Introduction to Biopharmaceutics and Pharmacokinetics

Introduction to Biopharmaceutics and Pharmacokinetics
Course Teacher: Sabrina Rahman Archie

Pharmaceutics, Biopharmaceutics & Pharmacokinetics
Pharmaceutics- Pharmaceutics is the general area of study concerned with the formulation, manufacture, stability and effectiveness of pharmaceutical dosage forms. Biopharmaceutics is the science that examines this interrelationship of the physicochemical properties of the drug, the dosage form in which the drug is given, and the route of administration on the rate and extent of systemic drug absorption. Bio= life

Biopharmaceutics involves factors that influence-
The stability of the drug within the drug product. The release of the drug from the drug product. The rate of dissolution/ release of the drug at the absorption site. The systemic absorption of the drug.

Pharmacokinetics- - refers to what the body does to the drug and It involves the absorption, distribution, metabolism and excretion of the drug. Drug Disposition- Description of drug distribution and excretion is referred to as drug disposition.

ADME Absorption- Absorption is defined as the process by which a drug proceeds from the site of administration to the site of measurement (usually blood, plasma or serum). Distribution- The dispersion of a drug throughout fluids and tissues of the body. It is a reversible process. Metabolism- The irreversible transformation of parent compounds to daughter compounds (also called biotransformation). Elimination- Irreversible loss of drugs from the site of measurement. Excretion- Excretion is the removal of drug from the body in an unchanged form through various routes. Ex- urine, saliva, sweat, respiratory route, biliary secretion.

Pharmacodynamics- Refers to the relationship between drug concentration at the site of action and the pharmacological response, including biochemical and physiological effects that influence the interaction of the drug with the receptor.

Process for reaching dosage decisions with therapeutic drug monitoring

Task What is pharmacokinetics? Discuss briefly the application of pharmacokinetics in the field of pharmacy? (Marks: 3+12) Hint: Discuss clinical pharmacokinetics, TDM, MEC, MTC. You can use schematic diagram, flow chart to explain. 2. Define toxicology and clinical toxicology? (Marks: 2+3)

Measurement of Drug Concentrations
Drug concentrations are measured in biologic samples, such as milk, saliva, plasma, and urine. General analytical method used- Chromatography

Sampling of Biologic Specimens
Invasive methods include sampling blood, spinal fluid, synovial fluid, tissue biopsy, or any biologic material that requires parenteral or surgical intervention in the patient. In contrast, noninvasive methods include sampling of urine, saliva, feces, expired air, or any biologic material that can be obtained without parenteral or surgical intervention.

Sampling of Biologic Specimens
The measurement of drug and metabolite concentration in each of these biologic materials yields important information, such as -the amount of drug retained in, or transported into, that region of the tissue or fluid, -the likely pharmacologic or toxicologic outcome of drug dosing, -and drug metabolite formation or transport.

Drug Concentrations in Blood, Plasma, or Serum
Measurement of drug concentration (levels) in the blood, serum, or plasma is the most direct approach to assessing the pharmacokinetics of the drug in the body. Whole blood contains cellular elements including red blood cells, white blood cells, platelets, and various other proteins, such as albumin and globulins. In general, serum or plasma is most commonly used for drug measurement.

Blood is the fluid most often sampled for determining drug concentration

To obtain serum, whole blood is allowed to clot and the serum is collected from the supernatant after centrifugation. Plasma is obtained from the supernatant of centrifuged whole blood to which an anticoagulant, such as heparin, has been added. Therefore, the protein content of serum and plasma is not the same. Plasma perfuses all the tissues of the body, including the cellular elements in the blood. Assuming that a drug in the plasma is in dynamic equilibrium with the tissues, then changes in the drug concentration in plasma will reflect changes in tissue drug concentrations.

Plasma Drug Concentration-Time Curve
The plasma level–time curve is generated by obtaining the drug concentration in plasma samples taken at various 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. The relationship of the drug level–time curve and various pharmacologic parameters for the drug is shown in Figure 1.

