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. Pharmacokinetics 2. Introduction to Pharmacokinetics. a. Mathematical model b. Drug levels in blood. c. Pharmacokinetic model d. Compartment models e. Pharmacokinetic study. With reference to pharm d sybullus
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I now have comprehensive content from Goodman & Gilman's and Lippincott's textbooks. Let me compile the full, structured notes.
Pharmacokinetics — Complete Notes (Pharm.D. Syllabus)
1. Introduction to Pharmacokinetics
Pharmacokinetics (PK) is the study of what the body does to a drug. It encompasses the time course of drug concentration in body fluids and tissues as a result of the processes of Absorption, Distribution, Metabolism, and Elimination (ADME).
"ADME, the absorption, distribution, metabolism, and elimination of drugs, are the processes of pharmacokinetics. Understanding these processes and their interplay and employing pharmacokinetic principles increase the probability of therapeutic success and reduce the occurrence of adverse drug events and drug-drug interactions." — Goodman & Gilman's The Pharmacological Basis of Therapeutics
Why Pharmacokinetics Matters:
- Establishes a quantitative relationship between dose and therapeutic effect
- Provides a framework to interpret drug concentrations in biological fluids
- Guides selection of appropriate dosage regimens
- Helps individualize therapy in special populations (renal/hepatic disease, pediatrics, elderly)
- Helps predict and avoid drug toxicity and drug–drug interactions
Pharmacokinetics vs. Pharmacodynamics:
| Parameter | Pharmacokinetics | Pharmacodynamics |
|---|---|---|
| Definition | What the body does to the drug | What the drug does to the body |
| Focus | ADME processes | Receptor binding, efficacy, toxicity |
| Determines | Drug concentration–time profile | Concentration–effect relationship |
2. Mathematical Models in Pharmacokinetics
Mathematical models in pharmacokinetics provide a concise, quantitative means of expressing the time course of drug concentrations throughout the body. They allow computation of key pharmacokinetic parameters and prediction of plasma drug concentrations under different dosing scenarios.
Key Mathematical Concepts
a) First-Order Kinetics
- Most drugs follow first-order (linear) kinetics: a constant fraction of drug is eliminated per unit time
- Rate of elimination is directly proportional to drug concentration:
$$\text{Rate of elimination} = k \cdot C$$
Where k = first-order elimination rate constant (units: time⁻¹)
- Since metabolizing enzymes and transporters are usually not saturated, the absolute rate of elimination is essentially a linear function of plasma concentration
b) Zero-Order Kinetics
- Occurs when elimination mechanisms become saturated (e.g., ethanol, high-dose phenytoin)
- A constant amount (not fraction) of drug is eliminated per unit of time
- Concentration declines linearly with time (not exponentially)
c) Michaelis-Menten Kinetics (Mixed-Order)
$$CL = \frac{V_m}{K_m + C}$$
Where:
- $V_m$ = maximal rate of elimination
- $K_m$ = concentration at which elimination rate is half-maximal
- At low concentrations (C << K_m): approaches first-order; at high concentrations (C >> K_m): approaches zero-order
d) The One-Compartment Equation (IV bolus)
$$C = \left[\frac{\text{Dose}}{V}\right] \cdot e^{-kt}$$
Where:
- C = plasma concentration at time t
- V = volume of distribution
- k = elimination rate constant
- e = Euler's number (base of natural logarithm)
e) The AUC (Area Under the Curve)
$$AUC = \frac{\text{Dose}}{CL}$$
AUC represents total drug exposure over time and is used to calculate bioavailability.
3. Drug Levels in Blood
Why Measure Drug Levels?
Blood/plasma drug concentration is the most accessible compartment that reflects drug concentration at its site of action. Therapeutic Drug Monitoring (TDM) uses measured drug levels to individualize dosing.
