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Idialized Drug Discovery
& development flow chart
Disease area
basic research;
Medical disease
understanding
Animal Models
Preclinical in-vivo
profiling
NDA
NEW DRUG
APPLICATION
Compound repository
Archive
Assay strategy
Assay development
Assay validation
Screening
Med. Chem.
optimization
Lead Selection
based on
«lead criteria»
Process development,
Disease marker,
endpoint definition
Clinical Phase III
Hit confirmation,
Hit validation
«counter screening»
Hit Selection
Hit to «Lead»
early chemistry
IND
Investigational New
Drug application
Clinical Phase I
Clinical Phase II
1
Animal experiments
Meet increasing resistance and pose ethical problems.
Consensus is that animal models are necessary to increase safety of clinical trial
& to verify treatment concepts in-vivo before human trials are undertaken.
Disease models are project specific and cannot be generalized
Pharmacokinetic and toxicity evaluation is more standardized:
PK data is generally obtained first in rhodents (mice &/or rats) & then in 1
«higher animal species» e.g. dogs, cats, rabbits, (hamster ).
Toxicity data is first evaluated in mice & preferrably in rats.
PK & toxicity (PD only in exceptional cases) is then normally evaluated in a
non-human primate experiment e.g. chimps, before phase I studies are started.
2
Schedule
1. single ascending dose studies (i.v.)
Q: what is the acute toxicity of my substance
Starting dose?
Investigation:
- overall clinical signs (weight, behavior, signs of pain, etc… )
- plasma levels e.g. 10 mins, 15 mins, 1 h, 6 h,
- tissue sampls (blood, fat tissue, muscle, kidney, spleen, liver, brain)
2. Multiple dosing study
Q: what is the chronic toxicity of my substance
Set-up: 1 week, 2, week, 4 week daily dosing (depending on indication)
Investigation:
- overall clinical signs (weight, behavior, signs of pain, etc… )
- plasma levels after multiple dosing
- phathological investigation
- phatohistology
- «clinical chemistry»: erythrocytes, thromobcytes, cytokines, etc..3
A simple sign for toxicity: weight change of animals
Average daily weight change [%] after 4 doses of SPK-843
1.04
1.02
1
NP1
0.98
NP2
0.11 ug/ml
IV
0.96
oral
0.19 ug/ml
0.94
0.92
0.9
0
01
2
1
32
43
54
65
76
87
9
Days
5 mg/kg dose applied
After 24 h, NP resulted in 57%
of SPK level in blood compared
to iv. injection
4
Example of histological analysis – Singe cell necrosis & NK infiltration
in liver after multiple dosing.
NK cell infiltration
( 24hrs)
5
Experiment size:
Deciding how large an experiment needs to be is of critical importance because of
the ethical implications of using animals in research.
An experiment that is too small may miss biologically important effects, whereas
an experiment that is too large wastes animals.
Power Analysis
A power analysis is the most common way of determining sample size.
The appropriate sample size depends on a mathematical relation between the
following:
(1) effect size of interest,
(2) Standard deviation (for variables with a quantitative effect),
(3) chosen significance level,
(4) chosen power,
1-4 are generally specified by the investigator and the experimental size
(number of animals) is calculated based on this.
6
Effect size (D):
Often specified in units of standard deviation e.g. treatment is expected to increase
litter size by 1 in mice (normal 5 mice per litter, std.dev: 0.8 -> D = 1/0.8 = 1.25
Significance Level
The significance level is the chance of obtaining a false positive result due to sampling
error (known as a Type I error). It is usually set at 5%, although lower levels are
sometimes specified.
Power
The power of an experiment is the chance that it will detect the specified effect size
for the given significance level and standard deviation and be considered statistically
significant. Choice of a power level is somewhat arbitrary and
usually ranges from 80 to 95%.
If too small numbers of animals (samples) are used, then the study is called
“underpowered” . This means, with high likelihood differences, even if present would
not have been detected/classified as statistically significant due to normal variations.
7
8
Different methods exist for e.g. sample size determination if a proportion of two
groups is measured e.g. % of successfully treated patients in two groups:
Successfully treated
with control:
Successfully
treated
with
new treatment
9
Sample size estimate – resource equation
Provides a simple alternative to accurate power analysis.
Especially useful in early stage research and when accurate assumptions on
expected effect sizes etc.. are not available.
Method is based on correlation between
Information content and E (degrees of
freedom in a data set)
Correlation function is steep but with a
saturation value between 10 and 20.