Figure 1: Plasma level – Time Curve

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.

The therapeutic window is the concentration between the MEC and MTC. Drugs with a wider therapeutic window are generally considered safer than drugs with a narrow therapeutic window. Sometimes the term therapeutic index is also used. Therapeutic index refers to the ratio between the toxic and therapeutic dose.

The time for peak plasma level is the time for maximum drug concentration in the plasma and is a rough marker of average rate of drug absorption. AUC (area under curve) is the amount of drug systemically absorbed.

Biological ½ life ½ life = how much time it takes for plasma drug concentration to decrease to half of what it was at equilibrium (t1/2)

Compartmental Models The handling of a drug by the body can be very complex, as several processes (such as absorption, distribution, metabolism, and excretion) work to alter drug concentrations in tissues and fluids. Simplifications of body processes are necessary to predict a drug’s behaviour in the body. One way to make these simplifications is to apply mathematical principles to the various processes. To apply mathematical principles, a model of the body must be selected. A basic type of model used in pharmacokinetics is the compartmental model.

Compartmental Models Compartmental models are categorized by the number of compartments needed to describe the drug’s behaviour in the body. There are one-compartment, two-compartment, and multi-compartment models. The compartments do not represent a specific tissue or fluid but may represent a group of similar tissues or fluids. These models can be used to predict the time course of drug concentrations in the body

Simple Compartment Model

Typical organ groups for central and peripheral compartments

Compartmental model representing transfer of drug to and from central and peripheral compartments

One-compartment model

Two compartment model

Drug Concentration Drug Concentration in a compartment is defined as the amount of drug in a given volume, such as mg/L.

Volume of Distribution
also known as Apparent volume of distribution, is used to quantify the distribution of a drug between plasma and the rest of the body after oral or parenteral dosing. It is called as Apparent Volume because all parts of the body equilibrated with the drug do not have equal concentration. It is defined as the volume in which the amount of drug would be uniformly distributed to produce the observed blood concentration.

Volume of distribution
Volume of distribution (V) is an important indicator of the extent of drug distribution into body fluids and tissues. V relates the amount of drug in the body (X) to the measured concentration in the plasma (C). Thus, V is the volume required to account for all of the drug in the body if the concentrations in all tissues are the same as the plasma concentration.

Volume of Distribution
A large volume of distribution usually indicates that the drug distributes extensively into body tissues and fluids. Conversely, a small volume of distribution often indicates limited drug distribution. Volume of distribution indicates the extent of distribution but not the tissues or fluids into which the drug is distributing. Two drugs can have the same volume of distribution, but one may distribute primarily into muscle tissues, whereas the other may concentrate in adipose tissues.

Volume of distribution
Approximate volumes of distribution for some commonly used drugs are shown in Table below.

Imagine the body as a tank!

volume of distribution
We can use the relationship given for volume, amount of drug administered, and resulting concentration to estimate a drug's volume of distribution in a patient. If we give a known dose of a drug and the concentration of that drug achieved in the plasma, we can calculate a volume of distribution.

Case Study !!! If 500 mg of drug X is administered intravenously and the plasma concentration is determined to be 25 mg/L just after the dose is given, then volume of distribution= ??? If the first 80-mg dose of gentamicin is administered intravenously and results in a peak plasma concentration of 8 mg/L, volume of distribution is?

PLASMA DRUG CONCENTRATION VERSUS TIME CURVES
With the one-compartment model, if we continuously measure the concentration of a drug in the plasma after an intravenous bolus dose and then plot these plasma drug concentrations against the times they are obtained, the curve would result as follows :

Note that this plot is a curve and that the plasma concentration is highest just after the dose is administered, at time zero (t=0). Because of cost limitations and patient convenience in clinical situations, only a small number of plasma samples can usually be obtained for measuring drug concentrations. From these known values, we are able to predict the plasma drug concentrations for the times when we have no samples. In clinical situations, it is rare to collect more than two samples after a dose.

Either take natural log or use semilog scale to plot the data

Semilog paper

Task !! A drug that follows a one-compartment model is given as an intravenous injection, and the following plasma concentrations are determined at the times indicated: Using semilog graph paper, determine the approximate concentration in plasma at 6 hours after the dose. A. 18 mg/L B. 30 mg/L C. <1 mg/L

Drug Concentrations in Tissues
Tissue biopsies are occasionally removed for diagnostic purposes, such as the verification of a malignancy. Usually, only a small sample of tissue is removed, making drug concentration measurement difficult. Drug concentrations in tissue biopsies may not reflect drug concentration in other tissues nor the drug concentration in all parts of the tissue from which the biopsy material was removed.

Drug Concentrations in Tissues
For example, if the tissue biopsy was for the diagnosis of a tumor within the tissue, the blood flow to the tumor cells may not be the same as the blood flow to other cells in this tissue. In fact, for many tissues, blood flow to one part of the tissues need not be the same as the blood flow to another part of the same tissue. The measurement of the drug concentration in tissue biopsy material may be used to ascertain if the drug reached the tissues and reached the proper concentration within the tissue.

Drug Concentrations in Urine and Feces
Measurement of drug in urine is an indirect method to ascertain the bioavailability of a drug. The rate and extent of drug excreted in the urine reflects the rate and extent of systemic drug absorption. Measurement of drug in feces may reflect drug that has not been absorbed after an oral dose or may reflect drug that has been expelled by biliary secretion after systemic absorption.

Drug Concentration in Saliva
Saliva drug concentrations have been reviewed for many drugs for therapeutic drug monitoring. Because only free drug diffuses into the saliva, saliva drug levels tend to approximate free drug rather than total plasma drug concentration.

Forensic Drug Measurements
Forensic science is the application of science to personal injury, murder, and other legal proceedings. Drug measurements in tissues obtained at autopsy or in other bodily fluids such as saliva, urine, and blood may be useful if a suspect or victim has taken an overdose of a legal medication, has been poisoned or has been using of drugs of abuse such as opiates, cocaine or marijuana.

Significance of Measuring Plasma Drug Concentrations / Plasma level –time curve
The plasma drug concentration versus time profile provides the basic data from which the various pharmacokinetic models can be developed that predict the time course of drug action, relates the drug concentration to the pharmacodynamic effect or adverse response and enables the development of individualized therapeutic dosage regimens and new and novel drug delivery systems.

Basic Pharmacokinetics and Pharmacokinetic Models
Drugs are in a dynamic state within the body as they move between tissues and fluids, bind with plasma or cellular components, or are metabolized. Mathematical models and statistics are used to estimate drug dosing and to predict the time course of drug efficacy for a given dose. A model is a hypothesis using mathematical terms to describe quantitative relationships concisely.

The key parameters in a process are commonly estimated by fitting the model to the experimental data, known as variables. A pharmacokinetic parameter is a constant for the drug that is estimated from the experimental data. For example, estimated pharmacokinetic parameters such as k depends on the method of tissue sampling, the timing of the sample, drug analysis, and the predictive model selected.

A pharmacokinetic function relates an independent variable to a dependent variable, often through the use of parameters. For example, a pharmacokinetic model may predict the drug concentration in the liver 1 hour after an oral administration of a 20-mg dose. The independent variable is time and the dependent variable is the drug concentration in the liver. Based on a set of time-versus-drug concentration data, a model equation is derived to predict the liver drug concentration with respect to time. In this case, the drug concentration depends on the time after the administration of the dose, where the time:concentration relationship is defined by a pharmacokinetic parameter, k, the elimination rate constant.

Such mathematical models can be devised to simulate the rate processes of drug absorption, distribution, and elimination to describe and predict drug concentrations in the body as a function of time. Pharmacokinetic models are used to: 1. Predict plasma, tissue, and urine drug levels with any dosage regimen. 2. Calculate the optimum dosage regimen for each patient individually. 3. Estimate the possible accumulation of drugs and/or metabolites.

