Biopharmaceutics and Pharmacokinetics Study Guide

Course Overview

• Course Title: PSW 313: Biopharmaceutics/Pharmacokinetics

• Instructor: Dr. G. Acquaah-Mensah

• Focus: Drug Elimination and Clearance

Objectives / Overview

• Key Topics:

  • Drug Excretion

  • Henderson Hasselbalch Equations

  • Clearance Models:

  • Compartmental Models

  • Physiologic Models and Extraction Ratio

  • Model-Independent Approaches

  • Renal Clearance

  • More on Compartmental Models

Drug Elimination: Introduction

• Definition of Drug Excretion:

  • Removal of unchanged drug, primarily via kidneys but also possible via lungs, breast milk, sweat, etc.

• Definition of Drug Biotransformation:

  • Enzymatic modification of the drug facilitating its excretion or altering pharmacodynamic potential.

  • Enzymes are typically hepatic but may be located in other tissues.

• Total Drug Elimination:

  • Formula: Drug Elimination = Drug Excretion + Biotransformation

• Elimination Rate Dynamics:

  • Unlike clearance, the elimination rate for first order processes varies based on the drug amount present at a given time.

Drug Excretion Mechanisms

• Schematic of Nephron Unit:

  • Pathway includes TO URETER, RENAL VEIN, RENAL ARTERY

  • Key Mechanisms:

  • Glomerular Filtration:

    • Involves a glomerular capillary network and Bowman’s capsule.

    • Small molecules free not protein bound.

    • Uses Inulin and Creatinine

  • Active Secretion:

    • Accommodates specific transport processes, requiring energy.

    • They go from a region of lower concentration to a region of higher concentration. Carrier mediated transport again concentration gradient.

    • Protein bound drugs can be excreted vi Active Secretion

    • Iodopyracet and p-amino-hippuric acid are used in this

    • Active secretion strips the drug of protein so it can be filtered. This process is crucial for eliminating waste products and ensuring that free drug levels remain manageable within the bloodstream.

  • Tubular Resorption:

    • Reabsorption of substances back into blood.

    • This can either be passive or active.

    • Unionized drugs are more lipid soluble therefore more absorbed.

    • The extent of dissociation is governed by the Henderson-Hasslebalch equation. Factors such as pH and pKa values play a crucial role in determining the degree of ionization, ultimately influencing the bioavailability of the drug.

Drug Elimination: The Kidney and Blood Supply

• Anatomy Reference: Basic understanding of kidney

• Renal Blood Flow (RBF):

  • Represents the volume of blood flowing through the kidney blood vessels per unit of time.

• Renal Plasma Flow (RPF):

  • RPF Formula: RPF = RBF (1 - Hematocrit)

  • Hematocrit (Hct) Assumption: Approximately 45% in average adults.

• Key Measurements:

  • Glomerular Filtration Rate (GFR): ~ 125 mL/min.

  • Filtration Fraction:

  • Formula: Filtration Fraction = GFR / RPF

Drug Elimination: The Kidney and Urine Formation

• Kidney Functions:

  • Regulation of fluid volume and various solute and electrolyte levels.

• GFR Regulation:

  • Controlled by hydrostatic pressure differences in the glomerulus, starting from an arterial pressure of approximately 100 mmHg, which drops to ~50 mmHg in the glomerulus.

• Average Urine Volume:

  • ~1-1.5 L/day.

Drug Elimination: The Kidney and Drug Excretion

• Components of Renal Drug Excretion:

  • Composite of glomerular filtration, active tubular secretion, and tubular reabsorption.

• Small Molecule Filtration:

  • Most small molecules with molecular weight (MW) < 500 undergo glomerular filtration.

• Proteins in Filtration:

  • Proteins and protein-bound drugs do not undergo glomerular filtration.

• GFR Correlation:

  • GFR of a drug correlates with the free drug levels in the blood.

• Inulin and Creatinine:

  • Neither are actively secreted nor reabsorbed; hence, their clearances reflect GFR (approximately 125 – 130 mL/min).

Drug Elimination: The Kidney and Drug Excretion II

• Active Tubular Secretion Mechanics:

  • A specialized, energy-consuming transport process that is carrier-mediated and occurs against concentration gradients.

  • Dependency:

  • It relies on renal blood flow.

• Measurement Agents:

  • Iodopyracet and p-amino-hippuric acid are cleared by glomerular filtration and actively secreted by tubule cells; their clearances indicate effective renal plasma flow (ERPF).

Drug Elimination: The Kidney and Drug Excretion III

• Carrier System Characteristics:

  • Saturable process subject to competition, especially with structurally similar drugs.

  • Distinction between carrier systems for weak acids and weak bases.

• Protein Binding Impact:

  • Drugs bound to plasma proteins dissociate rapidly in renal secretion; thus, protein binding does not significantly affect the elimination half-life of mainly secreted drugs.

Drug Elimination: The Kidney and Drug Excretion IV

• Tubular Reabsorption Types:

  • Can be either active or passive.

• Unionized Drugs:

  • Undissociated (unionized) drugs are more lipid-soluble and permeate cell membranes more easily, thus reabsorbed more efficiently.

• Dissociation Extent:

  • Governed by the Henderson-Hasselbalch equation, which relates urine pH and the drug's pKa.

