Clinical Pharmacokinetics: Principles and Goals

Clinical Pharmacokinetics Definition

• Clinical pharmacokinetics applies pharmacokinetic principles for safe and effective therapeutic drug management in individual patients.

Primary Goals of Clinical Pharmacokinetics

• Tailoring drug therapy to individual patients.
• Monitoring drugs with a narrow therapeutic index.
• Minimizing adverse effects while maximizing medication's response.
• Measuring bioavailability
• Understanding drug disposition and elimination per physiological and pathological conditions.
• Adjusting drug dosages in disease states when necessary.

Types of Pharmacokinetics

• Clinical Pharmacokinetics: Focuses on individual patient drug management.
• Population Pharmacokinetics: Studies pharmacokinetic differences in various population groups for individualization.
• Toxicokinetics: Applies pharmacokinetic principles to design and interpret drug safety evaluation studies.

Plasma Drug Concentration-Time Profile

• A direct relationship exists between drug concentration at the biophase (site of action) and plasma drug concentration.
• Two parameter categories can be evaluated from it: Pharmacokinetic and Pharmacodynamic.

Pharmacokinetic Parameters

• Peak Plasma Concentration (Cmax): the maximum drug concentration observed after administration.
  • It is also known as peak height concentration and maximum drug concentration.
  • Cmax is expressed in mcg/ml.
  • Affected by the administered dose, absorption rate, and elimination rate.
• Time of Peak Concentration (tmax): time it takes for a drug to reach maximum concentration in plasma post extravascular administration.
  • It influences onset time and onset of action.
  • Key parameter for assessing efficacy of drugs treating acute conditions.
• Area Under the Curve (AUC): Represents the total integrated area under the plasma level-time profile.
  • Expresses total amount of drug reaching systemic circulation post-administration.
  • It is expressed in mcg/ml X hours.
  • Most important parameter for evaluating bioavailability, reflecting the extent of drug absorption.

Peak Concentration Curve Sections

• The peak indicates when absorption and elimination rates of the drug are equal.
• The portion to the left indicates absorption phase, where absorption rate exceeds elimination.
• The portion to the right indicates the elimination phase, where elimination rate exceeds absorption.
• Peak concentration is related to pharmacological response intensity.
  • Ideally, stay above minimum effective concentration (MEC) and below maximum safe concentration (MSC).

Pharmacodynamic Parameters

• Minimum Effective Concentration (MEC).
• Maximum Safe Concentration (MSC).
• Onset of Action.
• Onset Time.
• Duration of Action.
• Intensity of Action: It is also called as peak response.
• Therapeutic Range.
• Therapeutic Index.

Onset Time

• Onset Time: Time taken to reach therapeutic range, initiating pharmacological response.
• Onset of Action: The beginning of pharmacological response
• Termination of Action: Time taken for plasma drug concentration to fall below minimum effective concentration (MEC).

Intensity of Action

• Intensity of Action: It is also called as peak response.
• Maximum pharmacological response is produced by peak plasma concentration of drug.

Therapeutic Range & Index

• Therapeutic Range: The drug concentration between MEC and MSC.

  • It is also known as therapeutic window.

• Therapeutic Index: The ratio of MSC to MEC.

  • It is also defined as the ratio of dose required to produce toxic or lethal effects to dose required to produce a therapeutic response

Pharmacokinetic-Pharmacodynamic Relationship

• Pharmacokinetics helps develop dosing that achieves therapeutic concentrations for desired response.
• Pharmacodynamics is the relationship between drug concentrations at the action site and the pharmacological response.

Mathematical Model Assumptions

• Drug molecules combining with receptor molecules is a bimolecular association.
  • The resulting drug-receptor complex disassociates as a unimolecular entity.
• Drug binding with the receptor is fully reversible.
• The base model has a single receptor binding site, with one binding site per molecule.
• Receptors with multiple sites can be modeled after this base model.

Drug Receptor Occupancy

• A greater pharmacodynamic response is obtained with more receptors occupied by drug molecules until maximum response is reached.

Relation of Dose to Pharmacologic Effect

• The onset, intensity, and duration of the effect depend on the dose and pharmacokinetics of the drug.
• Increased drug concentration at the receptor site results in increases of the effect up to a maximum.
• Plotting the effect to a dose yields a hyperbolic curve while compressing the same plotted on a log-linear scale yields a sigmoidal curve.
• Log dose-response curves demonstrate a linear relationship at dose ranges between 20% and 80% of the maximum drug response.
  • Log plasma drug concentration is proportional to the pharmacological response within its therapeutic range.