4. Correlate drug concentrations with pharmacologic or toxicologic activity. 5. Evaluate differences in the rate or extent of availability between formulations (bioequivalence) 6. Describe how changes in physiology or disease affect the absorption, distribution, or elimination of the drug 7. Explain drug interactions

Simplifying assumptions are made in pharmacokinetic models to describe a complex biologic system concerning the movement of drugs within the body. For example, most pharmacokinetic models assume that the plasma drug concentration reflects drug concentrations globally within the body.

A model may be empirically, physiologically, or compartmentally based. The model that simply interpolates the data and allows an empirical formula to estimate drug level over time is justified when limited information is available. Empirical models are practical but not very useful in explaining the mechanism of the actual process by which the drug is absorbed, distributed, and eliminated in the body.

Physiologically based models also have limitations. Apart from the necessity to sample tissue and monitor blood flow to the liver in vivo, the investigator needs to understand the following questions – What is the clinical implication of the liver drug concentration value? Should the drug concentration in the blood within the tissue be determined and subtracted from the drug in the liver tissue? What type of cell is representative of the liver if a selective biopsy liver tissue sample can be collected without contamination from its surroundings?

Depending on the spatial location of the liver tissue from the hepatic blood vessels, tissue drug concentrations can differ depending on distance to the blood vessel or even on the type of cell in the liver. Moreover, changes in the liver blood perfusion will alter the tissue drug concentration. If heterogeneous liver tissue is homogenized and assayed, the homogenized tissue represents only a hypothetical concentration that is an average of all the cells and blood in the liver at the time of collection.

A very simple and useful tool in pharmacokinetics is compartmentally based models. For example, assume a drug is given by intravenous injection and that the drug dissolves (distributes) rapidly in the body fluids. One pharmacokinetic model that can describe this situation is a tank containing a volume of fluid that is rapidly equilibrated with the drug. The concentration of the drug in the tank after a given dose is governed by two parameters: the fluid volume of the tank that will dilute the drug, and the elimination rate of drug per unit of time.

Though this model is perhaps an overly simplistic view of drug disposition in the human body, a drug's pharmacokinetic properties can frequently be described using a fluid-filled tank model called the one-compartment open model. In both the tank and the one-compartment body model, a fraction of the drug would be continually eliminated as a function of time (see next slide for figure 1). In pharmacokinetics, these parameters are assumed to be constant for a given drug. If drug concentrations in the tank are determined at various time intervals following administration of a known dose, then the volume of fluid in the tank or compartment (V D, volume of distribution) and the rate of drug elimination can be estimated.

Figure 1. Tank with a constant volume of fluid equilibrated with drug
Figure 1 . Tank with a constant volume of fluid equilibrated with drug. The volume of the fluid is 1.0 L. The fluid outlet is 10 mL/min. The fraction of drug removed per unit of time is 10/1000, or 0.01 min– 1.

In practice, pharmacokinetic parameters such as k and V D are determined experimentally from a set of drug concentrations collected over various times and known as data. The number of parameters needed to describe the model depends on the complexity of the process and on the route of drug administration. In general, as the number of parameters required to model the data increases, accurate estimation of these parameters becomes increasingly more difficult. With complex pharmacokinetic models, computer programs are used to facilitate parameter estimation. However, for the parameters to be valid, the number of data points should always exceed the number of parameters in the model.

Compartment Models If the tissue drug concentrations and binding are known, physiologic pharmacokinetic models, which are based on actual tissues and their respective blood flow, describe the data realistically. Physiologic pharmacokinetic models are frequently used in describing drug distribution in animals, because tissue samples are easily available for assay. On the other hand, tissue samples are often not available for human subjects, so most physiological models assume an average set of blood flow for individual subjects.

Compartment Models In contrast, because of the vast complexity of the body, drug kinetics in the body are frequently simplified to be represented by one or more tanks, or compartments, that communicate reversibly with each other. A compartment is not a real physiologic or anatomic region but is considered as a tissue or group of tissues that have similar blood flow and drug affinity. Within each compartment, the drug is considered to be uniformly distributed.

