3.4 Pharmacokinetics & Narrow Therapeutic Index Drugs

3.4 Pharmacokinetics & Narrow Therapeutic Index Drugs

Quick Reference: Pharmacokinetics (PK) quantitatively defines drug movement into, through, and out of the body via Absorption, Distribution, Metabolism, and Excretion (ADME). Mastery of PK equations, elimination rates, steady-state kinetics, and Therapeutic Drug Monitoring (TDM) protocols is critical for managing narrow therapeutic index (NTI) drugs safely.

Mathematical modeling of PK parameters enables clinical pharmacists to individualize dosing regimens, optimize therapeutic efficacy, and prevent severe adverse drug reactions.

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Fundamental Pharmacokinetic Parameters: ADME

1. Absorption & Bioavailability ($F$)

Bioavailability ($F$) is the fraction of an administered drug dose that reaches the systemic circulation in an active, unchanged form.

$$F = \frac{\text{AUC}_{\text{oral}}}{\text{AUC}_{\text{IV}}} \times 100\%$$

• Intravenous (IV) Route: $F = 1.0$ (100% bioavailability by definition).
• Oral Route Factors: Incomplete GI mucosal absorption, intestinal efflux transporters (P-glycoprotein), and first-pass hepatic metabolism (CYP3A4 extraction) reduce $F$ (e.g., morphine $F \approx 30\%$, propranolol $F \approx 25\%$).

2. Distribution & Volume of Distribution ($V_d$)

Volume of Distribution ($V_d$) is a theoretical volume relating the total amount of drug in the body ($D_{\text{body}}$) to its measured plasma concentration ($C_p$):

$$V_d = \frac{D_{\text{body}}}{C_p}$$

• Low $V_d$ ($< 5\text{ L}$ or $0.07\text{ L/kg}$): Confined to vascular plasma space. Highly plasma protein-bound (e.g., Warfarin $V_d \approx 8\text{ L}$). Acidic drugs bind primarily to Albumin.
• Moderate $V_d$ ($10–42\text{ L}$): Distributed throughout extracellular or total body water (e.g., Gentamicin $V_d \approx 0.25\text{ L/kg}$). Basic drugs bind to Alpha-1-Acid Glycoprotein.
• High $V_d$ ($> 42\text{ L}$ or $> 0.7\text{ L/kg}$): Extensively sequestered in peripheral tissue, fat, or cell membranes (e.g., Digoxin $V_d \approx 7\text{ L/kg}$, Chloroquine $V_d > 100\text{ L/kg}$). Hemodialysis is ineffective for high $V_d$ drug clearance.

3. Metabolism (Biotransformation)

• Phase I Reactions: Oxidation, reduction, hydrolysis. Introduced or unmasked polar functional groups ($-OH, -NH_2, -SH$). Mediated predominantly by microsomal Cytochrome P450 (CYP) enzymes.
  • Major Isoforms: CYP3A4 (metabolizes >50% of drugs), CYP2D6, CYP2C9, CYP2C19, CYP1A2.
  • Inducers ($\downarrow$ drug concentration): Rifampicin, Carbamazepine, Phenytoin, St John's Wort, Phenobarbital.
  • Inhibitors ($\uparrow$ toxicity risk): Ketoconazole, Erythromycin, Clarithromycin, Ciprofloxacin, Omeprazole, Grapefruit juice (intestinal CYP3A4).
• Phase II Reactions: Conjugation with endogenous polar substrates (Glucuronidation, Sulfation, Acetylation, Glutathione conjugation) producing inactive, hydrophilic metabolites excreted renally.

4. Clearance ($Cl$) & Elimination

Clearance ($Cl$) is the volume of plasma completely cleared of drug per unit of time (e.g., mL/min or L/h). Total systemic clearance is additive:

$$Cl_{\text{total}} = Cl_{\text{renal}} + Cl_{\text{hepatic}} + Cl_{\text{other}}$$

Renal elimination rate depends on Glomerular Filtration Rate (GFR), active tubular secretion, and passive tubular reabsorption (influenced by urinary pH: alkalinisation accelerates weak acid excretion).

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Quantitative Kinetics & Dosing Regimens

First-Order vs. Zero-Order Kinetics

• First-Order Kinetics (Linear PK):
  • A constant fraction (percentage) of drug is eliminated per unit time.
  • Elimination rate is directly proportional to plasma concentration ($C_p$).
  • Half-life ($t_{1/2}$) remains constant regardless of dose.
• Zero-Order Kinetics (Non-Linear / Capacity-Limited PK):
  • A constant amount (mass) of drug is eliminated per unit time due to saturation of metabolic enzymes or clearance mechanisms.
  • Clearance decreases and $t_{1/2}$ increases as plasma concentration rises.
  • Clinical Examples: Phenytoin (at therapeutic ranges), Ethanol, high-dose Aspirin.

Key Quantitative Equations

1. Elimination Rate Constant ($k_e$): $$k_e = \frac{Cl}{V_d}$$
2. Elimination Half-Life ($t_{1/2}$): $$t_{1/2} = \frac{\ln(2)}{k_e} = \frac{0.693 \times V_d}{Cl}$$
3. Time to Steady-State ($C_{ss}$): Achieved after 4 to 5 half-lives ($4-5 \times t_{1/2}$) of constant dosing.
4. Maintenance Dose ($MD$): $$MD = \frac{C_{ss} \times Cl \times \tau}{F}$$ (where $\tau$ is the dosing interval)
5. Loading Dose ($LD$): $$LD = \frac{C_{ss} \times V_d}{F}$$ (Used to immediately attain therapeutic concentrations for drugs with long $t_{1/2}$)

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Therapeutic Drug Monitoring (TDM) & Narrow Therapeutic Index (NTI) Drugs

Narrow Therapeutic Index drugs possess a narrow margin between efficacy and life-threatening toxicity ($TI < 2$). TDM optimizes individual patient dosing via precise serum concentration monitoring.

Clinical TDM Sampling Rules

1. Steady-State Confirmation: Always sample after achieving steady state ($4-5 \times t_{1/2}$), unless acute toxicity is suspected.
2. Trough Sampling: Draw blood samples within 30 minutes immediately before administering the next scheduled dose for most drugs (vancomycin, gentamicin, phenytoin).
3. Distribution Phase Delay: For drugs with prolonged distribution phases (digoxin, lithium), delay sampling until tissue distribution equilibrium is complete (6–8 hours for digoxin, 12 hours for lithium).