Finals 05 Drug Elimination, Clearance, and Renal Clearance PDF

BSPH-3101 | BIOPHARMACEUTICS AND PHARMACOKINETICS Drug Elimination, Clearance, and Renal Clearance 1st SEMESTER | FINALS Instructor: Mrs. Jonah Micah T. Jimenez-Madera, RPh _____________________________________________________________________________________________ DRUG ELIMINATION...

BSPH-3101 | BIOPHARMACEUTICS AND PHARMACOKINETICS Drug Elimination, Clearance, and Renal Clearance 1st SEMESTER | FINALS Instructor: Mrs. Jonah Micah T. Jimenez-Madera, RPh _____________________________________________________________________________________________ DRUG ELIMINATION This refers to the irreversible removal of drugs For intravenous (IV) administration, the dose can be from the body, involving two main components: calculated as: excretion and biotransformation. 1. Excretion: This is the removal of the intact DOSE=Cl×AUC0-inf drug from the body. Nonvolatile and polar More generally, when the absolute bioavailability (F) is drugs are primarily excreted through the unknown or unspecified, the dose is calculated as: kidneys into the urine. Other excretion pathways include bile, sweat, saliva, milk, DOSE=FCl​×AUC0-inf and expired air (for volatile drugs like gaseous anesthetics and alcohol). Here, Cl/F is referred to as the “apparent clearance”. 2. Biotransformation (Drug Metabolism): This DRUG CLEARANCE process chemically converts the drug into This is a pharmacokinetic term describing the metabolites, usually through enzymatic elimination of drugs from the body without reactions, primarily in the liver. Other organs specifying the mechanisms involved. It considers like the kidneys, lungs, small intestine, and the entire body as a single drug-eliminating system. skin also play a role. Instead of measuring the drug elimination rate in Clearance terms of the amount of drug removed per unit time the total sum of all different clearance (e.g., mg/h), drug clearance is described in terms of processes in the body, including renal the volume of fluid cleared of the drug per unit clearance (ClR) and hepatic clearance (ClH), time. occurring in parallel with cardiac blood flow, except for lung clearance. There are several definitions of clearance: is a key concept in drug elimination, Volume-Based describing the volume of fluid cleared of the ○ The body is viewed as a space containing drug per unit time, often measured in liters a definite volume of fluid (apparent volume per hour (L/h). of distribution, V or VD) in which the drug It is crucial for determining the appropriate is dissolved. Clearance is the fixed volume drug dosage to achieve therapeutic goals, as of this fluid cleared of the drug per unit it accounts for all elimination processes. time. is more clinically relevant than half-life because it directly relates to the systemic Rate-Based exposure of a drug, making it essential for ○ Clearance can also be defined as the rate calculating doses to reach desired of drug elimination divided by the plasma therapeutic levels. drug concentration, expressing drug elimination in terms of the volume of The clearance of a drug (Cl) is crucial as it directly plasma cleared of the drug per unit time. relates to the dose administered and the overall systemic exposure (AUC0-inf) achieved. This The two definitions are similar because dividing the relationship is expressed by the equation: elimination rate by the plasma concentration yields the volume of plasma cleared of the drug per minute. Cl=AUC0-infDOSE​ In first-order elimination processes, clearance The systemic exposure (AUC0-inf) correlates with the remains constant even as the plasma drug drug’s efficacy and toxicity, making clearance the concentration decreases. most important pharmacokinetic (PK) parameter. Clearance is the product of the volume of NOTE: Knowing the therapeutic goal in terms of distribution (VD) and a rate constant (k), both AUC0-inf allows for precise dose calculation based on of which are constants in linear the clearance value. pharmacokinetics. Albano S. C. BSPH-3101 | BIOPHARMACEUTICS AND PHARMACOKINETICS Drug Elimination, Clearance, and Renal Clearance 1st SEMESTER | FINALS Instructor: Mrs. Jonah Micah T. Jimenez-Madera, RPh _____________________________________________________________________________________________ Elimination Rate Constant (k or kel): Example Problem The overall elimination rate constant is the sum of the renal (kR), hepatic (kH), and other elimination rate constants (kother). Clearance Total clearance is the sum of renal clearance (ClR), hepatic clearance (ClH), and other clearance processes (Clother). Renal clearance ClR=kR×V Hepatic clearance ClH=kH×V Total clearance Cl=k×V=(kR+kH+kother)×V For a one-compartment model: Total body clearance (Cl) is the product of the elimination rate constant (lz) and the volume of distribution (Vss). For a multicompartment model: Total body clearance is the product of the elimination rate constant from the central compartment (k10) and the central volume of distribution (Vc). Renal clearance ClR=kR×Vc Hepatic clearance ClH=kH×Vc Total clearance Cl=k10×Vc=(kR+kH+kother)×Vc Clearance values are often adjusted based on: body weight (ABW), or; body surface area Clearance varies best allometrically with ABW, typically using an exponent of 0.75. This approach helps in predicting clearance across different individuals, such as between children and adults. Albano S. C. BSPH-3101 | BIOPHARMACEUTICS AND PHARMACOKINETICS Drug Elimination, Clearance, and Renal Clearance 1st SEMESTER | FINALS Instructor: Mrs. Jonah Micah T. Jimenez-Madera, RPh _____________________________________________________________________________________________ CLEARANCE MODELS Extraction Ratio (E): Fraction of drug extracted Calculating clearance using a rate constant and a by the organ, calculated as volume of distribution assumes a specific compartmental model, which may not always be accurate. Noncompartmental pharmacokinetic (PK) Range of E: From 0 (no drug removed) to 1 (100% approaches estimate clearance directly from the drug removed). plasma drug concentration-time curve without needing to specify the number of compartments. The elimination rate may or may not follow Hepatic Clearance: first-order kinetics. ClH=QH×EH Total Clearance: Sum of hepatic clearance (ClH) and non-hepatic clearance (ClNH). Physiologic Approach: Depends on blood flow rate and the organ’s ability to eliminate the drug. Measurement: Requires invasive techniques for blood flow and extraction ratio; commonly used for hepatic clearance. Renal Clearance: Measured directly through plasma drug concentration and urinary drug excretion. PHYSIOLOGIC MODEL NONCOMPARTMENTAL METHODS Clearance in Compartment Models are commonly Clearance is the fraction of blood volume containing used to describe first-order drug elimination in models the drug that flows through the organ and is like the one-compartment model. eliminated per unit time. Clearance Calculation: Can be calculated Noncompartmental Method for any organ involved in drug elimination. Estimates clearance directly from the plasma Organs Involved: Kidneys (excretion) and drug concentration-time curve without liver (metabolism) are the primary organs. assuming the number of compartments. Physiologic Models: Based on drug clearance Model-Dependent Assumption: Despite being through individual organs or tissue groups. called “model-independent,” it assumes the terminal phase decreases log-linearly and Cl (organ) = Q(organ) × E(organ) requires PK linearity. Albano S. C. BSPH-3101 | BIOPHARMACEUTICS AND PHARMACOKINETICS Drug Elimination, Clearance, and Renal Clearance 1st SEMESTER | FINALS Instructor: Mrs. Jonah Micah T. Jimenez-Madera, RPh _____________________________________________________________________________________________ Advantages of Noncompartmental Approach: Formula: Clearance is the product of a rate 1. Easy calculation of clearance without constant and a volume of distribution. assumptions about rate constants. 2. Volume of distribution is related to Models: Various pharmacokinetic models systemic exposure and dose. describe concentration-time profiles, with 3. Robust estimation with rich sampling data formulas varying by intravenous or extravascular and minimal modeling. administration. Clearance Calculation: Determined from the One-Compartment Model time-concentration curve using the area under the Intravenous Administration curve (AUC). Concentration-Time Profile: Decreases in a straight line on a semilog plot, described by monoexponential decline. Model: Simplest one-compartment model, suitable for polar drugs eliminated in urine (e.g., aminoglycoside antibiotics). AUC Calculation: Uses the trapezoidal rule from Clearance Formula: Cl = λz × Vss zero to infinity, assuming first-order elimination