B Pharmacy Sem 6: Biopharmaceutics & Pharmacokinetics

Subject 4: Biopharmaceutics & Pharmacokinetics

Unit 1 – Basic Principles (absorption, distribution)

Unit 2 – Elimination, Bioavailability, Bioequivalence

Unit 3 – Pharmacokinetic Models & Parameters (t₁/₂, Vd, AUC, clearance)

Unit 4 – Multi-compartment Models & Dosing Regimens

Unit 5 – Non‑linear Pharmacokinetics (Michaelis–Menten kinetics)

Unit 1: Basic Principles (Absorption & Distribution)

This unit introduces how drugs enter the body and reach their sites of action, focusing on the factors and processes that govern absorption and distribution—presented for easy learning and recall.

4.1 Absorption

The process by which a drug moves from its site of administration into the systemic circulation.

• Routes of Administration

  • Enteral: Oral, sublingual, rectal

  • Parenteral: IV, IM, SC

  • Others: Transdermal, inhalational

• Mechanisms of Drug Movement

  • Passive Diffusion (most common)

    • Driven by: Concentration gradient

    • Influenced by: Lipid solubility (↑ Log P ↑ diffusion), molecular size, degree of ionization (pH partitioning)

  • Facilitated & Active Transport

    • Requires: Carrier proteins (e.g., uptake of levodopa via LAT1)

    • Active: Energy‑dependent, saturable (e.g., P-gp efflux limits oral bioavailability of many drugs)

• Absorption Rate & Extent

  • Rate: Determines onset of action

  • Extent (F): Fraction of dose reaching systemic circulation (bioavailability)

  • Factors Affecting:

    • Gastric emptying & intestinal transit time

    • First‑pass metabolism (hepatic & gut wall)

    • Formulation factors (particle size, excipients)

4.2 Distribution

The reversible transfer of drug from the systemic circulation to tissues and organs.

• Volume of Distribution (Vd)

  • Definition: Apparent volume that would be needed to contain the drug amount in the body at the same concentration as in plasma

  • Interprets: Tissue binding vs. plasma binding

    • Low Vd (< 10 L): Largely confined to plasma (e.g., warfarin)

    • High Vd (> 40 L): Widely distributed into tissues (e.g., amiodarone)

• Plasma Protein Binding

  • Proteins: Albumin (acidic drugs), α₁‑acid glycoprotein (basic drugs)

  • Implication: Only unbound (free) drug is pharmacologically active and cleared

• Tissue Binding & Barriers

  • Lipid‑rich tissues: Lipophilic drugs accumulate in fat (e.g., diazepam)

  • Barriers:

    • Blood–Brain Barrier: Tight junctions + P-gp efflux (limits CNS penetration)

    • Placental Barrier: Partial; many drugs cross to fetus

• Perfusion vs. Permeation

  • Perfusion‑rate limited: Distribution determined by blood flow (e.g., heart, liver, kidneys)

  • Permeation‑rate limited: Cell membrane permeability is rate‑limiting (e.g., to CNS)

Key Exam Tips

• Absorption: “Rate for onset; extent (F) for amount”—think first‑pass, pH partitioning.

• Distribution: Vd tells you where drug goes—small Vd = plasma, large Vd = tissues.

• Binding: Only free drug acts & is eliminated—be mindful of drug–drug displacement interactions.

• Barriers: Remember P‑gp and tight junctions at BBB; fetal exposure via placenta is partial.

Unit 2: Elimination, Bioavailability & Bioequivalence

This unit focuses on how drugs are removed from the body and how bioavailability and bioequivalence assess the performance of different formulations—presented for clear understanding and quick recall.

4.2 Elimination

The irreversible removal of drug from the systemic circulation, comprising metabolism and excretion.

