# PLASMA HALF LIFE

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### Slide 1:

PLASMA HALF LIFE (t ½ )

### Slide 2:

Effective drug concentration: It is the concentration of the drug at the receptor site. The conc. at the receptor site is usually proportionate to the drug conc. in the plasma or whole blood at equilibrium (except topically applied drug).

### Slide 3:

Important Plasma Concentration Minimum Effective Concentration (MEC): The plasma drug concentration below which a patient’s response is too small for clinical benefit. Peak Plasma & Through Concentration : The maximum & minimum drug conc. achieved during repeated dosing cycles. Target Concentration : The plasma concentration required to produce desired therapeutic effect.

### Slide 5:

Plasma Half Life (t ½ ) Definition: It is the time required to change the amount of drug in the plasma to decrease to one half of its initial value during elimination. It is designated as t ½. It is a useful parameter derived from Vd & CL. t ½ is important for rational drug therapy because it helps in designing & planning the dosage regimens.

### Slide 6:

Determination of t ½ : 1: It can be calculated by following relationship: t ½ = 0.7 x Vd (0.7: Natural Log. Of 2) CL 2: Determined graphically from the plot of plasma conc. versus time, by measuring time between any 2 plasma conc. points on the elimination phase that differ by two fold.

### Slide 8:

The graph shows two phases: Initial rapidly declining ( α ) phase --- due to distribution ----- t ½ α . Later less declined ( β ) phase --- due to elimination ------ t ½ β .

### Slide 9:

Decline in Plasma Concentration Starting at any steady-state plasma concentration (100 %) of a drug , it will fall as follows: After 1 t ½ to 50 % After 2 t ½ to 25 % After 3 t ½ to 12.5 % After 4 t ½ to 6.25 % After 5 t ½ to 3.125 % t ½ 0 1 2 3 4 5 Plasma conc (mg) 100 50 25 12.5 6.25 3.125 In one t ½ conc. falls by 50 %. So 97 % drug is eliminated from the body in 5 t ½ . For complete elimination more time is required

### Clinical Significance of t ½ :

Clinical Significance of t ½ t ½ indicates rate of elimination. 97 % drug eliminated in 5 t ½ For complete elimination more than 7 t ½ are required 2 . The steady state (SS) reaches in 4-5 t ½ . 3. t ½ indicates the duration of action of a drug. The drugs with longer t ½ have greater duration of action and drugs having shorter t ½ have less duration of action. t ½ is important for designing a dosage regimen. 5. t ½ may be altered by many factors

### Slide 12:

Decline in Plasma Concentration Starting at any steady-state plasma concentration (100 %) of a drug , it will fall as follows: After 1 t ½ to 50 % After 2 t ½ to 25 % After 3 t ½ to 12.5 % After 4 t ½ to 6.25 % After 5 t ½ to 3.125 % t ½ 0 1 2 3 4 5 Plasma conc (mg) 100 50 25 12.5 6.25 3.125 In one t ½ conc. falls by 50 %. So 97 % drug is eliminated from the body in 5 t ½ . For complete elimination more than 7 t ½ is required

### Slide 13:

Change in plasma concentration following an i.v. bolus injection of a drug, in the elimination phase (the distribution phase, see text, is not shown); as elimination is a first-order process, the time taken for any concentration to fall by 50% (t ½) is the same.

### Slide 14:

Steady state (SS): In Pharmacokinetics the condition in which the average total amount of the drug in the plasma does not change over multiple dosing cycles. ( i.e the condition in which the Rate of elimination equals the Rate of drug administration). Time to reach SS --4-5 t ½ . 50% of SS reaches in one t ½ Time to reach SS is independent of dose.

### Rise in Plasma Concentration / time to reach steady state (SS):

Rise in Plasma Concentration / time to reach steady state (SS) If a drug is given by a constant I/V infusion, the plasma concentration will rise as follows: In 1 x t ½ to 100/2= 50 % In 2 x t ½ to 50/2 + 50= 75 % In 3 x t ½ to 75/2 + 50= 87.5 % In 4 x t ½ to 87.5/2 + 50= 93.75 % In 5 x t ½ to 93.75 /2+ 50= 96.87 % So SS (pleatue) is reached after 4-5 t ½ . Time to reach SS is not affected by dose of drug.

### Plasma Half Life of Some drugs:

Plasma Half Life of Some drugs Esmolol 09 Min Aspirin 15 Min Morphine 1.9 Hours Propranolol 3.9 Hours Digoxin 50 Hours Digitoxin 161 Hours

### Slide 18:

Designing a dosage regimen Dosage Regimen: It is a plan for drug administration over a period of time. The interval between doses should not be less than 4 t ½ . Drugs with short half life --- More frequent dosing. Drugs with long half life --- Less frequent dosing. Loading dose for drugs with large Vd .

### Slide 19:

Maintenance Dosage: Dosing rate = CL x Desired plasma conc. Bioavailability (F) Loading Dosage: Initial large dose given for drug with large Vd i.e. Digoxin, chloroquine. Loading dose= Vd x Desired plasma conc. Bioavailability (F) Adjustment of Dosage when Elimination is altered by disease: Corrected dose = Average dose x Pt’s creatinine CL 100 ml/min

### Factors Affecting t ½ :

Factors Affecting t ½ 1. Factors affecting CL & Vd independently will change t ½ . If both CL & Vd are altered there may not be any change in t ½ . e.g. Digoxin in chronic renal failure & Lidocaine in chronic heart failure. 2. Type of Kinetics------First order (constant t ½ ) /Zero order ( prolonged t ½ ) . 3. Diseases of organ of metabolism / excretion--- hepatic & renal disease ( prolonged t ½ ) . 4. Addition of second drug : Enzyme inducers - ----↑ metabolism (↓ t ½ ) . Enzyme inhibitors - ---- ↓ metabolism (↑ t ½ ) .

### Slide 21:

5. Active metabolites ( prolonged t ½ ) . 6. Entero hepatic re-circulation ( prolonged t ½ ) . 7. Decreased hepatic blood flow e.g. in cardiogenic shock, cardiac failure, hemorrahage ( prolonged t ½ of drugs with flow dependent CL / extensive hepatic first pass metabolism ) . 8. Displacement of a drug from PPB sites increasing its CL (↓ t ½ ) .

### Slide 22:

Therapeutic drug monitoring It is particularly useful in the following situations: Drugs with narrow therapeutic window (low safety margin) ---- Digoxin, Lithium, Theophylline. If individual variations are large---Antidepressants. Potentially toxic drugs used in the presence of renal failure---Aminoglycoside antibiotics. In case of poisoning. In case of failure of response without any apparent reason---Antimicrobials. To check patient compliance ---- Psycho pharmacological agents.

### Slide 23:

Therapeutic window: