Non linear pharmacokinetics


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Slide 2: 

A young child given an im injection might ask "How will that 'ouch' get from there to my sore throat"? The answer to this question is the basis of pharmacokinetics. That is, how drugs move around the body and how quickly this movement occurs. Many of the processes which control the absorption, distribution, metabolism, and excretion of drugs will be discussed. 10/25/2010 vikramjit singh ,"Dr.Nawazish alam" 2


PHARMACOKINETICS Definition : The study of the absorption, distribution, metabolism and excretion of drugs and their relationship to pharmacological response . In simple words : What the body does to the drugs. 10/25/2010 vikramjit singh ,"Dr.Nawazish alam" 3


NON-LINEAR PHARMAKOKINETICS Linear Pharmacokinetics:- In this the p’kinetic parameter for a drug would not change when different doses or multiple doses of a drug is given. Non-linear p'kinetic;- With some drugs, increased dose or chronic medication can cause deviation from the linear p’kinetics.this is known as non-linear p’kinetic. 10/25/2010 vikramjit singh ,"Dr.Nawazish alam" 4



Slide 6: 

Causes of non-linearity in p'kinetic:- Nonlinearities can occur in drug absorption,distribution,metabolism and excretion. Absorption:- Nonlinearity in drug absorption arise from 3 important sources: 1)When absorption is solubility or dissolution rate-limited e.g.Griseofulvin. 2)When absorption involves carrier mediated transport systems e.g. Riboflavin. 3)When presystemic gut wall or hepatic metabolism attains saturation e.g.Propanolol 10/25/2010 vikramjit singh ,"Dr.Nawazish alam" 6

Drug Absorption : 

10/25/2010 vikramjit singh ,"Dr.Nawazish alam" Drug Absorption oral administration plasma concentration time profile 7

10/25/2010 vikramjit singh ,"Dr.Nawazish alam" therapeutic response is dependent on drug achieving an adequate plasma concentration plasma conc’n Cp Therapeutic Window 8

Slide 9: 

Distribution: Nonlinearity in distribution of drugs administered at high doses may be due to: 1)Saturation of binding sites on plasma proteins e.g.Phenylbutazone. 2)Saturation of tissue binding sites.e.g.Methotrexate. Metabolism: Two important causes of nonlinearity in metabolism are: 1)Capacity limited metabolism due to enzyme and/or cofactor saturation.e.g.Theophylline. 2)Enzyme induction e.g.Carbamazepine. 10/25/2010 vikramjit singh ,"Dr.Nawazish alam" 9

Slide 10: 

Excretion: Two active processes in renal excretion of a drug that are saturable are: 1)Active tubular secretion e.g. Penicillin G. 2)Active tubular reabsorption e.g. Glucose. * Biliary excretion, which is also an active process, is also subject to saturation e.g. tetracycline. 10/25/2010 vikramjit singh ,"Dr.Nawazish alam" 10


EXCRETION Passage out of systemically absorbed drug. ROUTE Urine (through kidney ) Faeces ( through intenstine ) Exhaled air Saliva and sweat ( through skin ) Milk 10/25/2010 vikramjit singh ,"Dr.Nawazish alam" 11


KINETICS OF ELIMINATION Clearance (CL): The theoretical volume of plasma from which the drug is completely removed in unit time. CL = rate of elimination/plasma concentration(c) Two types: First order kinetics Second order kinetics 10/25/2010 vikramjit singh ,"Dr.Nawazish alam" 12


KINETICS OF ELIMINATION First order(exponential) kinetics: Rate of elimination is directly propotional to drug concentration. CL remains constant t½ remains constant Zero order(linear) kinetics: Rate of elimination is constant irrespective of drug concentration. CL decrease with increase in concentration. t½ increases with dose e.g. Ethyl alcohol 10/25/2010 vikramjit singh ,"Dr.Nawazish alam" 13

Slide 14: 

Michaelis-Menten equation and kinetics:- The elimination of a drug by a saturable enzymatic process is best described by Michaelis-Menten kinetics or equation: -dc/dt =vmaxc/km+c (1) Where, –dc/dt =rate of decline of drug concentration with time Vmax = theoretical maximum rate of process km = Michaelis constant C =concentration of drug 10/25/2010 vikramjit singh ,"Dr.Nawazish alam" 14

Slide 15: 

Vmax/2 ZERO ORDER RATE AT HIGH DOSE dc/dt MIXED ORDER RATE AT INTERMEDIATE DOSES Km FIRST ORDER RATE AT LOW DOSES C Fig: plot of M-M equation (elimination rate dc/dt versus concentration c) 10/25/2010 vikramjit singh ,"Dr.Nawazish alam" 15

Slide 16: 

Three situations can now be considered depending upon the values of Km and C:- 1)When Km =C:under this situation, the equation (1) reduces to: -dc/dt =Vmax/2 (2) i.e. the rate of process is equal to one half its maximum rate. 2)When Km >>C:Here,Km + C =Km and the equation reduces to: -dc/dt =VmaxC/Km (3) 3)When Km << C: under this condition,Km + C=C and the equation will become -dc/dt = Vmax (4) 10/25/2010 vikramjit singh ,"Dr.Nawazish alam" 16

