Michaelis-Menten kinetics is commonly used to describe non-linear pharmacokinetics when drug metabolism or elimination involves saturable enzyme systems. Non-linearity occurs when the capacity of the enzyme is exceeded, leading to saturation. This document discusses various causes and examples of non-linear pharmacokinetics, including saturation of absorption, distribution, metabolism and excretion processes. It also describes the two-compartment open model and how drug concentrations change in each compartment over time following intravenous bolus dosing.
Herbs, Herbal Drugs
Present Scope of Herbal Drug Industry
Scope of Herbal Drug Medicine and Industry
Indian Herbal Industry
International Scope of Herbal Medicines
World Wide Herbal Trade
Overview on plant based industries and research institutions in India
List of few herbal drug industries in India
List of few herbal research institution/ centres in India
General Introduction to Herbal Industry
Herbal drugs industry: Present scope and future prospects.
A brief account of plant based industries and institutions involved in work on medicinal and
aromatic plants in India.
Herbal excipients are non-active ingredients used in herbal medicines that help process, protect, support, enhance stability or patient acceptability of the active compounds. The document discusses various types of herbal excipients including colorants, sweeteners, binders, diluents, viscosity enhancers, disintegrants and flavors. For each type, examples of specific herbal sources are provided, including the plant name and family as well as the active constituent. Advantages and disadvantages of using herbal excipients are also summarized.
Nonlinear pharmacokinetics occurs when the body's processing of a drug is saturated at higher doses, causing kinetics parameters like clearance and half-life to change with dose. Michaelis-Menten kinetics are commonly used to model nonlinear metabolism, where the metabolic rate approaches a maximum (Vmax) at high concentrations. Parameters like Vmax and KM can be estimated from steady-state dosing and concentration data by linearizing the Michaelis-Menten equation. Drugs like phenytoin exhibit nonlinear kinetics due to capacity-limited hepatic metabolism.
1. Drug absorption involves the movement of unchanged drug molecules from the site of administration into systemic circulation. It occurs primarily through the gastrointestinal (GI) tract and is influenced by factors like solubility, permeability, and transport mechanisms.
2. There are three main mechanisms of drug transport across the GI tract - transcellular, paracellular, and vesicular. Transcellular transport occurs across cells and includes passive diffusion, active transport, and carrier-mediated transport. Paracellular transport is between cell junctions. Vesicular transport involves endocytosis within cells.
3. The most common mechanism is passive diffusion, which does not require energy. Other mechanisms like active transport and carrier-mediated transport use
1. The herbal drug industry in India has significant present scope and future prospects due to the increasing demand for herbal medicines that are safer, less toxic, and more affordable than synthetic drugs.
2. India has a large number of plant-based industries and research institutions involved in developing medicinal and aromatic plants, with over 2400 plant species used as raw drugs and 8000 plant varieties used in herbal medicines.
3. The herbal drug market in India is estimated at Rs. 7000 crore currently and is one of the fastest growing sectors due to the popularity of Ayurveda and other traditional Indian medicine systems.
This document describes the two compartment open model for drug distribution and elimination. It discusses:
- How the body is divided into a central compartment (blood, highly perfused tissues) and peripheral compartment (poorly perfused tissues)
- How drugs distribute between compartments according to first-order rate constants K12 and K21, and are eliminated from the central compartment at a rate of KE
- Equations that describe drug concentrations in each compartment over time after intravenous or oral administration
- Methods for determining pharmacokinetic parameters like absorption rate constant Ka, distribution and elimination rate constants, and compartment volumes from drug concentration-time data.
The document discusses the pH partition theory of drug absorption from the gastrointestinal tract. The theory states that a drug's absorption is governed by its dissociation constant (pKa), the lipid solubility of its unionized form, and the pH of the absorption site. According to the theory, only the unionized form of an acid or base drug can be absorbed if it is sufficiently lipid soluble. The fraction of a drug in its unionized form depends on the drug's pKa and the pH of the solution based on the Henderson-Hasselbalch equation. While the pH partition theory explains many observations, it has limitations such as not accounting for the presence of an unstirred water layer and virtual membrane pH at the absorption
Herbs, Herbal Drugs
Present Scope of Herbal Drug Industry
Scope of Herbal Drug Medicine and Industry
Indian Herbal Industry
International Scope of Herbal Medicines
World Wide Herbal Trade
Overview on plant based industries and research institutions in India
List of few herbal drug industries in India
List of few herbal research institution/ centres in India
General Introduction to Herbal Industry
Herbal drugs industry: Present scope and future prospects.
A brief account of plant based industries and institutions involved in work on medicinal and
aromatic plants in India.
Herbal excipients are non-active ingredients used in herbal medicines that help process, protect, support, enhance stability or patient acceptability of the active compounds. The document discusses various types of herbal excipients including colorants, sweeteners, binders, diluents, viscosity enhancers, disintegrants and flavors. For each type, examples of specific herbal sources are provided, including the plant name and family as well as the active constituent. Advantages and disadvantages of using herbal excipients are also summarized.
Nonlinear pharmacokinetics occurs when the body's processing of a drug is saturated at higher doses, causing kinetics parameters like clearance and half-life to change with dose. Michaelis-Menten kinetics are commonly used to model nonlinear metabolism, where the metabolic rate approaches a maximum (Vmax) at high concentrations. Parameters like Vmax and KM can be estimated from steady-state dosing and concentration data by linearizing the Michaelis-Menten equation. Drugs like phenytoin exhibit nonlinear kinetics due to capacity-limited hepatic metabolism.
1. Drug absorption involves the movement of unchanged drug molecules from the site of administration into systemic circulation. It occurs primarily through the gastrointestinal (GI) tract and is influenced by factors like solubility, permeability, and transport mechanisms.
2. There are three main mechanisms of drug transport across the GI tract - transcellular, paracellular, and vesicular. Transcellular transport occurs across cells and includes passive diffusion, active transport, and carrier-mediated transport. Paracellular transport is between cell junctions. Vesicular transport involves endocytosis within cells.
3. The most common mechanism is passive diffusion, which does not require energy. Other mechanisms like active transport and carrier-mediated transport use
1. The herbal drug industry in India has significant present scope and future prospects due to the increasing demand for herbal medicines that are safer, less toxic, and more affordable than synthetic drugs.
2. India has a large number of plant-based industries and research institutions involved in developing medicinal and aromatic plants, with over 2400 plant species used as raw drugs and 8000 plant varieties used in herbal medicines.
3. The herbal drug market in India is estimated at Rs. 7000 crore currently and is one of the fastest growing sectors due to the popularity of Ayurveda and other traditional Indian medicine systems.
This document describes the two compartment open model for drug distribution and elimination. It discusses:
- How the body is divided into a central compartment (blood, highly perfused tissues) and peripheral compartment (poorly perfused tissues)
- How drugs distribute between compartments according to first-order rate constants K12 and K21, and are eliminated from the central compartment at a rate of KE
- Equations that describe drug concentrations in each compartment over time after intravenous or oral administration
- Methods for determining pharmacokinetic parameters like absorption rate constant Ka, distribution and elimination rate constants, and compartment volumes from drug concentration-time data.
