PHARMACODYNAMIC MODELS AND PHARMACOKINETIC MODELS : PHARMACODYNAMIC MODELS AND PHARMACOKINETIC MODELS PRESENTED BY A.RAJU M.PHARMACY 1 st yr PHARMACEUTICS UNDER THE GIDENCE OF G.GURUNATH
CONTENTS :: Why Study PK/PD ? Application of PK/PD modeling in drug development Requirements to Characterize PK/PD Relationship Complexities in PK/PD Modeling Pharmacodynamic models Definition of pharmacodynamic Definition of pharmacodynamic models Types of pharmacodynamic models Pharmacokinetic models Definition Types 1.Compartmental models 2.Physiological models 3.Non-Compartmental model 4.Non linear pharmacokinetics Application CONTENTS :
Why Study PK/PD ?: Characterize time course of pharmacologic response (therapeutic &/or toxic effects) Understand complex relationships tolerance, sensitization, mechanistic delay Explain variability in response Identify biomarkers and validate surrogate endpoints Aid dose/dose regimen selection through simulation Bridge clinical efficacy and safety results across ethnic populations Bridge clinical results between adult and pediatric patients Why Study PK/PD ?
APPLICATION OF PK/PD MODELING IN DRUG DEVELOPMENT: Objectives of Early Drug Development Identification of critical risk factors prior to investment in full clinical development selection of better compounds Provide critical data to identify safe and effective dose and dose regimens more efficient development Requirements to Characterize PK/PD Relationship Validated biomarkers for therapeutic effects & toxicity Should be meaningful (relates to MOA), reproducible, quantitative and allows frequent sampling to characterize the time course of effect Validated Assay (reproducible, high precision….) Exposure-response relationship Understanding of pharmacologic behavior of the drug and pathophysiology of the disease Pharmacology and pharmacokinetic modeling APPLICATION OF PK/PD MODELING IN DRUG DEVELOPMENT
Complexities in PK/PD Modeling: Equilibration delay : example-the anticoagulant effect of dicoumarol is due to indirect inhibition and depletion of clotting factors. Protein Binding : Active Metabolite : example- imipramine,amitryptyline and propranolol Tolerance : example- carbamazepin & nitroglycerin Racemates : S(+) Isomer of Ibuprofen Complexities in PK/PD Modeling
Definition of pharmacodynamics: It is concerned with the biochemical and physiological effects of the drug and its mechanism of action (or) It is defined as a study of what the drug does to the body . Definition of pharmacodynamic models These are mathematical models that relate pharmacological effect to a measured drug concentration in plasma or at the effecter site can be used to develop quantitative relationships. Concentration response relationships The response produced by a drug can be classified into two categories. Definition of pharmacodynamics
A. Graded response: It is the one where intensity of effect increases with the dose or concentration of drug. B. Quantal response(All or none response) It is the one where the drug may either show their effect or not at all that is the responses are not observed on a continuous basis. Example: prevention of seizures by phenytoin . Types of modeling 1.Linear model 2.Non-linear (or) Logarithmic model 3.Emax (or) hyperbolic model 4.Hill (or) Sigmoid Emax model A. Graded response
1.Linear model: Pharmacological effect(E) is directly proportional to the drug concentration(C). These can be explained by the following equation by plotting the graph C Vs E , liner curve is obtained. Equation E=PC+E0 where P =The slope of the line obtained from a plot E0 =The extrapolated y-intercept called as baseline effect in the absence of drug 1.Linear model
2.Non linear (or) Logarithmic model: These can be explained by the following equation by plotting the graph Log concentration Vs Percentage effect E=P log C + I where I=empirical constant Large change in concentration produces slight changes in response. This transformation is the linear relationships between drug concentration & response at concentrations producing effect of between 20 to 80% of the maximum effect. Beyond this range, a larger dose produces a larger concentration of drug in the body. 2.Non linear (or) Logarithmic model
3.Emax (or) Hyperbolic Model: This model describe non-linear concentration-effect relationships. These can be explained by the Michaelis-Menten equation by plotting the graph Concentration Vs Percentage effect Equation E= Emax C C50 +C where Emax = maximum effect, C50=the concentration at which 50% of the effect is produced 3.E max (or) Hyperbolic Model
4.Hill (or) Sigmoid Emax model : Hill equation h E= E max C h C 50 +C where h=hill coefficient (shape factor) If h=1, a normal hyperbolic plot is obtained and the model is called E max model Larger the value of h, steeper the linear portion of the curve and greater its slope. Such a plot is often sigmoidal and thus, the Hill model is also called as Sigmoid Emax model 4.Hill (or) Sigmoid Emax model
