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Half life - Definition, Formula / Equation, Types (Biological) & more - ePharmacology

Updated on July 7, 2014

Definition of half life

It is the time by which the concentration or effect of a drug decline by one half or 50%.

Phases of half life

  1. α-half life - half life of distribution
  2. β-half life - half life of elimination

Classification of half life

1. 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%.

2. 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), fally by one half or 50%.

3. 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 :

1. Routes of administration

2. Dose of the drug

In case of Phenytoin:

Phenytoin
Half life
Low dose (25mg)
10-15 hours
High dose
60 hours
 
 

3. Dosage schedule

Dosage
Half life
Single dose
Increased
Repeated dose
Decreased
 
 

4. Tissue binding of a drug

The more the tissue binding of a drug, the longer the half life of that drug.

5. Distribution of drug

The more widely distributed a drug is the longer the half life.

6. Excretion of drug

The faster the excretion, the shorter the half life.

7. Age of the patient

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

8. Genetic factors:

Determines whether a person is fast or slow acetylator. For example in case of INH

Type of acetylator
Half life
Slow
3 hour
Fast
1 hour
 
 

9. Plasma protein binding of the drug

The more the plasma protein binding the longer is the half life of a drug and vice versa.

10. 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.

Source

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 | Source
Look at how long medicine keeps you pain free
Look at how long medicine keeps you pain free | Source

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

  1. High molecular weight
  2. Less lipid soluble
  3. Slow absorption from GIT
  4. High PPB
  5. Metabolism is less
  6. Elimination rate is Slow
  7. Tissue distribution is more
  8. More cumulative effect
  9. Less dose frequency
  10. Can not be used in emergency

What is the significance of plasma half life = 12 hour?

Plasma half life = 12 hours signifies

  1. 12 hour is taken for that specific drug to fall its plasma concentration by 50%
  2. Absorption is slow
  3. Plasma protein binding is high
  4. Metabolism is slow
  5. Excretion is less
  6. Slow & sustained action
  7. Suitable in chronic case
  8. Compliance of the patient is good
  9. Frequency of administration is twice a day

What Is the significance of plasma half life = 1 hour?

Plasma half life = 1 hour signifies:

  1. 1 hour is taken for that specific drug to fall its plasma concentration by 50%
  2. Absorption is rapid
  3. Plasma protein binding is less
  4. Rapid metabolism
  5. Rapid excretion
  6. Rapid action
  7. Suitable for emergency case
  8. Frequency of administration is more
  9. 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

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