Bio & Pharmacokinetics II PDF

Dr. HAFIZ MUHAMMAD ARSHAD Associate professor, Dept. of Pharmaceutics Faculty of Pharmaceutical Sciences Dow College of Pharmacy Dow University of Health Sciences, Karachi  COURSE OUTLINE INTRODUCTION TO PHARCOKINETICS Determination through plasma drug level studies. Application...

Dr. HAFIZ MUHAMMAD ARSHAD Associate professor, Dept. of Pharmaceutics Faculty of Pharmaceutical Sciences Dow College of Pharmacy Dow University of Health Sciences, Karachi  COURSE OUTLINE INTRODUCTION TO PHARCOKINETICS Determination through plasma drug level studies. Application of Pharmacokinetics in clinical situations. CONSEPT OF COMPARTMENT (S) MODELS: compartmental and non compartmental method of analysis i.e. One compartment open model and Two compartments open model method of analysis. BIOLOGICAL HALF-LIFE AND VOLUM OF DISTRIBUTION: Concept and Methods of determination. DRUG CLEARANCE: Mechanism, determination and relationship of clearance with half-life. IV INFUSION AND : MULTIPLE DOSAGE REGIMEN: CLINICAL HARMACOKINETICS:  RECOMMENDED BOOKS 1. Leon Shargel, Applied Pharmacokinetics and Bio Pharmaceutics. 2. Robert E. Notari, Bio-Pharmaceutics and clinical Pharmacokinetics, Marchel & Dakker. 3. Malcoln Rouland, Thomous N. Tozer, Clinical Pharmacokinetics and Pharmacodynamics. 4. Milo Gibaldi, Bio-Pharmaceutics and Clinical Pharmacokinetics, Marchel & Dakker.  LEARNING OBJECTIVES  Introduction to Pharmacokinetics and its importance.  Kinetics analysis of data (Order and rate constants)  Kinetics of Drug transport (movement of drug from one place to another) through membranes.  Model independent vs compartment model pharmacokinetic analysis.  Compare and contrast the terms variable, constant and parameters.  Describe the pharmacokinetic parameters i.e. apparent volume of distribution, elimination half life, first-order elimination rate constant and clearance ·  Determine pharmacokinetic parameters from either plasma or urinary data  Pharmacokinetics  Pharmacokinetics is a mathematical subject. It deals in quantitative conclusions, such as a dose or a concentration of drug in the blood or other body fluids.  Quantitative study of drug movement in, through and out of body  In other words, the magnitude of response (good or bad) depends on concentration of the drug at the site of action Cont…….. ‘‘Pharmacokinetics is the study of kinetics of absorption, distribution, metabolism and excretion (ADME) of drugs and their corresponding pharmacologic, therapeutic, or toxic responses in man and animals’’ (American Pharmaceutical Association, 1972)  Applications of pharmacokinetic studies :  Intended to define the time coarse of drug and major metabolite concentration in plasma and other biological fluids in order to obtain information on ADME  Bioavailability measurements.  Effects of physiological and pathological conditions on drug disposition and absorption.  Dosage adjustment of drugs in disease states, if and when necessary.  Correlation of pharmacological responses with administered doses.  Evaluation of drug interactions.  Using pharmacokinetic parameters to individualize the drug dosing regimen and thus provide the most effective drug therapy.  Study of drug(s) over time Tissue Site of action reservoirs (receptors) liver Free drug kidney Gut Plasma proteins metabolites Blood/ Plasma/ CC  ADME Most drugs are enter the body (by mouth or injection or any other route of administration)- must cross barriers to enter compartment are Distributed by the blood to the site of action - intra- or extra- cellular - cross barriers to distributed to different compartments , are Biotransformed perhaps to several different compounds by enzymes evolved to cope with natural materials - this may increase, decrease or change drug actions and are Excreted (by kidney or other route) which removes them and their metabolites from the body. “Pharmacokinetics is the quantification of all these processes”  Plasma Level–Time Curve  Blood-plasma or serum level demonstrate the concentration in blood, plasma or serum upon administration of a dosage form by various routes of administration.  The blood plasma level–time curve is generated by obtaining the drug concentration in plasma samples by venipuncture in certain time intervals after a drug product is administered.  The concentration of drug in each plasma sample is plotted on rectangular/coordinate graph paper against the corresponding time at which the plasma sample was removed.  As the drug reaches the general (systemic) circulation, plasma drug concentrations will rise up to a maximum. Usually, absorption of a drug is more rapid than elimination. As the drug is being absorbed into the systemic circulation, the drug is distributed to all the tissues in the body and is also simultaneously being eliminated. Elimination of a drug can proceed by excretion, biotransformation, or a combination of both.  