Download Calculate the elimination rate constant and half life.

Pharmacology in nuclear medicine
Prof Geoff Currie, BPharm, MMedRadSc, MAppMngt, MBA, PhD
Faculty of Science, Charles Sturt University
Faculty of Medicine and Health Sciences, Macquarie University
Rural Clinical School, University of NSW
May 28 – 30, 2015, Montréal, Québec
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Disclosure Statement: No Conflict of Interest
I do not have an affiliation, financial or otherwise, with a pharmaceutical company, medical
device or communications organization.
I have no conflicts of interest to disclose ( i.e. no industry funding received or other
commercial relationships).
I have no financial relationship or advisory role with pharmaceutical or device-making
companies, or CME provider.
I will not discuss or describe in my presentation at the meeting the investigational or
unlabeled ("off-label") use of a medical device, product, or pharmaceutical that is
classified by Health Canada as investigational for the intended use.
May 28 – 30, 2015, Montréal, Québec
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Pharmacology
• is the study of the action of drugs on living
systems and the interactions of drugs with
living systems
• Generally is divided into
•
•
Pharmacodynamics is the effects of the drug on
the body
Pharmacokinetics is the effects of the body on
drugs
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Drug
• is a chemical substance that produces a
biological effect and can be either
synthetic or derived from plant, animal or
mineral sources
• Generally is exogenous although
endogenous sources might also exist
•
for example, adenosine is an endogenous drug
produced by the body while dipyridamole is an
exogenous drug introduced to the body
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Receptor Principles
• Receptors are proteins (macromolecules)
that mediate drug activity
• The chemical signal (ligand) binds to a
specific site (receptor) and triggers a
response in the cells
• The intra-cellular changes initiated by the
ligand-receptor complex can be through
direct or indirect action, however, the
ligand generally functions as an agonist or
an antagonist
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Receptor Principles
• An agonist will mimic the endogenous
ligand to produce a similar response
• An antagonist blocks the usual ligand and,
thus, inhibits the physiological response
•
•
•
•
•
Antagonist can be reversible, partially reversible or
irreversible
Caffeine / adenosine
Beta blockers
CCB
Captopril (ACEI)
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Receptor Concept - Agonist
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Receptor Concept - Antagonist
No response
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Receptor Principles
• Specificity is the measure of a receptors
ability to respond to a single ligand
•
Low specificity generally results in physiological
responses not targeted or intended by the drug; side
effects provide a good example
• Selectivity defines the ability of the receptor
to distinguish between drugs and has the
same implications as specificity; indeed the
terms are often used interchangeably
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Receptor Principles
• Affinity defines the strength of attraction
between the drug and its receptor
•
A high affinity is generally associated with a lower
dose requirement (compared to low affinity for the
same receptor).
• Potency describes the relationship between
the drug dose and the magnitude of the
effect
•
•
High potency induces a maximum effect with a
minimum of drug.
Antagonist potency relates to dose required to inhibit
50% of biological effect of agonist
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Receptor Principles
• Efficacy is the invivo potency
•
Antagonist has no efficacy
• The interaction (eg. absorption, metabolism,
excretion) of the drug in the body may alter
the relative bioavailability and thus, change
the theoretical effect of the drug.
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Pharmacodynamics
• Used to explain the relationship between
the drug dose and response
•
•
Drug effects
Side effects
• The pharmacologic response depends on:
•
•
•
•
•
Drug binding to the target.
Concentration of the drug at the receptor site.
Disease states
Age and gender
Other drugs
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Dose-Response Relationships
• Concentration of the drug at the receptor
controls the effect
• Typically non-linear
• Drug effect is a function of dose and time
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Increased
efficacy
Increased
potency
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Antagonist
(eg caffeine on adenosine)
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Therapeutic Window
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Pharmacokinetics
• The underlying principle of
pharmacokinetics is consistent with the
philosophy of Paracelsus (medieval
alchemist)
“only the dose makes a thing not a poison”
• Within a window, a specific drug will offer
therapeutic benefit and outside that
window there will either be no therapeutic
benefit or toxicity.
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Pharmacokinetics
• A narrow therapeutic range (eg digoxin)
means small variations in blood
concentration may easily result in toxic or
sub therapeutic concentrations.
• To maintain concentrations within the
therapeutic range requires consistent
bioavailability.