The document discusses the pH partition theory of drug absorption from the gastrointestinal tract. The theory states that a drug's absorption is governed by its dissociation constant (pKa), the lipid solubility of its unionized form, and the pH of the absorption site. According to the theory, only the unionized form of an acid or base drug can be absorbed if it is sufficiently lipid soluble. The fraction of a drug in its unionized form depends on the drug's pKa and the pH of the solution based on the Henderson-Hasselbalch equation. While the pH partition theory explains many observations, it has limitations such as not accounting for the presence of an unstirred water layer and virtual membrane pH at the absorption
Methods for Measurement of bioavailability pharmacampus
Which are the Methods for Measurement of bioavailability?- Pharmacokinetic method- Plasma level time studies, Urinary excretion studies.
Pharmacodynamic method: Acute pharmacologic response, Therapeutic response.
This document discusses kinetics of multiple dosing, drug accumulation, and concepts of loading and maintenance doses. It provides definitions and formulas for calculating accumulation factor, steady state levels, loading doses, and maintenance doses. The key points are:
1) Multiple dosing leads to drug accumulation until steady state is reached when the drug entering and leaving the system are equal.
2) Loading doses provide rapid target concentrations while maintenance doses maintain therapeutic levels.
3) Calculations for loading and maintenance doses depend on clearance, volume of distribution, and bioavailability. Maintaining therapeutic levels with minimal fluctuations is the goal of multiple dosing regimens.
The document discusses nonlinear pharmacokinetics and chronopharmacokinetics. Nonlinear pharmacokinetics occurs when the body's absorption, distribution, metabolism, or excretion of a drug becomes saturated at higher doses. This can cause the rate of drug elimination to decrease. Examples of processes that can become saturated include drug metabolism and renal excretion. Circadian rhythms can also impact drug pharmacokinetics by influencing absorption, distribution, metabolism, and excretion over 24-hour periods. Accounting for these temporal changes can improve drug therapy for circadian phase-dependent diseases.
Methods of enhancing Dissolution and bioavailability of poorly soluble drugsRam Kanth
Bioavailability refers to the amount of drug that reaches systemic circulation after administration. It is reduced when drugs are administered orally rather than intravenously due to incomplete absorption and first-pass metabolism. The document discusses several methods for enhancing bioavailability of orally administered drugs with poor solubility or permeability. These include micronization, use of surfactants, salt forms, altering pH, polymorphism, complexation, molecular encapsulation, and forming solid solutions, eutectic mixtures or solid dispersions to improve solubility and dissolution rate.
The document discusses the pH partition hypothesis, which states that the absorption of drugs across biomembranes is governed by the drug's dissociation constant (pKa), lipid solubility of the un-ionized form, and the pH of the absorption site. According to the hypothesis, only the un-ionized form of an acid or base drug can be absorbed if it is sufficiently lipid soluble. The fraction of a drug in its un-ionized form can be calculated using the Henderson-Hasselbach equation based on the drug's pKa and the pH. However, the pH partition theory is an oversimplification and does not always accurately predict drug absorption behavior.
This document discusses factors that influence the absorption of drugs in the gastrointestinal tract. It outlines various physicochemical and dosage form factors that can impact a drug's solubility, dissolution rate, and absorption. The key physicochemical factors discussed are drug solubility, particle size, polymorphism, salt form, and lipophilicity. Theories of drug dissolution like the diffusion layer model and Danckwert's model are also summarized. The principle of bioequivalence studies and factors like disease state, gastrointestinal contents, and presystemic metabolism that can influence drug absorption are briefly covered as well.
ABSORPTION OF DRUGS - NON PER ORAL - EXTRA VASCULAR ROUTESRam Kanth
Greetings!
Good Day to All..
This presentation is all about ABSORPTION OF DRUGS - NON PER ORAL - EXTRA VASCULAR ROUTES which covers about the various route of administration which are administered other than oral route like
1. Buccal / Sublingual
2. Rectal
3. Topical & Transdermal
4. Parenteral
5. Pulmonary & Intra nasal
6. Intra ocular &
7. Vaginal Administration
Your suggestion and comments are welcome for further improvement in my presentations.
Thank you all for your valuable time.
Disclaimer Note: Some contents in the presentation were taken from online sources which is purely used for education purpose and for any personal financial or commercial aspects. I thank all the source providers in online for your efforts and support in sharing of knowledge.
The document discusses compartment modeling and one compartment open models. It describes how the body can be represented as a single well-mixed compartment and outlines the assumptions of compartmental models. It then covers one compartment open models for intravenous bolus administration, intravenous infusion, and extravascular administration. For intravenous bolus administration, the elimination phase can be characterized by parameters like elimination rate constant, half-life, and clearance. Intravenous infusion allows for constant rate input into the compartment. Extravascular administration models absorption as either zero-order or first-order kinetics.
ONE COMPARTMENT OPEN MODEL I.V BOLUS (Contact me: dr.m.bharathkumar@gmail.com)DR. METI.BHARATH KUMAR
The document appears to be a scanned receipt from a grocery store listing various food and household items purchased totaling $123.45. It includes the store name, date, time of purchase, payment method (credit card), and signature of the cashier. The receipt provides details of the transaction including item names, quantities, and individual prices.
This document provides information about the nutraceutical properties of various herbs and foods. It discusses the health benefits of nutraceuticals in treating diseases like diabetes, cardiovascular diseases, cancer, and gastrointestinal issues. Key points covered include the classification of nutraceuticals, probiotics and prebiotics, polyunsaturated fatty acids, vitamins, and the traditional and global market of nutraceuticals. Specific herbs discussed include alfalfa, chicory, ginger, fenugreek, garlic, and honey.
This document discusses linear and nonlinear pharmacokinetics. [1] Linear pharmacokinetics follow first-order kinetics where the rate of drug absorption, distribution, metabolism and excretion is proportional to dose. [2] Nonlinear pharmacokinetics occur when these processes become saturated at high doses due to limited enzyme or transporter capacity. [3] Michaelis-Menten kinetics are often used to model nonlinear processes and estimate parameters like Vmax and Km.
Phytosomes are advanced herbal formulations containing bioactive plant constituents bound to phospholipids. This improves absorption and bioavailability compared to conventional herbal extracts. Phytosomes are prepared by reacting phytoconstituents like flavonoids with phosphatidylcholine in solvent to form a complex. They have advantages like reduced dose requirements and synergistic effects when combined with hepatoprotective substances. Common phytosome applications include milk thistle for liver protection, grape seed for antioxidants, green tea for various health benefits, and curcumin for its anti-inflammatory properties.
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
Model approach, and
Model-independent approach (also called as non-compartmental analysis).
This document outlines World Health Organization (WHO) and International Council for Harmonization (ICH) guidelines for evaluating herbal drugs. It discusses evaluating the quality, safety, efficacy and intended use of herbal medicines according to WHO guidelines. This includes assessing the botanical identity and constituents of plant materials, manufacturing processes, stability testing, safety, efficacy based on literature and traditional use, and providing product information for consumers. ICH guidelines on quality and safety are also used to assess drug substances. The overall aim is to help regulatory authorities and manufacturers properly evaluate herbal drugs.
The document discusses the structure-activity relationship of quinolines as urinary tract anti-infective agents. It outlines that the 1,4-dihydro-4-oxo-pyridin-3-carboxylic acid moiety is essential for antibacterial activity, and it must be annulated with an aromatic ring. Substitutions at certain positions, like fluorine at position 6, lower alkyl groups at position 1, and amino at position 5 result in compounds with antibacterial activity. Piperazine, N-methyl piperazine and pyrrolidine ring substitutions at position 7 also lead to active compounds.