• Metabolism (Biotransformation)

  • Phase I Reactions

    • Processes: Oxidation (CYP450), reduction, hydrolysis

    • Outcome: Introduce or expose functional groups (–OH, –NH₂)

    • Example: Codeine → morphine (O‑demethylation)

  • Phase II Reactions

    • Processes: Conjugation (glucuronidation, sulfation, acetylation)

    • Outcome: Increase water solubility for excretion

    • Example: Morphine → morphine‐6‐glucuronide

• Excretion

  • Renal (primary route)

    • Glomerular Filtration: Free drug passes into filtrate

    • Tubular Secretion: Active transport of organic acids/bases (e.g., penicillins)

    • Reabsorption: Lipophilic drugs reabsorbed passively

  • Non‐Renal

    • Biliary: Large, polar conjugates excreted into bile → feces

    • Pulmonary: Volatile anesthetics eliminated via lungs

    • Others: Sweat, saliva, milk

• Clearance (Cl)

  • Definition: Volume of plasma cleared of drug per unit time (L/h or mL/min)

  • Total Clearance: Sum of clearances via all routes

  • Intrinsic Clearance: Liver’s inherent ability to eliminate drug (independent of blood flow)

  • Extraction Ratio (E): Fraction removed during one pass through eliminating organ

    • High‑extraction drugs (E > 0.7): Clearance ≈ hepatic blood flow

    • Low‑extraction drugs (E < 0.3): Clearance ≈ intrinsic clearance × fₕ

4.3 Bioavailability (F)

The fraction of an administered dose reaching the systemic circulation unchanged.

• Absolute Bioavailability

  $$F = \frac{\text{AUC}_{\text{oral}} \,/\, \text{Dose}_{\text{oral}}} {\text{AUC}_{\text{IV}} \,/\, \text{Dose}_{\text{IV}}}$$

  • Uses: Compare oral vs. IV formulation

• Relative Bioavailability

  • Compares two non‐IV formulations (e.g., two tablets)

• Factors Affecting F

  • First‑pass metabolism (hepatic & gut wall)

  • Drug formulation (particle size, excipients)

  • Gastrointestinal pH & motility

4.4 Bioequivalence

Assessment showing that two formulations of the same drug have no significant difference in rate and extent of absorption.

• Key Parameters

  • Cₘₐₓ: Peak plasma concentration

  • Tₘₐₓ: Time to reach Cₘₐₓ

  • AUC: Overall exposure

• Regulatory Criteria

  • 90 % confidence interval for the ratio (test/reference) of Cₘₐₓ and AUC must lie within 80–125 %

• Applications

  • Approval of generic drugs

  • Reformulations (e.g., tablet vs. capsule)

Key Exam Tips

• Clearance vs. half‑life: Cl and Vd determine t₁/₂ (t₁/₂ = 0.693 × Vd/Cl).

• High‑ vs. low‑extraction: Know which drugs are flow‑limited vs. capacity‑limited.

• Bioavailability formula: Always normalize AUC by dose.

• Bioequivalence window: 80–125 % for Cₘₐₓ and AUC—remember for generics.

Unit 3: Pharmacokinetic Models & Parameters (t₁/₂, Vd, AUC, Clearance)

This unit introduces basic compartmental modeling—how we describe drug concentration over time—and the four cornerstone pharmacokinetic parameters you must master for exams.

4.3.1 Pharmacokinetic Models

One‑Compartment Model (IV Bolus, First‑Order Elimination)

• Assumption: Body behaves as a single, well‑mixed compartment.

• Concentration–Time Profile:

  $$C(t) = C_0 \,e^{-k\,t}$$

  where C₀ is the initial concentration; k is the elimination rate constant.

• Use: Simplest model—suitable when distribution is rapid relative to elimination.

Zero‑Order vs. First‑Order Kinetics

• First‑Order: Rate ∝ concentration (most drugs).

  $$\frac{dC}{dt} = -k\,C$$

• Zero‑Order: Constant rate (e.g., high‑dose phenytoin, ethanol).

  $$\frac{dC}{dt} = -k_0$$

4.3.2 Half‑Life (t₁/₂)

• Definition: Time for plasma concentration to fall by 50%.