E=N-T-B
N = total number of animals in expriment - 1
T = total number of groups
B = number of subgroups -1
Example: Two treatments, 1 control in 3 groups of 8 animals each.
E = 23 (animals -1) - 3 (groups ) – 0 (no subgroups) = 20
E of 20 is > threshold of 10-20 and could be reduced.
10
Prodrugs
11
Prodrugs
• Concept: use of known in-vivo transformations or enzymatic processes in order to
optimize the properties of drug candidate molecules in terms of toxcicity,
therapeutic window, pharmakokinetics, dosing regimens, metabolism and
eliminiation routes.
• Delivered molecules ≠ the molecule which acts as the drug but a modified
«masked» version of it.
• Parameters most commonly addressed:
Aqueous Solubility
If concentration is not reached
Absorption and Distribution
If lipid/hydrophilic profile is not right
Site Specificity
If target tissue has unique enzymes
Instability
If metabolized before site of action reached
Prolonged release
If half-life is too short/inconvenient
Toxicity
If therapeutic window is too narrow
Poor patient acceptance
If unpleasant or painful or irritant etc..
Formulation problems
12
1. Carrier linked prodrugs
Example:
Brivanib (Bristol-Myers Squibb)
Anti-cancer drug candiate
Limited solubility/bioavailability
Ester pro-drugs:
Improved solubility/oral bioavailability
Estrification is the most common approach to pro-drugs
Ubiquitously present esterases will generate drug in-vivo
13
1. Carrier linked prodrugs
The «Carrier» has to…
Protect the drug until it is at the site of action
Localize the drug to the site of action
Allow for release via chemical or enzymatic mechanism
Minimize host toxicity, be non immunogenic
Be biodegradable
Most common activation method is hydrolysis (enzymatic or purely chemical)
14
15
DRUG
Choline esters can change the
overall characteristics of Carboxylic acid
DRUG
DRUG
DRUG
Succinate esters
16
Adefovir dipivoxil
Hepatitis B
Phosphate or sulfate drugs
normally not well absorbed in ionized form
Pro-drug oral bioavailability: 60%
Fostamatinib
(Syk kinase inhibitor)
Phosphate group increases solubility,
Activated at intestinal epithelium
17
Amides: not generally used, unless activated (carbamates, phenylcarbamates, etc..)
Alternative: Imines (Schiff Base)
Example:
Progabide (Sanofi-Aventis)
18
Dabigatran (anticoagulant, thrombin inhibitor)
i.v.
oral
Prevention of thromoembolic disease after planned surgery
(e.g. hip replacement)
19
Reductive cleavage mechanism:
X= NH or O, Y= O, S, Z = C, N
Tumor environment = hypoxic
Drawback =
Sulfonamides:
drug
Solubility enhancement
Plasma half-life 5 min
20
Prednisolon
Glucocorticosteroid,
Treatment of anaphylactic shock
Poor solublity
Succinate
Lyophilized powder for reconsitution
Sulfonate, carboxylates poorly hydrolyzed..
Solution shelf-life > 2 years
21
Prodrugs for Site Specific delivery:
This is feasible when physicochemical prpoerties of parent drug and prodrug
can be tuned optimally for the target site.
However, in general, increasing lipophilicity will increase passive transport to
most tissues.
Oxyphenisatin (laxative)
Oxyphenisatin acetate
Only deliverd rectally
Oral delivery
22
Brain targeting:
Crosses BBB
GABA + GABA aminotransferase
inhibitor
Is trapped in brain tissue
23
Liver targeting:
General approaches:
a) Very lipophilic substances
b) Phosphate or phosphonate moiety using aryl-substituted cyclic phosphodiesters
Activation: oxidative hydroxylation on benzylic position by liver specific isoform
of cytochrome P450. (free phosphate drug is trapped in hepatocytes due to poor
Membrane passage).
24
Adefovir
Reverse Transcriptase inhibitor
Hepatitis B
Suboptimal dosing regime –
Renal toxicity
60 fold higher liver c in liver
compared to Adefovir
& Kidney c 33% lower
25
Tumor microenvironment also contains increased phosphatases and proteases
Example: Delivery of dethylstilbestrol to prostate cancer tissue
Drawback: derivatives with poor membrane permeability -> poor distribution into
tissue…
26
glucuronation
Prodrugs for Stability:
What happens?