Compartment Models Mixing of the drug within a compartment is rapid and homogeneous and is considered to be "well stirred," so that the drug concentration represents an average concentration, and each drug molecule has an equal probability of leaving the compartment. Rate constants are used to represent the overall rate processes of drug entry into and exit from the compartment. The model is an open system because drug can be eliminated from the system. Compartment models are based on linear assumptions using linear differential equations.

Mammillary Model A compartmental model provides a simple way of grouping all the tissues into one or more compartments where drugs move to and from the central or plasma compartment. The mammillary model is the most common compartment model used in pharmacokinetics. The mammillary model is a strongly connected system, because one can estimate the amount of drug in any compartment of the system after drug is introduced into a given compartment. In the one-compartment model, drug is both added to and eliminated from a central compartment.

Mammillary Model The central compartment is assigned to represent plasma and highly perfused tissues that rapidly equilibrate with drug. When an intravenous dose of drug is given, the drug enters directly into the central compartment. Elimination of drug occurs from the central compartment because the organs involved in drug elimination, primarily kidney and liver, are well-perfused tissues.

Mammillary Model In a two-compartment model, drug can move between the central or plasma compartment to and from the tissue compartment. Although the tissue compartment does not represent a specific tissue, the mass balance accounts for the drug present in all the tissues. In this model, the total amount of drug in the body is simply the sum of drug present in the central compartment plus the drug present in the tissue compartment.

Mammillary Model Knowing the parameters of either the one- or two-compartment model, one can estimate the amount of drug left in the body and the amount of drug eliminated from the body at any time. The compartmental models are particularly useful when little information is known about the tissues

Mammillary Model Several types of compartment models are described in the following figure. The pharmacokinetic rate constants are represented by the letter k. Compartment 1 represents the plasma or central compartment, and compartment 2 represents the tissue compartment. The drawing of models has three functions. The model- (1) enables the pharmacokineticist to write differential equations to describe drug concentration changes in each compartment, (2) gives a visual representation of the rate processes, and (3) shows how many pharmacokinetic constants are necessary to describe the process adequately.

Catenary model In pharmacokinetics, the mammillary model must be distinguished from another type of compartmental model called the catenary model. The catenary model consists of compartments joined to one another like the compartments of a train. In contrast, the mammillary model consists of one or more compartments around a central compartment like satellites. Because the catenary model does not apply to the way most functional organs in the body are directly connected to the plasma, it is not used as often as the mammillary model.

Catenary model

Physiologic Pharmacokinetic Model (Flow Model)
Physiologic pharmacokinetic models, also known as blood flow or perfusion models, are pharmacokinetic models based on known anatomic and physiologic data. The models describe the data kinetically, with the consideration that blood flow is responsible for distributing drug to various parts of the body. Uptake of drug into organs is determined by the binding of drug in these tissues. In contrast to an estimated tissue volume of distribution, the actual tissue volume is used. Because there are many tissue organs in the body, each tissue volume must be obtained and its drug concentration described.

The model would potentially predict realistic tissue drug concentrations, which the two-compartment model fails to do. Unfortunately, much of the information required for adequately describing a physiologic pharmacokinetic model are experimentally difficult to obtain. In spite of this limitation, the physiologic pharmacokinetic model does provide much better insight into how physiologic factors may change drug distribution from one animal species to another.

Other major differences are described below. First, no data fitting is required in the perfusion model. Drug concentrations in the various tissues are predicted by organ tissue size, blood flow, and experimentally determined drug tissue–blood ratios (ie, partition of drug between tissue and blood). Second, blood flow, tissue size, and the drug tissue–blood ratios may vary due to certain pathophysiologic conditions. Thus, the effect of these variations on drug distribution must be taken into account in physiologic pharmacokinetic models.

