THE APhA COMPLETE REVIEW FOR PHARMACY, 7th Ed

6. Pharmacokinetics, Drug Metabolism, and Drug Disposition - Bernd Meibohm, PhD, Charles R. Yates, PharmD, PhD

6-1. Introduction

Introduction

Pharmacokinetics is the science of a drug's fate in the body. A drug's therapeutic potential is intimately linked to its pharmacokinetic profile. For example, a drug's pharmacologic response may be severely diminished by poor absorption, rapid elimination from the body, or both. The most important factors contributing to drug disposition include absorption, distribution, metabolism, and excretion.

Absorption

The rate and extent of drug absorption is referred to as bioavailability. The fraction of drug absorbed (fa), an important determinant of the extent of bioavailability (represented by F), is affected not only by the drug's physicochemical properties but also by physiologic barriers at the site of absorption. For example, intestinal expression of the drug efflux transporter P-glycoprotein is known to limit oral drugs.

Distribution

Many drugs circulate in the body bound to plasma proteins (e.g., human serum albumin). The fraction of drug not bound to protein (fup) is responsible for the pharmacologic effect. A drug may also bind significantly to tissue proteins (fut). Drugs with a large fup-to-fut ratio have a large volume of distribution, whereas drugs with a small fup-to-fut ratio are largely confined to the vascular space. Volume of distribution is directly related to half-life (t1/2), the time required to eliminate half the drug from the body.

Metabolism

Approximately 50% of drugs undergo some form of hepatic metabolism. The cytochrome P450 (CYP450) family of drug-metabolizing enzymes is primarily responsible for drug inactivation in the liver. Hepatic clearance depends on liver blood flow and the extraction ratio (ER). Hepatic ER can be used to estimate the fraction of drug escaping first-pass metabolism (F*), which is an important determinant of oral bioavailability. Intestinal inactivation of drugs by CYP450 enzymes in the gut is responsible for reduced F of a number of drugs.

Excretion

The primary purpose of hepatic metabolism is to increase a drug's water solubility to facilitate its renal elimination. The kidneys also serve as the primary eliminating organ for drugs that do not undergo hepatic metabolism. Renal clearance comprises three main physiologic processes: glomerular filtration, reabsorption, and secretion. Filtration clearance is the product of fup and glomerular filtration rate (a physiologic parameter that diminishes with age). Renal reabsorption is a predominantly passive process dependent on physicochemical drug properties and on urine drug concentration and pH, whereas secretion is an active process facilitated by various transport mechanisms. The net of filtration, reabsorption, and secretion determines a drug's total renal clearance.

Interindividual differences in drug pharmacokinetics can at least partially explain variability in drug response. Thus, a thorough understanding of the physiologic processes affecting drug disposition is essential to drug individualization and optimization.

6-2. Absorption and Disposition

Drug Input

Drugs are administered to the body by one of two routes, intravascular or extravascular. For intravascular administration, drugs are usually administered as in intravenous (IV) infusion (continuous, short term, or bolus). The concentration C is given by the following expressions.

IV bolus

000005

 

= (rate of drug elimination, or output rate)

 

K

= elimination rate constant = CL/V

 

CL

= clearance = Dose/AUC

 

V

= Volume

 

IV infusion

For drugs that are administered extravascularly (by mouth, intramuscularly, or subcutaneously) and act systemically, absorption must occur. See section 6-4.

First-order absorption

000100

where ka = first-order rate constant for drug absorption; absorption half-life = 0.693/kaK = first-order rate constant for drug elimination (CL/V); CL = F × Dose/AUC, oral clearance = CL/F = Dose/AUC; and F = bioavailability, or fraction of drug absorbed. F refers to the rate and extent of absorption.

6-3. Constant Rate Regimens

Introduction

For many drugs to be therapeutically effective, drug concentrations of a certain level have to be maintained at the site of action for a prolonged period (e.g., β-lactam antibiotics, antiarrhythmics), whereas for others, alternating plasma concentrations are more preferable (e.g., aminoglycoside antibiotics such as gentamicin).

Two basic approaches to administering the drug can be applied to continuously maintain drug concentrations in a certain therapeutic range over a prolonged period:

• Drug administration at a constant input rate

• Sequential administration of discrete single doses (multiple dosing)

Drug Administration as Constant Rate Regimens

At any time during the infusion, the rate of change in drug concentration is the difference between the input rate (infusion rate R0/volume of distribution V) and the output rate (elimination rate constant K × concentration C):

Rate of change = input rate - output rate

In concentrations:

000248

In amounts:

000251

R0

= infusion rate (in amount/time, e.g., mg/h)

 

V

= volume of distribution

 

CL

= clearance

 

K

= first-order rate constant for drug elimination (CL/V)

 

000253

Hence, the steady-state concentration Css is determined only by the infusion rate R0 and the clearance CL.

Drug concentration at steady state:

000254

Drug concentration before steady state:

000255

Time to Reach Steady State

For therapeutic purposes, knowing how long after initiation of an infusion reaching the targeted steady-state concentration Css will take is often of critical.

Concentration during an infusion before steady state:

000256

Concentration during an infusion at steady state:

000257

The fraction of steady-state f is then

000095

After a duration of infusion of

1.0 t1/2 ® 50% of steady state is reached

2.0 t1/2 ® 75% of steady state is reached

3.0 t1/2 ® 87.5% of steady state is reached

3.3 t1/2 ® 90% of steady state is reached

4.0 t1/2 ® 93.8% of steady state is reached

5.0 t1/2 ® 96.9% of steady state is reached

The following conclusions can be drawn:

• The approach to the steady-state concentration Css is exponential in nature and is controlled by the elimination process (elimination rate constant K), not the infusion rate R0.

• Only the value of the steady-state concentration Css is controlled by the infusion rate R0 (and of course by the clearance CL).

• Assuming for clinical purposes that a concentration of > 95% of steady state is therapeutically equivalent to the final steady-state concentration Css, approximately five elimination half-lives t1/2 are necessary to reach steady state after initiation of an infusion.

Concentration-Time Profiles Postinfusion

The plasma concentration postinfusion cannot be distinguished from giving an IV bolus dose. Because the drug input has been discontinued, the rate of change in drug concentration is determined only by the output rate. If the drug follows one-compartment characteristics, then the plasma concentration profile can be described by

C = C´ × e-K×tpi

where C´ is concentration at the end of the infusion and tpi is time postinfusion (i.e., time after the infusion has stopped).

Thus, a general expression can be used to calculate the plasma concentration during and after a constant rate infusion: 000096

where t is the elapsed time after the beginning of the infusion and tpi is the postinfusion time—that is, the difference between the duration of the infusion (infusion time Tinf) and t: tpi = t - Tinf. For describing concentrations during the infusion, tpi is set to zero. For describing concentrations postinfusion, t is set to Tinf.

Four different cases can be distinguished:

1. During the infusion, but before steady state is reached:

000064

2. During the infusion at steady state:

000190

3. After cessation of the infusion before steady state:

000262

4. After cessation of the infusion at steady state:

000263

Determination of Pharmacokinetic Parameters

The elimination rate constant K and the elimination half-life t1/2 can be determined from

• The terminal slope after the infusion has been stopped

• The time to reach half of Css

• The slope of the relationship of ln(Css - C) vs. t, based on

C = Css × (1 - e-K × t)

   and the resulting ln(Css - C) = ln Css - K × t

The clearance CL from the relationship can be determined from

000264

The volume of distribution from the relationship can be determined from

000062

Loading Dose and Maintenance Dose

The loading dose LD is supposed to immediately (t = 0) reach the desired target concentration Ctarget. It is administered as an IV bolus injection or, more frequently, as a short-term infusion. Following is an expression of target concentration calculated for a drug with one-compartment characteristics:

000265

The maintenance dose MD is intended to sustain Ctarget. It is administered as a constant rate infusion. The maintenance dose is the infusion rate necessary to sustain the target concentration:

000267

6-4. Multiple Dosing

Introduction

Continuous drug concentrations for a prolonged therapy can be maintained either by administering the drug at a constant input rate or by sequentially administering discrete single doses of the drug. The latter is the approach more frequently used and can be applied for extravascular as well as intravascular routes of administration.

Multiple-dose regimens are defined by two components, the dose D that is administered at each dosing occasion, and the dosing interval τ, which is the time between the administrations of two subsequent doses. Dose and dosing interval can be summarized in the dosing rate DR:

000269

Concentration-Time Profiles during Multiple Dosing

The multiple-dose function MDF can be used for calculating drug concentrations before steady state has been reached during a multiple-dose regimen: 000271

where K is the respective rate constant of the drug, τ is the dosing interval, and n is the number of the dose.

Once steady state has been reached, n approaches infinity, and MDF simplifies to the accumulation factor AF:

000272

Multiple-Dosing Regimens: Instantaneous Input (IV Bolus)

For an IV bolus multiple-dose regimen, the concentrations during the first dosing interval, the nth dosing interval, and at steady state are described by the relationships shown in

Table 6-1.

The peak and trough concentrations at steady state can thus be expressed as the peak and trough after the first dose multiplied by the accumulation factor AF:

000160

Average steady-state concentration

By definition, the average drug input rate is equal to the average drug output rate at steady state. Whereas the average input rate is the drug amount entering the systemic circulation per dosing interval, the average output rate is equal to the product of clearance

[Table 6-1. IV Bolus Multiple Dose Regimen]

CL and the average plasma concentration within one dosing interval Css,av:

000170

Thus, the average steady-state concentration Css,av during multiple dosing is determined only by the dose, the dosing interval τ (or both together as dosing rate DR = D/τ), and the clearance CL:

000241

The area under the curve resulting from administration of a single dose AUCsingle is equal to the area under the curve during one dosing interval at steady state AUCss if the same dose is given per dosing interval τ:

000171

Thus,

AUCsingle = AUCss

Extent of accumulation

The extent of accumulation during multiple dosing at steady state is determined by the dosing interval τ and the half-life of the drug t1/2 (or the elimination rate constant K):

000173

Thus, the extent of accumulation is dependent not only on the pharmacokinetic properties of a drug but also on the multiple-dosing regimen chosen.

Fluctuation

The degree of fluctuation between peak and trough concentrations during one dosing interval—that is, Css,max and Css,min—is determined by the relationship between elimination half-life t1/2 and dosing interval τ.

000174

Multiple-Dosing Regimens: First-Order Input (Oral Dosing)

The average steady-state concentration Css,av is now determined by the bioavailable fraction F of the dose D administered per dosing interval τ and the clearance CL:

000043

The concentration-time profile after a single oral dose is given by

000163

Hence, the concentration at any time within a dosing interval during multiple dosing at steady state is determined by

000259

Thus, the trough concentration is readily available, assuming that the absorption is completed:

000175

The peak concentration is assessable via the time-to-peak tmax, which is dependent on the rate of absorption and has to be determined through

000178

6-5. Volumes of Distribution and Protein Binding

Introduction

Drug distribution means the reversible transfer of drug from one location to another within the body. After the drug has entered the vascular system, it becomes distributed throughout the various tissues and body fluids. However, most drugs do not distribute uniformly and in a similar manner throughout the body, as reflected by the difference in their volumes of distribution. Thus, the following material focuses on the factors and processes determining the rate and extent of distribution and the resulting consequences for pharmacotherapy.

Factors affecting distribution are

• Binding to blood or tissue elements

• Blood flow (i.e., the delivery of drug to the tissues)

• Ability to cross biomembranes

• Physicochemical properties of the drug (lipophilicity, extent of ionization) that determine partitioning into tissues

Protein Binding

The fraction unbound in plasma varies widely among drugs. Drugs are classified as follows:

• Highly protein bound:

fu ≤ 0.1 (≤ 10% unbound, ≥ 90% bound)

• Moderately protein bound:

   fu = 0.1 - 0.4(10 - 40% unbound, 60 - 90% bound)

• Low protein bound:

fu = 0.4 (≥ 40% unbound, ≤ 60% bound)

Factors Determining the Degree of Protein Binding

The reversible binding of a drug to proteins obeys the law of mass action, 000179

where the expressions in brackets represent the molar concentrations of the components, and k1 and k2 are rate constants for the forward and reverse reactions, respectively. The equilibrium association constant Ka is defined as k1/k2.

This reaction results in the following relationship for the fraction unbound: 000181

where N is the number of available binding sites and Cu is the unbound concentration.

Binding Proteins

Human plasma contains more than 60 proteins. Of these, three proteins account for the binding of most drugs. Albumin, which comprises approximately 60% of total plasma protein, fully accounts for the plasma binding of most anionic drugs and many endogenous anions (high-capacity, low-affinity binding site). Many cationic and neutral drugs bind appreciably to α1-acid glycoprotein (high-affinity, low-capacity binding site) or lipoproteins in addition to albumin. Other proteins, such as transcortin, thyroid-binding globulin, and certain antibodies have specific affinities for a small number of drugs.

Volumes of Distribution

Volume of distribution at steady-state Vss

The volume of distribution at steady state is by definition the sum of the pharmacokinetic volumes of distribution for the different pharmacokinetic compartments. It is the theoretical 000273

where Vp is the volume of plasma (3 L); Vt is the volume of tissue water (total body water minus plasma volume: 42 - 3 = 39 L based on a "standard" person); and fu and fu,t are the fraction unbound for the drug in plasma and in tissue, respectively.

Besides physicochemical properties of the drug, the relationship for Vss shows that the extent of distribution is largely determined by the differences in protein binding in plasma and tissue, respectively:

000184

Unbound steady-state concentrations

The average steady-state concentration during a multiple-dose regimen or during a constant rate infusion is determined by

000186

The free steady-state concentration Css,u is given by

Css,u = fu × Css

Thus, the unbound steady-state concentration Css,u is determined by

000189

6-6. Bioavailability and Bioequivalence

Introduction

The FDA (21 Code of Federal Regulations 320) defines bioavailability as "the rate and extent to which the active ingredient or active moiety is absorbed from a drug product and becomes available at the site of action." Because, in practice, drug concentrations can rarely be determined at the site of action (e.g., at a receptor site), bioavailability is more commonly defined as "the rate and extent that the active drug is absorbed from a dosage form and becomes available in the systemic circulation."

Following are factors affecting bioavailability:

• Drug product formulation

• Properties of the drug (salt form, crystalline structure, formation of solvates, and solubility)

• Composition of the finished dosage form (presence or absence of excipients and special coatings)

• Manufacturing variables (tablet compression force, processing variables, particle size of drug or excipients, and environmental conditions)

• Rate and site of dissolution in the gastrointestinal tract

• Physiology

With respect to physiology, the following factors affect bioavailability:

• Contents of the gastrointestinal tract (fluid volume and pH, diet, presence or absence of food, bacterial activity, and presence of other drugs)

• Rate of gastrointestinal tract transit (influenced by disease, physical activity, drugs, emotional status of subject, and composition of the gastrointestinal tract contents)

• Presystemic drug metabolism or degradation (influenced by local blood flow; condition of the gastrointestinal tract membranes; and drug transport, metabolism, or degradation in the gastrointestinal tract or during the first pass of the drug through the liver)

Absolute Bioavailability

Absolute bioavailability is the fraction (or percentage) of a dose administered nonintravenously (or extravascularly) that is systemically available as compared to an intravenous dose. If given orally, absolute bioavailability (F) is

000188

Relative Bioavailability

Relative bioavailability refers to a comparison of two or more dosage forms in terms of their relative rate and extent of absorption:

000191

Bioequivalence

Two dosage forms that do not differ significantly in their rate and extent of absorption are termed bioequivalent. In general, bioequivalence evaluations involve comparisons of dosage forms that are

• Pharmaceutical equivalents: Drug products that contain identical amounts of the identical active drug ingredient (i.e., the same salt or ester of the same therapeutic moiety, in identical dosage forms)

• Pharmaceutical alternatives: Drug products that contain the identical therapeutic moiety, or its precursor, but not necessarily in the same amount or dosage form or as the same salt or ester

Biopharmaceutics Classification System

With minor exceptions, the FDA requires that bioavailability and bioequivalence of a drug product be demonstrated through in vivo studies. However, the Biopharmaceutics Classification System (BCS) can be used to justify the waiver of the requirement for in vivo studies for rapidly dissolving drug products containing active moieties or active ingredients that are highly soluble and highly permeable (Class 1 drugs).

