect Level and
human
 NOAEL = No Observed Adverse Effect Level extrapolati
 TWA = Time Weighted Average on

25.  Absorption :
passage of drug from the site of administration into
the blood stream.
 Bioavailability :
is defined as the amount or percentage of drug that
is absorbed from a given dosage form and reaches
the systemic circulation following non-vascular
administration
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26. Parameters for assessing bioavailability
 T max : time to peak plasma concentration
 depends on rate of absorption
 C max : peak plasma concentration
 AUC (area under the curve) (∫C dt): is a
P
measure of the total amount of the unaltered
drug that reaches systemic circulation
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27. 40
A Cmax
30
plasma Tmax
conc.20
(μg/ml) AUC
10 B
0 1 2 3 4
Time (hrs)
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29. • AUC 0-t
• AUC 0-∞
For the segment from Cp2 to Cp3: AUC2-3 = Cp2 + Cp3 x (t3 - t2)
2
AUC 0-∞ = AUC 0-t + Clast / k

30.  Describes the fraction of an administered dose of
unchanged drug that reaches the systemic circulation
 By definition, when a medication is
administered intravenously, its bioavailability is
100%

31. “The ratio of areas beneath the blood level-time curves
after oral administration to that following intravenous administration of
the same dose is a measure of the absorption of the drug administered”
Nimodipine AUC
Oral : 1.17 %
Nasal : 67.4 %
www.chinaphar.com

32. Apparent volume of distribution is the
theoretical volume that would have to be
available for drug to disperse in if the
concentration everywhere in the body were the
same as that in the plasma or serum, the place
where drug concentration sampling generally
occurs.

33.  VD is a theoretical Volume and
determines the loading dose
 Clearance is a constant and determines
the maintenance dose
 CL = kVD
 CL and VD are independent variables
 k is a dependent variable

34. Volume of Distribution, Clearance and
Elimination Rate Constant
V
Volume 100 L
Clearance
10 L/hr

35. Volume of Distribution, Clearance and
Elimination Rate Constant
V
V2
Cardiac and
Skeletal Muscle
Volume 100 L (Vi)
Clearance
10 L/hr

36. V2
Cardiac and
Skeletal Muscle
V
Volume 100 L (Vi)
Clearance
10 L/hr
Volume of Distribution =
Dose_______
Plasma Concentration

37. V2
Cardiac and
Skeletal Muscle
V
Volume 100 L (Vi)
Clearance
10 L/hr
Clearance =
Volume of blood cleared of drug per unit time

38. V2
Cardiac and
Skeletal Muscle
V
Volume 100 L (Vi)
Clearance
10 L/hr
Clearance = 10 L/hr
Volume of Distribution = 100 L
What is the Elimination Rate Constant (k) ?

39. CL = kV
k = 10 Lhr -1 = 0.1 hr -1
100 L
10 % of the “Volume” is cleared (of drug) per hour
k = Fraction of drug in the body removed per hour

40. CL = kV
If V increases then k must decrease as
CL is constant

41.  An abstract concept
 Gives information on HOW the drug is
distributed in the body
 Used to calculate a loading dose

42. Loading Dose
Dose = Cp(Target) x VD

43.  What Is the is the loading dose required
for drug A if;
 Target concentration is 10 mg/L
 VD is 0.75 L/kg
 Patients weight is 75 kg

44.  Dose = Target Concentration x VD
 VD = 0.75 L/kg x 75 kg = 56.25 L
 Target Conc. = 10 mg/L
 Dose = 10 mg/L x 56.25 L
 = 565 mg
 This would probably be rounded to 560 or even
500 mg.