The Concentration–Time Profile
Following drug administration, plasma concentration varies with time through distinct phases:
| Phase | Description |
|---|---|
| Absorption phase | Concentration rises as drug enters systemic circulation |
| Peak (C_max) | Maximum plasma concentration; time to peak = t_max |
| Distribution phase | Concentration falls rapidly as drug distributes to tissues |
| Elimination phase | Slower, log-linear decline as drug is metabolized/excreted |
| Steady state (C_ss) | Achieved after ~4–5 half-lives during repeated dosing |
Key Blood Level Parameters
| Parameter | Definition | Formula |
|---|---|---|
| C_max | Maximum plasma concentration | — |
| t_max | Time to reach C_max | — |
| AUC | Area under concentration–time curve; reflects total exposure | Dose / CL |
| t½ | Half-life: time for concentration to fall by 50% | 0.693 × V / CL |
| C_ss | Steady-state concentration during continuous dosing | F × Dosing rate / CL |
Therapeutic Window (Therapeutic Range)
- The range of plasma concentrations between the minimum effective concentration (MEC) and the minimum toxic concentration (MTC)
- Drugs with narrow therapeutic windows require TDM (e.g., digoxin, phenytoin, vancomycin, aminoglycosides, lithium)
Dosage Adjustment Using Blood Levels
If current plasma concentration is C₁ and target is C₂:
$$\text{Additional dose needed} = V_d \times (C_2 - C_1)$$
4. Pharmacokinetic Models
A pharmacokinetic model is a mathematical framework that simplifies the complex biological processes of drug disposition into manageable equations that describe drug concentration versus time.
Purpose of Pharmacokinetic Models
- Predict plasma concentrations at any time after dosing
- Determine optimal dosing intervals
- Assess the effect of disease on drug disposition
- Guide dose adjustments in special populations
- Design drug formulations
Types of Models
| Model Type | Description |
|---|---|
| Compartment models | Body divided into hypothetical compartments; most widely used |
| Physiologically-based PK (PBPK) | Uses actual organ volumes and blood flows; complex |
| Non-compartmental analysis (NCA) | Model-independent; uses AUC and statistical moments |
| Population PK | Accounts for inter-individual variability using mixed-effects modeling |
5. Compartment Models
Compartment models are the most commonly used pharmacokinetic models. They divide the body into hypothetical compartments that are not anatomically defined but represent groups of tissues with similar drug distribution characteristics.
"The body is treated as a series of compartments, often depicted as boxes, between which drug moves reversibly."
Key Assumptions
- Drug distributes instantly within each compartment (homogeneous mixing)
- Drug transfer between compartments follows first-order kinetics
- Elimination occurs from the central compartment
A. One-Compartment Open Model
The simplest model. The entire body is treated as a single, homogeneous compartment.
Assumptions:
- Drug distributes instantaneously throughout the body
- Elimination is first-order from this single compartment
- "Open" = drug can leave (be eliminated) from the system
IV Bolus Administration:
$$C(t) = C_0 \cdot e^{-kt}$$
Where:
- $C_0$ = initial plasma concentration (= Dose/V)
- $k$ = elimination rate constant
- $t$ = time post-dose
On a semi-log plot, this gives a straight line with slope = −k/2.303
Parameters:
| Parameter | Formula |
|---|---|
| Elimination rate constant (k) | = CL / V |
| Half-life (t½) | = 0.693 / k = 0.693 × V / CL |
| Volume of distribution (V) | = Dose / C₀ |
| Clearance (CL) | = k × V |
| AUC₀→∞ | = C₀ / k = Dose / CL |
IV Infusion (One-Compartment):
$$C_{ss} = \frac{R_0}{CL}$$
Where R₀ = infusion rate (dose/time)
B. Two-Compartment Open Model
The body is divided into two compartments:
- Central compartment (Compartment 1): Plasma + highly perfused tissues (liver, lungs, kidneys, heart)
- Peripheral compartment (Compartment 2): Poorly perfused tissues (muscle, fat, bone)
Drug Distribution:
- Drug distributes from central → peripheral compartment (rate constant k₁₂)
- Drug redistributes from peripheral → central (rate constant k₂₁)
- Drug is eliminated only from the central compartment (rate constant k₁₀)
Plasma Concentration–Time Equation (IV bolus):
$$C(t) = A \cdot e^{-\alpha t} + B \cdot e^{-\beta t}$$
Where:
- α (distribution rate constant): rapid decline phase = distribution
- β (elimination rate constant): slow decline phase = terminal elimination
- A and B = intercepts of the two exponential phases on the y-axis
The Bi-exponential Curve:
- Phase 1 (α phase): Rapid initial fall in plasma concentration as drug distributes from central to peripheral compartment
- Phase 2 (β phase): Slower terminal decline reflecting true elimination once distribution equilibrium is reached
Clinical Significance:
- Drugs like gentamicin, vancomycin, and propranolol follow two-compartment kinetics
- This explains why toxicity can occur after rapid IV bolus (high initial central compartment concentration)
- Loading doses must account for the volume of the central compartment
C. Three-Compartment Open Model (Multi-compartment)
Adds a third, deep peripheral compartment representing very poorly perfused tissues (e.g., bone, fat depots, CNS for some drugs).