The document discusses two-compartment pharmacokinetic models. A two-compartment model describes the distribution and elimination of drugs in the body using two interconnected compartments - a central compartment representing blood and highly perfused tissues, and a peripheral compartment representing slowly perfused tissues. Parameters like volume of distribution, clearance, half-life and rate constants can be estimated from the biexponential decline in drug concentration observed following intravenous administration. Clinical applications including intravenous infusion and factors affecting pharmacokinetic parameters are also covered.
The document discusses three main theories of drug dissolution:
1) Diffusion layer/film theory which describes dissolution as a two step process of drug dissolving from the solid to form a saturated film and then diffusing out of the film. The rate of dissolution is given by the Noyes-Whitney equation.
2) Danckwert's/surface renewal theory which accounts for eddies in the solution exposing new surface areas for dissolution. The rate is expressed as the product of the surface renewal rate and concentration gradient.
3) Interfacial barrier model which assumes the reaction at the solid surface is slower than diffusion, making interfacial transport the rate limiting step described by another equation.
This document provides an overview of pharmacokinetics, including definitions, compartment models, non-compartment models, physiological models, and a one-compartment open model. Pharmacokinetics describes the absorption, distribution, metabolism, and excretion of drugs in the body. Compartmental models represent the body as a series of compartments and use rate constants to describe drug movement between compartments. A one-compartment open model can be used to model intravenous bolus administration, where drug is eliminated from the body via first-order kinetics.
This document discusses multicompartment models, including two-compartment models. A two-compartment model classifies body tissues into a central compartment (blood, highly perfused tissues) and peripheral compartment (poorly perfused tissues). Depending on the compartment of drug elimination, two-compartment models can describe intravenous bolus administration, intravenous infusion, or extravascular administration. Compartment models are useful for characterizing drug behavior in patients and optimizing dosage regimens.
This document discusses multi-compartment pharmacokinetic modeling and nonlinear pharmacokinetics. It describes multi-compartment models with central and peripheral compartments and assumptions about drug distribution and elimination. Two-compartment open models are described along with intravenous bolus administration profiles. Causes of nonlinear pharmacokinetics are covered, including saturation of absorption, distribution, metabolism and excretion processes. Methods for determining kinetic parameters like Km and Vmax under nonlinear conditions are also summarized.
Methods for Measurement of bioavailability pharmacampus
Which are the Methods for Measurement of bioavailability?- Pharmacokinetic method- Plasma level time studies, Urinary excretion studies.
Pharmacodynamic method: Acute pharmacologic response, Therapeutic response.
This document discusses kinetics of multiple dosing, drug accumulation, and concepts of loading and maintenance doses. It provides definitions and formulas for calculating accumulation factor, steady state levels, loading doses, and maintenance doses. The key points are:
1) Multiple dosing leads to drug accumulation until steady state is reached when the drug entering and leaving the system are equal.
2) Loading doses provide rapid target concentrations while maintenance doses maintain therapeutic levels.
3) Calculations for loading and maintenance doses depend on clearance, volume of distribution, and bioavailability. Maintaining therapeutic levels with minimal fluctuations is the goal of multiple dosing regimens.
The document discusses nonlinear pharmacokinetics and chronopharmacokinetics. Nonlinear pharmacokinetics occurs when the body's absorption, distribution, metabolism, or excretion of a drug becomes saturated at higher doses. This can cause the rate of drug elimination to decrease. Examples of processes that can become saturated include drug metabolism and renal excretion. Circadian rhythms can also impact drug pharmacokinetics by influencing absorption, distribution, metabolism, and excretion over 24-hour periods. Accounting for these temporal changes can improve drug therapy for circadian phase-dependent diseases.
Methods of enhancing Dissolution and bioavailability of poorly soluble drugsRam Kanth
Bioavailability refers to the amount of drug that reaches systemic circulation after administration. It is reduced when drugs are administered orally rather than intravenously due to incomplete absorption and first-pass metabolism. The document discusses several methods for enhancing bioavailability of orally administered drugs with poor solubility or permeability. These include micronization, use of surfactants, salt forms, altering pH, polymorphism, complexation, molecular encapsulation, and forming solid solutions, eutectic mixtures or solid dispersions to improve solubility and dissolution rate.
The document discusses the pH partition hypothesis, which states that the absorption of drugs across biomembranes is governed by the drug's dissociation constant (pKa), lipid solubility of the un-ionized form, and the pH of the absorption site. According to the hypothesis, only the un-ionized form of an acid or base drug can be absorbed if it is sufficiently lipid soluble. The fraction of a drug in its un-ionized form can be calculated using the Henderson-Hasselbach equation based on the drug's pKa and the pH. However, the pH partition theory is an oversimplification and does not always accurately predict drug absorption behavior.
This document discusses factors that influence the absorption of drugs in the gastrointestinal tract. It outlines various physicochemical and dosage form factors that can impact a drug's solubility, dissolution rate, and absorption. The key physicochemical factors discussed are drug solubility, particle size, polymorphism, salt form, and lipophilicity. Theories of drug dissolution like the diffusion layer model and Danckwert's model are also summarized. The principle of bioequivalence studies and factors like disease state, gastrointestinal contents, and presystemic metabolism that can influence drug absorption are briefly covered as well.
ABSORPTION OF DRUGS - NON PER ORAL - EXTRA VASCULAR ROUTESRam Kanth
Greetings!
Good Day to All..
This presentation is all about ABSORPTION OF DRUGS - NON PER ORAL - EXTRA VASCULAR ROUTES which covers about the various route of administration which are administered other than oral route like
1. Buccal / Sublingual
2. Rectal
3. Topical & Transdermal
4. Parenteral
5. Pulmonary & Intra nasal
6. Intra ocular &
7. Vaginal Administration
Your suggestion and comments are welcome for further improvement in my presentations.
Thank you all for your valuable time.
Disclaimer Note: Some contents in the presentation were taken from online sources which is purely used for education purpose and for any personal financial or commercial aspects. I thank all the source providers in online for your efforts and support in sharing of knowledge.
The document discusses compartment modeling and one compartment open models. It describes how the body can be represented as a single well-mixed compartment and outlines the assumptions of compartmental models. It then covers one compartment open models for intravenous bolus administration, intravenous infusion, and extravascular administration. For intravenous bolus administration, the elimination phase can be characterized by parameters like elimination rate constant, half-life, and clearance. Intravenous infusion allows for constant rate input into the compartment. Extravascular administration models absorption as either zero-order or first-order kinetics.
ONE COMPARTMENT OPEN MODEL I.V BOLUS (Contact me: dr.m.bharathkumar@gmail.com)DR. METI.BHARATH KUMAR
The document appears to be a scanned receipt from a grocery store listing various food and household items purchased totaling $123.45. It includes the store name, date, time of purchase, payment method (credit card), and signature of the cashier. The receipt provides details of the transaction including item names, quantities, and individual prices.
This document provides information about the nutraceutical properties of various herbs and foods. It discusses the health benefits of nutraceuticals in treating diseases like diabetes, cardiovascular diseases, cancer, and gastrointestinal issues. Key points covered include the classification of nutraceuticals, probiotics and prebiotics, polyunsaturated fatty acids, vitamins, and the traditional and global market of nutraceuticals. Specific herbs discussed include alfalfa, chicory, ginger, fenugreek, garlic, and honey.