MEC and MTC represent the minimum effective concentration and minimum toxic concentration of drug, respectively.  The drug concentration in the plasma is in equilibrium with the tissues, the MEC reflects the minimum concentration of drug needed at the receptors to produce the desired pharmacologic effect. Similarly, the MTC represents the drug concentration needed to just barely produce a toxic effect.  The onset time corresponds to the time required for the drug to reach the MEC.  The intensity of the pharmacologic effect is proportional to the number of drug receptors occupied, which is reflected in the observation that higher plasma drug concentrations produce a greater pharmacologic response, up to a maximum.  The duration of drug action is the difference between the onset time and the time for the drug to decline back to the MEC. Plasma Concentration-Time Profile for a Drug Following a Single Oral Dose Rate of drug accumulation at any time: dDBODY/dt= dDABS/dt - dDELIM/dt Absorption Phase: dDABS/dt > dDELIM/dt At time of peak drug conc.: dDABS/dt = dDELIM/dt Post-absorption Phase: dDABS/dt < dDELIM/dt  ORDER OF REACTIONS  Zero-order reactions (order = 0) have a constant rate. This rate is independent of the concentration of the reactants. The rate law is:  Rate = k, with k having the units of M/sec.  Few drugs: rate of elimination remain constant irrespective of concentration  Cl decrease with increase of concentration  Constant amount of drug is eliminated in unit time.  First-Order Reactions A first order reaction (order = 1) has a rate proportional to the concentration of one of the reactants. A common example of a first-order reaction is the phenomenon of radioactive decay. The rate law is:  Rate = k[A] (or B instead of A), with k having the units of sec-1  Second-Order Reactions A second-order reaction (order = 2) has a rate proportional to the concentration of the square of a single reactant or the product of the concentration of two reactants:  rate = k[A]2 (or substitute B for A or k multiplied by the concentration of A times the concentration of B), with the units of the rate constant M-1sec-1  Mixed-Order or Higher-Order Reactions Mixed-order reactions have a fractional order for their rate:  e.g., rate = k[A]1/3  UNITS of Rate Constant  For zero order  For first order  For second order  Applications of pharmacokinetics  To understand process of absorption, distribution and elimination after administration of drug , Which affects onset and intensity of biological response.  To access drug moiety in terms of plasma drug conc. response which is now considered as more appropriate parameter then intrinsic pharmacological activity.  In design and utilization of in-vitro model system that can evaluate dissolution characteristics of new compound formulated as new drug formulations and establish meaningful in vivo-in vitro correlationship.  In design and development of new drug and their appropriate dosage regimen.  In safe and effective management of patients by improving drug therapy.  To understand concept of bioavailability which has been used by regulatory authorities to evaluate and monitor in vivo performance of new dosage forms and generic formulations.  To carry out bioavailability and bioequivalence studies.  We can used pharmacokinetic principles in the development of N.D.D.S like micro spheres and Nanoparticles. e.g. The drug with short half life about 2-6 h can be formulated as controlled release drugs by using polymers.  The lower bioavailability of the drugs can be increased by using different technique and several components.  Role of pharmacokinetics in drug design  Many drugs are investigated nowadays the estimation of activity and pharmacokinetics properties are important for knowing the ADME of that particular drug.  By understanding the mechanism of disease the drug design is done.The drug design is based on the mechanism of the particular disease.  Some newly discovered drugs that shows very high activity in-vitro but in in-vivo that drug not shows high activity or showing high toxic activity.  This toxic nature of the drug in in-vivo will be explained by studying the pharmacokinetics properties and the toxicity may result from the formation of reactive metabolites.  Some newly invented drugs showing undesirable p.k properties such as too long or too short t1/2 , poor absorption and extensive first pass metabolism. CONSEPT OF COMPARTMENT (S) MODELS  OBJECTIVES To understand the assumptions associated with the one and two models To understand the properties of first order kinetics and linear models To derive the differential equations for a simple pharmacokinetic model To derive and use the integrated equations for a one compartment linear model To define, use, and calculate the parameters, Kel (elimination rate constant), other rate constant(s), t1/2 (half-life), Cl (clearance), V (apparent volume of distribution), and AUC (area under the concentration versus time curve) as they apply to compartment model  PHARMACOKINETIC PARAMETERS In practice, pharmacokinetic parameters are determined experimentally from a set of drug concentrations collected over various times known as data. Parameters are also called as variables. Variables are of two types – Independent variables which are not affected by any other parameter, for example time. Dependent variables, which change as the independent variables change, for example, plasma drug concentration.  