The BCS divides drugs into classes on the basis of their solubility and permeability:

• Class 1: high solubility and high permeability

• Class 2: low solubility and high permeability

• Class 3: high solubility and low permeability

• Class 4: low solubility and low permeability

6-7. Elimination and Clearance Concepts

Clearance is defined as the irreversible removal of drug from the body by an organ of elimination. Because the units of CL are flow (e.g., mL/minute or L/h), CL is often defined as the volume of blood irreversibly cleared of drug per unit of time.

CL by the eliminating organ (CLorgan) is defined as the product of blood flow (Q) to the organ and the extraction ratio (ER) of that organ:

CLorgan = Q × ER

Individual organ clearances are additive. For the majority of drugs used clinically, the liver is the major—and sometimes only—site of metabolism; the kidneys are the major site of excretion for drugs and metabolites. Thus, the equation for total clearance can be written to include renal clearance (CLR) and hepatic clearance (CLH):

CL = CLR + CLH

The fraction of drug excreted unchanged by the kidneys (fe) indicates what fraction of the drug administered will be excreted into the urine:

000007

6-8. Renal Clearance

Introduction

Drugs may undergo three processes in the kidney. Two act to remove drug from the body: filtration and secretion. The other acts to return drug to the body: reabsorption. Thus, one may express renal clearance of a drug as follows:

CLR = [CLfiltration + CLsecretion] × (1-freabsorbed)

Calculating Filtration Clearance of Creatinine

Normal serum concentrations of creatinine are 0.8-1.3 mg/dL for men and 0.6-1.0 mg/dL for women.

Creatinine is a useful marker of renal function because it is an endogenous by-product of muscle breakdown. The kidney eliminates creatinine at a rate approximately equal to the glomerular filtration rate (GFR). A number of formulas have been developed that allow creatinine clearance (CLcr) to be estimated from serum creatinine concentrations. The most widely used clinically is the Cockroft-Gault equation: 000194

where Scr is the serum creatinine concentration in mg/dL, and IBW is the ideal body weight.

IBWmales (kg) = 50 + (2.3 × height in inches > 5 ft)

IBWfemales (kg) = 45.5 + (2.3 × height in inches > 5 ft)

Secretion Clearance

Drug in blood may also be secreted into the kidney tubule. This process occurs against a concentration gradient (concentration of drug in kidney tubule is very high because of water reabsorption) and therefore is an active process.

Cellular processes (e.g., presence of active transporters) exist to facilitate tubular secretion. The two most well characterized of these processes include transporters responsible for the secretion of basic (anionic) and acidic (anionic) drugs.

Reabsorption

Passive reabsorption of many drugs also occurs in the kidneys. Because reabsorption is a passive process (i.e., diffusion), reabsorption will depend on the physicochemical properties of the drug (e.g., molecular weight, polarity, and acid disassociation content pKa).

Weak bases: B + H+Û BH+

Low urine pH = more ionized, less reabsorption

High urine pH = less ionized, more reabsorption

Thus, only weak bases with pKa between 6 and 12 show changes in the extent of reabsorption (and thus CLR) with changes in urine pH.

Weak acids: HA Û A- + H+

Low urine pH = less ionized, more reabsorption

High urine pH = more ionized, less reabsorption

Thus, only weak acids with pKa in the range of 3.0 to 7.5 show changes in the extent of reabsorption (and thus CLR) with changes in urine pH.

All drugs that are not bound to plasma proteins are filtered; therefore, filtration clearance is

CLfiltration = fup × GFR = 125mL/minute

Some drugs are secreted or reabsorbed, or both. One can determine the net process a drug undergoes by calculating the excretion ratio (Eratio):

000198

6-9. Hepatic Clearance

Introduction

The fraction of drug escaping first-pass metabolism (F*) can be described in terms of the hepatic extraction ratio:

F* = 1 - ER

The overall oral bioavailability (F) of a drug is dependent on the fraction absorbed (fa), the fraction escaping metabolism in the intestinal wall (fg), and the fraction escaping hepatic first-pass metabolism (F*).

F = fa × fg × F*

Venous Equilibrium Model for Hepatic Clearance

The venous equilibrium model relates hepatic extraction ratio ER to its determinants as follows: 000200

and (remembering that CLH = QH × ERH)

000201

The fraction of drug escaping hepatic first-pass metabolism using the venous equilibrium model is

000033

Drugs undergoing hepatic metabolism can be divided into three broad categories:

1. Low-extraction drugs: ER < 0.3 and thus F* > 0.7

2. Intermediate-extraction drugs: 0.3 < ER < 0.7 and thus 0.3 < F* < 0.7

3. High-extraction drugs: ER > 0.7 and thus F* < 0.3

Determinants of Hepatic Clearance

Thus, the determinants of hepatic extraction ratio, hepatic clearance, and the fraction escaping hepatic first-pass metabolism are liver blood flow (Q), protein binding (fup), and CLint.

For some drugs, hepatic clearance is limited or restricted to the unbound or free drug (ER < fup). This is known as restrictive clearance. Because clearance is limited to unbound drug, changes in protein binding will alter the concentration of drug that is available for elimination.

Some drugs defy this principle so that the hepatic extraction ratio is greater than the fraction of drug unbound in plasma (ER > fup). When this occurs, it suggests that drug clearance is not restricted to unbound drug. Drugs behaving in this manner are said to undergo nonrestrictive clearance. Because nonrestrictive clearance is not limited to the fraction unbound in plasma, changes in protein binding will not alter the concentration of drug that is available for elimination (i.e., all drug is available for elimination regardless of whether it is bound or unbound).

Intrinsic clearance (CLint) is defined as the intrinsic ability of the hepatic enzymes to eliminate drug when blood flow or protein binding causes no limitations. CLint is a measure of the capacity and affinity of drug-metabolizing enzymes (e.g., CYP450s) for the drug. The determinants of CLint can be explained using the Michaelis-Menten equation: 000206

where υ is the rate of drug metabolism (amount/time), Vmax is the maximal rate of metabolism for a given metabolic pathway (amount/time), Km is the concentration of the drug at which the rate of metabolism is half-maximal (amount/volume), and Cu is the unbound drug concentration (amount/volume).

Physiologically, Vmax describes the quantity (capacity) of a drug-metabolizing enzyme to metabolize drug. Km describes the interaction between the drug-metabolizing enzyme and the drug.

Factors that affect CLint are

• Enzyme induction: Enzyme induction refers to an increased number (capacity) of drug-metabolizing enzymes, which results in an increase in clearance. An increased number (capacity) of drug-metabolizing enzymes results in an increase in Vmax and CLint.

• Enzyme inhibitors: Competitive inhibition of the drug-metabolizing enzyme by another drug increases the apparent Km (i.e., a higher concentration of drug will be required to achieve a half-maximal rate of metabolism). Increase in apparent Km results in decrease in CLint.

An extensive list of potential P450 inducers and inhibitors can be found at www.drug-interactions.com.

