One compartment model IV Infusion

short introduction on one compartment model IV infusion.

1. One Compartment M odel IV Infusion LAKSHMI CHANDRAN PHARM D SRM COLLEGE OF PHARMACY

2. Intravenous infusion When a drug is administered intravenously at a constant rate (zero order) over a long period of time , it is known as IV infusion. The duration of the constant rate infusion is much longer than the half life of the drug. E.g. antibiotics, theophylline, procainamide etc. Why IV infusion? When the drug has potential to precipitate toxicity When a stable concentration of the drug is to be maintained for the therapeutic effect. Advantages Ease of control of rate of infusion to fit individual patient needs. Prevents fluctuating maxima and minima (peak and valley) plasma level, desired especially when the drug has a narrow therapeutic index. Other drugs, electrolytes and nutrients can be conveniently administered simultaneously by the same infusion line in critically ill patients.

3. Zero - Order Kinetics The rate of change in concentration is expressed as : = - K . C n where n is the order of the reaction for zero order kinetics n=0 = - K C = - K ( zero order rate constant in mg/min) Rearranging the equation we get: dC= - K t Integrating both sides C-C = - K t C= C - K t C is conc of drug at t=0 C is conc of drug yet to Undergo reaction at time t   Zero order processes can be defined as the one whose rate is independent of the concentration of drug undergoing reaction i.e. the rate cannot be increased further by increasing the concentration of reactants.

4. IV Infusion Model DRUG BLOOD AND OTHER BODY TISSUES ELIMINATION R K E Zero-order Infusion rate R - Zero order infusion rate K E - Elimination rate constant

5. At any time during infusion , the rate of change in the amount of drug in the body, dX/ dt is the difference between the zero order rate of drug infusion R and first order rate of elimination, -K E X = R – K E X - (1) Integrating eq.(1) yields X (1 - ) - (2) Since X= V d .C where V d is the volume of distribution and C is the Conc. of drug , eq. (2) can be transformed as: C = (1- = (1- ) - (3)  

6. Plasma concentration – Time profile Initially the drug enters the body at constant rate The infusion rate R > K E X (elimination rate). As infusion time progresses the rate of infusion equalizes with the elimination rate of the drug This stage is called the steady state concentration /plateau/ infusion equilibrium. (C SS ) At this stage concentration of drug in plasma approaches a constant value.

7. At steady state , the rate of change of amount of drug in the body is zero, hence the eq. (1) becomes: = R – K E X -(1) 0= R – K E X SS R = K E X SS - (4) Transforming to concentration terms and rearranging the equation: C SS = = - (5) K E - Elimination rate constant C SS - Concentration of the drug at steady state X SS - Amount of the drug in the body at steady state  

8. Calculating K E by using semi logarithmic plot Alternative method : During infusion the KE can be calculated: = C SS -(5) C= C SS ( 1- ) - (6) [ ] = - (7) l og [ ] = - (8)  

9. H alf life of drug in IV infusion The time to reach steady state concentration is dependent upon the elimination half life and not on the infusion rate. If n is the number of half lives passed since the start of infusion, the eq. (6) can be written as: C= C SS { 1- ( ) n } Where C is the concentration of the drug after n th half life The percent of C SS achieved at the end of each half life is the sum of C SS at previous half life and the concentration of drug remaining after a given half life   Half life % remaining % C SS achieved 1 50 50 2 25 50+25=75 3 12.5 75+ 12.5= 87.5 4 6.25 87.5+ 6.25= 93.75 5 3.125 93.75+ 3.125= 96.875 6 1.562 96.875+ 1.562= 98.437 7 0.781 98.437+ 0.781= 99.218 For therapeutic purpose, more than 90% of C SS is desired which is reached in 3.3 half lives. It takes 6.6 half lives to reach 99% of C SS . Shorter the half life, sooner the C SS reached. E.g. Penicillin G with half life of 30 mins .

10. Infusion plus Loading Dose What is loading dose? For drugs having longer half lives, like phenobarbital (5 days), it takes longer time to achieve the steady state concentration. To overcome the sub therapeutic concentration of these drugs, an IV loading dose large enough is administered to reach the steady state immediately After the loading dose is administered, the IV infusion is given immediately at a rate enough to maintain this concentration. Some i mportant drugs that require loading dose: Amiodarone- Loading dose of 150 mg IV in 10 minutes slowly, followed by IV infusion of 540 mg over 18 hours. Streptokinase- Loading dose of 250,000 IU, followed by IV infusion of 100,000 IU/ hr for 72 hours for recurring pulmonary emboli and DVT. Succinylcholine- Loading dose of 0.3-1.1 mg/kg over 30 sec for surgical procedures and a continuous IV infusion of 0.5-1.0 mg/min for prolonged muscle relaxation.

11. Calculating the loading dose X= V d .C Taking X 0,L as the loading dose, X 0,L = C SS . V d - (9) Substituting C SS = R / K E V d in eq. (9) X 0,L = - (10) Hence the eq. describing the plasma conc. Following the IV loading dose and IV infusion is: C= + ( 1- ) - (11)  

12. Assessment of Pharmacokinetic Parameters Apparent volume of distribution V d = Total systemic clearance Cl T = These two parameters can also be calculated from the total area under the curve (AUC) till the end of infusion: AUC = = = C SS . T Where T is the infusion time.  

13. References: Biopharmaceutics and Pharmacokinetics by D. M. Brahmankar and Sunil B. Jaiswal Guidance on Drug Doses Loading Doses for Primary Care Health Care Professionals by NHS http:// www.southernhealth.nhs.uk/EasySiteWeb/GatewayLink.aspx?alId=30182