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SEMINAR ONNonlinear pharmacokinetics                          1ST Year M. Pharma                         Dept. Of Pharmace...
contents• Introduction• Pharmacokinetics & Pharmacodynamic• Nonlinearity• Causes of nonlinearity• Michaelis – menten equat...
Phama               r cokinet &. Phama                       ics     r codynamics       Phama          r cokinet          ...
Objectives:• To understand the schemes & differential equations associated  with non linear pharmacokinetic models.• To un...
Linear and Nonlinear Pharmacokinetics• In case of therapeutic dose of drug, at single or multiple doses, the  process foll...
Detection of non-linearity in pharmacokinetics•     There are several tests to detect non –linearity in      pharmacokinet...
Reasons for non         linearity:•   Saturation of the enzymes and of the active transport systems for the    drug.    Dr...
Causes of non-linearity• Drug absorption:-• Three causes:- I) solubility/ dissolution of drug is rate-  limited           ...
Drug distribution• Drug distribution:- at high doses non-linearity due to• Two causes:- I) binding sites on plasma protein...
Drug metabolism• Drug metabolism:- non-linearity occurs due to capacity limited  metabolism, small changes in dose adminis...
Drug excretion• Drug excretion:- two active processes which are saturable          I) active tubular secretion- penicillin...
Examples of drugs showing nonlinear pharmacokinetics              causes                                   drugsGI absorpt...
• In order to determine whether a drug is following dose  dependent kinetics.• The drug is given at various dose levels an...
MICHAELIS MENTEN EQUATION• The kinetics of capacity limited or saturable processes is best  described by Michaelis-Menten ...
1)   If a drug at low conc. Undergoes a saturable biotransformation      then KM>>C:•    here , KM +C =KM and eq. I reduce...
Zer or r t a high doses                             o der ae t                  M or r t a                    ixed der ae ...
Estimation of Vmax & KM• The parameters Km and Vmax can be assessed from the  plasma conc.-time data collected after i.v. ...
• A semi log plot of C versus t yields a curve with a terminal  linear portion having slope –Vmax/ 2.303 Km and when back ...
•   a plot of drug given a IV bolus with nonlinear elimination               L Co                og           Y           ...
Lineweaver-Burk Plot• An alternation approach of estimating Vmax and KM is  determining the rate of change of plasma drug ...
Hanes-Woolf Plot Cm         KM            Cm      =            +                 … … … .. XV                              ...
Calculation of KM & Vmax steady-state                       concentration• If drug is administered for constant rate IV in...
Cur e foradr folow nonl rkinet         v        ug l ing inea       ics  Bypl t t st dy- ae conc. a instdosing r t     oti...
•    There are three methods which are used to define the KM     & Vmax at steady-state with appreciable accuracy:•    Lin...
Dir l rpl forest t ofKM &V x             ect inea ot        imaion         ma                a st dy- ae conc. Ofadr      ...
1)   Graphical method:-•    In this method by rearranging eq.(2) we get                         KM DR             … … … .....
• On solving above eq. 5& 6 we get                 DR-DR1   2     KM =                                      … … … .. (7)  ...
Bioavailability dependent nonlinear                    pharmacokinetics• The bioavailability of drugs that follows nonline...
1     Cb            Kd Cr                 … … … .. (2)                                          ………            =          ...
References• Biopharmaceutics and clinical pharmacokinetics by Milo  Gibaldi 4th edition 1991• Biopharmaceutics and pharmac...