PHARMACOKINETIC MODELS Drug movement within the body is a complex process. The major objective is therefore to develop a generalized and simple approach to describe, analyse and interpret the data obtained during in vivo drug disposition studies. The two major approaches in the quantitative study of various kinetic processes of drug disposition in the body are 1. Model approach, and 2. Model-independent approach (also called as non-compartmental analysis). Pharmacokinetic Model Approach A model is a hypothesis that employs mathematical terms to concisely describe quantitative relationships. Pharmacokinetic models provide concise means of expressing mathematically or quantitatively, the time course of drug(s) throughout the body and compute meaningful pharmacokinetic parameters. Applications of Pharmacokinetic Models – 1. Characterizing the behaviour of drugs in patients. 2. Predicting the concentration of drug in various body fluids with any dosage regimen. 3. Predicting the multiple-dose concentration curves from single dose experiments. 4. Calculating the optimum dosage regimen for individual patients. 5. Evaluating the risk of toxicity with certain dosage regimens. 6. Correlating plasma drug concentration with pharmacological response. 7. Evaluating the bioequivalence/bioinequivalence between different formulations of the same drug. 8. Estimating the possibility of drug and/or metabolite(s) accumulation in the body. 9. Determining the influence of altered physiology/disease state on drug ADME. 10. Explaining drug interactions. Types of Pharmacokinetic Models Pharmacokinetic models are of three different types – Compartment models – are also called as empirical models, and Physiological models – are realistic models. Distributed parameter models – are also realistic models. Compartment Models Compartmental analysis is the traditional and most commonly used approach to pharmacokinetic characterization of a drug. These models simply interpolate the experimental data and allow an empirical formula to estimate the drug concentration with time. Depending upon whether the compartments are arranged parallel or in a series, compartment models are divided into two categories — 1. Mammillary model 2. Catenary model. Since compartments are hypothetical in nature, compartment models are based on certain assumptions – 1. The body is represented as a series of compartments arranged either in series or parallel to each other, that communicate reversibly with each other. 2. Each compartment is not a real physiologic or anatomic region but a fictitious or virtual one and considered as a tissue or group of tissues that have similar drug distribution characteristics (similar blood flow and affinity). This assumption is necessary because if every organ, tissue or body fluid that can get equilibrated with the drug is considered as a separate compartment, the body will comprise of infinite number of compartments and mathematical description of such a model will be too complex. 3. Within each compartment, the drug is considered to be rapidly and uniformly distributed i.e. the compartment is well-stirred. 4. The rate of drug movement between compartments (i.e. entry and exit) is described by first-order kinetics. 5. Rate constants are used to represent rate of entry into and exit from the compartment. Mammillary Model This model is the most common compartment model used in pharmacokinetics.  The number of rate constants which will appear in a particular compartment model is given by R. For intravenous administration, R = 2n – 1 For extravascular administration, R = 2n where n = number of compartments. Catenary Model Physiological Models These models are also known as physiologically-based pharmacokinetic models (PB-PK models). They 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. Organs or tissues such as bones that have no drug penetration are excluded.  Compartment Model  After administering a dose, the change in drug concentration in the body with time can be described mathematically by various equations, most of which incorporate exponential terms (i.e. ex or e-x )  This suggests that ADME processes are ‘‘first order’’ in nature at therapeutic doses and, therefore, there is a directly proportional relationship between the observed plasma concentration and/or the amount of drug eliminated in the urine and the administered dose of the drug.  