• Formula (First‑Order):

  $$t_{1/2} = \frac{0.693}{k}$$

• Significance:

  • Determines dosing interval (≈ 3–5 × t₁/₂ to reach steady state).

  • Affected by both Vd and Clearance (t₁/₂ = 0.693 × Vd / Cl).

4.3.3 Volume of Distribution (Vd)

• Definition: Theoretical volume required to contain total drug amount at plasma concentration.

• Formula (IV Bolus):

  $$V_d = \frac{\text{Dose}}{C_0}$$

• Interpretation:

  • Low Vd (< 10 L): Drug largely in plasma (e.g., warfarin).

  • High Vd (> 40 L): Extensive tissue binding (e.g., amiodarone).

• Clinical Use:

  • Guides loading dose:

    $$\text{LD} = V_d \times C_{\text{target}}$$

4.3.4 Area Under the Curve (AUC)

• Definition: Total drug exposure over time.

• Calculation:

  • Non‑compartmental (Trapezoidal Rule): Sum of areas between measured concentrations.

• Units: Concentration × time (e.g., mg·h/L).

• Relation to Clearance:

  $$\text{AUC} = \frac{\text{Dose}}{\text{Cl}}$$

• Use:

  • Compare bioavailability (oral vs. IV).

  • Adjust dosing in renal/hepatic impairment.

4.3.5 Clearance (Cl)

• Definition: Volume of plasma cleared of drug per unit time.

• Formula:

  $$\text{Cl} = \frac{\text{Dose}}{\text{AUC}}$$

• Components:

  • Renal Clearance: filtration + secretion – reabsorption.

  • Hepatic Clearance: extraction by liver (Cl ≈ Qₕ × Eₕ for high‐extraction drugs).

• Clinical Significance:

  • Determines maintenance dose:

    $$\text{MD} = \text{Cl} \times C_{\text{target}}$$

Key Exam Tips

• Link parameters: t₁/₂ depends on Vd and Cl; AUC links dose to Cl.

• Formulas to memorize:

  • t₁/₂ = 0.693/k

  • Vd = Dose/C₀

  • Cl = Dose/AUC

• Model choice: One‑compartment gives exponential decline; recognize when zero‑order applies.

• Dose calculations: Use Vd for loading dose; Cl for maintenance dose.

Unit 4: Multi‑Compartment Models & Dosing Regimens

This unit expands on the one‑compartment framework to multiple compartments, then applies models to design dosing regimens that achieve and maintain therapeutic drug levels.

4.4.1 Multi‑Compartment Models

Two‑Compartment Model

• Concept: Body represented by a central compartment (plasma + highly perfused tissues) and a peripheral compartment (less‑perfused tissues).

• Phases of Concentration–Time Curve:

  1. Distribution Phase (α phase): Rapid decline as drug moves from central to peripheral.

  2. Elimination Phase (β phase): Slower decline once distribution equilibrium is reached.

• Mathematical Representation:

  $$C(t) = A\,e^{-\alpha t} \;+\; B\,e^{-\beta t}$$

  where A, B are intercepts; α, β are rate constants.

• Clinical Relevance:

  • Important for drugs with significant tissue binding (e.g., digoxin).

  • Guides interpretation of plasma levels and half‑lives (distribution vs. elimination half‑lives).

n‑Compartment Models

• Extension: More compartments (e.g., deep tissue depot) when needed.

• Use: Rare in routine dosing; applied in research and complex PK analyses.

4.4.2 Dosing Regimens

Designing dose amount and frequency to reach and maintain target plasma concentration (Cₜₐᵣgₑₜ).

Loading Dose (LD)

• Purpose: Rapidly achieve Cₜₐᵣgₑₜ before steady state.

• Formula:

  $$\text{LD} = \frac{V_d \times C_{\text{target}}}{F}$$

  where F is bioavailability (use 1 for IV).