Pow pointT aes   er     empl t   3 ge 3                    1                    Pa 1
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Non linear biopharmaceutics

  1. 1. SEMINAR ONNonlinear pharmacokinetics 1ST Year M. Pharma Dept. Of Pharmaceutics, KLES’s College Of Pharmacy Belgaum . Pow pointT aes er empl t 1Pa 1 ge
  2. 2. contents• Introduction• Pharmacokinetics & Pharmacodynamic• Nonlinearity• Causes of nonlinearity• Michaelis – menten equation• Estimation of Km and Vmax• Estimation of Km and Vmax steady-state conc.• Bioavailability dependent nonlinear pharmacokinetics• Non-linear pharmacokinetics due to drug- protein binding Pow pointT aes er empl t 2Pa 2 ge
  3. 3. Phama r cokinet &. Phama ics r codynamics Phama r cokinet ics Phama r codynamics A ion oft bodyon t chemica ct he he l A ion oft chemica on t body ct he l heSyst A pt distibut em: bsor ion, r ion, Syst Biol ll nds orot t r s in em: ogica iga her aget met bol el t (A E a ism, iminaion DM ) t biopha he se.Out : Concentaion-ime put rt t Out : Biol lr put ogica esponse r aionships el t Pow pointT aes er empl t 3 ge 3 Pa
  4. 4. Objectives:• To understand the schemes & differential equations associated with non linear pharmacokinetic models.• To understand the effect of parallel pathways.• To estimate the parameters KM & VM.• To design appropriate dosage regimen for drugs with non linear elimination. Pow pointT aes er empl t 4 ge 4 Pa
  5. 5. Linear and Nonlinear Pharmacokinetics• In case of therapeutic dose of drug, at single or multiple doses, the process follows first order or linear kinetics if drug in the body/ the change in plasma conc. due to ADME is proportional to dose.• In first order/ linear kinetics processes, the plot of log C vs. t for different doses on a semilog paper, are superimposable. This is known as principle of superposition.• But there are some drugs that do not follow first order/ linear kinetics. In such situations, a first order kinetic transformed in to a mixture of first order and zero order rate processes and the pharmacokinetic parameters change with the size of administered dose.• The pharmacokinetic s of such drugs are said to be dose dependent.• The other term synonymous with it are mixed-order, non linear, capacity limited kinetics. Pow pointT aes er empl t 5Pa 5 ge
  6. 6. Detection of non-linearity in pharmacokinetics• There are several tests to detect non –linearity in pharmacokinetics but the simplest ones are: First test:- Determination of steady state plasma concentration at different doses. Second test:- Determination of some important pharmacokinetic parameters such as fraction bioavailability, elimination half life or total systemic clearance at different doses of drug .any change in these parameters which are usually constant, is indicative to non-linearity. Pow pointT aes er empl t 6 ge 6 Pa
  7. 7. Reasons for non linearity:• Saturation of the enzymes and of the active transport systems for the drug. Drugs which show capacity limited elimination by the kidneys & capacity limited biotransformation exhibit non linearity at high doses. EX: salicylates & naproxen-capacity limited elimination. vitamin C- capacity limited absorption.• Changes in protein binding characteristics.• Variations in blood flow around the site of absorption.• Low solubility of drug, erratic dissolution behavior from dosage form.• Changes in Ph at the site of absorption. Pow pointT aes er empl t 7 ge 7 Pa
  8. 8. Causes of non-linearity• Drug absorption:-• Three causes:- I) solubility/ dissolution of drug is rate- limited Griseofulvin- at high conc. in intestine. II) carrier-mediated transport system ascorbic acid- saturation of transport system. III) Presystemic gut wall /hepatic metabolism attains saturation ; Propranolol• Above three factors affects F, Ka,KE,ClR,ClH• First two factors causes decrease in above parameters, while last factor causes er T ain parameters Powincrease t point empl es 8 ge 8 Pa
  9. 9. Drug distribution• Drug distribution:- at high doses non-linearity due to• Two causes:- I) binding sites on plasma proteins get saturated Phenylbutazone. II) tissue binding sites get saturated• In both cases there is increase in plasma drug conc.• Increase in Vd only in I)• Clearance with high ER get increased due to saturation of Pow pointT aes er empl t 9 ge 9 binding sites. Pa
  10. 10. Drug metabolism• Drug metabolism:- non-linearity occurs due to capacity limited metabolism, small changes in dose administrations- large variations in plasma conc. at steady state- large intersubject variability.• Two imp causes:- I) capacity-limited metabolism- enzyme &/ cofactor saturation; phenytoin, alcohol. II) enzyme induction-decrease in plasma conc. Carbamazepine.• Autoinduction in dose dependent conc.• Saturation of enzymes- decrease in ClH- increase in Css.• In case of enzyme induction reverse condition.• Other reasons includes saturation oftbinding sites, inhibitory10 ge 10 Pow pointT aes er empl Pa
