Pharma co kinetics compartmental modeling

Pharma co-kinetics compartmental modeling, Non Linear Pharma co kinetics and Drug Interactions.

1. PHARMACOKINETIC MODELS Name: Manjit Kaur Roll No. 1481311 M. Pharmacy (2 nd Sem.) Department Of Pharmaceutics Sri Sai College Of Pharmacy

2. PHARMACOKINETIC MODELS Basic considerations in pharmacokinetics • Compartment models • One compartment model • Assumptions • Intravenous bolus administration • Intravenous infusion • Extravascular administration (zero order and first order absorption model) • Multi-compartment model

3. Non linear pharmacokinetics Causes Michaelis- Menten equation Estimation of K max and V max Drug interactions

4. BASIC CONSIDERATIONS IN PHARMACOKINETICS • Pharmacokinetic parameters • Pharmacodynamic parameters • Zero, first order & mixed order kinetic • Rates and orders of kinetics • Plasma drug conc. Time profiles • Compartmental models – physiological model • Applications of pharmacokinetics • Non compartment model

5. MIXED ORDER KINETICS Kinetics of a pharmacokinetic process changes from First order to Zero order with increasing dose or chronic medication. Deviations from original Linear kinetic profile – Non Linear kinetics. Dose dependent kinetics Seen when P’kinetic process Carriers / Substrates (Capacity Limited – get saturated at Higher drug Conc ).

6. MICHAELIS – MENTEN KINETICS Describes velocity of Capacity limited, enzyme reactions and non linear pharmacokinetics. MICHAELIS MENTON EQUATION IS -DC/DT = V MAX . C / KM + C KM = Michaelis constant, Vmax = Theoretical maximum rate of process Some examples; Absorption (Vitamin C), Distribution (Naproxen), and Elimination (Riboflavin)

7. PLASMA DRUG CONCENTRATION – TIME PROFILE Effectiveness of Dosage Regimen Concentration of Drug in the Body Conc. at Site of action Conc. in whole Blood (Plasma, Serum), Saliva, Urine, PK Parameters determine drug Conc. Three important parameters useful in assessing the bioavailability of a drug from its formulation are:

8. Peak plasma concentration ( cmax ): The point at which, maximum concentration of drug in plasma. Units : µg/ml Peak conc. Related to the intensity of pharmacological response, it should be above MEC but less than MSC. The peak level depends on administered dose and rate of absorption and elimination.

9. Time of peak concentration ( tmax ): The time for the drug to reach peak concentration in plasma (after extra vascular administration). Units : hrs Useful in estimating onset of action and rate of absorption. Important in assessing the efficacy of single dose drugs used to treat acute conditions (pain, insomnia).

10. Area under curve (AUC): It represents the total integrated area under the plasma level-time profile and expresses the total amount of the drug that comes into systemic circulation after its administration. Units : µg/ml x hrs

11. PHARMACODYNAMIC PARAMETERS Minimum effective concentration (MEC ): Minimum concentration of drug in plasma/receptor site required to produce therapeutic effect. Antibiotics - MEC 2. Maximum safe concentration (MSC): Concentration in plasma above which adverse or unwanted effects are precipitated. Onset time: Time required to start producing pharmacological response. Time for plasma concentration to reach MEC after administrating drug.

12. Onset of action: The beginning of pharmacologic response. It occurs when plasma drug concentration just exceeds the required MEC. Duration of action: The time period for which the plasma concentration of drug remains above MEC level. Intensity of action: It is the minimum pharmacologic response produced by the peak plasma conc. Of drug. Therapeutic range: the drug conc. between MEC and MSC.

13. CONCEPT OF “HALF LIFE” ½ Life = how much time it takes for blood levels of drug to decrease to half of what it was at equilibrium. There are really two kinds of ½ life. 1. “Distribution” ½ life = when plasma levels fall to half what they were at equilibrium due to distribution to/storage in body’s tissue reservoirs. 2. “Elimination” ½ life = when plasma levels fall to half what they were at equilibrium due to drug being metabolized and eliminated. It is usually the elimination ½ life that is used to determine dosing schedules, to decide when it is safe to put patients on a new drug.

14. PHARMACOKINETIC MODELS AND COMPARTMENTS Pharmacokinetic Modelling Compartment Models: a. Caternary Model b. Mamillary Model Non-Compartment Models AUC, MRT, MAT, Cl, VSS Physiologic Models

15. PHARMACOKINETIC MODELS: Means of expressing mathematically or quantitatively, time course of drug through out the body and compute meaningful pharmacokinetic parameters. Useful in : Characterize the behaviour of drug in patient. • Predicting conc. Of drug in various body fluids with dosage regimen. Calculating optimum dosage regimen for individual patient. Evaluating bioequivalence between different formulation. Explaining drug interaction.