This document discusses linear and nonlinear pharmacokinetics. [1] Linear pharmacokinetics follow first-order kinetics where the rate of drug absorption, distribution, metabolism and excretion is proportional to dose. [2] Nonlinear pharmacokinetics occur when these processes become saturated at high doses due to limited enzyme or transporter capacity. [3] Michaelis-Menten kinetics are often used to model nonlinear processes and estimate parameters like Vmax and Km.
Phytosomes are advanced herbal formulations containing bioactive plant constituents bound to phospholipids. This improves absorption and bioavailability compared to conventional herbal extracts. Phytosomes are prepared by reacting phytoconstituents like flavonoids with phosphatidylcholine in solvent to form a complex. They have advantages like reduced dose requirements and synergistic effects when combined with hepatoprotective substances. Common phytosome applications include milk thistle for liver protection, grape seed for antioxidants, green tea for various health benefits, and curcumin for its anti-inflammatory properties.
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
Model approach, and
Model-independent approach (also called as non-compartmental analysis).
This document outlines World Health Organization (WHO) and International Council for Harmonization (ICH) guidelines for evaluating herbal drugs. It discusses evaluating the quality, safety, efficacy and intended use of herbal medicines according to WHO guidelines. This includes assessing the botanical identity and constituents of plant materials, manufacturing processes, stability testing, safety, efficacy based on literature and traditional use, and providing product information for consumers. ICH guidelines on quality and safety are also used to assess drug substances. The overall aim is to help regulatory authorities and manufacturers properly evaluate herbal drugs.
The document discusses the structure-activity relationship of quinolines as urinary tract anti-infective agents. It outlines that the 1,4-dihydro-4-oxo-pyridin-3-carboxylic acid moiety is essential for antibacterial activity, and it must be annulated with an aromatic ring. Substitutions at certain positions, like fluorine at position 6, lower alkyl groups at position 1, and amino at position 5 result in compounds with antibacterial activity. Piperazine, N-methyl piperazine and pyrrolidine ring substitutions at position 7 also lead to active compounds.
The document discusses two-compartment pharmacokinetic models. A two-compartment model describes the distribution and elimination of drugs in the body using two interconnected compartments - a central compartment representing blood and highly perfused tissues, and a peripheral compartment representing slowly perfused tissues. Parameters like volume of distribution, clearance, half-life and rate constants can be estimated from the biexponential decline in drug concentration observed following intravenous administration. Clinical applications including intravenous infusion and factors affecting pharmacokinetic parameters are also covered.
The document discusses three main theories of drug dissolution:
1) Diffusion layer/film theory which describes dissolution as a two step process of drug dissolving from the solid to form a saturated film and then diffusing out of the film. The rate of dissolution is given by the Noyes-Whitney equation.
2) Danckwert's/surface renewal theory which accounts for eddies in the solution exposing new surface areas for dissolution. The rate is expressed as the product of the surface renewal rate and concentration gradient.
3) Interfacial barrier model which assumes the reaction at the solid surface is slower than diffusion, making interfacial transport the rate limiting step described by another equation.
This document provides an overview of pharmacokinetics, including definitions, compartment models, non-compartment models, physiological models, and a one-compartment open model. Pharmacokinetics describes the absorption, distribution, metabolism, and excretion of drugs in the body. Compartmental models represent the body as a series of compartments and use rate constants to describe drug movement between compartments. A one-compartment open model can be used to model intravenous bolus administration, where drug is eliminated from the body via first-order kinetics.
This document discusses multicompartment models, including two-compartment models. A two-compartment model classifies body tissues into a central compartment (blood, highly perfused tissues) and peripheral compartment (poorly perfused tissues). Depending on the compartment of drug elimination, two-compartment models can describe intravenous bolus administration, intravenous infusion, or extravascular administration. Compartment models are useful for characterizing drug behavior in patients and optimizing dosage regimens.
This document discusses multi-compartment pharmacokinetic modeling and nonlinear pharmacokinetics. It describes multi-compartment models with central and peripheral compartments and assumptions about drug distribution and elimination. Two-compartment open models are described along with intravenous bolus administration profiles. Causes of nonlinear pharmacokinetics are covered, including saturation of absorption, distribution, metabolism and excretion processes. Methods for determining kinetic parameters like Km and Vmax under nonlinear conditions are also summarized.
Non-linear pharmacokinetics occurs when the rate of absorption, distribution, metabolism, or excretion of a drug depends on the dose administered. This can be due to saturation of enzymes involved in drug metabolism or transporters involved in absorption and excretion. According to the Michaelis-Menten equation, the rate of drug clearance will approach a maximum theoretical rate (Vmax) as the drug concentration increases, leading to non-linear kinetics. In linear kinetics, pharmacokinetic parameters are constant regardless of dose, while in non-linear kinetics they are dose-dependent.
Nonlinear pharmacokinetics can occur when the rate processes of drug absorption, distribution, metabolism, or excretion become dependent on dose size due to saturation of carrier proteins or enzymes. Some specific causes of nonlinearity include saturation of transporters during drug absorption, saturation of plasma protein binding sites or tissue binding sites during distribution, capacity-limited drug metabolism by enzyme saturation, and saturation of active tubular secretion or reabsorption processes during excretion. The Michaelis-Menten equation can describe the kinetics of these saturable, capacity-limited processes.
This document discusses linear and non-linear pharmacokinetics. Linear pharmacokinetics follow first-order kinetics where the rate of drug elimination is directly proportional to drug concentration. With non-linear kinetics, the rate of elimination appears zero-order at higher concentrations as a constant amount is eliminated per unit time. Non-linear kinetics occur when absorption, distribution, metabolism or excretion processes become saturated at higher doses. This can be detected by determining how pharmacokinetic parameters change with different doses. Causes of non-linearity include saturation of transporters, binding proteins, metabolic enzymes and renal reabsorption/secretion mechanisms.
non linear pharmakokinetic causes of nonlinearityamartya2087
This document discusses nonlinear pharmacokinetics, which occurs when the rate processes of drug absorption, distribution, metabolism, or excretion are dependent on carrier proteins or enzymes that have a limited capacity and can become saturated at high drug concentrations. This results in pharmacokinetic parameters like clearance and half-life varying with dose. Nonlinearity can be detected by determining parameters like bioavailability, elimination half-life, and clearance at different doses. It is commonly caused by saturation of absorption, distribution, metabolic or excretory pathways. Some examples of drugs that exhibit nonlinear kinetics due to different mechanisms like saturation of plasma protein binding or metabolic enzymes are provided.
University Institute of Pharmaceutical Sciences is a flag bearer of excellence in Pharmaceutical education and research in the country. Here is another initiative to make study material available to everyone worldwide. Based on the new PCI guidelines and syllabus here we have a presentation dealing with pharmacokinetics : concept of linear and non-linear compartment models.
Thank you for reading.
Hope it was of help to you.
UIPS,PU team
This document provides an overview of basic concepts in biopharmaceutics including pharmacokinetic models and parameters. It discusses pharmacokinetic concepts like dosage regimen, pharmacokinetics, plasma drug concentration profiles, and pharmacokinetic parameters including Cmax, tmax, AUC, etc. It also covers pharmacokinetic models including compartment models, physiological models, and non-compartmental analysis. Specific compartment models like one-compartment open model for IV bolus and IV infusion are explained. Rate constants, orders of reactions, and processes like zero-order, first-order, and mixed-order kinetics are defined. Methods for estimating pharmacokinetic parameters from plasma concentration-time data are also summarized.