Propranolol (beta-blocker)
(see day 1)
Oral application of the drug
has a much lower activity
than IV injection.
-> strong «first pass effect»
Hydroxylation, glucuronation
Prodrug:
Succinate ester has 8x higher plasma
Levels after oral dosing.
27
Prodrugs for slow & prolonged release
Advantages:
(1) Reduces number & frequency of dosing
(2) Can eliminate night-time adminsitration
(3) Greater patient compliance
(4) More constant, lower drug dose in system with less peak levels
(5) Less toxicity (due to lower constant dose)
General strategy: Make long-chain fatty acid esters or PEG esters and use
intra-muscular injection
Example:
Haloperidol (Haldol)
A potent, orally active CNS depressant,
sedative & tranquilizer.
Peak plasma levels observed 2-6 h after
administration.
Decanoate ester (Haldol decanoate) is
injected intramuscularly
-> antipsychotic activity lastst 1 month.28
Example 2:
Tolmetin sodium (Tolectin)
is a nonsteroidal ntiinflammatory drug
with peak concentration duration of 1 h
Tolmetin glycine amide
Higher potency & extension of peak concentration to 9 h
(slow hydrolysis of amide)
29
30
Prodrugs to minimize Toxicity
Side effects of long-term usage of painkillers and antiinflammatory drugs e.g.
Aspirin, paracetamol, Ibuprofen are associated with liver damage gastrici irritation
and bleeding.
Ulcerogenicity and gastric bleeding associated with aspirin may be due to
accumulation of the acid in gastric mucosal cells.
Deacetylation
half-life 2h
in plasma
Estrification reduces
Ulcerogenicity. But…
deacetylation half-life 1-3 min
Quicker ester hydrolysis
removes deacetylation
problem
31
Prodrugs for patient acceptance
Clindamycin
Bacterial protein synthesis
Inhibitor; bacteriostatic
i.v. application causes pain,
Oral use – bitter taste
Well tolerated,
Hydrolysis t1/2= 10 min
Clindamycin Palmitate
Pediatric use in cherry-flavored syrup
32
Bioprecursor Prodrugs
Rely predominantly on redox transformation to generate the active form of the drug,
which is administered as inactive precursor.
Example: Proton pump inhibitors
Day 1 we had talked about discovery of anti-histminergica as anti-ulcer drugs.
A second approach is based on H+/K+ ATPase (proton-pump) inhibitors .
The enzyme catalyzes an exchange of K+ for H+ in the parietyl cells in the gastric mucosa
(the cells responsible for secretion of acid) and thereby increases the acidity
of the stomach.
Starting point: Screening for compounds which block gastric acid secretion.
Lead compound identified:
Exhibited Liver toxicity -> attributed to thiamide
33
Exhibited Liver toxicity
-> attributed to thiamide
Sulfur analog with good activity
Series of
Heterocycle analogs
Metabolism studies
(dogs)
Timoprazole
More potent but iodine uptake blockage
Picoprazole
(no thyrooid uptake inhibition )
Omeprazole (Prilosec, Astra Zeneca)
one of the most widely prescribed medicines
34
Omeprazole (Prilosec, Astra Zeneca)
one of the most widely prescribed medicines
Accumulates in gastric mucosa. Omeprazole is weakly basic (pKa of only 4).
-> pyridine ring is not protonated at physiolog. pH. pH in parietal cell is much lower,
pH = 1. -> drug is protonated inside the cells and undergoes a transformation.
Thereby the drug covalently binds to ATPase.
Secondarily, the drug inhibits carbonic anhydrase.
ATPase
35
Example: Antiviral drugs - Acyclovir
Acyclovir
Nobel price in 1988 to Elion &Hitchings for this molecule (amongst others).
Open chain mimick of 2´-deoxyguanosine, the precursor of GTP.
Acyclovir is inactive – but is activated by viral thymidine kinase to
monophosphate.
Viral Thymidine kinase
Selective for infected cells
36
guanylkinase
Phosphoglycerat kinase
and others
Further selectivity of acyclovir is obtained by the fact that Acyclovir-triphosphate
has a ~ 40times higher affinity for viral a-DNA polymerase than for normal
cellular a-DNA polymerase. -> «Dead end complex» during viral replication.
Even if access phosphorylated drug is released form an infected cell
(because of cell death… ) Acyclovir-PP and Acyclovir-PPP is not taken up in new cells
Due to poor cell penetration because of high polarity (negative charged molecules)
Acylovir is a prodrug with an exceptionally high degree of selectivity!