Third, and most important of all, physiologically based pharmacokinetic models can be applied to several species, and, for some drugs, human data may be extrapolated. Extrapolation from animal data is not possible with the compartment models, because the volume of distribution in such models is a mathematical concept that does not relate simply to blood volume and blood flow. To date, numerous drugs (including digoxin, lidocaine, methotrexate, and thiopental) have been described with perfusion models. Tissue levels of some of these drugs cannot be predicted successfully with compartment models, although they generally describe blood levels well.

Pharmacokinetic model of drug perfusion

Explanation of the symbols of Pharmacokinetic model of drug perfusion
The k's represent kinetic constants: k e is the first-order rate constant for urinary drug excretion and k m is the rate constant for hepatic elimination. Each "box" represents a tissue compartment. Organs of major importance in drug absorption are considered separately, while other tissues are grouped as RET (rapidly equilibrating tissue) and SET (slowly equilibrating tissue). The size or mass of each tissue compartment is determined physiologically rather than by mathematical estimation. The concentration of drug in the tissue is determined by the ability of the tissue to accumulate drug as well as by the rate of blood perfusion to the tissue, represented by Q.

The number of tissue compartments in a perfusion model varies with the drug. Typically, the tissues or organs that have no drug penetration are excluded from consideration. Thus, such organs as the brain, the bones, and other parts of the central nervous system are often excluded, as most drugs have little penetration into these organs. To describe each organ separately with a differential equation would make the model very complex and mathematically difficult. A simpler but equally good approach is to group all the tissues with similar blood perfusion properties into a single compartment.

A criticism of physiologic pharmacokinetic models in general has been that there are fewer data points than parameters that one tries to fit. Consequently, the projected data are not well constrained. The real significance of the physiologically based model is the potential application of this model in the prediction of human pharmacokinetics from animal data. The mass of various body organs or tissues, extent of protein binding, drug metabolism capacity, and blood flow in humans and other species are often known or can be determined.

Q. What are reasons to use a multicompartment model instead of a physiologic model?
Ans. Physiologic models are complex, and require more information for accurate prediction compared to compartment models. Missing information in the physiologic model will lead to bias or error in the model. Compartment models are more simplistic in that they assume that both arterial and venous drug concentrations are similar. PTO

Answer continued : The compartment model accounts for a rapid distribution phase and a slower elimination phase. Physiologic clearance models postulate that arterial blood drug levels are higher than venous blood drug levels. In practice, only venous blood samples are usually sampled. Organ drug clearance is useful in the treatment of cancers and in diagnosis of certain diseases involving arterial perfusion. Physiologic models are difficult to use for general application.

Practical Focus In pharmacokinetics and therapeutics, plasma or tissue samples are often monitored to determine if a prescribed dose needs to be adjusted. Most potent drugs are dosed precisely for the individual patient, and the body weight of the patient should be known. Some physicians prescribe a drug dose based on body weight, whereas others prefer the body surface area method. Significant differences in plasma drug concentrations may result if the dose is based on a different method. Drug concentrations may also be different if a dose is injected rapidly versus infused over a period of time.

Practical Focus For example, theophylline is dosed at 5 mg/kg. Since the body weight (BW) of individuals may vary with age, sex, disease, and nutritional state, an individualized dose based on body weight will more accurately reflect the appropriate therapy needed for the patient. For drugs with a narrow therapeutic index and potential for side effects, dosing based on body surface is common. During chemotherapy with antitumor drugs, many drugs are dosed according to the body surface area (BSA) of the patient.

Practical Focus The body surface area may be determined from the weight of the patient using the empirical equation BSA = (BW ) 0.73 X m2 70kg where BSA = body surface area in m2, and BW = body weight in kg.

Practice Problem Q. The volume of distribution of theophylline is 0.7 L/kg. In most patients, the optimal benefits of theophylline therapy are seen at serum concentration of >10 mg/L; setting a plasma drug concentration of 5 mg/L lower therapeutic limit may result in reduced clinical efficacy. What is the volume of distribution in a 20-year-old male patient weighing 70 kg? What is the total dose for the patient if he is dosed at 5 mg/kg?