for ○ λz: Rate constant describing extrapolation. concentration-time profile. Observed vs. Extrapolated AUC: AUC0-t is ○ Vss: Total volume of distribution. observed, while AUCt-∞ is extrapolated; good Terminal Half-Life: T1/2 = 0.693 / λz practice limits extrapolation to less than 20%. Steady-State Clearance: At steady state, the Oral Administration amount of drug administered equals the amount Clearance Formula: Cl/F = λz × Vss/F eliminated over the dosing interval. ○ Includes absorption process in addition to elimination Absorption vs. Elimination: ○ If faster absorption: λz describes elimination ○ If slower absorption (flip-flop Consistency in Linear PK: Clearance calculated kinetics): λz reflects absorption after a single dose and at steady state will be the same if the drug exhibits linear pharmacokinetics. Noncompartmental Approach After IV Administration: ○ Cl: Dose / AUC₀-inf COMPARTMENTAL METHODS ○ MRT: Mean residence time = 1 / λz ○ Vss: Dose / (AUC₀-inf × λz) After Extravascular Administration: ○ Cl/F: Dose / AUC₀-inf ○ Vss/F: Dose / (AUC₀-inf × λz) ○ MTT: Mean transit time = MAT + MRT Calculated Parameters Clearance: Direct measure of drug elimination MAT: Mean absorption time from the central compartment, which includes MRT: Mean residence time = 1 / λz Vss/F: Dose / (AUC₀-inf × λz) plasma and highly perfused tissues (kidney and MTT: Subtract MRT from MTT to get MAT liver). Central Compartment: Comprises plasma and rapidly equilibrating tissues like the kidney and liver. Albano S. C. BSPH-3101 | BIOPHARMACEUTICS AND PHARMACOKINETICS Drug Elimination, Clearance, and Renal Clearance 1st SEMESTER | FINALS Instructor: Mrs. Jonah Micah T. Jimenez-Madera, RPh _____________________________________________________________________________________________ Two-Compartment Model Changes in Parameters: Intravenous Administration Changes in clearance might not affect Concentration-Time Profile: Characterized by volume of distribution, and vice versa. two different exponentials/straight lines on a Changes in clearance or volume will affect semilog plot. rate constants. Model: Describes pharmacokinetics of less polar drugs that distribute into a poorly Clinical Example: perfused second compartment (e.g., Significant changes in body weight (ABW) vancomycin). can affect both clearance and volume without changing rate constants. Example: Sudden edema increases both Clearance Formula: Cl = k10 × Vc clearance and volume, but half-life remains ○ k10: Rate constant for unchanged. disappearance from central volume Implication: Dosing interval remains (Vc). constant, but the dose may need to be ○ Cld: Distributional clearance increased due to larger volume and between central (Vc) and peripheral clearance. (Vp) compartments. SUMMARY Biexponential Decline Methods of Calculation: λ1: Describes rapid distribution phase. Physiologic, compartmental, or λz: Describes terminal elimination phase. noncompartmental methods. All methods yield the same results if applied Equations for Rate Constants correctly with sufficient data. λ1: [((Cl + Cld)/Vc + Cld/Vp) + SQRT(((Cl + Cld)/Vc + Cld/Vp)² - 4 × Cl/Vc × Cld/Vp))] / 2 Noncompartmental Equations λz: [((Cl + Cld)/Vc + Cld/Vp) - SQRT(((Cl + Cld)/Vc + Cld/Vp)² - 4 × Cl/Vc × Cld/Vp))] / 2 Single Dose Steady-State Administration Conditions Cl = (Dose × F) / AUC₀-inf Cl = (Dose × F) / AUCt(ss) Half-Lives T1/2(λ1): 0.693 / λ1 Constant Infusion until Steady-State T1/2(λz): 0.693 / λz Cl = F × R₀ / Css Compartmental Equations Volume of Distribution For any compartment (Simplified) For Vss: Vc + Vp model with linear one-compartment pharmacokinetics models Noncompartmental Equations Cl = k10 × Vc Cl = λz × Vss Cl = Dose / AUC₀-inf MRT = Vss / Cl Where: λz = k10, Vss = Vc Compartmental Equations Cl = k10 × Vc Vss = Vc + Vp Organ-Specific Clearance: Based on blood flow and extraction ratio. MRT = (Vc + Vp) / (k10 × Vc) Hepatic clearance example ClH = QH × EH RELATIONSHIP BETWEEN RATE CONSTANTS, VOLUMES OF DISTRIBUTION, AND where QH is hepatic blood flow and EH is CLEARANCES hepatic extraction ratio. Clearance Formulas: Cl = k10 × Vc for two-compartment models. For drugs eliminated solely by the liver Simplifies to Cl = λz × Vss for Cl = ClH one-compartment models Parameters: Clearance and Volume: Considered independent. Rate Constants: Considered dependent (e.g., k10, λz). Albano S. C. BSPH-3101 | BIOPHARMACEUTICS AND