37
Most severe weakness of Acyclovir is that only 15-20% of oral dose is absorbed.
Prodrugs of the prodrug have been designed…
Adenosin deaminase
6-deoxyacyclovir
18 times more water-soluble than acyclovir.
Plasma concentrations were 5x-6x
higher after oral dose than for Acyclovir.
38
Prodrugs of the prodrug have been designed…
Valacyclovir (Valtrex)
3x-5x higher oral bioavailiablity than Acyclovir
Ganciclovir, even closer
mimick of natural template.
Higher activity aginst human
cytomegalo virus
Penacyclovir
Longer acting
Famicyclovir
Longer acting
39
- Oral Hepatitis C treatment
- FDA approved in 2013
- Most expensive drug in history
- Price: 1000 US$ per tabet, 84000$
for 12 weeks treatment course.
- Drug cured > 90% patients in clinical
trial
Sofosbuvir (Sovaldi, Gilead)
Diisobutyrate ester prodrug of fluoro analog uridinmonophosphate
40
Delivered
In-vivo as
Starting point:
Fluoro-Cytidine analog
Active in-vitro as Tri-phosphate
Di-isobutylester analog
Active in-vivo
Metabolis studies however showed that…
First activation step - conversion of Uridyl analog to
Uridyl-phosphate does not work in-vivo
Uridyl analog more potent
Monophosphate had
to be delivered
41
First pass
42
43
Activation mechanism:
44
Case study: Dopamine
In the brain there is a balance of inhibitory neurotransmitter dopamine &
excitatory neurotransmitter acetylcholine.
Parkinson`s disease is characterized by a loss of dopaminergic neurons and a
deficiency of dopamne.
Treatment by supplementation of a high dose of dopamine does not work as
dopamine does not cross the BBB (bisphenol – deprotonated negative charges)
Making use of the L-amino acid transport system, L-dopa (levodopa) is used
to deliver a precursor of dopamine to the brian where it is decarboxylated.
Dopamine
L-dopa
45
Major complication arises because L-amino acid decarboxylase also exists
outside the CNS and >95% of L-dopa is decarboxylated after oral dosing due
to first-pass in the liver and in kidneys -> only 1% of dose elicits the effect.
Inhibition of peripheral L-amino acid decarboxylase can increase efficiency,
Effective dose of L-dopa can be reduced by 75%.
Peripheral decarboxylase inhibitors:
Carbidopa
Benserazide
Dopamine also increases renal blood flow and systolic and puls blood pressure.
If only renal vasodilation is desired a kidney specific delivery is used:
Kidneys have high concentrations of g-glutamyl transpeptidase:
g-Glutamyltranspeptidase
46
Macromolecular drug carriers
Concept: use of a «macromolecular» delivery platform to which the
pharmacologically active substance is conjugated in a way to allow
release at target site.
• Pharmacokinetic properties can be tuned independent of drug structure
• Pharmacokinetic properties now depend on characteristics of polymer
• Medium sized molecules (peptides) are protected from glomerular filtration
• Bound drug less toxic
• Drug carrier allows also to incorporate specific targeting funtions to deliver
drug to site of action
- Macromolecular carriers may be unsuitable for oral administration
- Immunogenic
- Release might be inefficient
47
Simple polymers
Aspirin linked to
Polyvinylalcohol:
Less side effects long term
treatment
Polylysine methotrexate
Folate reductase inhibitor
Improved uptake & therapeutic window
Ibuprofen linked PEG
- Sustained release,
- Prolonged action
- Higher plasma half-life
Polyglutamate norethindrone
9-month release contraceptive
48
Pharmacokinetics
49
Pharmacokinetics is the study of drug absorption,
distribution within body, and drug elimination over
time.
Absorption depends on the route of administration,
Drug distribution depends on lipophilicity of the drug (to
pass through membranes) and on the extent to which the
drug binds to blood proteins (plasma protein binding)
Drug elimination is accomplished by excretion into urine
and/or by inactivation by enzymes in the liver
50
Dose-response curve:
Effective doses must be reached and maintained to generate
the desired therapeutic effect. Overdosing causes risk of toxicity
51
Toxic
Potentially Toxic
Therapeutic
Potentially therapeutic
Subtherapeutic
100×
10×
52
53
The disposition of chemicals entering the body (from C.D. Klaassen, Casarett and Doull’s Toxicology, 5th ed., New York:
McGraw-Hill, 1996).
