Seminar on pharmacokinetic parameters of two compartment open model
PHARMACOKINETIC PARAMETERS OF TWO COMPARTMENT OPEN MODELSeminar ByAjmeera DivyaM. Pharmacy (Pharmaceutics)St. Peter’s Institute of Pharmaceutical Sciences,Hanmakonda. 1
CONTENTSI. INTRODUCTIONII. TWO COMPARTMENT OPEN MODEL - IV BOLUSIII. TWO COMPARTMENT OPEN MODEL - IV INFUSIONIV. TWO COMPARTMENT OPEN MODEL - EXTRAVASCULAR ADMINISTRATIONV. CONCLUSIONVI. REFERENCES 2
INTRODUCTION PHARMACOKINETICS:Pharmacon-Drug Kinesis-Motion/ Change of Rate‘‘Pharmacokinetics is the study of kinetics of absorption,distribution, metabolism and excretion (ADME) of drugs and theircorresponding pharmacologic, therapeutic, or toxic responses inman and animals’’ (American Pharmaceutical Association, 1972). 3
PHARMACOKINETIC MODELS PHARMACOKINETIC MODELSCOMPARTMENT NONCOMPARTMENT PHYSIOLOGICAL MODEL MODEL MODEL
COMPARTMENT MODELS•Compartment models are classical pharmacokinetic models thatsimulate the kinetic process of drug ,absorption, distribution andelimination with little physiologic detail. OPEN AND CLOSED MODEL Open: Administered drug dose is eliminated from the body by an excretory mechanism. Closed: The drug dose is not eliminated from the body.
COMPARTMENTS Poorly Highly Perfused Perfused Tissue Negligible Perfused Fat group Tissue Group(a) Classification of human body intocompartments 6
COMPARTMENT MODELS COMPARTMENT MODELMAMMILLARY CATERNARY MODEL MODEL(B) Classification of compartment modelbased on arrangement 7
TWO-COMPARTMENT OPEN MODELCENTRAL COMPARTMENT:• Blood, extracellular fluid, and highly perfused tissues.• The drug distributes rapidly and uniformly in the centralcompartment.TISSUE OR PERIPHERAL COMPARTMENT:• Tissues in which the drug equilibrates more slowly.• Drug transfer between the two compartments is assumed to takeplace by first-order processes. 8
TWO-COMPARTMENT OPEN MODEL K12 Peripheral CentralModel A: compartment compartment K21 KE k12 Central PeripheralModel B: compartment compartment k21 kE K12 Central Peripheral Model C: compartment compartment K21 KE KE
TWO COMPARTMENT OPEN MODEL-IV BOLUS ADMINISTRATION: k12 1 2 central peripheral k21 kE•After the iv bolus of a drug the decline in the plasma conc. is bi-exponential.•Two disposition processes- distribution and elimination.
Figure 1: Changes in the drug concentrations in thecentral(plasma) and peripheral(tissue )compartment afteri.v. bolus of a drug that fits two-compartment model 11
•The rate of change in drug concentration in the centralcompartment is given as: dCcdt = K21 Cp – K12 Cc – KE Cc (1) Cc= drug concentration in central compartment Cp= drug concentration in peripheral compartment K12= first order distribution rate constant from central to peripheral compartment K21=FIRST order distribution rate constant from peripheral to central compartment KE= elimination rate constant from central compartment 12
• Extending the relationship X= Vd C X=amount of drug in the body at any time t remaining to be eliminated C=drug concentration in plasma Vd =proportionality const apparent volume of distribution dCc = K21 Xp – K12 Xc – KE Xc dt Vp Vc Vc (2) Xc and Xp=amt of drug in C1 and C2 Vc and Vp=apparent volumes of C1 and C2
• The rate of change in drug concentration in the peripheral component is given by: dCp/dt=K12 Cc – K21 Cp (3) =K12 Xc/ Vc – K21 Xp/Vp (4)• Integration of the equations (3) and (4) gives conc of drug in central and peripheral compartments at any given time t : Cc = Xo/Vc [(K21 – α/ β-α ) e-αt + (K21- β/β-α) e-βt] (5) Cp = Xo/ Vc [( K21 – α/β – α )e-αt + (K12 – b/α– β )e-βt] (6) Xo = iv bolus dose α and β = hybrid first order constants for rapid dissolution phase and slow elimination phase respectively.