Slide 17: 

Estimation of Km and Vmax Km and Vmax is graphically computed in 3 ways: 1)Lineweaver-Burk plot: It is given by the following equation: 1/Dr =Km/Vmax Css +1/Vmax (5) A plot of 1/Dr versus 1/Css yields a straight line with slope Km/Vmax and y-intercept 1/vmax. 2)Direct linear plot: As shown in graph a pair of Css viz.Css.1 and Css.2 obtained with 2 different dosing rates DR1 and DR2 are plotted. The points Css.1 and Dr1 and Css.2 and DR2 are joined to form the lines. The points where these 2 lines intersect each other is extrapolated on DR axis to obtain Vmax and on x-axis to get Km. 10/25/2010 vikramjit singh ,"Dr.Nawazish alam" 17

Slide 18: 

Vmax DR DR1 DR2 Css.1 Css.2 Km Css O Km Fig. direct linear plot for estimation of Km and Vmax at steady-state concentration of a drug given at different dosing rates. 10/25/2010 vikramjit singh ,"Dr.Nawazish alam" 18

Slide 19: 

3)Graphical method: It is given by following equation: DR =Vmax-Km DR/Css (6) A plot of DR versus DR/Css yields a straight line with slope –Km and y-intercept Vmax. 10/25/2010 vikramjit singh ,"Dr.Nawazish alam" 19


PROTIEN-DRUG BINDING Determination of binding sites and binding constants: In-vitro methods (Known protein concentration): A plot of ratio of ‘ r ’ (moles of drug bound per mole of protein) versus free drug concentration[D] is shown in fig. Velocity of metabolism is given by the equation V = Vmax [D] / [D] + Km (7) Which shows that as free drug conc. Increases, the no. of moles of drug bound per mole of protein becomes saturated and plateaus.Thus,drug protein binding resembles a Langmuir adsorption isotherm, 10/25/2010 vikramjit singh ,"Dr.Nawazish alam" 20

Plasma protein binding : 

Plasma protein binding Acidic drugs generally binds to plasma albumin Basic drugs generally binds to α1 acid glycoprotein Plasma concentration of drug = bound form(with plasma protein) + unbound form(free drug) 10/25/2010 vikramjit singh ,"Dr.Nawazish alam" 21

Plasma protein binding : 

Plasma protein binding Bound form responsible for restrict drug to vascular compartment No action Longer action(no metabolism/excretion) Unbound form Free drug in plasma Responsible for action Toxicity 10/25/2010 vikramjit singh ,"Dr.Nawazish alam" 22

Slide 23: 

saturation of binding sites of high concentration Free drug conc.[D] Moles of drug bound per mole of protein [r] Fig: Graph showing saturation of protein at high drug concentrations. 10/25/2010 vikramjit singh ,"Dr.Nawazish alam" 23

Non-linear kinetics : 

Non-linear kinetics 10/25/2010 vikramjit singh ,"Dr.Nawazish alam" 24

General relationship between reaction rate and substrate concentration for any enzyme catalysed reaction : 

General relationship between reaction rate and substrate concentration for any enzyme catalysed reaction Rate Substrate concentration Graph becomes flatter as the enzyme becomes saturated with substrate. 10/25/2010 vikramjit singh ,"Dr.Nawazish alam" 25

Specific case of ...Drug elimination : 

Specific case of ...Drug elimination Elimination rate Drug concentration 10/25/2010 vikramjit singh ,"Dr.Nawazish alam" 26

For most drugs : 

For most drugs Drug concentration Elimination rate Highest concentrations actually seen in real therapeutic use. Too little to saturate the enzyme. Almost no curvature. 10/25/2010 vikramjit singh ,"Dr.Nawazish alam" 27

For most drugs[Expansion of the relevant part of the graph] : 

For most drugs[Expansion of the relevant part of the graph] Drug concentration Elimination rate Graph would start to curve if we went to much higher concentrations and began to saturate the enzyme. 10/25/2010 vikramjit singh ,"Dr.Nawazish alam" 28

Exceptions ... : 

Exceptions ... There are a small number of drugs where concentrations seen in real life use are high enough to saturate the eliminating enzymes. The best known are: Phenytoin - The only case of real clinical significance Salicylates Ethanol There is also some evidence that Theophylline may approach saturation but, in practice, it can be treated as following linear kinetics. 10/25/2010 vikramjit singh ,"Dr.Nawazish alam" 29

Slide 30: 

Rate of eliminat’n Rate of eliminat’n Blood drug conc Blood drug conc Linear kinetics (most drugs) Non-linear kinetics (e.g. phenytoin) 10/25/2010 vikramjit singh ,"Dr.Nawazish alam" 30

Slide 31: 

Rate of elim = Rate of admin Rate of elim = Rate of admin Blood drug conc Blood drug conc Blood drug conc Rate of admin Rate of admin Blood drug conc Linear Non-linear At steady state ... 10/25/2010 vikramjit singh ,"Dr.Nawazish alam" 31