54
Routes of Administration
Enteral
Parenteral
i.v.
subcutaneous
Inhalation
Intramuscular
Rectal
Oral
Routes of Administration
Plasma concentration following i.v. and oral application
A drug given by the i.v. route will have an
absolute bioavailability of 1 (F=1 or 100%
bioavavailable)
While drugs given by other routes usually
have an absolute bioavailability of
less than one.
The absolute bioavailability is the
area under curve (AUC) non-intravenous
divided by AUC intravenous
57
Definitions
Exposure:
A measure for the amount of drug that an organism has really
"seen"
Bioavailability
A measure for the proportion of the dose that reaches the
systemic circulation (not the same as exposure)
Clearance
A measure of the elimination of a compound from the blood
given as volume cleared/time
Volume of
Distribution
A measure of the theoretical volume that a compound
distributes to.
Half-Life
A measure of the time it takes for the organism to decrease
the concentration of the drug by 50%
58
A Pharmacokinetic Study
Rats were dosed with compound xx and Blood samples were
collected over 96 hours after oral and Intravenous dosing
(h)
0
0.166
0.333
0.666
1
2
4
7
24
30
48
72
96
(ug/l)
0
2422.971
4435.444
7552.264
7421.424
5572.851
2784.17
2270.989
1046.388
714.68
445.44
108.63
5.046
(h)
0
0.0833
0.166
0.333
0.666
1
2
4
7
24
30
48
72
96
(ug/l)
-37700
28600
25500
18100
15700
12200
4200
2200
1630
932
108
130
36
59
Measuring drug concentration in circulation
Blood component
How Obtained
Components
Whole blood
Venous puncture – collected in
tube with anticoaggulant
Contains all cellular & protein
components
Serum
Is liquid obtained from whole
blood after clotting
Does not contain cells, fibrinogen
and other clotting factors
Plasma
Is liquid obtained after
centrifugation of whole blood
treated with anticoagulant
Non-cellular liquid fraction
contiaing all protein components
• Measuring drug concentrations ensures that therapeutic levels are reached
• Measurments of PK allow model building and prediction of drug concentrations
• PK data allow individual ajustment for patients
60
Plasma concentration after 5 mg/kg oral dosing
61
Rat plasma Concentrations of BAY XX-XXXX after
5 mg/kg oral administration to rats
Cmax
BAY XX-XXXX (ug/l)
8000
6000
4000
2000
0
0
2
Absorption Phase
4
6
Time (h)
62
Distribution
63
Absorption
• Most Drugs administered orally as pills
• Absorbed largely from small intestine
•Some Sublinqual absorption
•Rectal Absorption (suppository)
•Some Absorption from stomach (rare)
• Molecules need to be near the intestinal
mucosa to be absorbed
•Compound should be soluble in gut
contents or in vehicle
• Crystals are not well absorbed
• Gummy stuff is not well absorbed
64
Passive Transport normally
thought to be the major Route
65
PK models are usually built using abstract compartment models.
A compartment symbolizes the volume of liquid in which a drug distributes/ dilutes.
Observed drug Blood/Plasma/tissue concentrations are used to model drug behaviour
using differential equations.
In practice: accurate measurements of drug in different discrete tissues is difficult,
also, perfusion rates are not exactly known – therefore compartments are abstract
and virtual constructes without exact physical equivalence.
Comparment
1
In which drug distributes
66
Example: 1 comparment model – i.v. bolus administration
Entire body is described as one continous compartment
VD = apparent volume of distribution
Cp = concentration of drug in Plasma at t=0 after it has equilibrated
D0 = Dose of drug administered
k = elimination rate constant
AUC = area under the curve
Comparment
1 distributes
In which drug
k
Volume of distribution, VD
Cp = D0/VD In practice Cp is not easily accessible
D0 = k x VD x AUC
67
The apparent Volume of distribution, VD
The apparent VD is a specific number and differs from drug to drug
The apparent VD (expressed as % body weight) is constant for a
given drug between patients
The apparent VD indicates how much of the drug is distributed into the tissue
The apparent VD determines how high a doses is required to achieve effctive
concentrations
Most drugs have an apparent VD smaller or equal to the body mass (1kg = 1L)
However, in some cases VDs of several times the body mass have been measured
Volume of plasma for an adult is ca. 3 liter
Apparent volume of distribution is normally > 3 liter
Polar drugs: VD = 8-10 L
Lipophilic drugs: VD can be 20-30 Liter
68
k
D1B , VD
k = km + ke
DB = Cp x VD
dDB
dt
DB… drug in body
First order rate constants
log DB =
-kt
+ log DB0
2.3
DB cannot be measured
directly … but ..
