Understanding the Half Life of a Drug: Definition, Types, Formula, and Equation
Definition:
It is the time by which the concentration or effect of a drug decline by one half or 50%.
Phases:
- α-half life - half life of distribution
- β-half life - half life of elimination
Classifications:
- Biological effective half life: It is the time in which the pharmacological effect of the drug and its active metabolites falls by one half or 50%.
- Elimination half life: It is the time in which the total amount of drug within the body, after equilibrium of plasma with other compartment (fat/muscle), falls by one half or 50%.
- Plasma half life (t 1/2): It is the time in which the concentration of the drug in plasma fall by 50%.
Example: 40 mg drug is administered (I/V) and after 2hr, concentration becomes 20mg, i.e. reduced by 50% of its original value. So the half life of the drug is 2 hours.
Plasma half life depends on:
- Routes of administration
- Dose of the drug
- Dosage schedule
- Tissue binding - The more the tissue binding of a drug, the longer the half life of that drug.
- Distribution - The more widely distributed a drug is the longer the half life.
- Excretion - The faster the excretion, the shorter the half life.
- Age of the patient
- Genetic factors - Determines whether a person is fast or slow acetylator.
- Plasma protein binding of the drug - The more the plasma protein binding the longer is the half life of a drug and vice versa.
- Drug biotransformation - If a patient suffers from cardiac or liver disease and there is decreased drug biotransformation then the half life of drugs increases. This is also true for enzyme inhibitors which inhibit the metabolizing enzymes. On the other hand, enzyme inducers increase the biotransformation of drug and thus decrease the half life of drugs.
| Phenytoin | Half life |
|---|---|
Low dose (25mg) | 10-15 hours |
High dose | 60 hours |
|
|
| Dosage | Half life |
|---|---|
Single dose | Increased |
Repeated dose | Decreased |
|
|
| Drug | Half life in neonates | Half life in adults |
|---|---|---|
Diazapam | 25-100 hour | 40-50 hour |
Salicylate | 5-11 hour | 10-15 hour |
Digoxin | 60-70 hour | 30-60 hour |
INH
| Type of acetylator | Half life |
|---|---|
Slow | 3 hour |
Fast | 1 hour |
|
|
Half life formula (half life equation)
Half life = 0.693/k
k = first order rate constant
See the video below for more details.
How to do half life calculation?
Examples of half life of drugs:
| Long half life | Short half life |
|---|---|
Digoxin 1-5 day | Dopamine 2 minute |
Digitoxin 7 day | Benzylpenicillin 30 minute |
Warfarin 25-60 hour | Insulin 10 minute |
Phenylbutazone 60 hour | Tubocurarine 60 minute |
Doxycycline 18 hour | Lidocaine 2 hour |
Diazepam 40-50 hour |
Look at how long medicine keeps you pain free
Look at how long medicine keeps you pain free
Clinical situation in which half life is increased
1. Diminished renal blood flow due to
- Cardiogenic shock
- Haemorrhage
- Heart failure
2. With addition of 2nd drug that displaces the first drug from albumin and thus increases the volume of distribution
eg. phenylbutazone + OHA. Phenylbutazone displaces OHA from binding site, thus increases the half life of OHA.
3. With decreased extraction ratio in renal disease
4. With decreased metabolism, for example when another drug decreases its biotransformation or hepatic insufficiency as with liver disease.
Extraction ratio
This ratio is the decline of drug concentration in the plasma from the arterial to the venous side of the kidney.
Drug entering the kidney at concentration = c1
Drug exiting the kidney at concentration = c2
So extraction ratio = c2/c1
Importance of half life
1. Half life gives a gross idea about the pharmacokinetic and pharmacodynamic of a drug
2. To predict the duration of action of a drug
3. To formulate a dosage schedule (amount of drug and frequency of interval)
- long half life : Should be given once/twice daily to prevent accumulation
- short half life : Should be give repeatedly
4. To handle a case of overdose of a drug
5. To determine the time to achieve steady state plasma concentration
6. It also give general knowledge:
- Whether the drug is metabolized or eliminated unchanged.
- Whether the drug itself is active or converted into active metabolite or both eg. Diazepam
- Whether the drug has irreversible action or not eg. Reserpine.
- Presence of disease in the organ of metabolism or excretion
Characteristics of a drug with long half life
- High molecular weight
- Less lipid soluble
- Slow absorption from GIT
- High PPB
- Metabolism is less
- Elimination rate is Slow
- Tissue distribution is more
- More cumulative effect
- Less dose frequency
- Can not be used in emergency
What is the significance of plasma half life = 12 hour?
Plasma half life = 12 hours signifies
- 12 hour is taken for that specific drug to fall its plasma concentration by 50%
- Absorption is slow
- Plasma protein binding is high
- Metabolism is slow
- Excretion is less
- Slow & sustained action
- Suitable in chronic case
- Compliance of the patient is good
- Frequency of administration is twice a day
What Is the significance of plasma half life = 1 hour?
Plasma half life = 1 hour signifies:
- 1 hour is taken for that specific drug to fall its plasma concentration by 50%
- Absorption is rapid
- Plasma protein binding is less
- Rapid metabolism
- Rapid excretion
- Rapid action
- Suitable for emergency case
- Frequency of administration is more
- Compliance of the patient is less good
How half life of a drug can be changed?
1. By tagging new chemical substances with drug
- Insulin is quickly metabolised in the body. If protamine-zinc-insulin complex is used the half life increases and the patient does not have to take it up to 24 hours.
- In rheumatic fever penicillin is injected but it produces severe pain. When benzathine is tagged with it, it can produce effect for one month.
2. By decreasing the elimination of drug
- Penicillin is secreted through kidney. If probenecid is administered it competes with penicillin, so penicillin excretion is delayed, and so the half life of penicillin is increased.
Advantage and Disadvantage of long half life
| Therapeutic disadvantage | Therapeutic advantage |
|---|---|
Cannot be given in emergency by oral route | Long duration of action |
More cumulative effect e.g. Diazepam-next day hangover | Less dose frequency |
More drug interaction as it is highly protein bound | Better patient compliance |
Chance of toxicity is more as it is less rapidly metabolised or eliminated | Can be used in prophylaxis, eg salmeterol to prevent night asthma |
| Tolerance does not develop |
| Therapeutic disadvantage | Therapeutic advantage |
|---|---|
Short duration of action so cannot be used as prophylactic measure | Can be given in emergency to prevent acute attack e.g GTN in acute angina |
More dose frequency | Rapidly excreted so less chance of toxicity |
Development of tolerance is more if frequently used | No cumulative effect |
| No drug interaction |
Dosing schedul from the knowledge of half life
1. Half life < 3 hour:
- If the half life is extremely short (dopamin half life = 2 min), then continuous IV infusion should be given.
- If the tl/2 is not extremely short (Lidocaine tl/2 = 2 hr), then initial loading dose followed by continuous IV infusion should be given.
2. Half life = 6-12 hour:
- Dosing interval should be equal to the plasma half life i.e. every 6-12 hrly
3. Half life > 24:
- Once daily dose
That's all for now!
That's it for today! Keep coming back as I will be adding more pharmacology articles soon!