This document provides an overview of basic concepts in biopharmaceutics including pharmacokinetic models and parameters. It discusses pharmacokinetic concepts like dosage regimen, pharmacokinetics, plasma drug concentration profiles, and pharmacokinetic parameters including Cmax, tmax, AUC, etc. It also covers pharmacokinetic models including compartment models, physiological models, and non-compartmental analysis. Specific compartment models like one-compartment open model for IV bolus and infusion administrations as well as extravascular administration are explained. Methods for estimating pharmacokinetic parameters from these models are also summarized.
This document provides an overview of basic pharmacokinetic concepts including dosage regimens, pharmacokinetic parameters, pharmacokinetic models, and compartment modeling. Some key points:
- Pharmacokinetics describes the absorption, distribution, metabolism and excretion of drugs over time. Parameters like Cmax, tmax, AUC can be evaluated from plasma concentration-time profiles.
- Reaction rates can follow zero-order, first-order or mixed-order kinetics depending on how the reaction rate is influenced by the drug concentration. Half-life concepts differ between these orders.
- Compartmental modeling represents the body as hypothetical compartments that communicate reversibly. Mammillary and catenary models differ in compartment arrangement
This document discusses linear and nonlinear pharmacokinetics. It defines linear pharmacokinetics as processes where drug parameters are proportional to dose. Nonlinear pharmacokinetics occurs when absorption, distribution, or metabolism pathways become saturated at high doses. Michaelis-Menten kinetics are used to model saturation effects. Methods for determining the Michaelis-Menten constants Km and Vmax using steady state drug concentrations include Lineweaver-Burk plots, direct linear plots, and graphical methods. Common drugs exhibiting nonlinear behavior and their causes are also outlined.
The presentation concisely describes the different pharmacokinetic parameters and basics of compartment modelling. It will help undergraduate students to understand the basic concepts of Biopharmaceutics.
This document discusses various pharmacokinetic concepts including dosage regimen, pharmacokinetics, plasma drug concentration-time profiles, pharmacokinetic parameters, rate and order of reactions, zero-order and first-order kinetics, mixed-order kinetics, pharmacokinetic models, compartment models, and physiological models. It provides definitions and examples of these key pharmacokinetic terms.
This document discusses saturation kinetics and nonlinear pharmacokinetics. It explains that drug clearance follows first-order kinetics at low concentrations but can become saturated and shift to zero-order kinetics at high concentrations due to limited enzyme capacity. This nonlinear behavior is described by Michaelis-Menten kinetics. A few drugs like phenytoin exhibit saturation kinetics in the therapeutic range, making their dosing more complex due to changing half-lives with concentration. Understanding saturation and nonlinear pharmacokinetics is important for safely dosing drugs that exhibit these behaviors.
This document discusses non-linear pharmacokinetics and pharmacodynamics. It begins by defining basic kinetic parameters like absorption and elimination rate constants, volume of distribution, and bioavailability fraction. It then explores possible causes of non-linearity, including saturation of absorption, distribution, metabolism and excretion processes. Non-linear binding due to saturation of plasma protein binding sites is also covered. The document concludes by giving an example of non-linear pharmacological responses with phenytoin, where capacity-limited metabolism leads to fluctuating clearance and half-life with changing plasma concentrations.
This document summarizes a seminar on computational methods for drug disposition. It discusses two approaches to modeling drug disposition: qualitative and quantitative. The quantitative approach uses pharmacophore modeling and docking to study drug interactions, while the qualitative approach uses QSAR and QSPR to correlate molecular descriptors with ADMET properties. The document also reviews the key processes of drug disposition: absorption, distribution, metabolism, and excretion. It provides examples of two research articles, one on the placental disposition of the immunosuppressant tacrolimus, and another on the pharmacokinetics of miltefosine in mice and hamsters infected with Leishmania.
pharmacokinetics is the important topic in both pharmacology and pharmaceutics in degree and masters level . the thorough knowledge in the fiels of pharmacokinetics will helps to choose the proper medicine to treat a particular disesse
This document discusses linear and nonlinear pharmacokinetics. Linear pharmacokinetics follow first-order kinetics and the concentration of a drug is proportional to the administered dose. Nonlinear pharmacokinetics occur when absorption, distribution, metabolism or excretion processes become saturated, leading to dose-dependent changes in pharmacokinetic parameters. Nonlinearity can be detected by examining steady state plasma concentrations and pharmacokinetic parameters at different doses. Causes of nonlinearity include saturation of drug transporters, plasma protein binding sites, metabolic enzymes, and renal excretion mechanisms.
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1. Department: Pharmacy
Class: BPharm
Semester: VI Sem
Subject: Biopharmaceutics & Pharmacokinetics (BP604T)
Topic: NON-LINEAR PHARMACOKINETICS
Disclaimer:
The presented matter is compilation of various online materials available on the topic with
modification and simplification. The content is presented here for student’s easy accessibility
as online study material and not for commercial purpose.
2. Unit-V
NON-LINEAR PHARMACOKINETICS
It is a Dose Dependent Pharmacokinetics. Nonlinear pharmacokinetic models imply that
some aspect of the pharmacokinetic behaviour of the drug is saturable.
CAUSES OF NON-LINEARITY
Saturation of enzymes in process of drug
Pathologic alteration in drug ADME
EXAMPLES
Amino glycoside may cause renal nephrotoxicity thereby altering renal drug excretion
Obstruction of the bile duct to the formation of gallstone will alter biliary drug
excretion
PROCESS SATURATED
Absorption
Nonlinearity in drug absorption can arise from 5 important sources;
1. When absorption is solubility or dissolution rate-limited. e.g. griseofulvin
3. 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.
2. When absorption involves carrier-mediated transport systems
e.g. absorption of riboflavin, ascorbic acid, cyanocobalamin, etc.
Saturation of the transport system at higher doses of these vitamins results in nonlinearity.
3. When presystemic gut wall or hepatic metabolism attains satura-Tion
e.g. propranolol, hydralazine and verapamil.
Saturation of presystemic metabolism of these drugs at high doses leads to increased
bioavailability.
The parameters affected will be F, Ka, Cmax and AUC, A decrease in these parameters is
observed in the former two cases and an increase in the latter case. Other causes of
nonlinearity in drug absorption are changes in gastric emptying and GI blood flow and other
physiological factors. Nonlinearity in drug absorption is of little consequence unless
availability is drastically affected.
4. Distribution
Nonlinearity in distribution of drugs administered at high doses may be due to-
1. Saturation of binding sites on plasma proteins e.g. phenylbutazone and naproxen. 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.
2. Saturation of tissue binding sites e.g. thiopental and fentanyl. With large single bolus doses
or multiple dosing, saturation of tissue storage sites can occur. In both cases, the free plasma
drug concentration increases but Vd increases only in the former case whereas it decreases in
the latter.
Clearance is also altered depending upon the extraction ratio of the drug. Clearance of a drug
with high ER is greatly increased due to saturation of binding sites. Unbound clearance of
drugs with low ER is unaffected and one can expect an increase in pharmacological response.
Metabolism
The nonlinear kinetics of most clinical importance is capacity-limited metabolism since
small changes in dose administered can produce large variations in plasma concentration
at steady-state. It is major sources of large inter subject variability in pharmacological
response. Two important causes of nonlinearity in metabolism are;
1. Capacity-limited metabolism due to enzyme and/or cofactor satu- ration. Typical
examples include phenytoin, alcohol, theophylline, etc.