PHARMACOKINETIC MODELS: Pharmacokinetics is the study of drug and/or metabolite kinetics in the body. The body is a very complex system and a drug undergoes many steps as it is being absorbed , distributed through the body, metabolized or excreted ( ADME ). Pharmacokinetic models Means of expressing mathematically or quantitatively, time course of drug through out the body and compute meaningful pharmacokinetic parameters. Types 1.Compartmental models 2.Physiological models 3.Non-Compartmental model 4.Non linear pharmacokinetics PHARMACOKINETIC MODELS
1.COMPARTMENT MODELS: These are used to analysis the pharmacokinetic characterization of a drug. These models simply interpolate the experimental data and allow an empirical formula to estimate the drug concentration with time. 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. Mammillary model : One or more peripheral comparetments connected to the central compartment. Caternary model : compartments are joined to one another in a series like compartments of atrain . 1.COMPARTMENT MODELS
ASSUMPTIONS: The body is represented as a series of compartments arranged either in series or parallel to each other, which communicate reversibly with each other. Each compartment is not a real physiological or anatomical region but a fictitious or virtual one and considered as a tissue or a group of tissues that have similar drug distribution characteristics. Within each compartment, the drug is considered to be rapidly and uniformly distributed i.e. the compartment is well stirred. The rate of drug movewment between compartments is described by first order kinetics. Rate constants are used to represent rate of entry into band exit from the compartment. ASSUMPTIONS
COMPARTMENT MODELS: COMPARTMENT MODELS a. One compartment model Intravenous bolus administration Intravenous infusion Extravascular administration (zero order and first order absorption model ) Multi- Compartment models b.Two -Compartment Open model Intravenous bolus administration Extravascular administration c.Three -Compartment Open model Applications of compartment models COMPARTMENT MODELS
One Compartment : One Compartment One Compartment
PowerPoint Presentation: Two compartment Open model-iv bolus administration: Elimination from central compartment Fig After the iv bolus of a drug the decline in the plasma conc. is bi-exponential. Two disposition processes- distribution and elimination. 1 Central 2 peripheral
PowerPoint Presentation: These two processes are only evident when a semilog 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. A pseudo-distribution equilibrium occurs between the two compartments following which the subsequent loss of drug from the central compartment is slow and mainly due to elimination. This second, slower rate process, is called as the post-distributive or elimination phase. In contrast to this compartment, the conc of drug in the peripheral compartment first increases and reaches its max. Following peak, the drug conc declines which corresponds to the post-distributive phase . dC c = K 21 C p – K 12 C c – K E C c dt
PowerPoint Presentation: Extending the relationship X= V d C dC c = K 21 X p – K 12 X c – K E X c dt V p V c V c X=amt. of drug in the body at any time t remaining to be eliminated C=drug conc in plasma V d =proportionality const app. volume of distribution X c and X p =amt of drug in C1 and C2 V c and V p =apparent volumes of C1 and C2 The rate of change in drug conc in the peripheral component is given by: dC p =K 12 C c – K 12 C p dt =K 12 X c – K 21 X p V c V p
PowerPoint Presentation: On integration equation gives conc of drug in central and peripheral compartments at any given time t : Cc = X o [(K 21 – a) e -at + (K 21 - b) e - bt ] b – a a - b Cp = Xo [( K 21 – a)e -at + (K 12 – b)e - bt ] Vc b – a a – b Xo = iv bolus dose a and b = hybrid first order constants for rapid dissolution phase and slow elimination phase, which depend entirely on 1 st order constants K12, K21, KE The constants K12, and K21 that depict the reversible transfer of drug between the compartments are called micro or transfer constants. The relation between hybrid and microconstants is given as : a + b = K12 + K21 + KE a b = K21 KE
PowerPoint Presentation: Cc = A e -at + Be - bt Cc=distribution exponent + elimination exponent A and B are hybrid constants for two exponents and can be resolved by graph by method of residuals. A = X 0 [K 21 - a] = C o [K 21 – a] V c b – a b – a B = X 0 [K 21 - b] = C o [K 21 – b] V c a – b a – b C o = plasma drug conc immediately after i.v . injection Method of residuals : the biexponential disposition curve obtained after i . v. bolus of a drug that fits two compartment model can be resolved into its individual exponents by the method of residuals.
PowerPoint Presentation: C = A e -at + B e - bt From graph the initial decline due to distribution is more rapid than the terminal decline due to elimination i.e. the rate constant a >> b and hence the term e -at approaches zero much faster than e – bt C = B e - bt log C = log B – bt /2.303 C = back extrapolated pl. conc A semilog plot of C vs t yields the terminal linear phase of the curve having slope –b/2.303 and when back extrapolated to time zero, yields y-intercept log B. The t 1/2 for the elimination phase can be obtained from equation t 1/2 = 0.693/b. Residual conc values can be found as- C r = C – C = Ae -at log Cr = log A – at 2.303 A semilog plot Cr vs t gives a straight line.