= -kDB
DB0
log Cp =
Cp
-kt
2.3
+ log Cp0
0
VD= DB0/Cp0
Slope
-k/2.3
Log [DB]
Log [Cp]
0
0
[t]
[t]
69
Clearance
Reason for clearance to be a first-order process is that filtration rate of kindeys
is relatively constant (120 ml/min in humans).
Therefore elimination of drug from plasma depends on plasma concentration.
The mechansimsm of drug elimination may be complex, but collectivley drug
elimination can be quantitated with the concept of clearance.
Clearance (CL) refers to volume of plasma fluid eliminated per unit of time.
Example:
Dose = 100 mg
VD = 10 ml
Cp = 10 mg/ml
Volume eliminated / minute:
1 ml/min
Clearance for a first-order process is constant regardless of drug concentration because
it is expressed in volume/unit time instead of drug amount per unit time.
CL = k x VD
t1/2= 0.693/k…… k = obtained via semilog cp vs t
70
Multicompartimental models
What if log Cp vs time is not linear?
Distribution phase
Plasma
c
Log [Cp]
Elimination phase
tissue
0
0
[t]
[t]
PK models are used to simplify all the complex processes that occur during drug
administration, including distribution & elimination in the body.
Model simplification is necessary becasue of the inability to measure quantitatively
all the rate processes in the body.
71
Compartimental models are classical PK models that simulate the kinetic processes
of adsorption, distribution and elimination with little physiological detail.
2-Compartment model
Central compartment
D V1 C
p
p
ke
p
Peripheral compartment
1
Dt Vt Ct
Drug tissue concentration Ct is assumed to be uniform within a given hypothetical
compartment.
Since no data can be collected on Ct; Ct is only theoretical.
However, Cp are simulated assuming the presence of a tissue compartment.
In contrast to Ct, which is not useful, Dt is a usful parameter as it allows to assess how
much drug accumulates extravascularly in the body. -> tracking mass balance.
72
Multicompartment models provide answers such as:
(1) How much of a dose is eliminated?
(2) How much drug remains in the plasma compartment?
(3) How much drug accumulates in the tissue compartment
Multicompartment models explain the observation that after a rapid IV bolus dose ,
The plasma level – time curve does not decline linearly.
Nonlinear plasma drug level – time decline occurs because the drug distributes
into different types of tissues with lower perfusion rates.
The highly perfused tissues and blood makes up the central compartment,
while lower perfused tissues like fat body, mucle, etc.. makes up the peripheral
compartment.
Kinetic analysis of multi-compartment models assumes that all transfer rate processes
between compartments are first-order processes.
Blood supply
Tissue Group
Highly perfused
Heart, brain, kidney, hepato-portal system,
Medium perfused
Adipose tisuse, muscle, connective t.
Slowly perfused
Bone, ligaments, cartilage, hair, teeth
73
Blood flow to human tissues
Tissue
% Body weight
%cardiac output
Blood Flow
ml/100g per min
Kidney
0.4
24
450
Thyroid
0.04
2
400
2
5
20
20
75
Heart
0.4
4
70
Brain
2
15
55
Muscle
40
15
3
Fat
15
2
1
Liver Hepatic
Portal
74
Practical example:
The following time course was recorded:
Time
Cp (observed
0.25
43
0.5
32
1.0
20
1.5
14
2.0
11
4.0
6.5
8.0
2.8
12.0
1.2
16.0
0.52
blood level (ug/ml)
plasma level ug/ml)
10
1
0
2
4
6
8
10
12
14
16
Time (h)
Clearly, not a 1-compartment kinetics
Step 1: Fit a bi-exponential decay: Cp = Ae-at + Be-bt
i.e. fit terminal phase to a linear equation log Cp’ = -bt/2.3 + log B -> gain B (intercept)
75
Clearly, not a 1-compartment kinetics
Step 1: Fit a bi-exponential decay: Cp = Ae-at + Be-bt
i.e. fit terminal phase to a linear equation log Cp’ = -bt/2.3 + log B -> gain B (intercept)
blood level (ug/ml)
B = 15 ug/ml
t1/2 = 0.693/b = 3.3 h
10
Slope= -bt/2.3
b = 0.21 h-1
1
0
2
4
6
8
10
12
14
16
Time (h)
Now, distribution phase can be obtained by substraction of Cp’ from Cp.