Cont….  There are several assumption associated with the modeling of drug behavior in the body as: i. The volume of each compartment remains constant. ii. Once the drug enter the compartment, it is immediately & uniformly distributed through out the entire compartment, so the sampling on any portion of the compartment will give the drug concentration of the entire compartment. iii. The drug passes freely into & out of compartment, so it is called as open system. It follow the first order kinetics which shows that a constant fraction of drug is eliminated per unit time.  Types of Compartment Model Mammillary compartment: it is most useful compartment model in PK.  It consist of one or more peripheral compartment is connected with central compartment.  The peripheral comartment are directly combined with the central compartment in the form of satellite. Caternary Compartment: it is also consist of central compartment and one or more peripheral compartment which are attached to the central in a series like a train.  “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.  Concept of Open One Compartment Model Drug in dosage form Input Body volume Output Drug in urine, feces, sweat, expired air, at administration site concentration milk One Compartment Model Drug Administration I V Volume of Distribution k Model =V1, k10 One Compartment Model, Intravenous (IV) Bolus Administration Assumptions 1. One compartment The drug in the blood is in rapid equilibrium with drug in the extravascular tissues. This is not an exact representation however it is useful for a number of drugs to a reasonable approximation. 2. Rapid Mixing We also need to assume that the drug is mixed instantaneously in blood or plasma. 3. Linear Model We will assume that drug elimination follows first order kinetics. 2. Rapid Mixing We also need to assume that the drug is mixed instantaneously in blood or plasma. 3. Linear Model We will assume that drug elimination follows first order kinetics.  Two compartment model Drug Administration I V2 k 12 V1 Peripheral Central k 21 Compartment Compartmen k 10 Model =V1, k10, k12, k21 V2 = V1 k12 / k21 CL1 = V1 k10 CL2 = V1 k12  Three compartment model Drug Administration I V2 k 12 V1 k 13 V3 Rapidly Central Slowly k 21 k 31 Equilibrating Equilibrating Compartmen k 10 Model =V1, k10, k12, k21, k13, k31 V2 = V1 k12 / k21 V3 = V1 k13 / k31 CL1 = V1 k10 CL2 = V1 k12 CL3 = V1 k13  Elimination rate constant Suppose we choose the following two points to determine the slope of the straight line :  x1= ---- hr, y1 = ------ mcg/ml, and x2 = -----hr, y2 = ---- mcg/ml. then ln y2 – ln y1 ln---- – ln ----- Slope = = = x2 – x1 ---- hr – --- hr = - ----------- = - --------/ hr ---------- hr Therefore Ke = - slope = - (---------/hr) = ----------/hr KE = Ke + Km +Kb +Kl +….. KE is overall elimination rate constant  Elimination half life 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. It is define as: “The time taken by the drug, blood or plasma concentration to decrease to one half of its original concentration.” OR  Cont……. “Elimination half life is the time required for the plasma concentration (or total body stores) of drug to fall to half of the concentration.” t1/2= 0.693/Kel Half life is represented by time in scond, min, hr, days. Kel is represented in time inverse i.e. /hr, /min, /sec.  CLASSIFICATION  On the basis of half life, most of the drugs are classified into 4 categories: UFD: half life 1or less than 1 hr. for e.g.: insuline, cefalaxine are administered more frequently to maintain desirable plasma conc. FD: half life is 1-4hr. E.g: Acetaminophen, Ampicillin MD: half life is 4-8hr e.g. tetracycline, lincomycin and theophyline etc. SD: half life 8-24hr or greater than 24hr. e.g. Atropine, diazepam, barbital and digoxin etc.  VOLUME OF DISTRIBUTION  “Ratio of the amount of drug in the body to the plasma drug concentration.” OR  “A hypothetical volume of the body fluid that would be required to dissolve the total amount of drug as the same concentration as that found in the blood.”  There are two types of distribution volume: 1. Apparent volume of distribution 2. Actual volume of distribution  Apparent volume of distribution The apparent volume of distribution is simply a proportionality constant relating the plasma concentration to the total amount of drug in the body. Depending on the degree of binding to plasma proteins and tissues, the apparent volume of distribution of a drug may very in man from 0.04L/kg(plasma volume) to 20L/kg or more.  Actual volume distribution  The actual distribution volume of drug is related to body water; it can never exceed total body water that is about 60% of body weight or a 42L in a normal 70-kg man.  