PowerPoint Presentation: C0 = A + B KE = a b c A b + B a K12 = A B (b - a) 2 C0 (A b + B a) K21 = A b + B a C0 For two compartment model, KE is the rate constant for elimination of drug from the central compartment and b is the rate constant for elimination from the entire body. Overall elimination t1/2 can be calculated from b. Area Under (AUC) = A + B the Curve a b App. volume of Central = X0 = X0 compartment C0 KE (AUC)
PowerPoint Presentation: App. volume of = VP = VC K12 Peripheral compartment K21 Apparent volume of distribution at steady state or equilibrium Vd,ss = VC +VP Vd,area = X0 b AUC Total systemic Clearence = ClT = b Vd Renal Clearence = ClR = dXU = KE VC dt The rate of excretion of Unchanged drug in urine can be represented by : dXU = KE A e -at + KE B e - bt dt The above equation can be resolved into individual exponents by the method of Residuals.
c.THREE COMPARTMENT MODEL: Gibaldi & Feldman described a three compartment open model to explain the influence of route of administration .i.e. intravenous vs. oral, on the area under the plasma concentration vs. time curve. Portman utilized a three compartment model which included metabolism & excretion of hydroxy nalidixic acid. Three compartment model consist of the following compartments . Central compartment. Tissue compartment. Deep tissue compartment. In this compartment model drug distributes most rapidly in to first or central compartment. Less rapidly in to second or tissue compartment . Very slowly to the third or deep tissue compartment. The third compartment is poor in tissue such as bone & fat. c.THREE COMPARTMENT MODEL
PowerPoint Presentation: CENTRAL COMPARTMENT TISSUE COMPARTMENT DEEP TISSUE COMPARTMENT DRUG INPUT K 10 THREE COMPARTMENT CATENARY MODEL THREE COMPARTMENT MAMMILLARY MODEL TISSUE COMPARTMENT CENTRAL COMPARTMENT DEEP TISSUE COMPARTMENT K 10 DRUG INPUT DRUG OUTPUT K 21 K 13 K 12 K 31 RAPID IV 25 November 2010 26 KLECOP, Nipani
Applications and advantagesof compartment models: It gives a visual representation of various rate processes involved in drug disposition. It shows how many rate constants are necessary to describe these processes. It is important to development of dosage regimens. Useful in predicting drug concentration time profile in both normal physiological and in pathological conditions. It is useful in relating plasma drug levels to therapeutic and toxic effects in the body. It enables monitoring of drug concentration change with time with a limited amount of data. Only plasma concentration data or urinary excretion data is sufficient. It enables the pharmacokinetic ist to write differential equations for each of the rate processes in order to describe drug concentration changes in each compartment. Applications and advantagesof compartment models
PowerPoint Presentation: Disadvantages The model may vary within a study population. The approach can be applied only to a specific drug under study. The model is based on curve fitting of plasma concentration with complex multiexponential mathematical equations. Difficulties genrally arise when using models to interpret the differences between results from human and animal experiments. The drug behaviour within the body may fit different compartmental models depending upon the route of administration. Extensive efforts are required in the development of an exact model that predicts and describes correctly the ADME of a certain drug.
2.Physiological Model: Physiological Models are drawn on the basis of known anatomic and physiological data and thus present a more realistic picture of drug disposition in various organs and tissues. The number of compartments to be included in the model depends upon the disposition characteristics of the drug. The rate of drug carried to a tissue/organ or tissue drug uptake is depend upon a. Rate of blood flow to the organ, and b. Tissue/blood partition coefficient or diffusion coefficient of drug that governs its tissue permiability . Types : a. Blood flow rate limited model b. Membrane permeation rate limited model 2.Physiological Model
a. Blood flow rate limited model: The drug movement within a body region is much more rapid than its rate of delivery to that region by the perfusion blood. Applicable only to the highly membrane permeable drugs i.e. low molecular weight, poorly ionised and highly lipophilic drugs, ex: thiopental,lidocaine,etc . b. Membrane permeation rate limited model These models are applicable to highly polar, ionised and charged drugs, in which case the cell membrane acts as a barrier for the drug that gradually permeates by diffusion. ADVANTAGES Mathematical treatment is straight forword . Mechanisam of ADME of drug can be esily explained. It is a realistic approach, the model is suitable where tissue drug concentration and binding are known. a. Blood flow rate limited model
PowerPoint Presentation: The method is frequently used in animals because invasive methods can be used to collect test samples. The model gives exact description of drug concentration-time profile in any organ or tissue and thus better picture of drug distribution characteristics in the body. DISADAVANTAGES Obtaining the experimental data is a very exhaustive process. The number of data points is less than the pharmacokinetic parameters to be assessed. Monitoring of drug concentration in body is difficult since exhaustive data is required. Most physiological Models assue an average blood flow for individual subjects and hence prediction of individualized dosing is difficult.