Basic Pharmacokinetics Topics

• Order and rate constants.
• Pharmacokinetic models.
• Compartmental models.
• Physiologic (perfusion models).
• Model-independent methods (statistical moment theory).
• Non-linear pharmacokinetics.

Kinetics

• The rate of a chemical reaction or process is the velocity at which the reaction occurs.
• Given drug A turns into drug B: drug A→ drug B
• If the amount of drug A is decreasing with respect to time then the rate of this reaction can be expressed as: -dA/dt
• If the amount of drug B is increasing with respect to time, the rate of the reaction can also be expressed as: +dB/dt
• Generally, only the parent or pharmacologically active drug is measured experimentally.
• Metabolites of the drug or decomposition products may not be known or difficult to quantitate.
• The rate of a reaction is measured experimentally by measuring the disappearance of drug A at given time intervals.

Reaction Order

• Refers to how concentration of drug or reactants influences the rate of a reaction or process.
• The manner in which the concentration of drug (or reactants) influences the rate of reaction or process

First Order Kinetics

• The most common process for many drugs
• The rate at which absorption, distribution, metabolism, and excretion occur is proportional to the concentration of drugs.
  • A constant fraction of a drug disappears in each interval of time.

Zero Order Kinetics

• The process is independent of the amount of drug present at the absorption or elimination sites.
• Few drugs follow this process like ethanol and phenytoin.
• A constant amount of the drug is eliminated in each equal interval of time
• A repeated administration leads to drug accumulation potentially causing toxic reactions.

Rate Constant: Zero-Order Reactions

• If the amount of drug A decreases at a constant time interval t, the disappearance rate of drug A is: dA/dt = -ko

• k(0) is the zero-order rate constant expressed in mass/time units like mg/min.

• Integration yields A = -k(0)t + A(0)

• A(0) represents drug amount at t=0.

• The y-intercept equals A(0), and the slope equals k(0).

• A graph of A versus t produces a straight line

• Drug concentration can be measured directly using C=-kt +C(0)

• C(0) is the drug concentration at time 0.

• Graphing the drug concentration over time will yield a straight line and results in zero order decline

Rate Constant: Zero-Order Example

• A pharmacist dissolves 10 g of a drug in 100 mL of water.
• The solution is stored at room temperature. Samples are removed periodically and assayed for the drug.
• Plotting concentration versus time yields a straight line, meaning the rate of decline follows zero order.
• Using this data, zero order rate constant k(0) can be found by the slope of the line.
• If C(0) = 100 mg/ml at t=0 and C = 90 mg/ml at t=4 hr, then
  • 90 = -K(0)(4) + 100 resulting in K(0) = 2.5 mg/ml hr
• Drug declines by 5mg/ml every 2 hours. The zero-order rate constant is 5mg/ml / 2 hr = 2.5 mg/ml hr.

Rate Constant: First-Order Reactions

• If the amount of drug A decreases at a rate proportionally to the amount of drug A remaining, the rate's expression is dA/dt = -kA.
• k is the first-order rate constant is expressed in time-1 units, e.g., hr-1.
• Integration produces in A = -kt + ln A(0)

Applying Logarithms

• In A = -kt + ln A(0) can be expressed as A = A(0)e-kt

• Since ln = 2.3log, the equation becomes log A = -kt / 2.3+ log A(0)

• With drug decomposition in a solution with initial concentration C0, the rate of change in decomposition, dC/dt, is expressed in drug concentration C. Hence- dC/dt = -kC

• ln C= -kt + ln C0

• log C = -kt/2.3 + log C0

• A graph of log A versus t yields a straight line, with y intercept log A0, and a slope of -k/2.3.

• Since convenience, C versus t can be plotted on semilog paper without having to convert C to log C

Half Life

• Half-life (t1/2) is the duration for a drug amount or concentration to decrease by one-half.
• In a first-order reaction, t1/2 is constant.
  • Time required for concentration to decrease by one-half is constant regardless initial amount/concentration.