6-10. Drug, Disease, and Dietary Influences on Absorption, Distribution, Metabolism, and Excretion

Introduction

Pharmacokinetics is the science of a drug's fate in the body. Typical reported pharmacokinetic parameters are determined in healthy individuals. However, drugs are prescribed to individuals with one or more altered physiological or pathological conditions. Clinical pharmacokinetics focuses on tailoring therapeutic dosing regimens to individuals on the basis of these altered physiological and pathological states. Thus, it is important to consider patient-specific factors that potentially contribute to drug interactions: drug-drug, drug-disease, and drug-dietary factors.

Drug interactions alter the effects of a drug by reaction with another drug or drugs, with foods or beverages, or with a preexisting medical condition. Drug interactions can be broadly classified as

• Drug-drug

• Drug-disease

• Drug-dietary

Drug-Drug Interactions

• Induction of CYP450 enzymes

• An increased number (Vmax) of drug-metabolizing enzymes leads to increased clearance.

• Example: Rifampin increases clearance of warfarin.

• Inhibition of cytochrome P450 enzymes

• Competitive inhibition of the drug-metabolizing enzyme by another drug leads to increase in apparent Km, which leads to decreased clearance.

• Example: Cimetidine decreases the clearance of warfarin.

• Inhibition of drug efflux transporter P-glycoprotein

• Competitive inhibition of P-glycoprotein occurs.

• Decreased renal clearance for drugs undergoing net secretion

• Example: Quinidine inhibits the renal secretion of digoxin.

• Increased fa and F

• Example: Ketoconazole increases the oral absorption of cyclosporine.

• Protein-binding displacement

• A drug or drugs is displaced from major binding proteins.

• Increased fup

• Increased volume of distribution

• Increased clearance for restrictively cleared drugs

• Example: Aspirin displaces warfarin from albumin, leading to an increased distribution and clearance for warfarin.

Drug-Disease Interactions

Cardiovascular disease

Reduced cardiac output associated with congestive heart failure leads to reduced perfusion of key eliminating organs such as the liver and kidney. The following pharmacokinetic effects have been reported:

• Decreased absorption rate (e.g, digoxin, hydrochlorothiazide, procainamide, and quinidine)

• Prolonged hepatic clearance for high extraction (E > 0.7) drugs (e.g., lidocaine and theophylline)

• Reduced volume of distribution (e.g., digoxin)

Renal disease

Creatinine clearance is commonly used to assess renal function, and the CLR of many drugs is known to vary in proportion to CLcr. Thus, renal impairment can be inferred from changes in CLcr.

CLcr is most often estimated by measuring serum creatinine concentration, using the Cockroft-Gault equation, as discussed previously.

Serum creatinine concentrations remain relatively constant (about 1 mg/dL) in adults over age 20. However, patients with compromised renal function may exhibit higher concentrations.

Renal function RF in a patient may be estimated by comparing the patient's creatinine clearance to what CLcr would be in a normal individual (i.e., fup × GFR or 125 mL/minute).

000207

Use of this equation to estimate RF assumes the intact nephron hypothesis (i.e., that renal disease results in the dysfunction of a certain fraction of nephrons but allows the remaining nephrons to remain intact).

To individualize drug treatment in patients with renal impairment, you need to know the drug clearance in your patient. This knowledge will allow you to calculate the dose rate of the drug that will maintain an individualized Ctarget. Clearance in your patient with renal impairment will be designated CL*. Three parameters are needed to calculate CL*:

• CL of the drug and fe in normal subjects. These values can be found in textbooks, primary literature, or package inserts.

• RF in your patient is usually estimated using a recent serum creatinine concentration and the equations presented above.

You can then calculate clearance in your patient with renal impairment using the following equation:

CL* = CL × [1 - fe × (1 - RF)]

CL* represents total clearance in the renally impaired individual.

Liver disease

Hepatic disease results in numerous pathophysiologic changes in the liver that may influence drug pharmacokinetics, including the following:

• Reduction in liver blood flow

• Decreased clearance for high-extraction drugs

• Reduction in number and activity of hepatocytes

• Decreased first-pass metabolism for high-extraction drugs

• Decreased clearance for low-extraction drugs

• Impaired production of human serum albumin

• Increased distribution of drugs

Drug-Diet Interactions

• Drug-food interactions

• Type I: Ex vivo bioinactivation

• Type II: Interactions affecting oral absorption

• Type III: Interactions affecting systemic disposition

• Type IV: Interactions affecting either renal or hepatic clearance

• Ex vivo bioinactivation

• It typically occurs in the delivery device before drugs enter body.

• Interaction occurs between the drug and the nutritional element or formulation through biochemical or physical reactions.

• Interaction examples include hydrolysis, oxidation, neutralization, precipitation, and complexation.

• High ethanol content may precipitate inorganic salts present in enteral feeding formulas.

• Syrups are acidic solvents and may cause precipitation of inorganic salts.

• Interactions affecting absorption

• This type of interaction affects drugs and nutrients delivered by mouth only.

• It may result in either an increase or a decrease in oral bioavailability.

• The interacting agent may alter function of either the metabolizing enzyme (e.g., CYP3A4) or the active transport protein (e.g., P-glycoprotein).

• Meal intake alters oral absorption through mechanisms involving altered (1) gastric pH, (2) gastrointestinal transit time, and (3) dissolution of solid dosage forms.

• Grapefruit juice inactivates gut CYP3A4, enhancing oral absorption of CYP3A4 substrates (e.g., cyclosporine, midazolam, and nifedipine).

• Interactions affecting systemic disposition

• These interactions occur after drug or nutrient has entered the systemic circulation.

• They involve alteration in tissue disposition or response.

• Example: Foods high in vitamin K (e.g., broccoli) can alter systemic clotting factors, reducing effectiveness of warfarin.

• Interactions affecting either renal or hepatic clearance

• These interactions arise from modification of drug elimination mechanisms in liver, kidney, or both.

• Acute ethanol ingestion may potentiate central nervous system effects of benzodiazepines (e.g., alprazolam).

6-11. The Pharmacokinetic-Pharmacodynamic Interface

Pharmacokinetics (PK) establishes the relationship between dose and concentration. Pharmacodynamics (PD) establishes the relationship between concentration and effect. When individualizing pharmacotherapy, it is important to account for both PK and PD variability. For a number of drugs, the PK variability is much larger than the PD variability. Thus, concentration-based therapeutic drug monitoring is useful for a number of drugs (e.g., theophylline). However, for some drugs, PD variability exceeds PK variability.

Linking the PK and PD allows a more thorough understanding of the effect of dosage adjustments on pharmacologic response.

The simple Emax model represents the most widely used model to describe the relationship between drug concentration and effect: 000204

where Emax is the maximum effect possible (intrinsic activity) and EC50 is the concentration achieving 50% maximal effect (potency).

Figure 6-1 illustrates the three concentration-dependent phases as follows:

• Linear phase (1)

• Drug concentration is much smaller than EC50 (C << EC50).

• A linear relationship exists between concentration C and effect E:

000199

• Constant phase (3)

• Drug concentration much larger than EC50 (C >> EC50).

• Effect E is independent of concentration:

E = Emax

• Log-linear phase (2)

• A log-linear relationship exists between C and E when E is between 20% and 80% of EmaxEmax/4 is the slope describing this relationship:

000177

6-12. Hysteresis

Response is linked to concentration and time. In other words, a given concentration may have a different effect depending on time. Therefore, the concentration-effect relationship is described by a hysteresis loop, which may be either clockwise or counterclockwise.