PHARMACOKINETICS Drug Elimination, Clearance, and Renal Clearance 1st SEMESTER | FINALS Instructor: Mrs. Jonah Micah T. Jimenez-Madera, RPh _____________________________________________________________________________________________ THE KIDNEY Blood Supply The main drug-eliminating organs are the liver and Body Weight: Kidneys are 0.5% of total body kidney. weight. Cardiac Output: Receive 20%-25% of cardiac Kidney Functions: output. Excretory Role: Removes metabolic waste Renal Artery: Supplies blood, subdivides into products, maintains fluid volume and interlobar arteries and afferent arterioles. electrolyte balance. ○ Afferent Arterioles: Deliver blood to nephron's glomerulus (Bowman’s Endocrine Functions: capsule). 1. Secretion of Renin: Regulates ○ Filtration: Occurs in glomeruli within blood pressure. Bowman’s capsule. 2. Secretion of Erythropoietin: ○ Efferent Arterioles: Carry blood out, Stimulates red blood cell forming a capillary network around production. tubules. Anatomical Considerations Renal Blood Flow and Renal Plasma Flow Kidney Location: In the peritoneal cavity. RBF: Volume of blood through renal vasculature, Kidney Zones: Outer cortex and inner medulla. >1.2 L/min (1700 L/day) Nephrons RPF: RBF minus red blood cells volume. - Basic functional units ○ Formula: RPF = RBF × (1 - Hct). - ~1-1.5 million per kidney ○ Assumption: Hct ~0.45, resulting in RPF - responsible for waste removal and ~0.66 L/min (950 L/day) water/electrolyte balance Glomerular Filtration Rate (GFR) ○ Cortical Nephrons: Short loops of Henle. Average GFR: ~120 mL/min in adults. ○ Juxtamedullary Nephrons: Long loops of Filtration Fraction: GFR/RPF, indicating efficiency Henle for concentrated urine production. of filtration. Regulation of Renal Blood Flow (RBF) Blood Flow to an Organ ○ directly proportional to arteriovenous pressure difference, and; ○ inversely proportional to vascular resistance Renal Arterial Pressure ○ normally ~100 mm Hg ○ decreases to 45-60 mm Hg in glomerulus due to increased vascular resistance Albano S. C. BSPH-3101 | BIOPHARMACEUTICS AND PHARMACOKINETICS Drug Elimination, Clearance, and Renal Clearance 1st SEMESTER | FINALS Instructor: Mrs. Jonah Micah T. Jimenez-Madera, RPh _____________________________________________________________________________________________ GFR Control: Controlled by changes in glomerular capillary hydrostatic pressure. 2. Active Tubular Secretion RBF and GFR: Remain constant despite large An active transport process differences in mean systemic blood pressure due Carrier-mediated, and requires energy to autoregulation. Is capacity limited and may be saturated. Autoregulation: Maintains constant blood flow Systems for weak acids (OAT) and weak and filtration fraction (GFR/RPF) within a specific bases (OCT) pressure range. Rapid for drugs like p-amino-hippuric acid (PAH) and iodopyracet (Diodrast), reflects effective renal plasma flow Glomerular Filtration and Urine Formation (ERPF). Normal adult has a GFR of ~120 mL/min ○ varies from 425 to 650 mL/min Kidneys filter ~180 L of fluid per day, but average urine volume is 1-1.5 L. Active tubular secretion rate is dependent Up to 99% of filtered fluid is reabsorbed. on RPF. Kidney regulates fluid, solutes, and electrolytes ○ ERPF is determined by both RPF retention/excretion. and the fraction of drug that is Filtrate Composition effectively extracted by the kidney ○ Ions relative to the concentration in the ○ Glucose renal artery ○ Essential nutrients ○ Waste products 3. Tubular Reabsorption occurs after the drug is filtered through the Reabsorption Sites: glomerulus and can be an active or a ○ Proximal tubule passive process involving transporting ○ Loops of Henle back into the plasma ○ Distal tubules Active or passive process, influenced by urine pH and drug pKa Mechanisms: Involves both active reabsorption If a drug is completely reabsorbed (eg, and secretion. glucose), then the value for the clearance Urine Composition: High concentration of of the drug is approximately zero metabolic wastes and eliminated drug products. For drugs that are partially reabsorbed Transporters and Enzymes: without being secreted, clearance values ○ P-glycoprotein and Efflux Proteins: are less than the GFR of 120 mL/min Influence urinary drug excretion. ○ CYP Enzymes: Impact drug clearance by Reabsorption Factors metabolism. ○ Influenced by pH and pKa pKa = constant Renal