Body water may be divided into 3 compartments:  Vascular fluid,  Extracellular fluid  Intracellular fluid  Factors affecting on Vd  Blood flow rate in a different tissues  Lipid solubility of drug  Partition co-efficient of drug and different type of tissue  pH  Binding to biological materials  Volume of distribution is proportional to the body weight However, obesity and edema produce abnormal deviation.  Cont……… In obesity, the Vd of hydrophilic drugs is lower than expected from the body weight. Vd is an important indicator of the extent of drug distribution into body fluids and tissues. For polar drug with low lipid solubility the apparent volume is generally small. Drugs with high peripheral tissue binding also contribute to a large Vd and it is known as apparent volume of distribution,. Half life is depends on both Cl & Vd , such that a decrease in clearance, increase the Vd will prolong the half life and lead to a longer dosage interval. In edematic patients, the Vd of hydrophilic drugs is larger than expected from the body weight. IMPORTANCE: i. Estimate the plasma drug conc. After a known conc. Of drug is given to the body. ii. Estimate the dose of drug in plasma drug conc iii. Also calculate the total clearence i.e. Cl=kV  Biological half-life Ke = 0.693 t1/2 , therefore 0.693 t½ = Ke  Area under curve Area from 0 to 7.0 hours – AUC0-7.0 by trapezoidal rule = ---------- mcg.hr/ml AUC0-7.0 by counting squares = ---------- mcg.hr/ml  Total area under curve  This is a two step method, first determine AUC0-t , then determine AUCt-∞ Ct -----mcg/ml AUC t- ∞ = = = ------ mcg. hr/ml Ke -------/hr Adding this value to AUC 0-7.0, we have AUC0-infi = AUC0-t + AUCt-∞ = ---------mcg.hr/ml + -------mcg.hr/ml = ----------------mcg.hr/ml C0 --------mcg / ml AUC0-∞ = = = ------ mcg.hr /ml Ke ------------ hr  Volume of distribution : Dose Vd = Co -------------mg = ----------- mcg / ml = ----------- L NON COMPARTMENTAL ANALYSIS  Non Compartmental Analysis Quantification method are based on theory of statistical moment. Individual particles are assumed to move independently among kinetic spaces according to fixed transfer probabilities The behavior of drug particles is described by the statistical moments. A complete discussion of the potential utility of statistical moments in Pk analysis was reported by Yamaoka and cutler in 1978. Also known as model-independent analysis.  CONT……..  The zero moment of the drug concentration in plasma verses time curve is the total AUC from time zero to infinity.  The total area under the c-t verses time plot is termed the AUMC. PLOT DESCRIBED  Non-compartmental analysis  S0 by the arithmetic trapezoidal rule C0 +C1 AUC1 = x (t1 - t0) C0 2 C1 C2 C3 extrapolation area AUC1 AUC2 AUC3 t0 t1 t2 t3 AUCTOT = S1 =  AUC1 + AUC2... AUCn + extrapolation area  Cont……  Computation of S1 = AUMC with the arithmetic trapezoidal rule t0 x C0 + t1 x C1 C0 AUMC1 = x (t1-t0) 2 C1 C2 area to extrapolate C3 AUMC1 AUMC2 AUMC3 t0 t1 t2 t3 AUMCTOT = S2 = AUMC1 + AUMC2 +... AUMC extrapolated  Non-Compartmental Analysis Based On: i. MRT, MTT, MAT ii. BA iii. Clearance iv. Apparent volume of distribution v. Half life vi. Fraction of drug eliminated  Total body clearance  It relate the dosing rate of a drug to its steady state concentration and it is use to calculate the maintenance dose regimen.  An estimate of the total clearance is obtained by IV data by IV dose administration. Clt = Xo/AUC0-∞ Where, Xo = drug dose Clt= total clearance  Mean residence time (MRT)  The average total time molecules of a given dose spend in the body. Thus, this can only be measured after instantaneous administration. MRT = AUMC/AUC Mean Transit Time (MTT):  The average time molecules of a given dose spend in the kinetic system. When determined after non- instantaneous administration, the MTT will be the sum of the MRT and the MAT MTT = MRT + MAT  Mean Absorption Time (MAT)  The fraction of an oral dose that actually reach the systemic circulation can be estimated from the ratio of AUC after oral administration to AUC after iv administration of equivalent doses of the same drug. The extent of absorption of drug in test dosage form relative to its absorption from a standard dosage form.  Non compartmental methods for estimating the rate of absorption of a drug after extra vascular administration are based on differences in MRT after different modes of administration. Where, MAT = MRT ni - MRTiv MRT ni is the mean residence time after administration of the drug in a non-instantaneous manner, such as oral, im, iv infusion and MRTiv is the mean residence time after iv bolus adm.  Cont…. i. Clearance = Dose / AUC ii. Vss = Dose x AUMC/ (AUC)2 iii. MRT = Vss / Cl = AUMC / AUC iv. %F = AUC EV / AUC IV DEV = DIV  Numerical  A dose of 300 mg of a drug was administered to a patient by iv bolus. Blood samples were taken obtained of the following indicated time: Time (hr) 0.25 0.5 1 3 6 12 18 Conc (mg/L) 8.21 7.87 7.23 5.51 3.09 1.11 0.4 i. Using non-compartmental method calculate the clearance, volume of distribution at steady state (Vss) and MRT.