45.  Ability of organs of elimination (e.g.
kidney, liver to “clear” drug from the
bloodstream
 Volume of fluid which is completely
cleared of drug per unit time
 Units are in L/hr or L/hr/kg
 Pharmacokinetic term used in
determination of maintenance doses

46.  Major Factors
 Drug delivery α Q
 Extraction Ratio (ER) = (Cin – Cout) / Cin
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47. Total Body Clearance
 ClTotal = ClHepatic + ClRenal + ClOthers
 ClTotal = aVd * Ke
 ClTotal = Dose / AUC
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48. RCR = ClDrug / ClCreatinine
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49.  Maintenance Dose = CL x CpSSav
 CpSSav is the target average steady state drug
concentration
 The units of CL are in L/hr or L/hr/kg
 Maintenance dose will be in mg/hr so for total
daily dose will need multiplying by 24

50.  What maintenance dose is required for
drug A if;
 Target average SS concentration is 10 mg/L
 CL of drug A is 0.015 L/kg/hr
 Patient weighs 75 kg

51.  Maintenance Dose = CL x CpSSav
 CL = 0.015 L/hr/kg x 75 = 1.125 L/hr
 Dose = 1.125 L/hr x 10 mg/L
= 11.25 mg/hr
 So will need 11.25 x 24 mg per day
= 270 mg

52.  Half-life is the time taken for the drug
concentration to fall to half its original
value
 The elimination rate constant (k) is the
fraction of drug in the body which is
removed per unit time.

53. Biological half-life
 Time it takes for the blood plasma concentration of a
substance to halve ("plasma half-life") its steady-state
 First-order elimination
 Proportional to the initial concentration of the drug A0 and inversely
proportional to the zero-order rate constant k0
 Logarithmic process
 Fall in plasma concentration:
Ct is concentration after time t
C0 is the initial concentration (t=0)
k is the elimination rate constant

54.  The relationship between the elimination rate constant
and half-life is given by the following equation:
 Half-life is determined by clearance (CL) and volume of
distribution (VD)
 In clinical practice, this means that it takes 4 to 5 times the half-
life for a drug's serum concentration to reach steady state after
regular dosing is started, stopped, or the dose changed.

55. Drug Concentration
C1
Exponential decay
dC/dt  C
= -k.C
C2
Time

56. Log Concn.
C0
C0/2
t1/2
t1/2
t1/2
Time
Time to eliminate ~ 4 t1/2

57. Integrating:
Cp2 = Cp1 .e -kt
Logarithmic transform:
lnC2= lnC1 - kt
logC2 = logC1 - kt/2.303
Elimination Half-Life:
t1/2 = ln2/k
t1/2 = 0.693/k

58.  Steady-state occurs after a drug has been given
for approximately five elimination half-lives.
 At steady-state the rate of drug administration
equals the rate of elimination and plasma
concentration - time curves found after each
dose should be approximately superimposable.

59. Accumulation to Steady State
100 mg given every half-life
194 … 200
187.5
175
150
100
97 … 100
87.5 94
75
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60.  Rate in = Rate Out
 Reached in 4 – 5 half-lives (linear kinetics)
 Important when interpreting drug
concentrations in TDM or assessing
clinical response

62.  Develops ADMET modeling and simulation
software
 GastroPlusTM predicts the absorption,
pharmacokinetics, for drugs administered orally.
 ADMET Predictor TM  Estimate kinetics based on
chemical structure
 ClassPharmerTM  Estimate screening data analysis
 DDDPlusTM  simulates the in vitro disintegration
and dissolution of solid dosage forms

63.  Metabolism
 Human liver microsomes
Human intestinal microsomes
Human kidney microsomes
Human hepatocytes
Recombinant CYP and UGT enzymes
 PK profiles
 Prediction of volume of distribution based on lipophilicity,
ionisation, protein binding and tissue composition
 Drug – drug interactions
 Competitive enzyme inhibition (including auto-inhibition)
Enzyme-induction (including auto-induction)

66.  Continuous line of heterogeneous human
epithelial colorectal adenocarcinoma cells
 When cultured under specific conditions the cells become
differentiated and polarized such that their phenotype,
resembles the enterocytes lining the small intestine
 Used as a model to estimate absorption of drugs at pre-
clinical stage of development
 Other cell cultures with expression of transporters and
enzymes are used in calculation of PK parameters
 E.g.: P-glycoprotein (ABCB1) and BCRP (ABCG2)

68. HPLC
Colorimeter
Spectrophotometer
Spectrophotofluorimeter
GLC
Flame photometry
19/11/2008 Dept.of Pharmacology Grant Medical College

69.  High ER (Liver, Blood, Lungs) indicates high
PRE-SYSTEMIC ELIMINATION
(Lidocaine in liver)
 Maximal clearance = Blood flow
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