Drug Excretion normal urinary pH = 4.5 to Is the major route of drug elimination 8.0, depending on diet, Is key for nonvolatile, water-soluble, low MW pathophysiology, and drug drugs, or those slowly metabolized by the liver intake Processes Involved: Undissociated drugs (more 1. Glomerular Filtration lipid-soluble) are easily reabsorbed For small molecules (MW < 500) driven by ○ Can significantly reduce the amount hydrostatic pressure of drugs excreted Protein-bound drugs are not filtered here is directly related to the free or nonprotein-bound drug concentration in Protein Binding: the plasma → increased renal clearance Affects elimination half-life for drugs excreted GFR Measurement by glomerular filtration, less so for those by ○ Using drugs like inulin and active secretion creatinine. GFR ~120 mL/min. Because drug protein binding is reversible, Relates to free drug concentration drug bound to plasma protein rapidly in plasma. dissociates as free drug is secreted by the ○ The value for the GFR correlates kidneys fairly well with body surface area. Albano S. C. BSPH-3101 | BIOPHARMACEUTICS AND PHARMACOKINETICS Drug Elimination, Clearance, and Renal Clearance 1st SEMESTER | FINALS Instructor: Mrs. Jonah Micah T. Jimenez-Madera, RPh _____________________________________________________________________________________________ Penicillins are extensively protein bound, ○ alkaline urine increases but their elimination half-lives are short due reabsorption to rapid elimination by active secretion ○ acidic urine increases excretion. Urinary pH: Urine-Plasma (U/P) Ratios: Varies with diet, pathophysiology, drug intake a concentration ratio for the distribution of a ○ Vegetable and fruit diets (alkaline weak acid or basic drug between urine and residue diet) → higher urinary pH plasma, derived From the ○ Protein diet → lower urinary pH Henderson-Hasselbalch relationship Can be altered by intravenous fluids, For weak acids affecting drug reabsorption and excretion ○ bicarbonate or ammonium chloride, are used in acid-base therapy to alkalize or acidify the For weak bases urine, respectively the initial morning urine generally is more acidic and becomes more alkaline later in the day ascorbic acid and antacids such as sodium carbonate may decrease (acidify) or Examples: increase (alkalinize) the urinary pH, Amphetamine respectively ○ Weak base ○ Reabsorbed in alkaline urine (more Henderson-Hasselbalch Equation: lipid-soluble species are formed), Determines percentage of ionized weak excreted faster in acidic urine (more acid/base drugs at a given pH ionized, forming salt) For weak acids Salicylic acid ○ Weak acid ○ Reabsorbed in acidic urine, excreted faster in alkaline urine For weak bases Ionization Fraction: Calculated using the fraction of drug ionized. Affects dissociation in varying pH environments (e.g., urinary pH). Weak Acids: Dissociation affected by urinary pH, especially for drugs with pKa 3-8 ○ More affected in pKa of 5 than with pKa of 3 ○ pKa of 2 → highly ionized at all SUMMARY urinary pH values, and are only Renal Drug Excretion: slightly affected by pH variations Combination of passive filtration, active Example secretion, and reabsorption. ○ acidification increases reabsorption ○ Active secretion: Saturable ○ alkalinization increases excretion enzyme-mediated process. ○ Reabsorption: Influenced by urine Weak Bases: pH and drug ionization. Greatest urinary pH effect on reabsorption Although reabsorption of drugs is mostly a for pKa 7.5-10.5 passive process, the extent of reabsorption Example of weak acid or weak base drugs is Albano S. C. BSPH-3101 | BIOPHARMACEUTICS AND PHARMACOKINETICS Drug Elimination, Clearance, and Renal Clearance 1st SEMESTER | FINALS Instructor: Mrs. Jonah Micah T. Jimenez-Madera, RPh _____________________________________________________________________________________________ influenced by the pH of the urine and the Increase in Urine Flow: degree of ionization of the drug. Caused by ethanol, large fluid intake, and Increased kidney blood flow (caused by methylxanthines (e.g., caffeine, alcohol consumption or diuretic therapy) theophylline). decreases reabsorption, increases excretion Reduces reabsorption time, promoting drug excretion. Clinical Application Sulfisoxazole (Gantrisin) and Forced Diuresis: Sulfamethoxazole/Trimethoprim (Bactrim) Using diuretics can increase renal drug Both are combined upon