• Counterclockwise hysteresis

• Distributional delay to effect site

• Indirect response mechanism

• Active metabolite (agonism)

• Sensitization

[Figure 6-1. The Three Concentration-Dependent Phases]

• Clockwise hysteresis

• Functional tolerance

• Active metabolite (antagonism)

6-13. Clinical Examples

Clinical Example 1

A patient (55 years old, weighing 73 kg) was started on a multiple-dose regimen with gentamicin 80 mg every 8 hours given as IV short-term infusion over 30 minutes. Because his infection is serious, it is decided to target for a peak concentration of 10 mg/L and a trough concentration of 1 mg/L. Three blood samples were drawn 30 minutes prior to the third dose and 30 minutes and 7 hours after the end of the infusion of the third dose, respectively. The measured plasma concentrations are 1.73, 5.96, and 1.80 mg/L, respectively.

Optimize the gentamicin dosing regimen on the basis of the individual pharmacokinetic parameters of the patient to achieve the therapeutically targeted concentrations.

• Step 1: Calculate the elimination rate constant K:

000054

• Step 2: Calculate volume of distribution V:

000057

• Step 3: Calculate recommended dosing interval τ:

000060

   The practically reasonable, recommended dosing interval is 12 hours.

• Step 4: Calculate recommended dose D:

000063

   The recommended dosing regimen is 140 mg every 12 hours.

• Step 5: Check expected peak Css,max and trough Css,min:

000065

Clinical Example 2

A 70-year-old white male weighing 95 lbs is 5 feet tall and has a serum creatinine of 1.1 mg/dL. He is admitted to the hospital complaining of shortness of breath; he denies chest pain. Digoxin is prescribed for him. You are asked to design a dosage regimen using tablets for him to achieve and maintain a Ctarget,ss of 1 ng/mL. The PK parameters for digoxin are as follows: CL = 2.7 mL/minute/kg (total body weight, or TBW); fe = 0.68; Vss = 6.7 L/kg (IBW); F of tablet = 0.75.

• Step 1: Estimate CL, CLcrRF, and CL* of digoxin in this patient.

   IBW = 45.5 kg; TBW = 43 kg. Therefore, use TBW for all calculations.

   CL for a normal 43 kg patient = 116 mL/minute.

   CLcr and RF are

000067

• Step 2: Estimate CL*, clearance of digoxin in this patient with renal impairment:

CL*

= 116 mL/minute × [1 - 0.68 (1 - 0.304)]

 
 

= 61.1 mL/minute

 

• Step 3: Calculate Dose Rate*:

000069

• Step 4: Determine dosing interval τ* by estimating the half-life of digoxin:

000071

   Vss (Vd) for digoxin from PK tables is 6.7 L/kg, or 289 L in this patient. Thus,

000075

   Digoxin is normally administered every 24 hours (τ = 24 h); it could be administered 0.25 mg every 48 hours (τ = 48 h). Here, however, changing the dosing interval is not recommended, because 24 hours is very convenient, and the resultant peak:trough ratio would be lower with τ = 24 h as compared with τ = 48 h.

Clinical Example 3

A. M. is a 61-year-old white male, 6 feet tall, weighing 195 lbs. He has a diagnosis of pneumonia. His serum creatinine is 2.3 mg/dL. Design a dosage regimen of gentamicin to achieve Cpeak and Ctrough values of 8 mg/L and 1 mg/L, respectively. Vd = 0.2 L/kg IBW.

• Step 1: The CL of gentamicin is 85 mL/minute and the fe = 1.0. Calculate the degree of renal impairment:

000076

• Step 2: Calculate the CL of gentamicin in this patient:

CL*

= 85 mL/minute × [1 - 1 × (1 - 0.296)]

= 25.2 mL/minute = 1.5 L/h

 

• Step 3: Calculate the elimination rate constant in this patient:

000077

• Step 4: Calculate the infusion rate and dosing interval:

000080

Clinical Example 4

Patient D. M. is a 50-year-old white male (74.1 kg) who is being treated for seizure control with phenytoin (Vd = 0.6 L/kg), 300 mg/d, using the capsule formulation. He has been taking phenytoin for 2 weeks. He experienced a seizure on day 14 of treatment. His blood level was 5.2 mg/L. His dose rate was increased to 400 mg/d of the capsule formulation. Three weeks later his blood level was 11.8 mg/L.

• Phenytoin capsules and parenteral solution = sodium phenytoin

• Phenytoin tablets and suspension = phenytoin acid

• 100 mg phenytoin sodium = 92 mg phenytoin acid

• Step 1: The Vmax (mg/d) for phenytoin in patient D. M. is

a. 491

b. 499

c. 542

d. 590

e. 614

   Because D. M. is using capsules, you need to multiply the original dose rate by 0.92.

Dose rate (mg/day)

Css (mg/L)

Dose rate/Css (L/day)

 

300 × 0.92 = 276

5.2

53.08

 

400 × 0.92 = 368

11.8

31.19

 

000082

   Y-intercept = Vmax = 499 mg/d phenytoin slope = - Km = - 4.2 mg/L; therefore

Km = 4.2 mg/L

• Step 2: What dosage regimen would you recommend to achieve an average steady-state phenytoin concentration of 15 mg/L in patient D. M. using the capsule formulation?

a. 100 mg q6h

b. 100 mg q8h

c. 200 mg q6h

d. 200 mg q8h

000084

   390 mg/d phenytoin = 424 mg/d sodium phenytoin

   Recommend 400 mg Dilantin Kapseals in three or four divided doses (e.g., 100 mg q6h).

• Step 3: Estimate the time required to achieve steady-state levels of phenytoin in patient D. M. at the dosage regimen if it were changed to 100 mg capsule q6h.

a. 1 day

b. 5 days

c. 9 days

d. 13 days

e. 17 days

000187

   About 9 days are needed to reach 90% of new steady-state plasma concentration.

• Step 4: Calculate the loading dose of phenytoin in this patient that would be needed to achieve a phenytoin blood level of 12 mg/L. (Assume that blood levels of phenytoin = 0 at time of administration of the loading dose.)

a. 491 mg

b. 535 mg

c. 580 mg

d. 603 mg

LD =

Css,target × Vss = 12 mg/L phenytoin × 0.6 L/kg

 
 

× 74.1 kg = 534 mg of phenytoin

 

=

580 mg of phenytoin sodium (parenteral)

 

Clinical Example 5

To treat her asthma exacerbation, L. Y., a 68-year-old woman who weighs 55 kg, has received a continuous infusion of aminophylline (infusion rate 0.45 mg/kg/h) for 5 days. This morning, she suffers from theophylline toxicity indicated by tachycardia, headache, and dizziness. A blood sample is drawn, and the theophylline plasma concentration is 24.3 mg/L. The therapeutic range is 10-20 mg/L; the population average of the volume of distribution is 0.5 L/kg.

• Step 1: What is the theophylline clearance in this patient under the assumption that steady state had already been reached at the time the blood sample was obtained?

a. 0.81 L/h

b. 0.95 L/h

c. 1.35 L/h

d. 2.15 L/h

e. 2.80 L/h

000061

• Step 2: To what aminophylline infusion rate should the infusion be reduced to achieve a steady-state concentration in the middle of the therapeutic range, that is, 15 mg/L?

a. 0.17 mg/kg/h

b. 0.18 mg//kg/h

c. 0.20 mg/kg/h

d. 0.22 mg/kg/h

e. 0.28 mg/kg/h

MD

Ctarget × CL = 15 mg/L × 0.81 L/h

= 12.15 mg/h theophylline

= 15.2 mg/h aminophylline

 

   Because the patient weighs 55kg, MD = 0.28 mg/kg/h.