5. 2. Enzyme induction e.g. carbamazepine, where a decrease in peak plasma concentration
has been observed on repetitive adminis- tration over a period of time. Autoinduction
characterized in this case is also dose-dependent. Thus, enzyme induction is a common
cause of both dose- and time-dependent kinetics.
3. Saturation of enzyme results in decreased ClH and therefore in- creased Css Reverse is
true for enzyme induction. Other causes of nonlinearity in biotransformation include
saturation of binding sites, inhibitory effect of the metabolite on enzyme and pathological
situations such as hepatotoxicity and changes in hepatic blood flow.
Excretion
The two active processes in renal excretion of a drug that are;
1. Active tubular secretion e.g. penicilin G. After saturation of the carrier-system, a decrease
in renal clearance occurs.
2. Active tubular reabsorption e.g. water-soluble vitamins and glucose. After saturation of the
carrier-system, an increase in renal clearance occurs. Other sources of nonlinearity in renal
excretion include forced diurebiliary secretion, which is also an active process.
A summary of outcome of saturation (nonlinearity) in various ADME is changes in urine pH,
nephrotoxicity and saturation of binding sites. e.g. tetracycline and indomethacin.
6.
7. MICHAELIS MENTEN EQUATION
Michaelis–Menten kinetics is one of the best
after German biochemist Leonor Michaelis and Canadian physician Maud Menten.
Michaelis-Menten equation is commonly used to describe the kinetics of in
well as certain in-vitro processes that are k
of drugs by a saturable enzymatic process
If C is the concentration of drugs in the plasma then
Where
Vm is t
Km i
A typical p
MICHAELIS MENTEN EQUATION
Menten kinetics is one of the best-known models of enzyme kinetics. It is named
Leonor Michaelis and Canadian physician Maud Menten.
equation is commonly used to describe the kinetics of in
vitro processes that are known to be catalysed by enzymes
drugs by a saturable enzymatic process is described by Michaelis-Menten Kinetics.
If C is the concentration of drugs in the plasma then Elimination rate
Where C is the plasma concentration
Vm is the maximum rate of process
Km is the Michaelis-Menten constant
A typical plot of Michaelis-Menten equation
known models of enzyme kinetics. It is named
Leonor Michaelis and Canadian physician Maud Menten. The
equation is commonly used to describe the kinetics of in-vitro, in-situ as
nown to be catalysed by enzymes. The elimination
Menten Kinetics.
8. Case I: Km=c
The value for Km is equal to the concentration at which the rate of process is half (1/2) the
maximum rate Vm.
-dc/dt=Vmax/2
Case II where Km > C
At low concentration, where Km> C , Km + C is approximately equal to Km,
As Vm/Km is a constant term, the equation can be described as a first order equation with
Vm/Km as the first order kinetics is expected. Usually in most of the case of the cases Km is
larger than the plasma concentration that is achieved.
Case III:
In some cases at higher doses C > Km, then
Km+ C is approximately equal to C.
Summary:
Condition I When Km = C -dc/dt=Vmax/2
Condition II When Km>>C -dc/dt=Vmax.c/Km
Condition III When Km<<C -dc/dt=Vmax
When given in the therapeutic doses, most drugs produce plasma drug concentration
well below the Km for all carrier mediated enzyme systems affecting the
pharmacokinetics of the drugs. Therefore, most drugs at normal therapeutic
concentration follow 1st order rate process
9. A few drugs such as salicylate and phenytoin saturate the hepatic mixed function
oxidase at higher therapeutic doses.
Later part of the graph describes here zero order kinetics. Thus at high plasma
concentration, first order kinetics are not seen.
With these drugs, elimination kinetics are first order at low doses and mixed at high
doses and may approach zero-order at very high therapeutic doses
10. Suggested References/Sources
1. https://www.slideshare.net/bharathpharmacist/non-linear-pharmacokinetics-
39686259?qid=ab58fcd5-fe1f-4203-b07a-111e806a20c7&v=&b=&from_search=6
2. Ritschel, Wolfgang A. "Handbook of basic pharmacokinetics." (1976).
3. Brahmankar, D. M., and Sunil B. Jaiswal. Biopharmaceutics and pharmacokinetics: A
treatise. Vallabh prakashan, 2005.
4. Shargel, Leon, Susanna Wu-Pong, and Andrew BC Yu. Applied biopharmaceutics &
pharmacokinetics. McGraw-Hill, 2007.
5. Gibaldi, Milo. Biopharmaceutics and clinical pharmacokinetics. Lea & Febiger,
1977.
6. Winter, Michael E. Basic clinical pharmacokinetics. Eds. Mary Anne Koda-Kimble,
and Lloyd Y. Young. Philadelphia: Lippincott Williams & Wilkins, 2004.
7. Welling, Peter G. Pharmacokinetics: processes, mathematics, and applications. Amer
Chemical Society, 1997.
11. Department: Pharmacy
Class: BPharm
Semester: VI Sem
Subject: Biopharmaceutics & Pharmacokinetics (BP604T)
Topic: Two compartment open model with first order elimination
kinetics, pharmacokinetics of single and multiple dose administration, as
applied to intravenous (rapid/bolus)
Disclaimer:
The content present here is part of the project which was submitted to www.cec.nic.in for e-
content development. Here, it is presented again for student’s easy accessibility as online
study material.
12. Various mathematical models can be devised to simulate the rate processes of drug
absorption, distribution, metabolism, and elimination. These mathematical models
are useful in the development of equations to describe drug concentration in the
body as a function of time. Pharmacokinetic models are divided into the:
1. Compartment models
2. Physiologic pharmacokinetic models
3. Non-compartmental pharmacokinetics
4. Non-linear pharmacokinetics
Compartment Model
In a pharmacokinetic analysis of the data, the living system is assumed to consist of
a number of interconnected compartments. A compartment is defined as a group of
tissues which behaves uniformly with respect to the drug movement. Each
compartment behaves differently regarding the drug concentration time course data.
As you know that one – compartment model describes pharmacokinetics of many
drugs. Instantaneous distribution equilibrium is assumed in such cases and decline
in the amount of drug in the body with time is expressed by an equation with a mono-
exponential term (i.e. elimination). However, instantaneous distribution is not truly
possible for an even larger number of drugs and drug disposition is not mono-
exponential but bi-or multi-exponential.
This is because the body is composed of a heterogeneous group of tissues each
with different degree of blood flow and affinity for drug and therefore different rate of
equilibration. Ideally, a true pharmacokinetic model should be the one with a rate
constant for each tissue undergoing equilibrium, which is difficult mathematically.
The best approach is therefore to pool together tissues on the basis of similarity in
their distribution characteristics.
As for one-compartment models, drug disposition in multi-compartment systems is
also assumed to occur by first-order. Multi-compartment characteristics of a drug are
best understood by giving it as i.v. bolus and observing the manner in which the
plasma concentration declines with time.
13. TWO COMPARTMENT OPEN MODEL
In a two compartment open model, the body tissues are broadly classified into two
categories.
1. Central Compartment or Compartment 1
It is comprised of blood and highly perfused tissues like liver, lungs, kidneys, etc.
that equilibrate with the drug rapidly. Elimination usually occurs from this
compartment.
2. Peripheral or Tissue Compartment or Compartment 2
It is comprised of poorly perfused and slow equilibrating tissues such as muscles,
skin, adipose, etc. and considered as a hybrid of several functional physiological
units.
