Multicompartment Models PDF

OBJECTIVES  To understand kinetic analysis of a multicompartment model.  To MULTICOMPARTMENT MODELS Winter, Part1 TWO COMPARTMENT OPEN MODEL  Most common model  Body tissues two broad categories:  Central Compartment:  Group of tissues which equilibrate instantaneously are supposed to re...

OBJECTIVES  To understand kinetic analysis of a multicompartment model.  To MULTICOMPARTMENT MODELS Winter, Part1 TWO COMPARTMENT OPEN MODEL  Most common model  Body tissues two broad categories:  Central Compartment:  Group of tissues which equilibrate instantaneously are supposed to reside in central compartment.  Sampled compartment ( though such sampling is not always necessary). know various Distribution factors.  To learn more about Two Compartment Open Model.  Highly  liver, perfused tissues : lungs, kidney etc.  Peripheral  Contains or Tissue Compartment: slowly equilibrating tissues  Drug requires some length of time for equilibration.  This model assumes  Drug eliminated from compartment. central  Possible to have  Part of an organ in the central compartment and  Rest in the tissue compartment.  Determining factor for classification Rate of equilibration.  Categorization of two compartment model  Depending upon the compartment from which the drug is eliminated TWO COMPARTMENT OPEN MODEL: INTRAVENOUS INJECTION (I.V. BOLUS ADMINISTRATION)  1.Two compartment model with elimination from central compartment  2.Two compartment model with elimination from peripheral compartment  3.Two compartment model with elimination from both the compartments.  Drug that follows two compartment kinetics  After an intravenous injection  Decline in plasma conc. :  Biexponential  Two disposition processes  Distribution and  Elimination  Rapid decline due to  Distribution into more slowly perfused tissues.  Initial rapid decline in the central compartment  distribution phase sometime,  pseudo-distribution equilibrium achieved between two compartments of the curve.  After  State of equilibrium between central compartment and more poorly perfused tissue compartment.  After this equilibrium is established,  loss of drug from central compartment appears to be single first-order process  It is due to  overall processes of elimination of drug from the body.  The second, slower rate process  elimination phase.  Two compartment model assumes  t = 0 there is no drug in the tissue compartment.  Tissue drug level curve after a single intravenous dose of drug shown in fig.  The tissue drug level will eventually peak  start to decline as conc. gradient between two compartment narrows.  Theoretical tissue conc. together with the blood conc.,  IDEA OF : total amount of drug remaining in the body at any time.  This information would not be available without using pharmacokinetic models.  Samples of blood removed from central compartment - analyzed for presence of drug.  Distribution Phase  Elimination phase  Distribution phase may take minutes or hours  may be missed entirely if blood is sampled too late after administration of the drug.  In the model depicted above  K12 and K21 : first order rate constants  Depict drug transfer between central and peripheral compartments.  Let the subscript c and p define central and peripheral compartment respectively. Relationship between amount of drug in each compartment and the conc. of drug in each compartment :  Xc  Cc = ---------(2)  Vc  Xp  Cp = ---------(3)  Vp  Where  Xc = Amount of drug in the central compartment  Xp = Amount of drug in the peripheral compartment   The rate of drug change in tissues :  d Cp  ---------- = K12 Cc - K21 Cp  dt  (1)  = Volume of drug in the central compartment  Vp = Volume of drug in the peripheral compartment  Eqn 1 becomes  Rate d Cp  ---------- = K12 Xc / Vc - K21 Xp / Vp  dt   Vc  (4) of change in drug conc. in central compartment : d Cc  ---------- = K21 Cp - K12 Cc - KeCc dt  (5) d Cc ---------- = K21 Xp / Vp - K12 Xc / Vc - Ke Xc / Vc  dt ( 6)   PHARMACOKINETIC PARAMETERS  Single compartment  pharmacokinetic calculations relatively simple.  Situations HAVING two, and occasionally more than two compartments  drug distribution, elimination and pharmacologic effect.  First compartment  smaller, rapidly equilibrating volume,  usually made up of plasma or blood and  those organs or tissues that have high blood flow  are in rapid equilibrium with the blood or plasma drug conc.  First compartment  volume : Vi or  initial volume of distribution.  Second compartment  Equilibrates over a somewhat longer period.  This volume referred to as V t or tissue volume of distribution. OBJECTIVES  To study Effects of a Two – Compartment Model on the loading dose and plasma conc.( C )  To learn Consequences of an inaccurate prediction  To learn how the problems can be circumvented  Half life for distribution phase  alpha half life  Half life for drug elimination  beta half life.  Sum of Vi and Vt : apparent volume of distribution (V). Drugs are assumed to enter into and be eliminated from Vi.  Any drug that distributes into tissue compartment (Vt ) must reequilibrate into Vi before it can be eliminated.  Effects of a Two – Compartment Model on the loading dose and plasma conc.( C )  Some time required for a drug to distribute into Vt,  Rapidly administered loading dose calculated on the basis of V ( Vi+ Vt)  Consequences of  Result in an initial C  higher than predicted  Why ?  initial volume of distribution (Vi) is always smaller than V.  