16. Pharmacokinetic models Pharmacokinetic models are hypothetical structures that are used to describe the fate of a drug in a biological system following its administration. Model is the Mathematical representation of the data and It is just hypothetical.

17. COMPARTMENTAL MODELS: A compartment is not a real physiological or anatomic region but an imaginary or hypothetical one consisting of tissue/ group of tissues with similar blood flow & affinity. Our body is considered as composed of several compartments connected reversibly with each other.

18. ADVANTAGES: Gives visual representation of various rate processes involved in drug disposition. Possible to derive equations describing drug concentration changes in each compartment. One can estimate the amount of drug in any compartment of the system after drug is introduced into a given compartment.

19. DISADVANTAGES: Drug given by IV route may behave according to single compartment model but the same drug given by oral route may show 2 compartment behaviour. The type of compartment behaviour i.E. Type of compartment model may change with the route of administration.

20. Central compartment: Blood & highly perfused tissues such as heart, kidney, lungs, liver, etc. Peripheral compartment: Poorly per fused tissues such as fat, bone, etc. MODELS: “OPEN” and “CLOSED” models: The term “open” itself mean that, the administered drug dose is removed from body by an excretory mechanism (for most drugs, organs of excretion of drug is kidney). If the drug is not removed from the body then model refers as “closed” model.

21. LOADING DOSE: A drug dose does not show therapeutic activity unless it reaches the desired steady state. It takes about 4-5 half-lives to attain it and therefore time taken will be too long if the drug has a long half-life. A simple equation for calculating loading dose is : xo,l = css,av vd / F

22. ASSUMPTIONS One compartment: The drug in the blood is in rapid equilibrium with drug in the extra-vascular tissues. This is not an exact representation however it is useful for a number of drugs to a reasonable approximation. Rapid mixing: We also need to assume that the drug is mixed instantaneously in blood or plasma. Linear model: We will assume that drug elimination follows first order kinetics.

23. ONE COMPARTMENT MODEL: One compartment model can be defined: a. One com. Open model – i.V. Bolus. b. One com. Open model - cont. Intravenous infusion. c. One com. Open model - extra vas. Administration (zero-order absorption) d. One com. Open model - extra vas. Administration (First-order absorption)

24. INTRAVENOUS (IV) BOLUS ADMINISTRATION INTRAVENOUS (IV) BOLUS ADMINISTRATION RATE OF DRUG PRESENTATION TO BODY IS: If rate out or elimination follows first order kinetic Dx/dt = - k e x ----------------(1) ELIMINATION PHASE: Elimination phase has three parameters: Elimination rate constant, Elimination half- life, Clearance ELIMINATION RATE CONSTANT: Integration of equation (1) In x = ln xo – ke t -----------(eq.2)

25. Elimination half -life can be readily obtained from the graph of log c versus t. Half-life is a secondary parameter that depends upon the primary parameters such as clearance and volume of distribution. T 1/2 = 0.693 V d / Cl T

26. APPARENT VOLUME OF DISTRIBUTION: defined as volume of fluid in which drug appears to be distributed. Vd = amount of drug in the body (x) / Plasma drug concentration (C) CLEARANCE: rate of elimination / Plasma drug conc.. ORGAN CLEARANCE: Rate of elimination by organ= rate of presentation to the organ – rate of exit from the organ. Clorgan = Q.Er …………….( eq 22) Extraction ratio: ER= ( C in - C out )/ C in

27. ONE COMPARTMENT MODEL: EXTRA VASCULAR ADMINISTRATION (ZERO ORDER ABSORPTION) This model is similar to that for constant rate infusion. Rate of drug absorption as in case of CDDS , is constant and continues until the amount of drug at the absorption site (Ex. GIT) is depleted. All equations for plasma drug conc. Profile for constant rate I.V. Infusion are also applicable to this model.

28. ONE COMPARTMENT MODEL: EXTRA VASCULAR ADMINISTRATION (FIRST ORDER ABSORPTION): Drug that enters the body by first order absorption process gets distributed in the body according to one compartment kinetic and is eliminated by first order process. The model can be depicted as follows and final equation is as follows Blood & other Body tissues C=K a F X o / V d (K a -K E ) [e - Ket -e -Kat ]

29. MULTI- COMPARTMENT MODELS: Ideally a true pharmacokinetic model should be the one with a rate constant for each tissue undergoing equilibrium. Therefore, best approach is to pool together tissues on the basis of similarity in their distribution characteristics. The drug disposition occurs by first order. Multi-compartment characteristics are best described by administration as i.v bolus and observing the manner in which the plasma concentration declines with time. The no. Of exponentials required to describe such a plasma level-time profile determines the no. Of kinetically homogeneous compartments into which a drug will distribute.