• Step 3: How long does it take approximately to achieve the new steady state after the infusion rate has been changed?

a. 26 hours

b. 68 hours

c. 118 hours

d. 156 hours

e. 192 hours

   Estimated V = 55 kg × 0.5 L/kg = 27.5 L

000036

   Time to new steady state approximately 5 t1/2 ≈ 118 hour

• Step 4: The pharmacist suggests that the new target concentration can be achieved faster if the first infusion with the higher infusion rate is completely stopped and the second infusion with the lower infusion rate is not initiated until the plasma concentration has decreased to 15 mg/L, the target concentration. Calculate the time the therapy has to pause (i.e., the time one waits after cessation of the first infusion before the second infusion is started).

a. 14.7 hours

b. 16.4 hours

c. 20.7 hours

d. 36.1 hours

e. 55.1 hours

000230

6-14. Key Points

• The clearance CL can be determined from the relationship

000089

• The volume of distribution can be determined from the relationship

000090

• The average steady-state concentration Css,av during multiple dosing is determined only by the dose, the dosing interval τ (or both together as dosing rate DR = D/τ) and the clearance CL:

000093

• The area under the curve resulting from administration of a single dose AUCsingle is equal to the area under the curve during one dosing interval at steady-state AUCss, provided that the same dose is given per dosing interval τ:

000094

• The volume of distribution at steady state is by definition the sum of the pharmacokinetic volumes of distribution for the different pharmacokinetic compartments. It is the theoretical

000098

   where Vp is the volume of plasma (3 L), Vt is the volume of tissue water (total body water minus plasma volume: 42 - 3 = 39 L based on a "standard" person), and fu and fu,t are the fraction unbound for the drug in plasma and tissue, respectively.

• Clearance is defined as the irreversible removal of drug from the body by an organ of elimination. CL by the eliminating organ (CLorgan) is defined as the product of blood flow to the organ (Q) and the extraction ratio of that organ (ER). The fraction of drug escaping first-pass metabolism (F*) can be described in terms of the hepatic ER (F* = 1 - ER).

• The venous equilibrium model relates hepatic ER to hepatic blood flow Q, unbound drug fraction fup, intrinsic clearance CLint:

000039

• The venous equilibrium model can be simplified for drugs with low ER (< 0.3) and high ER (> 0.7). For low-ER drugs, CLH ≈ fup * CLint. For high-ER drugs, CLH ≈ Q.

• Bioavailability is the fraction (or percentage) of a dose administered nonintravenously (or extravascularly) that is systemically available as compared to an intravenous dose. The overall oral bioavailability (F) of a drug is dependent on the fraction absorbed (fa), the fraction escaping metabolism in the intestinal wall (fg), and the fraction escaping hepatic first-pass metabolism (F*).

• Drugs may undergo three processes in the kidney. Two act to remove drug from the body: filtration and secretion. The other acts to return drug to the body: reabsorption. The net process a drug undergoes can be determined by calculating the excretion ratio (Eratio) using total renal clearance (CLR) and filtration clearance (CLF):

000006

6-15. Questions

1.

A pediatric patient receives an immunosuppressive therapy with oral cyclosporine solution. His concentration-adjusted dosing regimen is 85 mg every 12 hours. Because of a recent change in his insurance coverage, he needs to be switched from the drug product he is currently using to a generic solution dosage form of cyclosporine that is covered by his insurance. The bioavailability of the dosage form he previously used is 43%; the bioavailability of the generic dosage form is 28%. What is the appropriate dosage regimen for the generic dosage form to maintain the same systemic exposure as obtained from the previously used dosage form?

A. 25 mg every 12 hours

B. 55 mg every 12 hours

C. 184 mg every 12 hours

D. 130 mg every 12 hours

E. 305 mg every 12 hours

 

2.

A drug is administered via continuous infusion at a rate of 60 mg/h, resulting in a steady-state plasma concentration of 5 mcg/mL. If the plasma concentration is intended to be doubled to 10 mcg/mL, the infusion rate must be

A. left the same.

B. increased by 30 mg/h.

C. increased by 60 mg/h.

D. increased by 120 mg/h.

E. decreased by 30 mg/h.

 

3.

Jonathan R. (72 kg, 23 years old) has been admitted to the emergency room with acute asthma symptoms. He will be started on a continuous infusion of aminophylline with a target theophylline concentration of 12 mg/L (therapeutic range 10-20 mg/L). To achieve the target concentration more rapidly, medical personnel will administer an additional loading dose as a short-term infusion over 30 minutes. The population mean values for clearance and volume of distribution of theophylline are 2.7 L/h and 34 L, respectively. What aminophylline loading and maintenance dose should be given? (Select practically useful doses. Remember that aminophylline contains 80% theophylline.)

 

3a.

Loading dose:

A. 400 mg

B. 450 mg

C. 500 mg

D. 550 mg

E. 600 mg

 

3b.

Maintenance dose:

A. 35 mg/h

B. 40 mg/h

C. 45 mg/h

D. 50 mg/h

E. 55 mg/h

 

4.

Lidocaine will be given as a constant rate infusion for the treatment of ventricular arrhythmia. A plasma concentration of 3 mcg/mL was decided on as the therapeutic target concentration. The concentration of the infusion solution is 20 mg/mL lidocaine. The average volume of distribution of lidocaine is 90 L; the elimination half-life is 1.1 hours. What infusion rate (in mL/minute) has to be set on the infusion pump to achieve the desired target concentration?

A. 5 mL/h

B. 8.5 mL/h

C. 14 mL/h

D. 23.5 mL/h

E. 194 mL/h

 

5.

After termination of an intravenous constant rate infusion, the plasma concentration of a drug declines monoexponentially (C = C0 × e-k × t). Concentrations measured at 2 hours and 12 hours after the end of the infusion are 12.9 mcg/mL and 6.0 mcg/mL, respectively. Calculate the initial concentration at the end of the infusion, and predict the concentration 24 hours after termination of the infusion.

A. 13.5 and 2.9 mcg/mL

B. 16.5 and 3.8 mcg/mL

C. 16.5 and 1.3 mcg/mL

D. 15 and 2.4 mcg/mL

E. 15 and 1.3 mcg/mL

 

6.

Margaret Q. (100 kg, 26 years old) presents to the emergency room with acute symptoms of asthma. She recently started smoking again and has been taking oral theophylline for several years. The immediate determination of her theophylline plasma concentration results in a level of 4 mg/L.

Theophylline population pharmacokinetic parameters: CL 0.04 L/h/kg; V 0.5 L/kg Therapeutic range: 10-20 mg/L

What is the appropriate intravenous loading dose of aminophylline for Margaret to achieve a target concentration of 12 mg/L?

A. 300 mg

B. 400 mg

C. 500 mg

D. 600 mg

E. 750 mg

 

7.

For a drug product in clinical drug development, an oral dosing regimen needs to be established for a phase III study that maintains an average steady-state concentration of 50 ng/mL. In single-dose studies, an oral dose of 80 mg resulted in an AUC of 962 ng h/mL and an elimination half-life of 10.3 hours. What dosing regimen should be used?

A. 35 mg every 12 hours

B. 50 mg every 12 hours

C. 72 mg every 12 hours

D. 95 mg every 12 hours

E. 125 mg every 12 hours

 

8.

Mary D. (47 years old, 68 kg) has recently received her first 0.25 mg dose of digoxin. Plasma digoxin concentrations 12 and 24 hours following oral administration of this dose are 0.72 and 0.33 mcg/L, respectively. The therapeutic plasma concentration range is 0.8-2.0 mcg/L. Predict Mary's digoxin trough concentration at steady state, assuming that oral digoxin therapy is continued at a dose rate of 0.25 mg once daily.

A. 0.62 mcg/L

B. 0.93 mcg/L

C. 1.32 mcg/L

D. 1.57 mcg/L

E. 1.95 mcg/L

 

9.

The population average values for the clearance and volume of distribution of nifedipine have been reported as 0.41 L/h/kg and 1.2 L/kg. What would be the maximum dosing interval you can use for a multiple-dose regimen with an immediate-release oral dosage form of nifedipine if peak-to-trough fluctuation should not exceed 100%?

A. 2 hours

B. 4 hours

C. 6 hours

D. 8 hours

E. 12 hours

 

10.