In these instances  when loading doses are calculated based on the total volume of distribution,  conc. of drug delivered to the target organs could be much higher than expected and  produce toxicity if loading dose is not administered appropriately. an inaccurate prediction depend on  Whether target organ behaves as though it were located in Vi or Vt. Examples:  Lidocaine, Phenobarbital, procainamide, and theophylline exert therapeutic and toxic effects on target organs that behave as though they are located in Vi.  Problem can  First be circumvented by calculating loading dose based on the total volume of distribution ( V ),  Then administering the loading dose at a rate slow enough to allow for drug distribution into Vt.  This approach is common in clinical practice,  Guidelines for rates of drug administration are often based on the principle of two-compartment modeling with  Receptors for clinical response ( toxic or therapeutic) responding as though they were located in Vi.  Second approach  To administer loading dose in sufficiently small individual bolus doses  such that C in Vi does not exceed some predetermined critical conc.  Potassium is a good example of a drug that follows this principle of two-compartment modeling with the end-organ being located in Vi.  When  Potassium is primarily an intracellular electrolyte  Its cardiac effects parallel the plasma conc.  In addition, there is slow equilibrium between plasma and tissue potassium concs. potassium is given intravenously  rate of administration must be carefully controlled  serious cardiac toxicity and death will occur if patient experiences excessive plasma (Vi) concs.  Concept of two compartment modeling also important in evaluating the offset of drug effect.  For drugs with end organ for clinical response located in Vi  Rapid achievement of a therapeutic response  Followed quickly by loss of therapeutic response  may be the result of  drug being distributed into larger volume of distribution rather than drug being eliminated from the body.  When the drug’s target organ is in second or tissue compartment, Vt  e.g. digoxin, lithium  high C, which may be observed before distribution occurs, is not dangerous.  However plasma concs that are obtained before distribution is complete will not reflect the tissue conc. at equilibrium.  This  These plasma samples cannot be used to predict therapeutic or toxic potential of these drugs.  Clinicians usually wait for 1-3 hours after an intravenous bolus dose of digoxin before evaluating the effect delay allows  Digoxin to distribute to site of action (myocardium) so that the full therapeutic or toxic effects of a dose can be observed.  Slow drug distribution into the tissue compartment can pose problems in accurate interpretation of drug conc. when a drug is given by intravenous route.  These  Generally not a problem when a drug is given orally.  Rate of absorption is usually slower than the rate of distribution from Vi to Vt.  Digoxin and lithium are exceptions to this rule.  For these two drugs  Receptors in end-organs behave as though they are located in more slowly equilibrating tissue compartment  Vt. drugs given orally:  several hours required for complete absorption and distribution.  Digoxin  Plasma samples obtained less than 6 hours after an oral dose  lithium  oral dose of lithium less than 12 hours :  questionable value.  Plasma concs obtained during the distribution phase ( before equilibrium with the deep tissue compartment is complete) will be increased,  Pharmacologic response will be much less than the plasma concs would indicate. DRUGS WITH SIGNIFICANT AND NONOBJECTIVES  To learn about drugs with significant and non-significant two compartment modeling.  To understand the drugs that border on having significant two compartment modeling means  If patient not harmed by initially elevated drug conc. in alpha phase and  no drug samples are taken in alpha phase,  Then  Drug can be successfully modeled as one-compartment drug  (i.e only the elimination or beta phase is considered). SIGNIFICANT TWO COMPARTMENT MODELING  Alpha phase for most drugs represents distribution of drug from Vi into Vt  Relatively little drug eliminated during distribution phase.  Drugs that behave in this way are generally referred to as nonsignificant two compartment drugs.  Non-significant  For some drugs,  Increased drug plasma concs during the alpha phase can be clinically significant  Why?  serious toxicity  If end organ behaves as though it lies within the initial volume of distribution (Vi)  Drugs  These drugs considered to exhibit “nonsignificant ” two compartment modeling only after alpha phase or distribution has been completed.  Plasma samples obtained for pharmacokinetic modeling only during beta or elimination phase.  Drugs that border on having significant two compartment modeling  lithium and lidocaine.  When a one-compartment model is used for drugs that exhibit significant drug elimination in the alpha phase,  Actual trough concs will be lower than those predicted by onecompartment model. with “ significant ” two compartment modeling  Those eliminated to significant extent during initial alpha phase.  Example:  Methotrexate  alpha phase cannot be thought of simply as distribution,  Why?  Significant elimination occurs as well.  Two-compartment computer models are available for therapeutic drug monitoring.  If care taken to avoid obtaining samples in distribution phase,  Very similar pharmacokinetic interpretations are usually arrived at using simpler one-compartment model. LEARNING OUTCOMES  At the end of the chapter the student will be able to:  Adjust the administration of doses depending on the target organs location.  To distinguish between significant and insignificant compartment modelling.