Classification of particular tissue, for example brain, into central or peripheral
compartment depends upon the physicochemical properties of the drug. A highly
lipophilic drug can cross the BBB and brain would then be included in the central
compartment. In contrast, a polar drug cannot penetrate the BBB and brain in this
case will be a part of peripheral compartment despite the fact that it is a highly
perfused organ.
Following I.V. bolus, if a drug distributes to some tissue which are not highly
perfused with blood, the distribution of the drug to tissue may take a longer time to
establish equilibrium between the central compartment and the tissue compartment.
During this time the drug levels in the central compartment will fall because of two
14. reasons. 1. Distribution of the drug from the central compartment to peripheral
compartment. 2. Elimination of the drug levels from the central compartment by the
all possible pathways of elimination. It means the decrease in drug level in the
central compartment can be described by biexponential equation. This part of the
plasma level time curve is called distribution phase. Once equilibrium is established
between the amount of the drug present in the central compartment and that of the
peripheral compartment, a decline in the plasma level takes place mono
exponentially. This decline is only because of elimination of the drug from the body
and is called elimination phase.
The following points should be considered in developing the equation for a
two-compartment open model:
1. In this model, the drug distributes in two compartments, the central
compartment and the tissue compartment.
2. Drug transfer between the two compartments is assumed to take place by a
first-order process.
3. There are three possible types of two compartment systems. Depending upon
the compartment from which the drug is eliminated, the two-compartment
model can be categorized into 3 types:
I. Two –compartment model with elimination from central compartment.
II. Two–compartment model with elimination from peripheral compartment.
III. Two- compartment model with elimination from both the compartments.
In the absence of information, elimination is assumed to occur exclusively from
central compartment.
4. Elimination of the drug from the body is assumed to follow first order kinetics.
5. The concentration of the drug in a compartment is assumed to be uniform in
its volume of distribution.
Two compartment models assume that at t=0 there is no drug in the tissue
compartment. After an I.V. dose, drug levels in the tissue compartment will first
increase, reach maximum and then decline.
PHARMACOKINETICS OF I.V BOLUS SINGLE DOSE ADMINISTRATION
After the i.v. bolus of a drug that follows two-compartment kinetics, the decline in
plasma concentration is bi-exponential indicating the presence of two disposition
15. processes viz. distribution and elimination. These two processes are not evident to
the eyes in a regular arithmetic plot but when a semilog plot of C versus t is made,
they can be identified.
You can see figure 1. Initially, the concentration of
declines rapidly, this is due to the distribution of drug from the central compartment
to the peripheral compartment. The phase during which this occurs is therefore
called as the distributive phase.
After sometime, a pseudo distribution equilibrium is achieved 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 elim
compartment, the drug concentration in the peripheral compartment first increases
and reaches a maximum. This corresponds with the distribution phase. Following
peak, the drug concentration declines which correspo
phase.
Figure 2: Changes in drug concentration in the central (plasma) and the
peripheral compartment after i.v. bolus of a drug that fits two
You can see figure 2 in which two compartment IV bolus model ha
with elimination from the central compartment
processes viz. distribution and elimination. These two processes are not evident to
the eyes in a regular arithmetic plot but when a semilog plot of C versus t is made,
You can see figure 1. Initially, the concentration of drug in the central compartment
declines rapidly, this is due to the distribution of drug from the central compartment
to the peripheral compartment. The phase during which this occurs is therefore
called as the distributive phase.
do distribution equilibrium is achieved 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
distributive or elimination phase. In contrast to the central
compartment, the drug concentration in the peripheral compartment first increases
and reaches a maximum. This corresponds with the distribution phase. Following
peak, the drug concentration declines which corresponds to the post
Figure 2: Changes in drug concentration in the central (plasma) and the
peripheral compartment after i.v. bolus of a drug that fits two
model
You can see figure 2 in which two compartment IV bolus model has been depicted
with elimination from the central compartment
processes viz. distribution and elimination. These two processes are not evident to
the eyes in a regular arithmetic plot but when a semilog plot of C versus t is made,
drug in the central compartment
declines rapidly, this is due to the distribution of drug from the central compartment
to the peripheral compartment. The phase during which this occurs is therefore
do distribution equilibrium is achieved 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
ination phase. In contrast to the central
compartment, the drug concentration in the peripheral compartment first increases
and reaches a maximum. This corresponds with the distribution phase. Following
nds to the post-distributive
Figure 2: Changes in drug concentration in the central (plasma) and the
peripheral compartment after i.v. bolus of a drug that fits two-compartment
s been depicted
16. (2)
(3)
Figure 1: Scheme for I.V. Bolus Two-Compartment Pharmacokinetic Model
Where:
X0 = I.V. dose given as bolus
Xc = Amount of the drug in the central compartment at any time (Compartment 1)
Xt = Amount of drug in the tissue compartment at any time (Compartment 2)
X3 = Amount of drug eliminated to time t.
Vc = Volume of distribution of drug in the central compartment.
Vt = Volume of distribution of the drug in the tissue compartment.
C = Concentration of the drug in the central compartment at any time.
Ct = Concentration of the drug in the tissue compartment at any time.
Calculation of pharmacokinetic parameters
Let K12 and K21 be the first-order distribution rate constants depicting drug transfer
between the central and the peripheral compartments and let subscript c and t define
central and peripheral compartment respectively. The constants K12 and K21 that
depict reversible transfer of drug between compartments are called as micro-
constants or transfer constants. Ke is the elimination rate constant.
Equation that describes the time course of drug concentration in the central
compartment and peripheral compartment following I.V. bolus can be developed as
described below.
According to mass balance equation,
X0 = Xc + Xt + X (1)
The rate of change in the amount of the drug in central compartment is the net
balance of rate of input (K21 Xt) and output (K12 Xc and K13 Xc)
dXc
dt
= K X − K X − K X
The rate of change in drug concentration in the tissue compartment is given by
equation:
K13
K12
K21
Ka
Xo
1 2
Xc = Vc.C Xt = Vt.Ct
X3
17. (4)
(5)
(6)
(7)
(8)
(9)
dXt
dt
= K X − K X
The rate of elimination of drug from the central compartment is given by,
dX
dt
= K X
Integrating the equation (4) and substituting the value of X3 in equation (1) it will yield
a biexponentail curve in the form of,
= +
Where
=
0 ( − )
( − )
and
=
0 ( − )
( − )
Substituting the values of A’ and B’ in equation 5, we get
=
0 ( − )
( − )
+
0 ( − )
( − )
A linear relationship exists between the drug concentration in plasma and the
amount of the drug in the central compartment.
Xc = Vc. C
Where, Vc is the apparent volume of distribution of the drug in the central
compartment. This relationship enables the conversion of equation 6 from amount-
time to a concentration-time equation, which can be expressed as,
C =
( )
( )
e +
( )
( )
e
or in simpler form,
C = A e + B e
Where, A =
( )
( )
and B =
( )
( )
18. Where Xo = i.v. bolus dose, α and β are hybrid first-order constants for the rapid
distribution phase and the slow elimination phase respectively which depends
entirely upon the first order rate constants K12, K21 and KE
Method of Residuals: The bi-exponential disposition curve obtained after i.v. bolus
of a drug that fits two compartment models can be resolved into its individual
exponents by the method of residuals.
C = A e-αt
+ B e-βt
(9)
As apparent from the bi-exponential curve given in Fig. 3., the initial due to
distribution is more rapid than the terminal decline due to elimination i.e. the rate
constant α > >β and hence the term e-αt
approaches zero much faster than does e-βt
.