  11. 11. Drug excretion• Drug excretion:- two active processes which are saturable I) active tubular secretion- penicillin G II) active tubular reabsorption - water soluble vitamins &glucose.• Saturation of carrier systems- decrease in renal clearance in case of I & increase in II. Half life also increases.• Other reasons like forced diuresis, change in urine pH, nephrotoxicity, & saturation of binding sites.• The AUC is not proportional to amount of bioavailable drug.• In case of biliary excretion non-linearity due to saturation- tetracycline & indomethacin. T aes Pow point empl t er 11 ge 11 Pa
  12. 12. Examples of drugs showing nonlinear pharmacokinetics causes drugsGI absorption:-Saturable transport in gut wall Riboflavin, gabapentinSaturable GI decomposition Penicillin G, omeprazoleIntestinal metabolism Propranolol, salicylamideDistribution:-Saturable plasma protein binding Phenylbutazone, lidocaineTissue binding ImipramineMetabolism:-Saturable metabolism Phenytion, salicylic acidEnzyme induction CarbamazepineMetabolite inhibition DiazepamRenal elimination:-Active secretion Para- aminohippuric acidTubular reabsorption Ascorbic acid, riboflavinChange in urine pH Pow pointT aes acid, dextroamphetamine ge 12 er Salicylic empl t 12 Pa
  13. 13. • In order to determine whether a drug is following dose dependent kinetics.• The drug is given at various dose levels and a plasma concentration level time curve is obtained for each dose.• The curve should exhibit parallel slopes if the drug fallows a dose dependent kinetics.• Alternatively, a plot of the areas under the plasma level time curves at various doses should be linear. Pow pointT aes er empl t 13 ge 13 Pa
  14. 14. MICHAELIS MENTEN EQUATION• The kinetics of capacity limited or saturable processes is best described by Michaelis-Menten equation. dC V xC ma = … … … .. I ……… dt KM+ C• Where ,• -dC/dt= rate of decline of drug conc. with time• Vmax= theoretical maximum rate of the process• KM=Michaelis constant• Three situation can now be considered depending upon the value of Km and C.1) when KM=C:• under this situation , eq I reduces to,• -dC/dt=Vmax/2 ...................II• The rate of process is equal to half of its maximum rate.• This process is represented er the empl t dc/dt vs. C. shown in fig. 1 Powin Tplot es point aof 14 Pa 14 ge
  15. 15. 1) If a drug at low conc. Undergoes a saturable biotransformation then KM>>C:• here , KM +C =KM and eq. I reduces to, -dC/dt =Vmax C /KM………………III• above eq. is identical to the one that describe first order elimination of drug, where Vmax/KM= KE.3) when KM<<C:• Under this condition ,KM +C= C and eq. I will become, -dC/dt =Vmax …………….IV above eq. is identical to the one that describe a zero order process i.e. the rate process occursPowconstant aes Vmax and is independent of at er T rate point empl t 15 ge 15 Pa drug conc.
  16. 16. Zer or r t a high doses o der ae t M or r t a ixed der ae t int mediaed doses er tdcdt F stor r t a l doses ir der ae t ow C fig.1 Apl ofM E ot M Pow pointT aes er empl t 16 ge 16 Pa
  17. 17. Estimation of Vmax & KM• The parameters Km and Vmax can be assessed from the plasma conc.-time data collected after i.v. bolus administration of a drug with non linear characteristics• Rewriting eq. I dC Vmax C - = … … … .. X ……… dt KM +C• integration of above eq. we get Co- C V xt ma InC = InCo + - … … … .. XI ……… KM KM• If above eq. is converted to log base 10, we get L C= l 0 + og ogC (C0-C) – Vmax t … … … .. XII ……… 2.303 KM 2.303 KM Pow pointT aes er empl t 17 ge 17 Pa
  18. 18. • A semi log plot of C versus t yields a curve with a terminal linear portion having slope –Vmax/ 2.303 Km and when back extrapolated to time zero gives y- intercept log Co . The equation that describe this line is:• l = l Co – ogC og Vmax t … … … .. XIII ……… 2.303 Km• At low plasma conc. , eq. XII and XIII are identical . equating the two and simplifying further , we got: (Co- C) Co = log … … … .. XIV ……… 2.3 3Km 0 Co• from above eq. KM can be obtained. The value KM on Pow pointT aes er empl t 18 ge 18 substituting in the slope value gives Vmax Pa
  19. 19. • a plot of drug given a IV bolus with nonlinear elimination L Co og Y L Co og T mina l rporion of er l inea t L C og T cur e ha ing sl he v v ope= -V x/ 0 KM ma 2.3 3 t X Fig.4 Pow pointT aes er empl t 19 ge 19 Pa
