Compartment Models PDF

 To understand one compartment model.   Body is considered as composed of several compartments that communicate reversibly with each other. A compartment is not a real physiologic or anatomic region, but is considered as a tissue or group of tissues which have similar blood flow and drug af...

 To understand one compartment model.   Body is considered as composed of several compartments that communicate reversibly with each other. A compartment is not a real physiologic or anatomic region, but is considered as a tissue or group of tissues which have similar blood flow and drug affinity.    Simplest model Predicts the body as single, kinetically homogenous unit that has no barriers to movement of drug and final distribution equilibrium between drug in plasma and other body fluids is attained instantaneously and maintained at all times. Homogenous does not mean equal conc.     It simply means that an equilibrium is reached between plasma and various tissues and fluids in the body and any change in plasma conc. can be attributed to elimination of drug from the body rather than uptake by tissues. ka ke Metabolism. Drug → → Blood and other body tissues → → (Absorption input) ( Elimination output) ‘ Excretion    One compartment open model assumes that any changes that occur in plasma levels of a drug reflect proportional changes in tissue drug levels. Model does not assume that the drug conc. in plasma is equal to that in other body tissues. Open reflects that the absorption and elimination are unidirectional and that the drug can be eliminated from the body.      Various one-compartment open models based on the rate of input are as follows: 1. One Compartment open model, intravenous adm 2. One compartment open model, continuous intravenous infusion 3. One compartment open model extravascular admn., first order absorption 4. One-compartment open model, extravascular admn., zero order absorption     One Compartment Open Model After administration, a drug may distribute into all of the accessible regions instantly. It is called 'one compartment' because all of the accessible sites have the same distribution kinetics as if the drug is dissolved in a beaker containing a single solvent. It is 'open' because unlike the beaker model the drug is eliminated from the container.    The time course of a drug which is handled in the body according to a one compartment open model depends upon the concentration which was initially introduced into the body (Co) and KE. Note that e-KE is the fraction already (t) eliminated: C = Co e-KE t (8) A plot of C versus t will be curvelinear on a linear paper and will be linear on a semi-log paper.    When drug given in form of rapid intravenous injection(IV bolus), entire dose of drug enters body immediately. Rate of absorption is neglected in calculations. In most cases drug distributes via the circulatory system to all the tissues in body and equilibrates rapidly in body.       Rate of process involves first-order kinetics dx/dt = -K e X (1) dx/dT = rate of process K e = elimination rate constant X= amount of drug in body at any time t remaining to be eliminated Negative sign indicates that drug is lost from the body      Elimination phase can be characterized by three parameters: 1. Elimination rate constant 2. Elimination half life 3. Clearance Substituting plasma drug conc C in place of amount of drug in the body X in eqn 1       dc/dt = K e C (3) Integration of eqn 3 gives ln C = ln C0 - K e t (4) Where C0 = plasma drug conc at time t=0 i.e plasma conc immediately after i.v. injection or conc. extrapolated to time zero on plasma conc: time profile Eqn 4 can also be written in exponential form as : C = C0 e - K e t (5)     Eqn 5 shows that disposition of drug that follows one compartment kinetics is monoexponential. Transforming eqn 4 in to common logarithm gives: K et log C = log C0 - -----------(6) 2.303   When log c is plotted against time t on semilog paper we get a straight line with slope = overall elimination rate constant and log C0 as Y intercept. Elimination rate constant has units of min-1 Linear plot is easier to handle mathematically than a curve which is obtained by eqn 5. Plot of C versus time gives an exponential curve that is cartesian plot.      For each drug the apparent Vd is constant. In certain pathologic cases apparent Vd for the drug may be altered if distribution of drug is changed. For example in edematous conditions total body water and total extra cellular water increase. This is reflected in a larger apparent Vd value for a drug that is highly water soluble. Similarly changes in total body weight and lean body mass which normally occurs with age may also affect the apparent Vd. Several advantages in giving a drug by intravenous infusion at zero-order rate.  1. In critically ill, antibiotics and drugs can often be conveniently administered by infusion together with IV fluids, electrolytes or nutrients.  2. The rate of infusion can be easily regulated to fit individual patient needs.  3. Constant infusion prevents a fluctuating peak (max.) and valley( min.) blood levels. Desirable if drug has narrow therapeutic index.   Conc. of drug in plasma by IV infusion at a constant rate is shown in fig. After a while the drug accumulates to reach a plateau or steady state level. Plateau level is called the steady-state conc., the point at which the rate of drug leaving the body and rate of drug entering the body (infusion) are the same.    Time required to reach steady-state drug conc. in blood is primarily dependent on elimination half-life. Time reqd to reach 90%, 95% and 99% of steady-state conc. is generally calculated. For therapeutic purpose, more than 95% of steady-state drug conc in blood is desired.   This is reached in period of time equal to six times the elimination half-life. If drug is given at a higher infusion rate, a higher steady-state level is obtained, but the time needed to reach steady state remains the same as shown is fig.     Model can be represented as follows: Intravenous infusion Ke Drug →→ →→ Blood and other body tissues → Elimination R (zero-order Infusion rate) Constant intravenous infusion involves zero order input since the rate of input remains constant.    Change of amount of drug in the body, assuming instantaneous distribution is given by: dX/dt = K0 – Ke X (22) Since at any time during infusion, rate of change in amount of drug in body, dX/dt is the difference between the zero-order rate of drug infusion K0 and first order rate of elimination -KeX    Amount of drug in the body is zero when constant rate of infusion is started and there is no elimination. As time passes, amount of drug in the body rises gradually until rate of infusion equals rate of elimination. i.e conc. of drug in plasma approaches a constant value called as steady state or plateau. At this stage e –ket becomes negligible.     At steady state the rate of change of amount of drug in the body is zero, hence eqn 22 becomes: Zero = K0 – Ke XSS Or Ke XSS = K0 ( 26 ) K0 XSS = ---------Ke