First-Order Half-Life

• The t1/2 for a first-order reaction found by 𝑡1/2 = 0.693 / k
• In contrast to first-order 𝑡1/2, a zero-order process cannot be constant.
• A zero-order 𝑡1/2 is proportional to the initial drug amount/concentration but is inversely proportional to the rate constant k0.
• Because 𝑡1/2 varies as drug concentrations decline, zero-order 𝑡1/2 has little practical value

Zero-Order Half-Life

• Zero-order 𝑡1/2 can be found by 𝑡1/2 = 0.5A0/ k0

Half-Life Example

• A pharmacist dilutes 10g of a drug with 100ml of water and obtains the following data.
• Based on this example the 𝑡1/2 is 4 hours.
• The first order is by the following, obtaining 2.3 times the slope or dividing (0.693/ 𝑡1/2 )

Pharmacokinetic Models

• Handling of drugs by the body can be very complex due to several concurrent processes.
• Simplifications of body processes are needed to be able to predict a drug's behavior.
• Simplifications are made by applying mathematical principles.
• To apply mathematical principles, a model of the body must be selected

Elements of Pharmacokinetic Models

• These models are a hypotheses employing mathematical terms that concisely describe quantitative relationships
• They provide concise mean to express mathematically or quantitatively the time course of drug(s) throughout the body and compute meaningful pharmacokinetic parameters

Utilities of Pharmacokinetic Models

• Pharmacokinetic models should allow one to:
• Predict plasma, tissue, and urine drug levels with any dosage regimen
• Calculate the optimum dosage regimen for each patient individually
• Estimate the possible accumulation of drugs and/or metabolites
• Correlate drug concentrations with pharmacological or toxicological activity
• Evaluate differences in the rate or extent of availability between formulations (bioequivalence)
• Describe how changes in physiology or disease affect the absorption, distribution, or elimination of the drug
• Explain drug interactions

Types of Pharmacokinetic Models

• Compartment models
• Physiological models
• Distributed Parameter models

Compartment Models

• Compartmental analysis is the traditional and most common approach to characterizing a drug's pharmacokinetics.
• Compartments don't represent specific tissues/fluids themselves; instead, they represent collections of similar tissue or fluid types.
• The following statements are true about models:
  • They can predict the time course drug in the body.
  • They are hypothetical in nature.
  • These models are based on certain assumptions.

Model Assumptions

• The body is represented as a series of compartments arranged in series or are parallel to each other, that communicate reversibly.

• Each compartment is not a real physiologic or anatomic region but a fictitious tissue or group.

  • They must also have similar drug distribution qualities (similar blood flow and affinity)

Compartment Uniformity

• Each compartment considers the drug to be rapidly and uniformly distributed.

  • The compartment itself are well-stirred

Rate of Drug Movement Between Compartments

• The rate of drug movement between compartments like entry and exist is described by first-order kinetics.
• Rate constants are used to represent the rate that compounds enter and exit compartments

Types of Models

• There are 3 types of compartment models: one, two, and three (or more).

One Compartment Model

• The most frequently used model in clinical practice.

  • Organs and tissues that demonstrate similar drug distribution are grouped.

  • The perfusion pattern is also to be considered, e.g., distribution into adipose tissue differs from distribution into renal tissue for most drugs.

• The highly perfused organs that include the heart muscles often have the same drug distribution

Two-Compartment Model

• Multicompartment models are not used frequently as they are difficult to apply.
• To describe the change over natural log that the plasma drug concentration versus time curve is not a straight line, a multi-compartment is used.
• All body fluids ad tissues are a part of this type of model

One-Compartment Open Model (Instantaneous Distribution)

• Is the simplest model option.

• Is based on underlying assumptions, namely, that the body's single, kinetically homogeneous unit includes no barriers to obstruct a drug's movement

• The following are considered in this model: -That final distribution equilibrium of equilibrium between drug in plasma and outer body fluids is attained.

  • That elimination is a first-order with overall the first-order-rate constant

  • rate of elimination is greater than the rate of output is greater than the rate of inputs

• The anatomical reference compartment is within plasma. concentration of frug in plasma is representative, of drug concentration in all body tissues

One-Compartment Open Model

• There are several models based on the rate of input:
  • IV bolus administration
  • Continuous IV administration
  • Extravascular administration, using zero-order absorption
  • Extravascular administration, using first-order absorption

Intravenous Bolus Administration Type

• Refers to a distributed drug that that given as a rapid IV by means of injection or slug.

• Takes approximately 3 minutes for complete circulation.

• The constant KE is used in calculations.

Formula Examples

• The general expression of drug presentation includes
  • dX /dtRate In — Rale Out

Estimation Of Parameters

• Elimination phase and rate constant follow: ln X = ln Xo – KE t
• In said expression, that X0 equals the amount of drug with time t = zero which is the amount injected to start.

Example 1

• log XX=-KET