  20. 20. Lineweaver-Burk Plot• An alternation approach of estimating Vmax and KM is determining the rate of change of plasma drug conc. at different times and using the reciprocal of equation I thus: - dC Vmax C = dt KM +C• Ignoring the – ve sign & writing reciprocal of the above eq. we get• If CM is the plasma conc. at the midpoint of the sampling interval, then on replacing C=Cm in above eq. 1 KM 1 = + … … … .. XV ……… dC/dt V x Cm ma Vxma• The Lineweaver-Burk Plot is obtained by ploting1/(dC/dt) vs.1/ Cm of the above eq. a straight line is obtained having slope = Pow pointT aes er empl t 20 ge 20 KM/Vmax & y-intercept = 1/Vmax. Pa
  21. 21. Hanes-Woolf Plot Cm KM Cm = + … … … .. XV ……… IdC/dt V x Cm ma Vx ma W f-A insson-Hofst Pl ool ugust ee ot dC dC/ dt KM … … … .. XV … … … II = Vx ma dt Cm Pow pointT aes er empl t 21 ge 21 Pa
  22. 22. Calculation of KM & Vmax steady-state concentration• If drug is administered for constant rate IV infusion/ in a multiple dosage regimen, the steady-state conc. is given in terms of dosing rate (DR): DR= Css ClT … … … .. (1) ………• If the steady-state is reached, then the dosing rate = the rate of decline in plasma drug conc.& if the decline occurs due to a single capacity-limited process then eq. I become as: V x Css ma DR = … … … .. (2) ……… KM+ Css• From a plot of Css vs. DR, a typical curve having a shape of hocky-stic is obtained which is shown in fig. 5 Pow pointT aes er empl t 22 ge 22 Pa
  23. 23. Cur e foradr folow nonl rkinet v ug l ing inea ics Bypl t t st dy- ae conc. a instdosing r t oting he ea st t ga aesCss Km V x/ ma 2 Vx ma DR(in mg/ ormg/ y) hr da Fig.5 Pow pointT aes er empl t 23 ge 23 Pa
  24. 24. • There are three methods which are used to define the KM & Vmax at steady-state with appreciable accuracy:• Lineweaver-Burk Plot: the reciprocal of eq. (2) we get 1 KM 1 = + … … … .. (3 ……… ) DR V x Css ma Vxma• If 1/DR is plotted against 1/Css a straight line is obtained having slope KM/Vmax & y-intercept 1/Vmax.2) Direct linear plot:-• Plotting a pair of Css, i.e.Css1,&Css2 against corresponding dosing rates DR1 & DR2 we get following fig. 5 which gives values KM &Vmax Pow pointT aes er empl t 24 ge 24 Pa
  25. 25. Dir l rpl forest t ofKM &V x ect inea ot imaion ma a st dy- ae conc. Ofadr t ea st t ug, w itis a hen dminist ed a differ dosing r t er t ent aes DR Vx ma DR1 DR2Css1 Css 2 KM Css 0 KM F 6 ig. Pow pointT aes er empl t 25 ge 25 Pa
  26. 26. 1) Graphical method:-• In this method by rearranging eq.(2) we get KM DR … … … .. (4 ……… ) DR = Vx ma Css• If DR is plotted against DR/Css, a straight line is obtained with slope –KM & y-intercept Vmax.• KM & Vmax can be estimated by simultaneous eq. as V x Css1 ma DR1 = KM+ Css1 V x Css2 ma DR = 2 … … … .. (6) ……… KM+ Css2 Pow pointT aes er empl t 26 ge 26 Pa
  27. 27. • On solving above eq. 5& 6 we get DR-DR1 2 KM = … … … .. (7) ……… DR 1 DR 2 - Css 1 Css 2• By substituting values of DR1, DR2,Css1 & Css2 we get value of KM & from KM we can found value of Vmax at steady-state conc.• From experimental observations, it shows that KM is much less variable than Vmax. Pow pointT aes er empl t 27 ge 27 Pa
  28. 28. Bioavailability dependent nonlinear pharmacokinetics• The bioavailability of drugs that follows nonlinear kinetics is difficult to estimate accurately.• In such cases in the presence of saturable pathways in drug ADME, drug bioavailability changes within single dose or subsequent doses.• The extent of bioavailability can also estimate from [AUC]0Φ Non-linear pharmacokinetics due to drug-protein binding … … … .. (1) ………• In case of protein binding drug the conc. of free drug can be obtained by• Cf = Cp (1- fraction bound)• in case of one compartmentpointT aes protein bounded drugge 28 Pow model, tthe er empl 28 Pa
  29. 29. 1 Cb Kd Cr … … … .. (2) ……… = 1 p 1+ ( K ) Cr d• Where Cb= plasma conc. Of bound drug. p= protein conc. in plasma Kd= K2/K1= dissociation constant of the protein drug complex. K1& K2= rate constants• The above eq. can be rearranged as p Cr Cb = = Cp - Cr … … … .. (3 ……… ) Kd Cr Pow pointT aes er empl t 29 ge 29 Pa
  30. 30. References• Biopharmaceutics and clinical pharmacokinetics by Milo Gibaldi 4th edition 1991• Biopharmaceutics and pharmacokinetics by D.M . Brahmankar and sunil.B. Jaiswal• Text book of Biopharmaceutics and pharmacokinetics by Dr.shobha rani r. hiremath ,2000• Biopharmaceutics and pharmacokinetics by G.R.chatwal, 1st edition.• Applied Biopharmaceutics and pharmacokinetics by Leon Shargel/ Andrew B.C 4th edition.• Drug disposition and pharmacokinetics by Curry Blackwell 3rd edition. Pow pointT aes er empl t 3 ge 3 0 Pa 0
  31. 31. Pow pointT aes er empl t 3 ge 3 1 Pa 1

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