Dosage adjustment : 

Dosage adjustment For most drugs, changes in dosage produce proportionate changes in blood concentrations. e.g. if you increase dose size by 25%, blood levels will also increase by 25%. For non-linear drugs (primarily phenytoin), an increase in dose size will cause a disproportionate increase in blood levels. A 25% increase in dose size might lead to a doubling in blood levels. So beware !!!! 10/25/2010 vikramjit singh ,"Dr.Nawazish alam" 32

What you should be able to do : 

What you should be able to do Explain why a small minority of drugs follow non-linear kinetics. Cite phenytoin as clinically the most significant example of a drug with non-linear kinetics. Describe the impact of non-linear kinetics upon dosage adjustment. Recognise drugs that have a low therapeutic index. Identify the mode of elimination of key drugs with low T.I.s Logically use the two pieces of information above to predict whether dosage adjustment will be necessary for a particular drug in a range of conditions. 10/25/2010 vikramjit singh ,"Dr.Nawazish alam" 33

Compartmental Analysis : 

10/25/2010 vikramjit singh ,"Dr.Nawazish alam" Compartmental Analysis objective is to represent complicated physiologic systems with simple mathematical models systems that are continuous and nonhomogeneous are replaced with compartments that are discrete and in which concentrations etc. are homogeneous 34

Slide 35: 

10/25/2010 vikramjit singh ,"Dr.Nawazish alam" 35

Open one-compartment model : 

10/25/2010 vikramjit singh ,"Dr.Nawazish alam" Open one-compartment model process of distribution to each compartment is much faster than absorption into blood and elimination drug concentration everywhere in the compartment is equal (CSTR) elimination processes are pseudo-1st order D ka DB Cp kel Vd 36

Plasma concentration curves (PCC) : 

Plasma concentration curves (PCC) The concentration of a drug in the plasma reflects many of its properties. A PCC gives a hint as to how the ADME processes interact. If we draw a PCC in a logarithmic scale after an i.v. dose, we expect to get a straight line since we assume the concentration of the drug in plasma to decrease exponentially. This is first order- or linear kinetics. The elimination rate is then proportional to the concentration in plasma. This model is approximately true for most drugs. 10/25/2010 vikramjit singh ,"Dr.Nawazish alam" 37

Plasma concentration curve : 

Plasma concentration curve 10/25/2010 vikramjit singh ,"Dr.Nawazish alam" 38

Slide 39: 

Pharmacokinetic models Various types of models 10/25/2010 vikramjit singh ,"Dr.Nawazish alam" 39

One-compartment model with rapid intravenous administration: The pharmacokinetics parameters : 

One-compartment model with rapid intravenous administration: The pharmacokinetics parameters Half life Distribution volume AUC Tmax and Cmax D: Dose VD: Volume k: Elimination rate Cl: Clearance 10/25/2010 vikramjit singh ,"Dr.Nawazish alam" 40

One compartment model : 

One compartment model General model Tablet IV 10/25/2010 vikramjit singh ,"Dr.Nawazish alam" 41

Slide 42: 

Complex picture of drug interactions in the body. This slide gives an idea of the complexity of drug disposition. Shown in this slide are many of the steps to getting drug from one site in the body to another. Many of these processes are enzyme induced. However the overall picture often is much simpler. Many of these processes maybe fast or not significant for any given drug. 10/25/2010 vikramjit singh ,"Dr.Nawazish alam" 42

Slide 43: 

Processes involved in drug transport. Here the major processes are represented in a less physiological fashion. It is with this approach that we will look at much of the course material. The headings Absorption, Distribution, Metabolism, and Excretion are important 10/25/2010 vikramjit singh ,"Dr.Nawazish alam" 43

Slide 44: 

One, two, and three compartment pharmacokinetic models. Fortunately many of the processes involved in drug movement around the body are not saturated at normal therapeutic dose levels. The pharmacokinetic - mathematical models that can be used to describe plasma concentration as a function of time can then be much simplified. The body may even be represented as a single compartment or container for some drugs. For other drugs a two or three compartment model is found to be necessary. 10/25/2010 vikramjit singh ,"Dr.Nawazish alam" 44

Slide 45: 

Body before and after a rapid I.V. bolus injection, considering the body to behave as a single compartment. In order to simplify the mathematics it is often possible to assume that a drug given by rapid intravenous injection, a bolus, is rapidly mixed. This slide represents the uniformly mixed drug very shortly after administration. 10/25/2010 vikramjit singh ,"Dr.Nawazish alam" 45

Slide 46: 

Oral curve and beakers. We can picture oral administration as water flowing from one bucket (representing the GI tract) into a second beaker (representing the body). At first drug flows into the 'body' beaker and the level rises, as drug concentration rises, then after peaking the levels start to fall as elimination overtakes absorption. 10/25/2010 vikramjit singh ,"Dr.Nawazish alam" 46

Slide 47: 

Questions Comments & 10/25/2010 vikramjit singh ,"Dr.Nawazish alam" 47