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Pharmacokinetics - ADME
• Absorption
•
Drug moves from site of administration to site of
measurement
• Distribution
•
Reversible drug transfer too and from site of
measurement (eg. compartments)
• Metabolism
•
Conversion of one species to another (eg. metabolites)
• Excretion
•
Irreversible loss of drug from site of measurement (eg.
kidneys, biliary, bowel)
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2 compartment
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Calculations
A patient weighing 70kg is given an IV bolus injection of 25mg of MDP.
Plasma concentrations after injection are tabulated.
Time (hours)
Plasma
concentration
(micrograms / L)
139
65.6
31.1
14.6
2
4
6
8
160
140
120
100
80
60
40
20
0
Cp
0
2
4
6
8
10
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Calculations
1.Calculate the elimination rate constant and half life.
Log / linear plot to confirm a single compartment mono-exponential curve.
Time (hours)
Plasma
concentration
(micrograms / L)
139
65.6
31.1
14.6
2
4
6
8
Log Cp
2.14
1.82
1.49
1.16
1000
100
Cp
10
1
0
2
4
6
8
10
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Calculations
Calculate the k and half life
C = C0 e-kt
k = ln2 / T0.5
14.6 = 139 e-k.6
T0.5 = ln2 / k
14.6 / 139 = e-k.6
T0.5 = ln2 / 0.3745
ln 0.1057 = -k.6
T0.5 = 1.85 hours
k = 0.3745
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Calculations
Calculate the AUC0-∞
AUC0-∞ = Cp0 / k
given k,
C = C0 e-kt
139 = C0 e-0.3745 x 2
139 = C0 x 0.4728
C0 = 139 / 0.4728
C0 = 294
AUC0-∞ = 294 / 0.3745 = 785ug or 0.785 mghrs /
litre
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Calculations
Calculate the clearance.
CL = dose / AUC
CL = 25000 / 785
CL = 31.84 litres / hour
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Calculations
The kidney concentrations of an IV DTPA are presented.
Time (min)
Plasma
concentration
(U / L)
0
31.3
49.3
58.6
62.5
62.8
58.1
50.6
36.1
25.3
0
1
2
3
4
5
7
10
16
24
70
60
50
40
Cp
30
20
10
24
22
20
18
16
14
12
10
8
6
4
2
0
0
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Calculations
Calculate the elimination rate constant and half life.
Log / linear plot to show mono-exponential clearance.
100
Cp
10
24
22
20
18
16
14
12
10
8
6
4
2
0
1
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Calculations
Time (mins)
0
1
2
3
4
5
7
10
16
24
Plasma
concentration
(U / L)
0
31.3
49.3
58.6
62.5
62.8
58.1
50.6
36.1
25.3
Elimination
curve
concentration
58.1
50.6
36.1
25.3
So.
C = C0 e-kt
25.3 = 58.1 e-k x 17
25.3 / 58.1 = e-k x 17
ln 0.4355 = -k x 17
k = 0.0489 (mins-1)
k = ln2 / T0.5
T0.5 = ln2 / k
T0.5 = ln2 / 0.0489
T0.5 = 14.17 mins
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Calculations
Calculate the absorption dose rate constant and half life.
Elimination
curve
concentration
81.8
77.9
74.0
70.7
67.1
64.1
58.1
50.6
36.1
25.3
R
(plasma –
elim)
81.8
46.6
24.7
12.1
4.6
1.3
C = C0 e-ka x t
12.1 = 46.6 e-ka x 2
12.1 / 46.6 = e-ka x 2
ln 0.2596 = -ka x 2
ka = 0.6742 (mins-1)
ka = ln2 / T0.5
T0.5 = ln2 / ka
T0.5 = ln2 / 0.6742
T0.5 = 1.03 Mins
100
Cp
10
Log Cp
24
22
20
18
16
14
12
10
8
6
4
1
2
0
1
2
3
4
5
7
10
16
24
Plasma
concentration
(ugm / ml)
0
31.3
49.3
58.6
62.5
62.8
58.1
50.6
36.1
25.3
0
Time (hours)
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Calculations
Calculate the Tmax
Tmax = (1/[ka-k]) ln (ka/k)
Tmax = (1/[0.6742-0.0489]) ln (0.6742/0.0489)
Tmax = (1/[0.6742-0.0489]) ln (13.8)
Tmax = 1.6 x 2.6
Tmax = 4.2 mins
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Nuclear Cardiology Case Study
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Pharmacologic Stress
• Exercise limited by beta blockers or calcium
channel blocker
• Stop xanthine drugs for 48 hours
• Stop caffeine for 12-48 hours (varies)
• We usually stop all stress patients with the
caffeine ‘in case’ they need pharmacologic
stress
• Why?