Henderson-Hasselbalch Equation for Weak Acids

• Equation Formulation:

  • $ext{pH} - ext{pKa} = rac{ ext{ionized}}{ ext{unionized}}$

  • Expressed as:

  • $ext{Fraction of ionized drug} = rac{1 + 10^{( ext{pH} - ext{pKa})}}{1 + 10^{( ext{pH} - ext{pKa})}}$

Henderson-Hasselbalch Equation for Weak Bases

• Equation Formulation:

  • $ext{pKa} - ext{pH} = rac{ ext{ionized}}{ ext{unionized}}$

  • Expressed as:

  • $ext{Fraction of ionized drug} = rac{1 + 10^{( ext{pKa} - ext{pH})}}{1 + 10^{( ext{pKa} - ext{pH})}}$

Example Calculations

Phenobarbital Example

• Given:

  • Weak acid with pKa of 7.2.

  1. Percent ionized in blood (pH 7.4): Calculation yields 61.48% ionized.

  2. Percent ionized in urine (pH 6.4): Calculation yields 13.67% ionized.

Itraconazole Example

• Given:

  • Weak base with pKa of 3.8.

  1. Percent ionized in blood (pH 7.4): Calculation yields 0.025% ionized.

  2. Percent ionized in stomach (pH 1.8): Calculation yields 99% ionized.

Clinical Application Example

• Patient Scenario:

  • 39-year-old woman with phenobarbital overdose. Urine pH changes from 5.8 to 8 following treatment.

  • Sodium Bicarbonate Administration:

  • Focus on resorption geneality calculation (30% phenobarbital is eliminated).

  • We use the formula for U/P Ratio:

  • $rac{(1 + 10^{( ext{pH}<em>{ ext{urine}} - ext{pKa})})}{(1 + 10^{( ext{pH}</em>{ ext{plasma}} - ext{pKa})})}$

Drug Clearance: Models

• Compartment Model:

  • $C_{I} = KVD$

• Physiologic Model:

  • $C_{I} = Q(ER)$

General Definitions of Clearance

• Total Clearance (ClT) Formula:

  • $ClT = ext{elimination rate} / ext{plasma concentration (C}_p ext{)}$

  • Rearranged:

  • $ext{elimination rate} = C<em>p imes Cl</em>T$

• Clearance Normalization:

  • Typically normalized to body weight, same as Volume of Distribution (VD).

Organ Clearance Models

• Physiological Approach:

  • Involves invasive parameters such as blood flow rate and extraction ratio (ER).

• General Clearance Formula:

  • $ext{Clearance} = Q imes ER$

Extraction Ratio Explanation

• Definition:

  • Ratio of concentrations of a drug in blood entering an organ (Ca) vs. leaving it (Cv).

  • $ER = rac{C<em>a - C</em>v}{C_a}$

  • The relationship between clearance and blood flow rate: $ext{Clearance} = Q$

Model-Independent Method for Clearance

• Definition of the Area Under the Curve (AUC):

  • Determined from plasma concentration-time curves.

  • Clinical importance: No need to calculate VD or k.

  • General Formula:

  • $Cl<em>T = rac{D</em>0}{ ext{AUC}}$

Renal Clearance Insights

• Renal Clearance Formula:

  • $C<em>R = rac{ ext{Rate of drug excreted in urine}}{C</em>p}$

  • Where:

  • $C_p = ext{Drug concentration in plasma}$

  • $Q_u = ext{Rate of urine flow}$

  • $C_u = ext{Drug concentration in urine}$

Renal Clearance Ratio

• Measurement Tools:

  • Inulin, which is solely cleared through glomerular filtration, serves as a reference.

• Calculative Index:

  • $ext{Clearance Ratio} = rac{C<em>{l, ext{drug}}}{C</em>{ ext{inulin}}}$

  • Interpretations:

  • If $C<em>{l, ext{drug}} / C</em>{ ext{inulin}} = 1$: ONLY filtration.

  • If < 1: Partial reabsorption.

  • If > 1: Active secretion.

Renal Clearance by Filtration Only

• Using Compartment Model for GFR:

  • $rac{dDU}{dt} = k<em>e V</em>D C_p$

• Using Physiologic Model:

  • $rac{dDU}{dt} = C<em>R C</em>p$

Renal Clearance by Filtration and Reabsorption

• Reabsorption Ratio Representation:

  • $C_R = GFR$

  • Where $f_r$ is the renal reabsorption ratio impacting overall clearance.

Practical Examples for Clearance

• Example Given:

  • Drug elimination via renal excretion and hepatic metabolism.

  • Calculate total body clearance, renal clearance, nonrenal clearance with provided parameters (e.g., total clearance normal values, % drug recovery).

Moderate Renal Failure Application

• Patient Case Study:

  • Adjustments in dose for renal function at 16% normal.

• Clearance Computation: Calculate systemic clearance using both renal and hepatic rates.

Drug Clearance: t1/2 and Volume of Distribution

• Total Clearance Relations:

  • $Cl<em>T = k V</em>D$

  • Meaning the total body clearance incorporates both the volume of distribution (V_D) and the elimination half-life (t1/2).

• Effect of Kidney Insufficiency:

  • May lead to decreased total clearance, subsequently increasing half-life.

Multicompartmental Models in Drug Clearance

• Central Compartment Understanding:

  • Clearance emerges from plasma perfusion in the kidney and liver, entities considered as part of the central compartment.

• Key Formula for Two-Compartment Models:

  • $Cl<em>T = k V</em>p$

  • Where $V_p$ represents the volume of the central compartment.

  • Other relationships include $Cl<em>T = b V</em>D^{\beta}$

  • Renal clearance expressed as $Cl<em>R = k</em>e V_p$

Summary

• Understanding drug elimination is essential in clinical applications involving renal function and pharmacokinetics.

• The interplay of kidney physiology, clearance mechanisms, and mathematical representations is vital for effective treatment regimens and monitoring of drug levels in patients.