$$C(t) = A \cdot e^{-\alpha t} + B \cdot e^{-\beta t} + G \cdot e^{-\gamma t}$$
- Three exponential phases: α (rapid distribution), β (slower redistribution), γ (terminal elimination)
- Applies to drugs like thiopental, amiodarone, and certain cytotoxics
Comparison of Compartment Models
| Feature | One-Compartment | Two-Compartment | Three-Compartment |
|---|---|---|---|
| Compartments | 1 | 2 | 3 |
| Phases | 1 (monoexponential) | 2 (biexponential) | 3 (triexponential) |
| Complexity | Simple | Moderate | Complex |
| Examples | Aminoglycosides (simple) | Propranolol, digoxin | Amiodarone, thiopental |
| Semi-log plot | Straight line | Biphasic curve | Triphasic curve |
6. Four Primary Pharmacokinetic Parameters
"The following are the four most important parameters governing drug disposition." — Goodman & Gilman's
1. Bioavailability (F)
- The fraction of administered dose that reaches the systemic circulation unchanged
- IV administration: F = 1.0 (100%)
- Oral drugs subject to first-pass metabolism have reduced F $$F = \frac{AUC_{oral}}{AUC_{IV}} \times \frac{Dose_{IV}}{Dose_{oral}}$$
2. Volume of Distribution (V_d)
$$V_d = \frac{\text{Amount of drug in body}}{C_{plasma}}$$
- A hypothetical volume — does not correspond to a real anatomical volume
- Large V_d → drug widely distributed in tissues (e.g., chloroquine: ~15,000 L; digoxin: ~667 L in 70 kg person)
- Small V_d → drug stays in plasma (e.g., warfarin, heparin)
3. Clearance (CL)
$$CL = \frac{\text{Rate of elimination}}{C}$$
- Volume of plasma cleared of drug per unit time (L/hr or mL/min)
- Most important parameter for designing maintenance dosing regimens
- At steady state: Dosing rate = CL × C_ss
- Hepatic clearance (most drugs), renal clearance (hydrophilic drugs), pulmonary clearance
4. Half-Life (t½)
$$t_{1/2} = \frac{0.693 \times V_d}{CL}$$
- Time for plasma concentration to fall by 50%
- Determines:
- Dosing interval
- Time to reach steady state (~4–5 × t½)
- Time for drug washout after discontinuation
- Increases if V_d increases OR CL decreases (e.g., renal/hepatic disease)
7. Pharmacokinetic Study Design
A pharmacokinetic study systematically measures drug concentrations in biological fluids over time to determine PK parameters for a new or existing drug.