3.Non-compartmental model: This method is based on the assumption that the drugs or metabolites follow linear kinetics,applied to any compartmental model. Statistical moments theory, involves collection of data following a single dose of drug. Equation MRT= AUMC AUC where AUMC=area under the first-moment curve AUC= area under the zero-moment curve MRT=mean residence time ( average amount of time spent by the drug in the body before being eliminated) 3.Non-compartmental model
APPLICATIONS: Estimate the important pharmacokinetic parameters like bioavailability, clearence apparent volume of distribution. The method is also useful in determining half-life, rate of sorption and first order absorption rate constant of the drug. ADVANTAGES Ease of derivation of pharmacokinetic parameters. The same mathematical treatment can be applied to almost any drug or metabolite provided they follows first order kinetics. DISADVANTAGES It provides limited information regarding the plasma drug concentration-time profile. The method does not adequately treat non-linear cases APPLICATIONS
4.Nonlinear pharmacokinetics: Determination of steady state plasma concentration at different doses. If the study state concentrations are directly proportional to the dose, then linearity in the kinetic exists. Such proportionality is not observable when there is nonlinearity. Determination of some of the important pharmacokinetic parameters such as fraction bioavailability, elimination half life or total systematic clearance at different doses of the drug. 4.Nonlinear pharmacokinetics
Causes of nonlinearity: 1.DRUG ABSORPTION: a. When absorption is solubility or dissolution rate limited. Ex: griseofulvin . At higher doses, a saturated solution of the drug is formed in the GIT or at any other extravascular site and the rate of absorption attains a constant value. b. When absorption involves carrier mediated transport systems. Ex: absorption of riboflavin, ascorbic acid, cyanocobalamin , etc. Saturation of the transport system at higher doses of these vitamins results non linearity. 2.DRUG DISTRIBUTION : a. Saturation of binding sites on plasma proteins. Ex. Phenyl butazone.There is a finite number of binding sites for a particular drug on plasma proteins and, theoretically, as the concentration is raised, so too is the fraction unbound. Causes of nonlinearity
PowerPoint Presentation: b. Saturation of tissue binding sites. Ex: thiopental. With large single doses or multiple dosing, saturation of tissue storage sites can occurs. 3.DRUG METABOLISAM: a. Capacity limited metabolism due to enzyme and or cofactor saturation. Ex: phenytoin , theophylline etc. b. Enzyme induction Ex: carbamazepine , where a decrease in peak plasma concentration has been observed on repetitive administration over a period of time. 4.DRUG EXCREATION : a. Active tubular secretion ex: penicillin G. After saturation of the carrier system, a decrease in renal clearence occurs. b. Active tubular reabsorption ex. Water soluble vitamins and glucose. After saturation of the carrier system, an increase in renal clearence occurs.
MICHELIS MENTEN EQUATION: The kinetics of capacity limited or saturable process is best described by MICHELIS MENTEN EQUATION - dC = V max dt K m +C - dC = rate of decline of drug concentration with time, dt V max = theoretical maximum rate of the process, and K m = Michaelis constant. 1. When K m =C 2. When K m C 3. . When K m C MICHELIS MENTEN EQUATION
Applications of pharmacokinetics: Characteriz the behavior of drug in patient. Predicting concentration of drug in various body fluids with dosage regimen. Predicting the multiple-dose concentration curves from single dose experiments. Calculating optimum dosage regimen for individual patient. Evaluating the risk of toxicity with certain dosage regimens. Correlating plasma drug concentration with certain dosage regimens. Determine the influence of altered physiology /disease state on drug ADME. Evaluating bioequivalence between different formulation. Estimating the posibility of drug and/or metabolite accumulation in the body. Explaining drug interaction. Applications of pharmacokinetics
References : : 1.Biopharmaceutics and pharmacokinetics. P L Madan,1st edition. 2.Biopharmaceutics and pharmacokinetics. D.M Brahmankar and Sunil. B .Jaiswal,1st edition 3.Applied Biopharmaceutics and pharmacokinetics Leon shargel and Andrew Yu, 4th edition. 4.Biopharmaceutics and clinical pharmacokinetics By Milo Gibaldi , 4th edition. 5.Biopharmaceutics and clinical pharmacokinetics. An introduction 4 th edition, revised and explained. Robert E.Notari 6.clinical pharmacokinetics and pharmacodynamics cancepts and applications 4 th edition Molcolm Rowland, Thamasn.Tozer 7.www.google.com 8. www.books.google.com References :
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