Using Cp’= 15e-0.21t
76
Time
Cp (observed
Cp’
Cp – Cp’
A = 45 ug/ml
0.25
43
14.5
28.5
0.5
32
13.5
18.5
1.0
20
12.3
7.7
1.5
14
11
3
2.0
11
10
1
4.0
6.5
8.0
2.8
12.0
1.2
16.0
0.52
blood level (ug/ml)
plasma level ug/ml)
10
a= 1.8 h-1
1
0
2
4
6
8
10
12
14
Time (h)
A number of PK parameters can be calculated:
77
16
A number of PK parameters can be calculated:
Elimination rate constant
transition rate constant central -> peripheral
compartment
transition rate constant peripheral ->
central compartment
Vt = Vp k12/k21
Once the PK parameters are determined for
an individual, the equations can be used to
extrapolate to different situations
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PK parameters for digoxin (heart failure drug)
for a normal patient and a patient with renal
impairment.
Q: when is the maximum tissue concentration
reached?
A: maximum tissue C is then when
Transfer from central compartment
to tissue is equal to transfer from
tissue to central compartment:
Dpk12 = Dtk21
Dp 1.02 = Dt 0.15
-> 3-4 hours for normal patient
Dp 0.45 = Dt 0.11 -> Dp = 0.24xDt
-> 7-8 hours for renal impaired patient
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Some more important relationships:
In the beginning, volume of distribution plasma is
In the beginning there is no elimination, therefore exponential terms are zero:
and
giving
Alternatively the volume of the central compartment can be calculated from the
Area under the curve:
From one compartment model:
Analog:
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Example:
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Constant infusion of drug:
In a constant i.v. infusion, drug solution is infused at a constant zero-order rate, R.
During infusion drug concentration in plasma increases and also the rate of
elimination increases (because elimination is concentration dependent = kCp). Cp
keeps increasing until steady state is reached (R = k DB).
R is rate of
infusion (mg/h)
% of Css reached
Number of half-lifes
90
3.32
95
4.32
99
6.65
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To reach steady state concentration faster,
a loading dose is normally used,
plus a maintenance dose.
Loading dose:
Dose = Cp(Target) x Vd
Q:
What 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
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Answer:
• 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 ~ 600 mg
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Maintenance Dose Calculation
• Maintenance Dose = CL x CpSS
• CpSS 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
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Q:
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
A:
Maintenance Dose = CL x CpSS
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
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Half life:
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.
t 1/2 = 0.693 / k
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Steady-State
• 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 after each dose should be approximately same
100 mg given every half-life:
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Q:
Determine the total body clearance for a drug in a 70kg patient.
The drug follows the kinetics of a one-compartment model
and has an elimination half-life of 3 hours with an apprent volume
of distribution of 100 mL/kg
A:
t1/2 = 0.693/k => 0.693/3= 2.31 h-1
CL = k * VD = 2.31 h-1 x 100 ml/kg -> 23.1 ml kg -1 h-1
CL for 70 kg patient: 1617 ml/h
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Oral dosing:
Extravascular routes, particularly oral dosing are
very popular for convenience.
PK models after extravasular administration must
take into account systemic drug absorption from
the administration site (gut, lung, etc..) into the
plasma.
The major advantage of intravenous admin. is
that the rate and extend of systemic absorption
can be more carefully controlled.
Systemic absorption from e.g. the GI depends on (1) physicochemical properties of the
drug (2) type and design of dosage form (3) anatomy & phsiology of drug absorption site.
In PK the overall rate of drug absorption may be described as either firt-order or zeroorder input process. (?)
90
1
4
2
3
91
ka
k
D1B , VD
DGI
F = fraction already absorbed
Amount in GI exp. declines
Integrated to
At the end of aborption e-kat = 0 ->
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ka can be determined as follows:
1. Fit a straight line to determine
y – intercept and slope -> k
2. Take 3 points on the extrapolated line
and determine corresponding
concentration points on the curve
3. Calculate differences between corresponding
points and plot -> straight line wiht slope
- ka/2.3
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Determined parameters can be used to calculate full curve and Cmax and t max.