Practice Problem Ans. Solution - (1) Volume of patient = 0.7 L/kg x 70 kg = 49 L (answer). (2) Dose for patient = 5 mg/kg x 70 kg = 350 mg (answer).

Clearance Another important parameter in pharmacokinetics is clearance. Clearance is a measure of the removal of drug from the body. Plasma drug concentrations are affected by the rate at which drug is administered, the volume in which it distributes, and its clearance. A drug's clearance and the volume of distribution determine its half-life.

Clearance contd. Clearance (expressed as volume/time) describes the removal of drug from a volume of plasma in a given unit of time (drug loss from the body). Clearance does not indicate the amount of drug being removed. It indicates the volume of plasma (or blood) from which the drug is completely removed, or cleared, in a given time period.

Drugs can be cleared from the body by many different mechanisms, pathways, or organs, including
hepatic biotransformation and renal and biliary excretion.

Clearance contd. Total body clearance of a drug is the sum
of all the clearances by various mechanisms.

Clearance contd. Let us consider a single well-perfused organ that eliminates drug. Blood flow through the organ is referred to as Q (mL/minute) , where Cin is the drug concentration in the blood entering the organ and Cout is the drug concentration in the exiting blood. If the organ eliminates some of the drug, Cin > Cout We can measure an organ's ability to remove a drug by relating Cin and Cout.

This extraction ratio (E):
This ratio must be a fraction between 0 and 1. Organs that are very efficient at eliminating a drug will have an extraction ratio approaching 1 (i.e., 100% extraction).

Clearance contd.

The drug clearance of any organ is determined by blood flow and the extraction ratio:
organ clearance = blood flow × extraction ratio If an organ is very efficient in removing drug (i.e., E= near 1) but blood flow is low , Cl will also be low . Also, if an organ is inefficient in removing drug (i.e., E =close to 0) even if blood flow is high, clearance would again be low.

Clearance can also be a useful parameter for constructing dosage recommendations in clinical situations. It is an index of the capacity for drug removal by the body organs.

Clinical correlate Propranolol is a drug that is eliminated exclusively by hepatic metabolism. The extraction ratio for propranolol is greater than 0.9, so most of the drug presented to the liver is removed by one pass through the liver. Therefore, clearance is approximately equal to liver blood flow (Cl = Q × E: when E ~ 1.0, Cl ~ Q). One indication of the high extraction ratio is the relatively high oral dose of propranolol compared with the intravenous dose; an oral dose is times the equivalent intravenous dose. The difference reflects the amount of drug removed by first-pass metabolism after absorption from the gastrointestinal tract and before entry into the general circulation. .

First order and zero order elimination
Most drugs are eliminated by a first-order process The amount of drug eliminated in a set amount of time is directly proportional to the amount of drug in the body. For zero-order elimination, the amount of drug eliminated for each time interval is constant, regardless of the amount of drug in the body

First order Fraction of drug eliminated over a given time remains constant
Zero order Fraction of drug eliminated over a given time varies

Rates and Orders of Reactions
The rate of a chemical reaction of process is the velocity with which the reaction occurs. Consider the following chemical reaction: Drug A > Drug B If the amount of drug A is decreasing with respect to time (that is, the reaction is going in a forward direction), then the rate of this reaction can be expressed as - dA dT

Since the amount of drug B is increasing with respect to time, the rate of the reaction can also be expressed as + dB dT Usually only the parent (or pharmacologically active) drug is measured experimentally. The metabolites of the drug or the products of the decomposition of the drug may not be known or may be very difficult to quantitate. The rate of a reaction is determined experimentally by measuring the disappearance of drug A at given time intervals.

Rate Constant The order of a reaction refers to the way in which the concentration of drug or reactants influences the rate of a chemical reaction or process.