intake (combination excretion. products) Useful in treating intoxicated patients by Used for urinary tract infections (UTIs) removing excessive drugs. Well absorbed orally Excreted in high urine concentrations RENAL CLEARANCE Urinary drug excretion rate (dDu/dt) divided by Metabolism plasma drug concentration (Cp) N-acetylated to less water-soluble Volume of drug removed by the kidney per unit metabolites time Solubility (both drug and metabolite): Less soluble in acidic conditions, leading to potential renal toxicity due to precipitation in renal tubules. More soluble in alkaline conditions Total Body Clearance: Sum of renal clearance (ClR) and nonrenal clearance (ClNR): Prevention of Crystalluria: Occur due to precipitation in the renal Cl = ClR + ClNR tubules Patients advised to take the drugs with high Therefore, fraction of Dose Excreted: fluid intake Maintain alkaline urine to prevent renal ClR = fe × Cl complications Practice Problem Using the noncompartmental formula for Cl studied earlier, we obtain: where: Ae₀-inf: Amount of drug eliminated unchanged in urine from time 0 to Infinity. In practice, it is not possible to measure the amount of drug excreted unchanged in the urine until infinity; therefore: Urine collection and AUC observation for >3-4 terminal half-lives to minimize error (less than 10%). Example: For a drug with a 12-hour half-life, collect urine for 48 hours. Urine pH and Flow Rate: Both influence drug reabsorption. Easier calculation occurs at steady-state, where all Normal Urine Flow: Approximately 1-2 mL/min excreted drug in urine (ClR(ss)) from one dose occurs Nonpolar and Nonionized Drugs: Sensitive to over one dosing interval. changes in urine flow, typically well reabsorbed Albano S. C. BSPH-3101 | BIOPHARMACEUTICS AND PHARMACOKINETICS Drug Elimination, Clearance, and Renal Clearance 1st SEMESTER | FINALS Instructor: Mrs. Jonah Micah T. Jimenez-Madera, RPh _____________________________________________________________________________________________ Where: Use the simplest identifiable model for t: Dosing interval until steady-state. accurate estimates. Aet(ss): Amount excreted in urine during dosing interval at steady state. Fitted Pharmacokinetic Parameters AUCt(ss): Area under the systemic Tlag: Time before absorption begins after concentration-time curve over the same dosing interval. ka: First-order absorption rate constant Vc/F: Apparent central volume of distribution Relative Bioavailability (F) (Cl/F - ClR): Apparent total clearance Not included in renal clearance calculations, excluding renal clearance only in total body clearance. ClR: Renal clearance ○ Apparent Clearance: Cl/F reported Cld/F: Apparent distributional clearance for extravascular administration if F between central and peripheral volumes is unknown. Vp/F: Apparent peripheral volume of ○ True Renal Clearance: ClR distribution calculated without F. Will be reported as an “apparent” Derived Pharmacokinetic Parameters clearance Apparent Total Clearance (Cl/F): Sum of ClR and (Cl/F - ClR) Apparent Total Volume of Distribution (Vss/F): Sum of Vc/F and Vp/F Rate Constants: ○ λ1 (Distribution) ○ λz (Terminal Elimination) The Nonrenal Clearance can be readily calculated Half-Lives when the drug product is administered Distribution Half-Life (T1/2(λ1)): 0.693 / λ1 intravenously, as ClNR = Cl - ClR. However, this Terminal Elimination Half-Life (T1/2(λz)): calculation is not possible after extravascular 0.693 / λz administration if the exact relative bioavailability is not known or assumed as the exact renal clearance can Comparison of Drug Excretion Methods be calculated (ClR), but only the apparent clearance Renal Clearance Measurement: Can be can (Cl/F). calculated without regard to physiologic mechanisms. Total and Nonrenal Clearance: However, from a physiological viewpoint, renal Cl = ClR + ClNR clearance may be considered the ratio of the sum ClNR = Cl - ClR (only if F is known or of glomerular filtration and active secretion rates assumed). minus the reabsorption rate, divided by plasma drug concentration. Mass Balance Approach: (Rate of drug passing through kidney = rate of drug excreted) ClR × Cp = Qu × Cu Relation to GFR: When reabsorption is negligible and drug is not actively secreted, renal Where: clearance relates to glomerular filtration rate Cp: plasma drug concentration (GFR). Qu: Rate of urine flow The renal clearance value