In simplified form Cc = A e-αt + Be-βtwhere, A = X0/ Vc [K21 – α/ (β-α) ] = Co/Vc [K21 – α/ (α-β)]and B = X0 /Vc [K21 – β/(α-β)] = Co/Vc [K21 – β/(α-β)] Co = plasma drug concentration immediately after i.v. injection 15
ASSESMENT OF TWO COMPARTMENT MODELMETHOD OF RESIDUALS C = A e-αt + B e-βt C = B e-βt log C = log B – βt/2.303 Figure 2: Resolution of the Bi exponential plasma concentration time curve by this method of residual for a drug that follows two compartment kinetics on16 i.v administration.
PHARMACOKINETIC PARAMETERS1. AREA UNDER THE CURVE2. VOLUME OF DISTRIBUTION3. RATE CONSTANTS OF DRUG TRANSFER4. HALF LIFE5. CLEARANCE6. ELIMINATION CONSTANT 17
• By proper substitution of the following values, the above listed parameters can be evaluated: C0 = A + B KE = αβC0 A β + Bα K12 = A B (β - α)2 C0 (A β + B α) K21 = A β + B α C0
• Area Under the Curve : (AUC) = A + B α β• Apparent volume of Central compartment : Vc = X0/ C0 = X0/KE(AUC)• Apparent volume of Peripheral compartment : VP= VcK12/K21• Apparent volume of distribution at steady state or equilibrium : Vd,ss = VC +VP 19
• Apparent volume of distribution from area : Vd,area = X0 βAUC• Haif life : t1/2=0.693/β• Total systemic Clearence : ClT = β Vd• Renal Clearence : ClR =dXU /dt = KE VC 20
TWO-COMPARTMENT OPEN MODEL INTRAVENOUS INFUSION R0 1 K12 2 Central Peripheral K21 KE• The plasma or central compartment concentration of a drug when administered as constant rate (zero order) i.v.infusion is given as: C = R0 [1+(KE -β)e-αt +(KE - α)e-βt] VC KE β–α α- β
• At steady state (i.e.at time infinity) the second and the third term in the bracket becomes zero and the equation reduces to: Css = R0 VC KE Now VC KE = Vd β CSS = R0 = R0 Vdβ ClT• The loading dose X0,L = Css Vc = R0/KE
TWO-COMPARTMENT OPEN MODEL- EXTRAVASCULAR ADMINISTRATION Ka 1 K12 2 Central peripheral K21 KE• The plasma concentration at any time t for a drug that enters thebody by a first-order absorption process and distributed accordingto two compartment model is given by : C = N e-kαt + L e-at + M e-βt C = Absorption + Distribution + Elimination exponent exponent exponent
Where•Ka is the first order absorption constant•α and β are hybrid first order constants for the rapiddistribution phase and slow elimination phase respectively•L,M,N are hypothetical coefficients. 24
True plasma conc log N Back extrapolatedlog L distribution curve log M First residual curve Back extra polated elimination log C Slope =-Ka/2.303 t figure3:Semi log plot of C versus t of a drug with two compartment characteristics if administered extravascularly 25
CONCLUSION• Pharmacokinetic models predict drug disposition after drugadministration.•Statistical methods are used for the estimation and datainterpretation of pharmacokinetic parameters• Useful in Drug formulation and treatment regimen• The drug behaviour within the body might be able to fit differentcompartmental models depending upon the route of drugadministration. 26
REFERENCES•Milo Gibaldi, Donald Perrier,pharmacokinetics, 2nd Edition, 1-89•Leon Shargel, Susanna W.U Pong, Andrew Bc.Yu, Applied Bio-Pharmaceutics And Pharmacokinetics, 5th Edition ,51-105•M.Blomhoj, T.H.Kjeldsen,j.Ottensen, Compartmental Modeling,1-32•Sunil S. Jambamkar, Sunil. B. Jaiswal , Basic Pharmacokinetis( Pharmaceutical Press) ,185- 289•Aldo Rescigno , Foundations of The Pharmacokinetics, 135 -149•P.L.Madan, Biopharmaceutics And Pharmacokinetics, 1st Edition ,173 -282 27
•Steven B Heymfield, Steven Litchman, Richard. N. Baumgartner, JackWong, Body Compositions Of Human, American Journal Of ClinicalNutrition, 52-59•Joseph T.Dipiro, William, Spruill, concepts In ClinicalPharmacokinetics, 4th Edition, 19-45• V. Venkateswar Rao, Fundamentals of Biopharmaceutics AndPharmacokinetics, 109-196•H.P.Tipnis, Amritha Bajaj, Principles And Application OfBiopharmaceutics And Pharmacokinetics, 213-259•Dm.Brahmamkhar, Sunil.B.Jaiswal, Biopharmaceutics AndPharmacokinetics : A Treatise, 212-272•J.S Kulakarni. Ap .Pawar, Vp Shedbalkar, Biopharmaceutics AndPharmacokinetics Cbs Publisher, 165-193 28