Thus, equation 9 reduces to:
C = Be (10)
In log form, the equation becomes:
log = log − .
(11)
Equations 10 and 11 describe the plasma drug-level time data during the elimination
phase.
A plot of the log plasma drug level versus time can be used to estimate various
pharmacokinetic parameters as shown in fig.3. An estimate of b can be made from
the slope of the terminal linear portion (slope = -βt/ 2.303) and the biological half-life
(t1/2) can be determined employing relationship t1/2 = 0.693/β.
19. Figure 3: Resolution of biexponential plasma concentration
method of residuals for a drug that follows two
administration
The zero time intercept obtained by extrapolation of the terminal linear phase
is log B. Application of the method of residual may be carried out by subtracting the
plasma drug level on the extended line at the same time point to obtain residual
concentration-time data. A plot of
line with a slope = -α/ 2.303 and an intercept = log A.
The constant A, B, a, and b may be obtained graphically as explained above.
Once these experimental constants are obtained, the pharmacokinetic par
Vc, K12, K13 and K21 can be generated by considering the following relationship.
Module 4: ESTIMATION OF PHARMACOKINETIC PARAMETERS
All the parameters of equation 9 can be resolved by the method of residuals as
described above. Other parameters o
derived by proper substitution of these values.
1. Vc
= C
f biexponential plasma concentration-time curve by the
method of residuals for a drug that follows two-compartment kinetics on i.v. bolus
The zero time intercept obtained by extrapolation of the terminal linear phase
of the method of residual may be carried out by subtracting the
plasma drug level on the extended line at the same time point to obtain residual
time data. A plot of residual concentration versus time gives a residual
α/ 2.303 and an intercept = log A.
The constant A, B, a, and b may be obtained graphically as explained above.
Once these experimental constants are obtained, the pharmacokinetic par
can be generated by considering the following relationship.
Module 4: ESTIMATION OF PHARMACOKINETIC PARAMETERS
All the parameters of equation 9 can be resolved by the method of residuals as
described above. Other parameters of the model viz. K12, K21, KE, etc. can now be
derived by proper substitution of these values.
C0 = A + B
time curve by the
compartment kinetics on i.v. bolus
The zero time intercept obtained by extrapolation of the terminal linear phase
of the method of residual may be carried out by subtracting the
plasma drug level on the extended line at the same time point to obtain residual
residual concentration versus time gives a residual
The constant A, B, a, and b may be obtained graphically as explained above.
Once these experimental constants are obtained, the pharmacokinetic parameters,
can be generated by considering the following relationship.
Module 4: ESTIMATION OF PHARMACOKINETIC PARAMETERS
All the parameters of equation 9 can be resolved by the method of residuals as
, etc. can now be
(12)
20. Therefore,
Vc = = =
. .
(13)
2. K21
K = (14)
3. K13
K =
( )
( )
(15)
4. K12 : By definition (α+β) = K12 + K13 + K21. Substituting K21 and K13 values
in the above equation and solving it for K12 we get
K =
( )
( )( )
(16)
It must be noted that for two-compartment model K13 is the rate constant for
elimination of drug from the central compartment and β is the rate constant for
elimination from the entire body. Overall elimination t1/2 should therefore be
calculated from β.
Drug level in tissue or peripheral compartment
The differential equation that describes the rate of change in the amount of the drug
in the tissue compartment is,
Xt = ( )
(e − e ) (17)
Equation 17 describes the time course of the amount of the drug in the peripheral
compartment following I.V. bolus. Thie equation may be useful in determining the
relationship between pharmacological action and the tissue level of the drug.
It is assumed that the drug in the tissue compartment distributes uniformly in its
volume of distribution, Vt, then equation 17 can be written in concentration terms.
Ct = ( )
(e − e ) (18)
Module 5: APPARENT VOLUME OF DISTRIBUTION
Even though the volume of distribution is fictive, it provides not only some insight into
distribution but also importantly relates to the rate of clearance of the drug from
plasma. In multiple compartments we may consider mathematically hypothetical
21. volumes, such as the volume of the central compartment and the volume of the
tissue or peripheral compartment.
In a two-compartment open model, the determination of the volume of
distribution, Vd is complicated by 1) The slow attainment of distribution equilibrium;
and, 2) The volume of distribution is changing continually during the distribution
phase. There are several volumes of distribution that may be considered for a drug
that follows a two-compartment open model.
Volume of distribution of central compartment (Vc)
The volume of distribution of the central compartment, Vc, is an important parameter
to understand distribution pattern of the drug in the body, to estimate drug clearance
and to describe the time course of plasma drug levels because the central
compartment is usually the sampling compartment.
At time zero, the total drug injected is in the central compartment. Hence Vc is
the ratio of I.V. dose and plasma drug concentration at t = 0 i.e., C0
Vc = I. V. Dose/C0 (19)
C0, can be estimated from equation
C = A e-αt
+ B e-βt
, at t = 0
C0 = A + B
Vc = (20)
A and B are estimated from the plasma drug level – time graph by the method of
residuals.
Alternatively, the volume of the central compartment may be calculated from [ ]
in a manner similar to the calculation for the apparent Vd in the one-compartment
model.
Vc = [ ]
(21)
The apparent volume of distribution at steady-state
The apparent volume of distribution at steady-state Vd,ss is equal to the total drug in
the body at steady state divided by the plasma drug concentration at that time.
, =
22. Total drug in the body = amount of the drug in the central compartment (Xc) +
amount of drug in the tissue compartment (Xt). Therefore,
, = (22)
At steady state condition the rate of drug entry into the tissue compartment from the
central compartment is equal to the rate of drug exit from the tissue compartment
into the central compartment. This steady-state condition may be exist for a moment,
theoretically, following I.V. bolus. Hence, at steady state condition
Vd, ss = Vc + Vc (23)
Volume of distribution by area can be given as:
Vd, area = (24)
I.V. Bolus – Unchanged drug in Urine
It is possible to obtain pharmacokinetics of a drug from urinary excretion data that
follows a two-compartment open model following an I.V. bolus administration. The
elimination of the drug from the body in such cases is by the parallel renal and extra-
renal elimination processes.
Figure 4: Scheme for I.V. Bolus Two-Compartment Pharmacokinetic Model
(Unchanged Drug in Urine)
Where:
Ke = Urinary excretion rate constant for unchanged drug.
Ky = Sum of all the rate constants of all the processes involved in the elimination of
drug other than renal excretion.
Xu = Cumulative amount of the unchanged drug excreted in urine.
Xy = Cumulative amount of drug eliminated by all other routes other than renal.
Xu
Ke
K12
K21
Ka
Xo
1 2
Xc = Vc.C Xt = Vt.Ct
Ky
Xy
23. The overall elimination rate constant from the central compartment, K13 is the sum of
the individual rate constants which characterize the parallel elimination processes
(K13 = Ke + Ky).
The excretion rate of unchanged drug, dXu/dt can be expressed as
= A"e + B"e (25)
Where A" = Ke X0
( )
( )
and B" = Ke X0
( )
( )
dXu/dt is the instantaneous rate of excretion of the drug, which cannot be
determined experimentally. Hence, instead of dXu/dt, the average excretion rate,
ΔXu/Δt, is used. ΔXu/Δt approximate dXu/dt if the sampling intervals are short.
Therefore,
= A"e + B"e ′ (26)
t’ = mid-point of urine collection period.
All pharmacokinetic parameters can be determined by applying method of residual.