for the drug is Cu: Urine drug concentration compared to that of a standard reference, such as inulin, which is cleared completely through Data Modeling and Fitting: the kidney by glomerular filtration only Another method of obtaining renal clearance ○ Clearance Ratio: Ratio of drug clearance The most accurate method will be to inulin clearance, indicating the simultaneous observation of systemic mechanism of renal excretion. concentrations and excreted urinary amounts (ideally over 3-4 terminal half-lives or longer) Albano S. C. BSPH-3101 | BIOPHARMACEUTICS AND PHARMACOKINETICS Drug Elimination, Clearance, and Renal Clearance 1st SEMESTER | FINALS Instructor: Mrs. Jonah Micah T. Jimenez-Madera, RPh _____________________________________________________________________________________________ Clearance decreases because excretion rate decreases. Clearance decreases because the total excretion rate of the drug increases to the point where it is approximately equal to the filtration rate. Compartmental Pharmacokinetics (PK): Modeling data helps describe drug elimination quantitatively, even without knowledge of GFR, secretion, or reabsorption Aids the ultimate development of a model consistent with physiologic functions of the body Creatinine Clearance (CrCl): Related to overall drug clearance in clinical practice, aiding dosage adjustments based on renal function. Filtration Only allows clinicians to adjust dosage of drugs depending on a patient’s observed renal Glomerular Filtration Sole Process: If it is the function only excretion process, the drug is unbound to plasma proteins and not reabsorbed. Renal Clearance (ClR) Formula: Amount Filtered: At any time (t) = Cp × GFR Renal clearance is a summation of filtration, Renal Clearance (ClR): secretion, and reabsorption; therefore: ○ If only by glomerular filtration (e.g., inulin): ClR = GFR ClR = Slope × CrCl + Intercept ○ Otherwise, ClR includes all processes: filtration, reabsorption, Where: and active secretion Intercept reflects reabsorption and secretion processes, assuming CrCl reflects GFR Total Clearance Formula: Filtration and Active Secretion Cl = (Slope × CrCl + Intercept) + ClNR Assuming nonrenal clearance (ClNR) remains constant unless severe renal impairment affects protein binding, enzyme, or transporter activity. Simplified Clearance Formula: Cl = (Slope × CrCl) + Intercept2 Where: Intercept2 often simplified to ClNR, representing kidney secretion, reabsorption, and nonrenal routes. For drugs primarily filtered and secreted with negligible reabsorption, overall excretion rate exceeds GFR. ○ At low plasma concentrations, active secretion is not saturated, leading to excretion by filtration and secretion. ○ At high concentrations, active secretion saturates, decreasing clearance as excretion rate equals filtration rate. Albano S. C. BSPH-3101 | BIOPHARMACEUTICS AND PHARMACOKINETICS Drug Elimination, Clearance, and Renal Clearance 1st SEMESTER | FINALS Instructor: Mrs. Jonah Micah T. Jimenez-Madera, RPh _____________________________________________________________________________________________ Example Problem #1 Example Problem #2 DETERMINATION OF RENAL CLEARANCE Graphical Methods Clearance is determined by the slope of a curve plotting the rate of drug excretion in urine (dDu/dt) against plasma concentration (Cp). ○ A steeper slope indicates greater clearance for rapidly excreted drugs, while; ○ a shallower slope indicates slower excretion By rearranging and integrating the relevant equations, one can express the cumulative drug excreted in relation to the area under the concentration-time curve (AUC). This relationship is used to graph cumulative drug excretion against AUC to determine renal clearance from the slope of the resulting curve. However, if data points are missing, calculating cumulative excretion becomes challenging, though accurate clearance determination is possible with complete data. Albano S. C. BSPH-3101 | BIOPHARMACEUTICS AND PHARMACOKINETICS Drug Elimination, Clearance, and Renal Clearance 1st SEMESTER | FINALS Instructor: Mrs. Jonah Micah T. Jimenez-Madera, RPh _____________________________________________________________________________________________ b. Renal clearance and nonrenal clearance c. Formation clearance of the parent drug to the metabolite: Midpoint Methods d. Other elimination or metabolic routes: The overall clearance equation is: The