• For how long?
• Lets ‘understand’ what we are doing.
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Purines
• Dipyridamole and Adenosine are not β agonists
• Adenosine is a purine:
• ATP breakdown
• Present in many tissues (CNS and peripheral)
• Acts on adenosine receptors (A1-4)
• Blocked by theophylline
• Vasodilator
• Block AV conduction
• Angina chest pain (stimulates nociceptive neurons)
• Broncho-constriction (contraindicated in asthma)
• Inhibits platelet aggregation
• Neuroprotection in cerebral ischaemia
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Adenosine
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Adenosine
There are four main adenosine receptor sub-types :
• A1, block atrioventricular (AV) conduction, reduce force
of cardiac contraction, decreased glomerular filtration
rate, cardiac depression, renal vasoconstriction,
decreased central nervous system (CNS) activity and
bronchoconstriction.
• A2A, anti-inflammatory response, vasodilation, decreased
blood pressure, decreased CNS activity, inhibition of
platelet aggregation and bronchodilation.
• A2B, stimulate phospholipase activity, release of mast
cell mediators, and actions on colon and bladder.
• A3, stimulate phospholipase activity and release of mast
cell mediators (contributes to bronchoconstriction).
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Figure 2
Rest
Stress
adenosine reuptake inhibition
(dipyridamole)
coronary
steal
vasodilation –
coronary flow reserve
(adenosine)
increased oxygen demand – induced ischaemia
(exercise / dobutamine)
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Adenosine and the Heart
• A1 receptors
• Causes transient heart block
• Relax arterial smooth muscle
• causes dilatation of the "normal" arteries
• but not where affected by plaque
• exaggerates blood flow difference between normal
and stenosed vessels
• Does not necessarily cause ischaemia
• Short half life
• Adenosine is also a CNS depressant!
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Xanthine / Methylxanthines
• Xanthine is a purine found throughout the body
• two of the building blocks of DNA itself are structural
analogues; adenine and guanine.
• basic xanthine structure below
• structural similarity with adenine part of adenosine means
potential antagonism of adenosine by xanthine based drugs.
• There are a number of xanthine derivatives that offer
bronchodilation and mild CNS stimulation by virtue of
antagonisms of adenosine.
• Methylation (substitution of H with CH3) of the xanthine
produces a number of variants called methylxanthines;
caffeine, theobromine and theophylline.
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Caffeine
Theobromine
Theophylline
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Caffeine
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Caffeine
• naturally occurring alkaloid
• purine structure binds to same receptors as
adenosine
• effects of adenosine blunted by
methylxanthines
• caffeine, found in coffee and tea,
• theobromine, found in chocolate
• CNS stimulant
• by blocking CNS depression by adenosine
• respiratory stimulant
• cardiac stimulant and diuretic
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Caffeine in MPS
• While 99% of caffeine is absorbed in the GI tract
within 45 minutes of consumption, plasma
concentrations following the same caffeine
ingestion can vary amongst individuals by as
much as a factor of 16
• The half life of caffeine is important but variable:
•
•
•
•
•
generally 4-6 hours biological half life
increased a bit by oral contraceptives (x2) or
pregnancy (15 hrs for last trimester)
increased substantially (96 hours) in liver disease
nicotine (smoking) can reduce the half life by 50%
Alcohol consumption decreases half life
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Caffeine in MPS
•
•
•
So why stop it for 48 hours?
Because that represents 8-10 half lives.
Same principle as decay by storage.
•
•
Does it make a difference?
The marginal improvement up to 24 hours is probably very
worthwhile.
The marginal improvement out to 48 hours (24-48 hrs) is
probably negligible.
•
•
•
•
Especially if they only have small amounts of caffeine.
So for the average person, 24 hours is more than enough
and indeed 12 hours would probably cover it.
People addicted to coffee and chocolate might need longer.
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Summary
• Adenosine and persantin act on adenosine
receptors so are not antagonised by β
blockers
• Exaggerates blood flow difference between
normal and atherosclerotic vessels
(vasodilation)
• Causes bronchoconstriction
• Persantin just increases the bioavailability of
adenosine
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Summary
•
•
•
•
•
Caffeine is an adenosine antagonist
Need to stop for persantin or adenosine
No need to stop for exercise or dobutamine
6-12 hours sufficient in normal use
Longer in liver disease or heavy consumption
• Shorter for smokers
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Questions?
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