Beth R. (63 years old, 58 kg) is suffering from symptomatic ventricular arrhythmia. She will be started on an oral multiple-dose regimen with the antiarrhythmic mexiletine. The population average values of mexiletine for clearance and volume of distribution are CL = 0.5 L/h/kg and V = 6 L/kg, respectively. Although a therapeutic range of 0.5-2.0 mg/L has been described, avoiding large peak-to-trough fluctuations is recommended. The available oral dosage forms are 150, 200, and 250 mg capsules with an oral bioavailability of F = 0.9. Design an appropriate and practically reasonable oral dosing regimen that keeps the plasma concentrations at an average concentration of approximately 1 mg/L, with a peak-to-trough fluctuation ≤ 100% (e.g. with concentrations within the limits of 0.75 and 1.5 mg/L).

A. 150 mg q6h

B. 200 mg q6h

C. 200 mg q8h

D. 250 mg q8h

E. 375 mg q12h

 

11.

Edgar W. (20 years old, 58 kg) is receiving 80 mg of gentamicin as IV infusion over a 30-minute period q8h. Two plasma samples are obtained to monitor serum gentamicin concentrations as follows: one sample 30 minutes after the end of the short-term infusion and one sample 30 minutes before the administration of the next dose. The serum gentamicin concentrations at these times are 4.9 and 1.7 mg/L, respectively. Assume steady state. Develop a practically reasonable dosing regimen that will produce peak and trough concentrations of approximately 8 and 1 mg/L, respectively.

A. 120 mg q8h

B. 160 mg q8h

C. 140 mg q12h

D. 180 mg q12h

E. 280 mg q24h

 

12.

A patient who is receiving chronic phenytoin therapy is hospitalized for an elective surgical procedure. Admission labs note that the patient has a phenytoin concentration of 8 mcg/mL (therapeutic range: 10-20 mcg/mL) and an albumin concentration of 3.0 g/dL. Phenytoin: F = 0.2-0.9, CL-variable, < 1% excreted unchanged in the urine, 88-93% bound to plasma proteins (primarily albumin). Given this information and the therapeutic range of phenytoin, you would recommend that the physician

A. decrease the dose of phenytoin, because high-extraction drugs (e.g., phenytoin) exhibit increased unbound concentrations with increases in fraction unbound in the plasma.

B. increase the dose rate of phenytoin, because low-extraction drugs (e.g., phenytoin) exhibit increased CL with increases in fraction unbound in the plasma.

C. not change the dose rate of phenytoin because low-extraction drugs (e.g., phenytoin) do not exhibit changes in unbound concentrations with increases in fraction unbound in the plasma.

D. not change the dose rate of phenytoin because low-extraction drugs (e.g., phenytoin) exhibit equal and offsetting changes in CL and F with increases in fraction unbound in plasma.

 

13.

Which of the following conditions indicate the possibility of renal clearance of a weakly acidic drug being sensitive to changes in urine pH?

I. It is secreted and not reabsorbed.

II. It has a pKa value of 5.0.

III. It has a small volume of distribution.

IV. All of the drug is excreted unchanged by the kidneys (i.e., fe = 1).

A. Only item I is correct.

B. Only item II is correct.

C. Only item III is correct.

D. Items II and III are correct.

E. Items II and IV are correct.

 

14.

A young man (age 28, 73 kg, creatinine clearance 124 mL/minute) receives a single 200 mg oral dose of an antibiotic. The following pharmacokinetic parameters of the antibiotic are reported in the literature:

• F = 90%

• Vd = 0.31 L/kg

• t1/2 = 2.1 h

• fup = 0.77

• 67% of the antibiotic's absorbed dose is excreted unchanged in the urine.


Determine the renal clearance of the antibiotic. What is the probable mechanism for renal clearance of this drug?

A. 84 mL/minute, glomerular filtration and tubular reabsorption

B. 98 mL/minute, glomerular filtration and tubular reabsorption

C. 112 mL/minute, glomerular filtration

D. 167 mL/minute, glomerular filtration and tubular reabsorption

E. 236 mL/minute, glomerular filtration and tubular secretion

 

15.

The pharmacokinetic parameters for captopril in healthy adults are

• Clearance: 800 mL/minute

• fe = 0.5

• Vss: 0.81 L/kg

• Plasma protein binding: 75%

 

15a.

Captopril is a weakly basic drug that is used in the treatment of hypertension. Assume a glomerular filtration rate of 125 mL/minute. What is (are) the mechanism(s) for renal clearance of captopril?

A. Filtration only

B. Reabsorption only

C. Secretion only

D. Filtration and net secretion

E. Filtration and net reabsorption

 

15b.

When cimetidine (a highly lipid soluble weak base that is highly secreted in the renal proximal tubules) and captopril are coadministered, the renal clearance of captopril is reduced to approximately 125 mL/minute. What is the most likely mechanism to account for this reduction in renal clearance?

A. Cimetidine reduces the filtration clearance of captopril.

B. Cimetidine enhances the reabsorption of captopril.

C. Cimetidine increases the unbound fraction of captopril.

D. Cimetidine blocks the renal secretion of captopril.

 

16.

One of the most severe drug interactions is that between digoxin and quinidine. Administration of quinidine to patients taking digoxin results in a two- to threefold increase in digoxin Css and AUC after oral and intravenous administration of digoxin. Digoxin and quinidine are substrates for the multidrug resistance transporter, P-glycoprotein. According to the following pharmacokinetic data for digoxin, what is the most likely mechanism to explain this drug-drug interaction?

CL: 125 mL/minute

Vss: 1.2 L/kg (IBW)

fe: > 0.99

fup: 0.25

A. Quinidine reduces the digoxin fraction escaping first-pass metabolism.

B. Quinidine inhibits renal secretion of digoxin by blocking P-glycoprotein.

C. Quinidine decreases digoxin fraction reabsorbed in the kidney tubule.

D. Quinidine reduces the fraction of digoxin absorbed.

 

17.

The drug transporter P-glycoprotein is involved in numerous processes in drug disposition. P-glycoprotein activity is directly responsible for the following processes:

I. Glomerular filtration

II. Transport of drug from hepatocytes into the bile

III. Transport of drug from the small intestine into the systemic circulation (i.e., bloodstream)

IV. Degradation of drug in the lumen of the duodenum

V. Maintenance of the integrity of the blood-brain barrier by transport of drug out of the brain

A. Only V

B. II and V

C. II and III

D. I, II, and V

E. All of the above

 

18.

A 59-year-old white female is hospitalized for a ruptured duodenal diverticulum. She is 5 feet 6 inches, weighs 65 kg, and has a serum creatinine of 1.5 mg/dL. Design a dosage regimen to achieve Cpeak and Ctrough values of 8.0 and 0.5 mg/L with an infusion time = 30 minutes. Assume Vd of gentamicin of 0.2 L/kg IBW in this patient. The typical population value of CL for gentamicin is 85 mL/minute/70 kg.

Which of the following dosage regimens would you recommend for this patient?

A. 100 mg q8h

B. 100 mg q18h

C. 100 mg q24h

D. 160 mg q12h

E. 160 mg q24h

 

19.

J. D. is a 47-year-old white male who has been prescribed codeine for lower back pain. The pharmacist dispensing the medication remembers reading a study in which patients who took codeine with grapefruit juice experienced an enhanced analgesic effect. The study found that grapefruit juice enhanced oral bioavailability (F) of codeine. Interestingly, there was no effect on codeine hepatic clearance or volume of distribution. Thus, the pharmacist counseled the patient not to take his codeine with grapefruit juice. Based on the pharmacokinetic data for codeine (listed below), what is the most likely explanation for the enhanced oral bioavailability of codeine?