equation simplifies renal clearance (Cl) to a relationship involving the 24-hour urinary excretion amount (Xu(0-24)), calculated by multiplying the total urine volume collected over 24 hours (Vu(0-24)) by the urinary concentration The drug does not undergo additional (Cu(0-24)), and the midpoint plasma concentration elimination or metabolic routes. (Cp12) measured at 12 hours. Although this method relies on a single plasma Overall, the analysis provides insights into the drug's concentration and may not be very robust, it is pharmacokinetics, revealing that it is eliminated solely useful in clinical settings where limited through renal and metabolic pathways, with no additional systemic routes involved. plasma samples can be obtained. While 24-hour collection is standard, different time intervals can also be utilized. Practice Problem #2 An antibiotic was administered via IV bolus injection at a dose of 500 mg, following a one-compartment Practice Problem #1 model. The drug had a total volume of distribution of In this scenario, a drug that is eliminated through 21 L and an elimination half-life of 6 hours. After first-order renal excretion and hepatic metabolism collecting urine for 48 hours, 400 mg of unchanged (following a one-compartment model) is drug was recovered. To determine the fraction of the administered as a single oral dose of 100 mg, with a 90% bioavailability. A total of 60 mg of unchanged dose excreted unchanged in urine (fe), the drug and 30 mg of metabolite (as milligram calculation is as follows: equivalents) are recovered in the urine. The drug has an elimination half-life of 3.3 hours and an apparent volume of distribution of 1000 L. This indicates that 80% of the administered dose was Solution: excreted unchanged in the urine.Calculations for a. Apparent clearance and clearance: various pharmacokinetic parameters are: Elimination rate constant (k): Renal elimination rate constant (kR): Albano S. C. BSPH-3101 | BIOPHARMACEUTICS AND PHARMACOKINETICS Drug Elimination, Clearance, and Renal Clearance 1st SEMESTER | FINALS Instructor: Mrs. Jonah Micah T. Jimenez-Madera, RPh _____________________________________________________________________________________________ Total Clearance (Cl): behavior of a drug is linear with respect to time and dose. Calculation Methods: Clearance can be calculated using various methods, including: Renal Clearance (ClR): ○ noncompartmental; ○ compartmental, and; ○ physiological approaches Nonrenal Clearance (ClNR): Compartment Models: In a specific compartment model, clearance equals the product of the elimination rate constant and the volume of distribution ○ In a one-compartment model, clearance is RELATIONSHIP OF CLEARANCE TO derived from the terminal elimination rate ELIMINATION HALF-LIFE AND VOLUME OF constant and total volume of distribution. DISTRIBUTION Students often find it confusing to understand the Relationship with Half-Life: Clearance is relationships between half-lives, volumes of inversely related to the elimination half-life of the distribution, clearances, and the differences drug. between noncompartmental and compartmental Organ Clearances: Organ clearances are approaches in pharmacokinetics (PK). generally additive, except for the lungs, with total CLEARANCES are consistently linked to a rate body clearance expressed as renal and nonrenal constant (k) and a volume of distribution (Vd), clearance. but these relationships can differ based on the mathematical model used to describe the drug's Renal Clearance Factors: Renal clearance pharmacokinetics. Table 7-6 is designed to clarify depends on renal blood flow, glomerular filtration, these relationships: drug secretion, and reabsorption. Reabsorption Process: Drug reabsorption is often passive and influenced by urine pH and the drug's ionization. Impact of Blood Flow: Increased renal blood flow (e.g., from diuretics or alcohol) reduces drug reabsorption and increases urinary excretion rate. CHAPTER SUMMARY Definition of Clearance: Refers to the irreversible removal of a drug from systemic circulation via all elimination routes; measured as the volume of fluid cleared of drug per unit time. Clinical Importance: Clearance is crucial for understanding systemic drug exposure, which affects efficacy and safety, as well as the administered dose. Constant Parameter: Clearance remains constant when the pharmacokinetic (PK) Albano S. C.