Cmax = Cp at Tmax
For oral dosing, a one compartment model is normally the model of choice.
There is more complex models but they all require also i.v. injection experiments
to determine k12 and k21 and other konstants to feed the model.
This level of complexity is not always desireable.
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Repetitive dosing – essential aspects
Ideally a dosing regimen is established for
each drug to provide the correct plasma level
without excessive fluctuation and drug
accumulation outside the therapeutic window.
2 main parameters:
- Dose applied
- t, the frequency of drug administration
Average concentration of drug at steady state is calculated by:
Can also be obtained from AUC
& F being the
fraction of dose absorbed
and
Concentration of drug x hours after n doses:
&after many doses
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Maximum and minimum amounts of drug between doses:
f = e-kt
f is fraction of dose left at end of dosing intervall
Cmax = Dmax/VD
Dmax = D0 / ( 1-f)
Dmin = Dmax – D0
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Example:
A patient receives 1000 mg of an antibiotic drug every 6 hours by i.v. bolus injection.
The drug has an elmination half-life of 3 hours and shows a volume of distribution of
20 L.
(1) What is the maximum and minimum amount of drug in the body between dosings
(2) What is the steady state average plasma concentration
(3) What is the plasma concentration 3 hours after the second dose?
1. Calculate k:
k = 0.693/t1/2 = 0.693/3 = 0.231 h-1
2. Calculate remaining dose at the end of dosing interval (f factor):
f = e-kt = e- 0.231x6 = 0.25 …. After dosing interval 0.25 is left of previous dose.
( with this information a table can be generated showing amount of drug after each
dose)
Dmax = D0/(1-f) = 1000/ (1-0.25) = 1333 mg -> maximum amount immediately after
dosing.
Dmin = Dmax – D0 = 1333 – 1000 = 333 -> minimum dose shortly before dosing. 97
Dmax = D0/(1-f) = 1000/ (1-0.25) = 1333 mg -> maximum amount immediately after
dosing.
Dmin = Dmax – D0 = 1333 – 1000 = 333 -> minimum dose shortly before dosing.
knowing that the Volume of distrubution is 20L we can calculate the cmax and cmin in
plasma between dosings:
cmax is 1333 mg/20000ml = 66 ug/ml
cmin is 333mg/20000ml = 16.5 ug/ml
Q2: (2) What is the steady state average plasma concentration?
F is 1 for an i.v. injection, therefore
Cav = 1000/(20x0.231x6) = 36 mg/L = 36 ug/ml
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(3) What is the plasma concentration 3 hours after the second dose?
n= 1, t=3
Cp =
1000
20
(
1-e-(2)(0.231)(6)
1-e- (0.231)(6)
)
e-(0.231)(3)
Dose # Before dosing
After dosing
1
0
1000
2
250
1250
3
312
1312
4
328
1328
5
332
1332
6
333
1333
7
333
1333
n
333
1333
= 31.3 mg/L = 31.3 ug/ml
-> amount of drug before and after
repetitive dosing with f= 0.25
This is influenced by Dose, interval and
Half-life (or elimination rate constant)
k = 0.693/t1/2
f = e- kt
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Example:
Tobramycin:
t1/2 = 2.15 h
VD = 33.5% of body weight
What is the correct dose for a 80kg patient if a average concentration of 2.5 ug/ml
is desired and the dosing regime is once every 8h?
k = 0.693/t1/2
D0 = 173 mg every 8 hours
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Dose and frequency of dosing
The size of drug dose is related to frequency at which it is given.
The more fequently a drug is given, the smaller the individual dose needed.
On the other hand, if dosing interval is too long, the dose required to keep a
desired average concentration increases and leads to higher Cmax and Cmin
differences.
In general, dosing interval for most drugs is determined by elimination half-life
Especially drugs with a narrow therapeutic window need to be given more
frequently to prevent cmax shooting over the toxic threshold.
Cmax
=
Cmin
1
e-kt
Example: antibiotic with 3 h half-life, VD = 20% body weight (200ml/kg),
Therapeutic range is 5 – 15 ug/ml. Serum concentrations > 20 ug/ml are toxic .
Calculate dosing regime which will maintain therapeutic levels betwen 5-15 ug.
1st calculate appropriate t:
15/5 = 1/e-(0.693/3)xt -> t = 4.76 h
For Cav= 10ug/ml
D= 0.01x200*0.693/3*4
D = 1.848 ug/kg
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