Kinetics of multiple dosing

KINETICS OF MULTIPLE DOSING under the Unit Multicompartment Models According to New PCI syllabus 2017 by Ms. Preeti Patil-Vibhute, Assistant Professor, Sarojini College of Pharmacy, Kolhapur.

1. BIOPHARMACEUTICS AND PHARMACOKINETICS UNIT NO.04: MULTICOMPARTMENT MODELS Lecture No. 02: Kinetics of Multiple Dosing PRESENTED BY: MRS. PREETI B. PATIL ASSISTANT PROFESSOR, DEPARTMENT OF PHARMACEUTICS, SAROJINI COLLEGE OF PHARMACY, KOLHAPUR

2. KINETICS OF MULTIPLE DOSING Many drugs such as antibiotics, antihypertensive, antiepileptic are usually given as multiple dose regimen to produce and maintain effective plasma concentration. In a single dose treatment , it is assumed that there is no drug in the body before the drug is administered and that no more is going to be administered after single dose given. However, in case of multiple dose administration we expected to give second and subsequent doses before the drug is completely eliminated from the body. Thus drug accumulation should be considered. On repeated drug administration, the plasma concentration will be repeated for each dose interval giving a STEADY STATE or PLATEAU with the plasma concentration fluctuating between a minimum and maximum value.

3. DRUG ACCUMULATION For single intravenous administration, Initial Plasma Concentration C is calculated as, C = X /V Where, X - Dose of drug V - Apparent volume of distribution of drug Fig.: 4.1 Plasma drug concentration after a single I.V. Bolus dose

4. If second drug dose is given at a time when the concentration of the first dose have fallen to approximately Zero then there is no drug accumulation in the body. Here we can see that C for the second dose is same as that of that for the first dose. This indicates that there is no drug accumulation in plasma. Fig.: 4.2 Plasma drug concentration after two I. V. Bolus doses with large time interval in- between

5. However, If the second dose is given after a short interval of time so that not all of the first dose is eliminated then the drug will start to accumulate and will get higher concentrations with the second dose. This summation of concentrations resulting from additional doses is termed as the PRINCIPLE OF SUPERPOSITION. Fig.: 4.3 Linear plot of Concentration versus Time showing doses given before complete elimination of the previous doses

6. The rate of elimination is equal to the amount of drug in the body multiplied by the rate constant for a First order elimination. As the plasma drug concentration increases the amount of drug eliminated during the dosing interval also increases. Thus, drug accumulation with each dose will be continued until the amount of drug eliminated during each dosing interval is equal to the amount of the dose. For example: If the amount of dose is 5mg/L then amount of drug eliminated during dosing interval should be 5mg/L. Here, the plasma drug concentration approaches a steady state or Plateau . Thus, Steady state conditions are attained when the rate of drug entering the systems equals the rate of drug leaving the system.

7. ACCUMULATION FACTOR OR ACCUMULATION INDEX ( R AC ) Definition: It is defined as the ratio between the highest, initial concentration at steady state, C max and the highest plasma concentration after the first dose (C ) i.e. C =X /V, and it is Expressed as: R ac = C max / C 1 R ac = 1 / 1-R R ac = 1 / 1-e –KƮ Significances: It gives idea about the quantity of drug accumulates during a multiple dosing regimen. It gives a direct measure of how much higher the concentrations are during a dosing interval at steady state compared with the concentration during the first dosing interval.

8. STEADY STATE DRUG LEVELS STEADY STATE OR PLATEAU PRINCIPLE The rate of elimination is equal to the amount of drug in the body(C) multiplied by the rate constant for a First order elimination (K). As the plasma drug concentration increases the amount of drug eliminated during the dosing interval also increases. Thus, drug accumulation with each dose will be continued until the amount of drug eliminated during each dosing interval is equal to the amount of the dose. For example: If the amount of dose is 5mg/L then amount of drug eliminated during dosing interval should be 5mg/L. Here, the plasma drug concentration approaches a STEADY STATE or PLATEU . Thus, Steady state conditions are attained when the rate of drug entering the systems equals the rate of drug leaving the system and no further drug accumulation occurs.

9. Changing the dose or dosing interval affect the concentrations attained at steady state, but not the time required to achieve steady state. The steady state (Plateau) is reached in approximately five half lives. At steady state the drug plasma concentrations ( C ss ), the peak (C max ) and trough (C min ) at any time during any dosing interval are similar. Under conditions of multiple I.V. bolus administration the plasma concentrations at steady state fluctuates (peaks and troughs) whereas under I.V. infusion conditions, plasma concentrations remain constant. Fig.: 4.4 Concentration-time profile associated with multiple I.V. bolus administration to steady state

10. Effect of Dose (X ) on steady state: The higher the dose, the higher the steady-state levels. The fluctuations in C max and C min are greatest with higher doses. Fig.: 4.5 Time profile of multiple I.V. bolus administration reaching steady state using different doses

11. Effect of dose interval(Ʈ) on steady state: When Ʈ< t 1/2 , The degree of accumulation is greater i.e. steady state levels are higher and there is less fluctuation in C max and C min ( Curve A). When Ʈ> t 1/2 , The degree of accumulation is less with greater fluctuation in C max and C min (Curve C). When Ʈ>> t 1/2 , There is no accumulation at all and C min approaches Zero. The plasma concentration- time profile will be the result of administration of series of single doses. Fig.: 4.6 Time profile for multiple I.V. bolus administration reaching steady state using different dose interval (Ʈ)

12. Time to Reach steady state: The time required to reach steady state is determined by the elimination rate constant (K)of the drug. It is directly proportional to the half-life. In practice, during a repeat-dose regimen, steady state is assumed to be reached in 5 half-lives unless dose interval is very much longer than t 1/2 . The time taken to reach steady-state does not depend on dose size, dosing interval and number of doses.