Types of Pharmacokinetic Studies
| Study Type | Purpose |
|---|---|
| Single-dose PK study | Determines C_max, t_max, AUC, t½, V_d, CL after one dose |
| Multiple-dose / steady-state study | Evaluates drug accumulation, steady-state concentrations, trough/peak levels |
| Bioavailability study | Measures F by comparing AUC of test vs. IV reference |
| Bioequivalence study | Compares generic vs. brand formulation (regulatory requirement) |
| Food-effect study | Determines if food alters drug absorption |
| Drug interaction study | Assesses effect of co-medications on PK parameters |
| Special populations study | PK in renal/hepatic impairment, elderly, pediatrics, pregnancy |
| Population PK study | Mixed-effects modeling of PK variability in large patient groups |
General Design Steps
- Subject selection: Healthy volunteers (Phase I) or patients (Phase II–IV)
- Dosing: Defined route, dose, formulation, fed/fasted state
- Sample collection: Serial blood (plasma/serum) and/or urine samples at pre-specified time points
- Bioanalytical method: Validated LC-MS/MS or immunoassay to measure drug/metabolite concentrations
- PK analysis:
- Non-compartmental analysis (NCA): Calculates AUC (trapezoidal rule), C_max, t_max, t½ directly from data
- Compartmental analysis: Fits data to one- or two-compartment model equations
- Population PK: NONMEM software; accounts for covariates (weight, age, creatinine)
- Parameter reporting: AUC₀–t, AUC₀–∞, C_max, t_max, t½, V_d, CL, bioavailability
Pharmacokinetic Study vs. Pharmacodynamic Study
| Aspect | PK Study | PD Study |
|---|---|---|
| Measures | Drug concentration vs. time | Drug effect vs. concentration |
| Samples | Blood, urine, tissue | Clinical endpoints, biomarkers |
| Output | AUC, CL, V_d, t½ | EC₅₀, E_max, Emin |
8. ADME — The Four Pharmacokinetic Processes
A. Absorption
- Movement of drug from administration site → systemic circulation
- Governed by: lipid solubility, molecular weight, degree of ionization (Henderson-Hasselbalch equation), formulation
- Mechanisms: Passive diffusion (majority), active transport, facilitated diffusion, endocytosis
- First-pass effect: Hepatic pre-systemic metabolism reducing oral bioavailability
B. Distribution
- Drug movement from blood → extracellular fluid and tissues
- Affected by: protein binding (albumin for acidic drugs; α₁-acid glycoprotein for basic drugs), tissue perfusion, lipid solubility, blood-brain barrier, placental barrier
- Volume of distribution is the key parameter
C. Metabolism (Biotransformation)
- Primarily hepatic; converts lipophilic → hydrophilic metabolites
- Phase I reactions: Oxidation, reduction, hydrolysis via CYP450 enzymes (CYP3A4 most important)
- Phase II reactions: Conjugation (glucuronidation, sulfation, acetylation) → inactive, water-soluble products
D. Elimination (Excretion)
- Renal excretion: Glomerular filtration + tubular secretion − tubular reabsorption
- Lipophilic drugs must first be metabolized; hydrophilic drugs excreted unchanged
- Ion trapping: alkaline urine favors excretion of weak acids; acidic urine favors excretion of weak bases
- Biliary/fecal excretion: Large molecular weight drugs (enterohepatic cycling)
- Other routes: Lungs (volatile agents), breast milk, saliva, sweat
Quick-Reference Summary Table
| Parameter | Definition | Units | Formula |
|---|---|---|---|
| F (Bioavailability) | Fraction reaching systemic circulation | dimensionless (0–1) | AUC_oral/AUC_IV |
| V_d (Volume of distribution) | Apparent volume containing drug | L or L/kg | Dose/C₀ |
| CL (Clearance) | Volume cleared per unit time | L/hr, mL/min | Dose/AUC or k × V_d |
| t½ (Half-life) | Time for 50% concentration decrease | hours | 0.693 × V_d/CL |
| C_ss (Steady state) | Plateau concentration at steady state | mg/L | F × Dose/(CL × τ) |
| AUC | Total drug exposure | mg·hr/L | Dose/CL |
| k (Elim. rate constant) | Fraction eliminated per unit time | hr⁻¹ | CL/V_d or 0.693/t½ |
Sources: Goodman & Gilman's The Pharmacological Basis of Therapeutics (13th ed.); Lippincott Illustrated Reviews: Pharmacology (8th ed.)
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