30. The simplest and commonest is the two compartment model which classifies the body tissues in two categories : Central compartment or compartment Peripheral or tissue compartment or compartment

31. TWO COMPARTMENT OPEN MODEL-IV BOLUS ADMINISTRATION: Elimination from central compartment • After the iv bolus of a drug the decline in the plasma conc. Is bi-exponential. • Two disposition processes- distribution and elimination. • These two processes are only evident when a semi log plot of C vs. T is made. • Initially, the conc. Of drug in the central compartment declines rapidly, due to the distribution of drug from the central compartment to the peripheral compartment. This is called distributive phase.

32. TWO-COMPARTMENT OPEN MODELEXTRAVASCULAR ADMINISTRATION: First - order absorption: For a drug that enters the body by a first-order absorption process and distributed according to two compartment model, the rate of change in drug conc. in the central compartment is described by three exponents: An absorption exponent, and the two usual exponents that describe drug disposition.

33. The plasma conc. at any time t is C = n e- kat + l e-at + m e- bt C = absorption + distribution + elimination exponent Besides the method of residuals, ka can also be found by loo-riegelman method for drug that follows two-compartment characteristics. Despite its complexity, the method can be applied to drugs that distribute in any number of compartments.

34. NONLINEAR PHARMACOKINETICS The rate process of drug’s ADME are depend upon carrier or enzymes that are substrate specific, have definite capacities and are susceptible to saturation at a high drug concentration. In such cases, an essentially first-order kinetics transform into a mixture of first-order and zero-order rate processes and the pharmacokinetic parameters are changed with the size of the administered dose. Pharmacokinetics of such drugs are said to be dose dependent. Terms synonymous with it are mixed-order, nonlinear and capacity-limited kinetics.

35. 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 is indicative to non-linearity which are usually constant.

36. CAUSES OF NON-LINEARITY DRUG ABSORPTION Three causes :- I) Solubility / dissolution of drug is rate-limited; Griseofulvin - at high concentration in intestine. II) Carrier - mediated transport system; Ascorbic acid - saturation of transport system. III) Pre-systemic gut wall / hepatic metabolism attains saturation; Propranolol. These parameters affected F, Ka , Cmax and AUC. • A decrease in these parameters is observed in former two causes and an increase in latter cause.

37. DRUG DISTRIBUTION At high doses non-linearity due to two causes: - Binding sites on plasma proteins get saturated; Phenylbutazone. Tissue binding sites get saturated. In both cases there is increase in plasma drug concentration. Increase in V d only in (I). Clearance with high ER get increased due to saturation of binding sites.

38. DRUG METABOLISM Non-linearity occurs due to : capacity limited metabolism small changes in dose administration large variations in plasma concentration at steady state

39. Two imp causes: - I) Capacity - limited metabolism - enzyme &/ cofactor saturation; Phenytoin, Alcohol. II) Enzyme induction - decrease in plasma concentration; Carbamazepine.

40. DRUG EXCRETION Two active processes which are saturable : - Active tubular secretion - Penicillin G 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. In case of biliary excretion non - linearity due to saturation - Tetracycline & Indomethacin.

41. MICHAELIS MENTEN ENZYME KINETICS It is also called as Capacity-limited metabolism or Mixed order kinetics . E + D = ED  E + M Enzymes usually react with the substrate to form enzyme substrate complexes; then the product is formed. The enzyme can go back to react with another substrate to form another molecule of the product.

42. MICHAELIS MENTEN EQUATION The kinetics of capacity limited or saturable processes is best described by Michaelis-Menten equation. -DC/DT = V MAX . C / KM + C ----------------(Eq.1) Where, - dC /dt = rate of decline of drug conc. with time Vmax = theoretical maximum rate of the process KM = Michaelis constant.

43. Three situation can now be considered depending upon the value of Km and C. 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 in the plot of dc/dt vs. C.

44. If a drug at low conc. undergoes a saturable biotransformation then KM>>C 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.

45. DRUG INTERACTIONS LINKED TRANSPORTS: INTRODUCTION: On its journey through the body, a drug needs to cross different biological barriers. These barriers can be - A single layer of cells (e.g. the intestinal epithelium), - Several layers of cells (e.g. in the skin), - Or the cell membrane itself (e.g. to reach an intracellular receptor). A drug can cross a cell layer either by traveling through the cells (transcellular drug transport) or through gaps between the cells (paracellular drug transport).

