CONCEPT OF PHARMACOKINETICS- ONE COMPARTMENT MODEL , DEPARTMENT OF PHARMACEUTICS

PHARMACOKINETICS: PHARMACOKINETICS It is defined as the Kinetics of drug absorption, distribution, metabolism, and excretion and their relationship with pharmacological, therapeutic or toxicological response in human and animals..,

A typical plot represents plasma concentration-time profile..

KEY PARAMETERS:- Pharmacokinetic parameters: Peak plasma concentration (Cmax), Peak time (tmax), Area under curve (AUC), t1/2(half life). Pharmacodynamic Parameters : Minimum effective concentration, Maximum safe concentration, Onset of action, duration of action, Therapeutic range and therapeutic Index.. 

PHARMACOKINETIC MODELS COMPARTMENTAL MODELS Mammillary model Caternary model NON COMPARTMENTAL MODELS PHYSIOLOGICAL MODELS

COMPARTMENTAL MODEL:- COMPARTMENTAL MODEL is Hypothetical space, bound by an unspecified membrane across which drugs are transferred in and out. Depending upon whether the compartments are arranged parallel or in a series classified as Mammillary model Caternary model…

Mammillary model Mammillary model consists of one (r) more periperal compartments connected to central compartment as like conection of satellite to a planet.(i.e they joined parallel to central compartment).. Central compartment comprises plasma & highly perfused tissues. Elimination too occur from it.

One, Two and Three Compartment Models :

Model-1 cc K10 One compartmental open model, INTRAVENOUS BOLUS Model-2 cc K10 K01 One compartmental open model, e.v administration

CC KE KE = Elimination rate constant.. ONE COMPARTMEN OPEN MODEL IV BOLUS ADMINISTRATION KE CC dX = Rate In – Rate Out dt dX = - Rate Out dt dX = - KEX dt.. KE = Elimination rate constant.. X = Amount of drug in the body..

dX = - KEX dt. Integrate the above eq.. ln X = ln X0 – KEt Transfer into log form.. Log X = Log X0 - KEt /2.303 BUT X=VdC Vd=Apparent volume of distribution(Constant) Log C = Log C0 - KEt /2.303 C = Concentration of drug in plasma..

SEMILOG PLOT CARTESIAN PLOT ONE COMPARTMEN OPEN MODEL IV BOLUS ADMINISTRATION

ELIMINATION RATE CONSTANT : The decline in plasma drug concentration is only due to elimination of drug from the body, the phage is called elimination phage.. It follows 1st order elimination process.. Elimination phase characterized by 3 parameters – elimination rate constant, elimination half life,clearence.. KE = Km + Ke

ELIMINATION HALF LIFE t1/2 = 0.693 / KE APPARENT VOLUME OF DISTRIBUTION For Compartment model) Vd=X/C For non compartment model Vd = X/KE.AUC(i.v bolus) Vd = X.Fo/KE.AUC(E.V adm.)

ClT=Clr+ClH+clothers Clearance The theoretical volume of body fluid containing drug from which the drug is completely removed in a given period of time.. ClT = [Rate of elimination/ Plasma drug conc.] Cl=dx/dt / C = KEX /C ClT=Clr+ClH+clothers

ORGAN CLEARANCE ER= Extraction ratio Rate of Elimination = Rate of Presentation – Rate of exist ( Q. C in - Q. Cout) Hepatic clearence = ClH = ClT+Clr ClH = QH.ERH ER= Extraction ratio

CC IV INFUSION KE dX = R0- KEX dt X = Ro/KE(1-ekEt) DRUG Ro dX = R0- KEX dt X = Ro/KE(1-ekEt) C = Ro/KEVd(1-ekEt) C = Ro/ClT(1-ekEt) CC

CSS Steady state Sope = -KE/2.303 INFUSION TIME

At steady state At steady state : Zero = R0 - KE Xss KE Xss = Ro Transform into conc. Terms & rearrange the eq. Css-c/Css = e-kEt Transfer into log form… log(Css-c/Css )= -KET/2.303

Semilog plot compute KE from infusion data upto steady -state.. Log[Css-C/Css] Sope = -KE / 2.303 time Semilog plot compute KE from infusion data upto steady -state..

INFUSION PLUS LOADING DOSE Intravenous infusion with LOADING DOSE..As the amount of bolus dose Falls,there is a complementary rise resulting from the infusion…

INFUSION PLUS LOADING DOSE The initial bolus dose of a drug, is used to obtain desire concentration as rapidly as possible.. Xo,L = CssVd But the loading dose simulates i.v loading dose(i.v bolus) & constant i.v infusion… C = XoL.e-KET/Vd +Ro/KEVd[1-e-KET]

CC Ka KE EXTRAVASCULAR ROUTE dx/dt = KaXa-KEX One compartment model with first order absorption dx/dt = KaXa-KEX Ka=first order absorption rate constant Xa = ARA Integrated & transform into concentration terms.., c = Ka F Xo/Ka-KE[e-KET – e-KaT ]

Assesment of pharmacokinetic parameters : tmax = 2.303 log(Ka/KE)/(Ka-KE) Cmax = 0.37FXo/Vd Elimination rate constant : logC = log [Ka F Xo/ Vd(Ka-KE)]- KE/2.303

Extravascular vascular adminstration of a single dose of drug

Absorption rate constant Ka It can be calculated by METHOD OF RESIDUAL [Feathering , peeling ,stipping] In which the plasma drug conc. Expressed by BIEXPONENTIAL equation c = Ka F Xo/Ka-KE[e-KEt – e-Kat ] C = Ae-KE t – A e-Kat

log Cr = log A – Kat /2.303 C =True plasma conc. Cr = Residual curve.. (C – C) = Cr = Ae-Kat C = The back extrapolated plasma conc. C =True plasma conc. Cr = Residual curve.. In log form the equation : log Cr = log A – Kat /2.303

Biexponential cuvre = Absorption + Elimination METHOD OF RESIDUALS Biexponential cuvre = Absorption + Elimination

EXCRETION RATE CONSTANT (KE) It can be calculated by URINARY EXCRETION DATA Determination of KE by Rate of excretion method Sigma minus method

Rate of excretion method

Transfer into log form.., log dXu/dt = log Ke Xo-KEt/2.303 Rate of excretion Rate of urinary drug excretion(dXu/dt) α Amount of drug in the body (X) dXu/dt = Ke X Ke= first order elimination rate constant.. dXu/dt = Ke Xoe-KEt Transfer into log form.., log dXu/dt = log Ke Xo-KEt/2.303

log(Xuα –Xu ) =log Xuα -KEt/2.303 Sigma minus method The plot drawn b/n cumulative amount of drug excreted unchanged in urine & time.. dXu/dt = Ke Xo e–KEt Integrate & rearrangement the above equation… Xuα – Xu = Xuα e-KEt log(Xuα –Xu ) =log Xuα -KEt/2.303

Sigma minus method : log(Xuα –Xu) Time(t)

REFERENCES: Bio-Pharmaceutics and Pharmacokinetics A Treatise by D.M BRAHMANKAR; SUNIL B. JAISWAL. Leon Shargel; et.al ; applied biopharmaceutics. Biopharmaceutics and pharmacokinetics by Venkateswarulu

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