Maintenance Dose (MD)

• Purpose: Replace drug eliminated to maintain steady‑state concentration.

• Formula:

  $$\text{MD} = \frac{\text{Cl} \times C_{\text{target}} \times \tau}{F}$$

  where τ is dosing interval.

Steady State & Fluctuation

• Time to Steady State: ≈ 3–5 × t₁/₂, independent of dose size.

• Peak–Trough Fluctuation: Controlled by dosing interval (shorter τ → less fluctuation).

Infusion Regimens

• Constant IV Infusion:

  • Rate in = Rate out at steady state.

  • Steady‑State Concentration:

    $$C_{ss} = \frac{\text{Rate of infusion}}{\text{Cl}}$$

• Loading Infusion:

  • Higher initial infusion rate to quickly reach Cₛₛ, then decrease to maintenance infusion rate.

Key Exam Tips

• Distinguish phases: In two‑compartment models, α = distribution, β = elimination.

• Loading vs. maintenance: LD uses Vd, MD uses Cl and τ.

• Infusion formulas: Cₛₛ = Rate/Cl; adjust Rate to achieve desired Cₛₛ.

• Steady state: Remember 3–5 half‑lives rule.

Unit 5: Non‑Linear Pharmacokinetics (Michaelis–Menten Kinetics)

This unit covers drugs whose elimination pathways become saturated, leading to dose‑dependent changes in clearance and half‑life. Understanding these kinetics is crucial for dosing drugs like phenytoin and ethanol.

4.5.1 Michaelis–Menten Elimination

• Concept: When metabolizing enzymes or transporters are saturated, elimination follows zero‑order above a certain concentration, rather than first‑order.

• Rate Equation:

  $$\text{Rate of elimination} = \frac{V_{\max} \times C}{K_m + C}$$

  • Vₘₐₓ: Maximum elimination rate (when enzymes saturated)

  • Kₘ: Drug concentration at which elimination rate is half Vₘₐₓ

  • C: Plasma concentration of drug

• Kinetic Phases:

  • First‑Order Region (C ≪ Kₘ): Rate ∝ C (linear)

  • Mixed Region (C ≈ Kₘ): Rate partly saturable

  • Zero‑Order Region (C ≫ Kₘ): Rate ≈ Vₘₐₓ (constant)

4.5.2 Clinical Examples

• Phenytoin

  • Therapeutic Range: 10–20 µg/mL, near Kₘ → small dose changes cause large concentration shifts

  • Implication: Careful monitoring; small dose increases can dramatically raise levels and toxicity

• Ethanol

  • Metabolism: Alcohol dehydrogenase follows saturation kinetics → constant rate of ~7–10 g/h at higher concentrations

• Aspirin (at high overdose levels)

  • Transition: From first‑order at low doses to zero‑order when metabolic pathways saturated

4.5.3 Pharmacokinetic Consequences

• Variable Half‑Life: t₁/₂ increases as C increases (no longer constant)

• Non‑Linear Dose–Response: Doubling the dose more than doubles the plasma concentration in the zero‑order region

• Accumulation Risk: Higher risk of toxicity with repeated dosing if near or above Kₘ

4.5.4 Dosing Considerations

• Therapeutic Drug Monitoring (TDM): Essential for drugs with narrow therapeutic index and non‑linear kinetics (e.g., phenytoin)

• Loading Doses: Calculated from Vd, but clearance changes with concentration—monitor and adjust

• Dose Adjustments: Small incremental changes; frequent level checks

Key Exam Tips

• Remember Vₘₐₓ and Kₘ: Kₘ analogous to “half‑speed” concentration.

• Identify drugs: Phenytoin and ethanol are classic examples.

• Clinical impact: Non‑linear → unpredictable concentration changes; necessitates monitoring.

• Half‑life isn’t constant: Emphasize changing t₁/₂ with dose.