46. Transcellular drug transport In order to travel through a cell or to reach a target inside a cell, a drug molecule must be able to transverse the cell membrane. Although cell membranes largely vary in their permeability characteristics depending on the tissue, the main mechanisms of drugs passing through the cell membrane are passive diffusion, carrier-mediated processes and vesicular transport.

47. The 3 steps involved in transcellular transport of drugs are Permeation of GI epithelial cell membrane, a lipoidal barrier- this is the major obstacle to drug absorption. Movement across the intracellular space (cytosol). Permeation of the lateral or basolateral membrane- this is of secondary importance.

48. a. Passive Transport: Passive diffusion is the process by which molecules spontaneously diffuse from a region of higher concentration (e.g. outside of the cell) to a region of lower concentration (e.g. inside the cell), and it is the main mechanism for passage of drugs through membranes. b. Carrier-mediated processes Many cell membranes possess specialized transport mechanisms that regulate entry and exit of physiologically important molecules and drugs. Such transport systems involve a carrier molecule, that is, a trans membrane protein that binds one or more molecules and releases them on the other side of the membrane.

49. c. Ion-Pair Transport Mechanism that explains the absorption of drugs like quaternary ammonium compounds and sulphonic acids, which ionize under all pH conditions, is ion-pair transport. d. Pore transport It is also known as Convective transport, bulk flow or filtration. This mechanism is responsible for transport of molecules into the cell through the protein channels present in the cell membrane.

50. Paracellular transport/Intercellular transport Drugs can also cross a cell layer through the small aqueous contact points (cell junctions) between cells. This paracellular drug transport can be initiated by a concentration gradient over the cell layer (passive diffusion), or By a hydrostatic pressure gradient across the cell layer (filtration).

51. Vesicular or Corpuscular Transport (Endocytosis) During vesicular transport the cell membrane forms a small cavity that gradually surrounds particles or macromolecules, thereby internalizing them into the cell in the form of a vesicle or vacuole.

52. CYTOCHROME P450 DRUG INTERACTION Humans constantly exposed to xenobiotics(usually non polar) that can cause harmful effect if not eliminated.  Biotransformation convert non polar compounds to polar and helps in their elimination.  Biotransformation occurs in 2 phases(phase1 &phase 2).  Cytochrome p-450 is a superfamily of enzymes that catalyse most of the oxidation reactions of phase 1.  Require both molecular oxygen and NADPH to effect reaction.  Also called mixed function oxidases and mono- oxygenases .

53. CYTOCHROME P450 ISOFORMS: Isoforms mean same enzyme that belong to cyp450 enzyme and which having ability to metabolized drug.  There are several isoforms of enzyme which is given below:- CYP1A2 CYP2C9 CYP2C19 CYP2D6 CYP2E1 etc.

54. CYP1A2…  Metabolize the chemical and environmental chemicals.  13% total hepatic content of isoenzyme.  Drug substrate E.g - caffein , theophylline, propanolol .  Drug inhibitor E.g - ciprofloxacin, cimetidine, erythromycin.  Drug inducer E.g - hydrocarbon, phenobarbital, rifampicin. CYP2C9…  Responsible for metabolism of ibuprofen, tolbutamide, torsemide.  Warfarin is mainly metabolized by this isoforms. 9  Inhibitor of warfarin E.g - fluconazole, metronidazole, amiodarone.

55. CYP2C19...  Responsible for metabolism of diazepam, omeprazole, lansoprazole.  Poor metabolizers. CYP2D6...  Enzyme not inducible by drug.  Most drug use in clinical evaluation metabolized by this isoforms.

56. INDUCTION AND INHIBITION OF CYP450: Induction of drug metabolism can lead to unexpected drops in drug concentration or the build-up of metabolites. The reverse can occur when there is inhibition of drug metabolism.  The major organ involved in metabolism is liver and the major enzyme system involved in drug metabolism is CYP 450, the well-known family of oxidative hemoproteins . Induction CYP 450 enzymes at the liver is responsible for induction of metabolism of many drugs.

57. INHIBITION OF CYP450: Decrease in the drug metabolism ability of enzyme by drug is called enzyme inhibition.  inhibition of CYP enzymes can be classified : 1.Reversible inhibition. 2.Irreversible inhibition.

58. Reversible inhibition...  Direct competition for binding site between substrate and inhibitor.  determination of potency of inhibitor.  for example :- cimetidine H2 receptor antagonist. 16 Irreversible inhibition...  It is occur by reactive metabolites generation.  first type of irreversible inhibition involves the formation of metabolic intermediate complexes.  inhibition of CYP3A by erythromycin.  Transformation reactions such as N-hydroxylation, N-demethylation, N-oxidation catalyzed by CYP3A.

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