Zero-Order Reactions If the amount of drug A is decreasing at a constant time interval t, then the rate of disappearance of drug A is expressed as dA = k (1) dT The term k 0 is the zero-order rate constant and is expressed in units of mass/time (eg, mg/min).

Zero-Order Reactions Integration of the Equation (1) yields the following expression: A = - k0t + A (2) where A 0 is the amount of drug at t = 0. Based on this expression, a graph of A versus t yields a straight line. The y intercept is equal to A 0, and the slope of the line is equal to k 0.

Zero-Order Reactions

Zero-Order Reactions Equation (2) may be expressed in terms of drug concentration, which can be measured directly. C = - k0t + C0 where C 0 is the drug concentration at time 0, C is the drug concentration at time t, and k 0 is the zero-order decomposition constant.

First-Order Reactions
Equation (2) may also be expressed as A = A0 e-kt Because ln = 2.3 log, Equation (2) becomes log A = -kt + log A (3) 2.3

When drug decomposition involves a solution, starting with initial concentration C 0, it is often convenient to express the rate of change in drug decomposition, dC/dt, in terms of drug concentration, C, rather than amount because drug concentration is assayed. Hence, dC = -kC (4) dt ln C = - kt + ln C (5)

Equation (5) may be expressed as C = C0 e-kt Because ln = 2.3 log, Equation (5) becomes log C = -kt + log C (6) 2.3

According to Equation (3), a graph of log A versus t will yield a straight line, the y intercept will be log A 0, and the slope of the line will be –k/2.3. Similarly, a graph of log C versus t will yield a straight line according to Equation (6). The y intercept will be log C 0, and the slope of the line will be –k/2.3.

Differences between Zero order Kinetics and First order Kinetics
Rate = k C = Co - kt C vs. t graph is LINEAR Equation of half life Rate = k C C = Co e-kt C vs. t graph is NOT linear, decaying exponential. Log C vs. t graph is linear. Equation of half life

Half-Life Half-life (t 1/2) expresses the period of time required for the amount or concentration of a drug to decrease by one-half. First-Order Half-Life The t 1/2 for a first-order reaction may be found by means of the following equation: t = 0.693 k

Zero-Order Half-Life In contrast to the first-order t 1/2, the t 1/2 for a zero-order process is not constant. The zero-order t 1/2 is proportional to the initial amount or concentration of the drug and is inversely proportional to the zero-order rate constant k 0: t1/2 = 0.5 A0 k0 Because the t 1/2 changes as drug concentrations decline, the zero-order t 1/2 has little practical value.

Q. What is the difference between a rate and a rate constant. Ans
Q. What is the difference between a rate and a rate constant? Ans. A rate represents the change in amount or concentration of drug in the body per time unit. For example, a rate equal to –5 mg/hr means the amount of drug is decreasing at 5 mg per hour. A positive or negative sign indicates that the rate is increasing or decreasing, respectively. Rates may be zero order, first order, or higher orders. For a first-order rate, the rate of change of drug in the body is determined by the product of the elimination rate constant,k, and by the amount of drug remaining in the body, ie, rate = –kD B, where k represents "the fraction" of the amount of drug in the body that is eliminated per hour. If k = 0.1 hr– 1 and D B = 10 mg, then the rate = 0.1 hr– 1 x 10 mg = 1 mg/hr. see next slide

Answer continued The rate constant in this example shows that one-tenth of the drug is eliminated per hour, whatever amount of drug is present in the body. For a first-order rate, the rate states the absolute amount eliminated per unit time (which changes with the amount of drug in the body), whereas the first-order rate constant, k, gives a constant fraction of drug that is eliminated per unit time (which does not change with the amount of drug in the body).

References Applied Biopharmaceutics and Pharmacokinetics – Leon Shargel, Sussana Wu-Pong, Andrew B.C. Yu, 6th Edition, Mc Graw Hill Inc. Chapter -1 and Chapter -2

Introduction to Biopharmaceutics and Pharmacokinetics

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Introduction to Biopharmaceutics and Pharmacokinetics

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