13. LOADING DOSE OR PRIMING DOSE (X L ) Definition: It is defined as the amount of an initial dose of a certain drug needed to reach a target plasma concentration. A loading dose is used to achieve therapeutic drug concentration in plasma rapidly without having to wait for the drug to reach the steady state level. It rapidly achieves the therapeutic response and subsequent doses maintain the response. It is a single or few quickly repeated doses given in the beginning to attain target concentration ( C ss , av ) rapidly followed by a maintenance dose to maintain the steady state so that the therapeutic effect is maintained. With a loading dose, the steady state is reached much quicker than using the maintenance dose only. Loading doses are larger than maintenance doses.

14. If a drug has long half-life, or if therapeutic levels must be attained immediately in serious conditions or emergency situations, an I.V. bolus loading dose can be administered. In practice, a loading dose may be administered as I.V. bolus dose or a short-term loading I.V. infusion. For example: Clopidogrel (Anti-platelet Drug) Intravenous Clopidogrel is given as a loading dose in percutaneous coronary intervention to prevent clotting straightway, and this is followed by oral maintenance doses to prevent coagulation, as the patient recovers from the surgery.

15. MAINTENANCE DOSE Definition: It is defined as the dose needed to maintain the concentration within the therapeutic window ( C ss ) when given repeatedly at a constant interval. Fig.: 4.7 Maintenance dose with and without loading dose

16. CALCULATIONS OF LOADING AND MAINTENANCE DOSE Loading doses and maintenance doses are mainly depends on, Clearance rate Volume of distribution Bioavailability Loading Dose Calculations: A simple equation for calculating loading dose (X L ) administered as I.V. Bolus is, X L = Css,av . V Where, Css,av- Average steady state plasma drug concentration to be achieved V- Apparent Volume of distribution of drug. For drugs not given I.V., X L need to be divided by the bioavailability fraction, F. If apparent volume of distribution of drug (V) is not known and loading dose (X L ) is administered a) As I.V. Bolus or when absorption is very rapid (then e -Ka Ʈ becomes Zero).

17. b ) For drugs not given I.V., or when K a >>K,

18. Maintenance Dose Calculations: Equations for calculating maintenance dose (X M ) administered as I.V. are, 1) X M = C ss,av . Cl T .Ʈ Where, C ss,av - Average steady state plasma drug concentration to be achieved Cl T - Total body Clearance Ʈ - Dosing interval 2) X M = ( C max ss - C minss ).V Where, C max ss - Maximum Concentration at steady state C minss - Minimum Concentration at steady state V - Apparent Volume of distribution of drug 3) X M = C ss,av. .V . Ʈ/ 1.44 . t 1/2 Where, C ss,av - Average steady state plasma drug concentration to be achieved V - Apparent Volume of distribution of drug Ʈ - Dosing interval t 1/2 - Half life of drug All the extracellular loading doses and maintenance doses have to be adjusted to bioavailability.

19. Dose Ratio Calculations: The dose ratio is equal to the loading dose divided by the maintenance dose. Dose ratio= X L / X M If the dosing interval (Ʈ) is equal to the drug’s elimination half life, then the dose ratio calculated and should be equal to 2.0. In other words, the loading dose will be equal to double the initial drug dose. When, Dosing interval (Ʈ)= t 1/2 , Dose ratio= 02 If , Ʈ> t 1/2 , then Dose ratio < 02 and Ʈ< t 1/2 , then Dose ratio > 02 These calculations for loading doses and maintenance doses are applicable to drugs that follow one compartment kinetics and not multicompartment kinetics. The equations for drugs that follow multicompartment kinetics can be much more complicated.

20. CLINICAL SIGNIFICANCES OF LOADING AND MAINTAINANCE DOSE The two phase dosing (loading dose+ maintenance dose) provides rapid therapeutic effect with long term safety. For example: Digogxin , Chloroquine, Doxycyclines , amiodarone etc. The concept of loading dose and maintenance dose is valid for short t 1/2 drugs and I.V. administration in critically ill patients. For example: Lidocaine (t 1/2 - 1.5 hrs.) used for cardiac arrhythmias is given orally as an I.V. Bolus dose followed by slow I.V. infusion or intermittent fractional dosing. Heparin when used to treat pulmonary embolism, may also need a loading dose to attain an immediate therapeutic effect.

21. ADULT LOADING AND MAINTENANCE DOSES OF SOME IMPORTANT DRUGS Drug Loading dose Maintenance dose Digoxin Atrial Fibrillation (oral) 10-15 mcg/kg 3.4-5.1 mcg/kg/day or 0.125-0.5 mg/day Amiodarone Arrhythmias (oral) 800-600mg/day for 1-3 weeks 400mg/day Chloroquine phosphate Malaria (oral) 1g 500mg at 6,24 and 48 hrs Heparin Pulmonary embolism (I.V. injection) 10,000 units I.V. 5000-10000 units I.V. every 4-6 hrs. Voriconazole Fungal Pneumonia (I.V.) 6mg/kg I.V. every 12 hours 4mg/kg every 12 hours

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