CL: 1,350 mL/minute

fe: 0.10

Vss: 3.3 L/kg

Plasma protein binding: 35%

A. Grapefruit juice increases the absorption (fa) of codeine.

B. Grapefruit juice decreases the fraction escaping first-pass metabolism (F*).

C. Grapefruit juice increases renal secretion of codeine.

D. Grapefruit juice increases the fraction escaping first-pass metabolism (F*).

 

20.

The pharmacokinetic parameters for codeine in healthy adults are as follows:

Oral F: 50%

fe < 0.01

Vss: 2.6 L/kg

Plasma protein binding: 7%


Codeine is well absorbed (fa = 1, fg = 0.8). You may assume that hepatic blood flow in a 70 kg adult is 1,350 mL/minute. The hepatic clearance of codeine is

A. 851 mL/minute.

B. 1,350 mL/minute.

C. 500 mL/minute.

D. 675 mL/minute.

 

6-16. Answers

1.

D. The systemic exposure or average steady-state concentration for an oral dosing regimen is given by

000086

where DR is the dose rate and F the oral bioavailability of the respective dosing regimens. If Css,av should be maintained constant, if follows that

000003

where the subscript denotes the different dosing regimens. Thus DR2, the dose rate for the generic dosage form, can be calculated as

000016

 

2.

C. Steady-state plasma concentration of a constant-rate infusion is directly proportional to the infusion rate R0 through

000004

Thus, R0 has to be doubled from 60 mg/h to 120 mg/h to increase Css from 5 to 10 mcg/mL, that is, an increase of infusion rate by 60 mg/h.

 

3a.

C. 500 mg for the loading dose.

 

3b.

B. 40mg/h for the maintenance dose.

The loading dose and maintenance dose can be calculated from target concentration and volume of distribution or clearance:

 

LD

Ctarget × V = 12 mg/L × 34 L

 
 

= 408 mg theophylline

 
 

= 510 mg aminophylline

 

MD

Ctarget × CL = 12 mg/L × 2.7 L/h

 
 

= 32.4 mg/h theophylline

 
 

= 40.5 mg/h aminophylline

 

4.

B. The infusion rate R0 or maintenance dose MD needed to achieve and maintain a steady-sate concentration of 3 mcg/mL is given by

000002

The infusion pump setting can then be calculated as

000197

 

5.

D. The first step is to calculate the elimination rate constant k from the measured plasma concentrations:

000260

The initial concentration C0 at the end of the infusion can then be back-extrapolated by solving the following relationship for C0:

000014

The concentration 24 hours after termination of the infusion can be predicted by

C24 h = 15 mcg/mL × e-0.077 h-1 × 24 h = 2.4 mcg/mL

 

6.

C. The loading dose can be determined on the basis of the target concentration to be achieved and the volume of distribution. The predose level of 4 mg/L needs to be subtracted from the target concentration, because the loading dose only has to account for the concentration difference. The calculated theophylline dose needs to be converted to aminophylline:

 

LD =

(Ctarget - Cpredose) × Vd

 

=

(12 - 4) mg/L × 0.5 L/kg

 
 

× 100 kg = 400 mg theophylline

 
 

A loading dose of 400 mg theophylline is equivalent to 500 mg aminophylline.

 

7.

B. The maintenance dose MD required to achieve an average steady-state concentration of 50 ng/mL for an oral dosing regimen is given by

MD = Css,av × CL/F

The oral clearance CL/F can be determined from the relationship between dose and area under the plasma concentration-time curve AUC:

000040

Thus, the required MD can be calculated as

000008

This corresponds to a dosing regimen of 50 mg (4.16 mg/hour × 12 hours) given every 12 hours.

 

8.

D. Because trough concentrations after the first dose are known (0.33 mcg/L), trough concentrations during multiple dose at steady state can be predicted by multiplying the trough after the first dose with the accumulation factor

000010

The dosing interval τ is 24 hours; k can be calculated from

000011

Thus,

000012

 

9.

A. For immediate-release formulations, upper limits for peak concentrations (Css,max) and lower limits for trough concentrations (Css,min) can be estimated by assuming immediate drug absorption. If fluctuation is equal to 100%, Css,min is exactly one-half of Css,max. This is the case when the dosing interval τ is equal to the elimination half-life t1/2 of the drug. A population average half-life for nifedipine can be calculated as

000035

Thus, τ has to be smaller than 2.03 hours to avoid peak-to-trough fluctuation exceeding 100%.

 

10.

D. Calculate necessary dose rate DR to maintain Css,avg = 1 mg/L:

000017

Determine the maximum dosing interval:

000021

Practical dosing interval: 8 hours

 

D

DRnecessary × τ = 32.22 mg/h × 8h

= 257.8 mg

 
 

Recommended dosing regimen: 250 mg every 8 hours

 

11.

C. Calculate the elimination rate constant k:

000023

Calculate the volume of distribution assuming steady state:

000218

Calculate the recommended dosing interval:

000009

Recommended dosing interval: 12 hours

Calculate the recommended dose:

000024

Recommended dosing regimen: 140 mg every 12 hours

 

12.

C. Phenytoin has to be a low-extraction drug because its bioavailability is as high as 90%. The large range in F is due to variability in the absorption of the drug. You know it is not high extraction because if it were, you could never get an F of 90%. Assume ER < 0.1, fup = 0.07-0.12. Low-extraction drug and restrictively cleared (assume all low-ER drugs are restrictively cleared for the purposes of this course). Normal albumin range: 3.5-5 gm/dL. Thus, patient probably has increased fup because of decreased albumin. Fup (according to the following equation) would be 0.14 (slightly elevated).

000027

Because phenytoin is a low-extraction drug, CL is dependent on fup and CLint. Increased fup would lead to increased CL and decreased total plasma concentrations (thus Cp of 8, which is below therapeutic range). However, unbound concentrations would be predicted to be normal (therapeutic) even though total concentration is low. You would not recommend an increase in patient's phenytoin dose because it may result in toxic concentrations. Obtaining free phenytoin plasma concentration, if available from the hospital's lab, may be reasonable to document therapeutic concentrations.

 

13.

B. Only item II is correct. Item I is incorrect. No pH sensitivity in CLR is expected unless the drug is reabsorbed (i.e., Eratio << 1). Item II is possible. Weakly acidic drugs with pKa values between 3.0 and 7.5 can be highly un-ionized in the range of urine pH (5-8) and can thus undergo significant reabsorption if the unionized form is nonpolar. Item III is incorrect. Clearance and volume have nothing to do with a drug's likelihood of being affected by changes in urine pH. Item IV is incorrect. The fraction excreted unchanged says nothing about the mechanisms of renal elimination. However, it is important to note that for drugs with high fe values that are susceptible to changes in urine pH, large changes in the PK of the drug (i.e., CLR) may be observed.

 

14.

A. The antibiotic's total clearance can be determined from the reported Vd and t1/2:

000029

Renal clearance CLR is then given by total clearance and the fraction excreted fe:

 

CLR

fe × CL = 0.67 × 7.47 L/h = 5.00 L/h

 
 

= 83.3 mL/minute

 
 

The predominant renal clearance mechanism can be estimated by determining the Eratio:

000185

The Eratio < 1 indicates that glomerular filtration and net reabsorption are the probable renal clearance mechanisms.

 

15a.

D.

000032

 

15b.

D. The most likely mechanism to account for this reduction in renal clearance is that cimetidine blocks the renal secretion of captopril.

 

16.

B.

000102

 

17.

B. The drug transporter P-glycoprotein is directly responsible for the transport of drug from hepatocytes into the bile and maintenance of the integrity of the blood-brain barrier by transport of drug out of the brain.

 

18.

C. Calculation of CL: IBW = 59.3 kg:

000107

CL of gentamicin is 85 mL/minute/70 kg TBW (1.2 mL/minute/kg). CL of gentamicin in this patient if she did not have renal impairment would be

000046

Calculate the dosing interval (τ) that you would recommend:

000030

Calculate the dose of gentamicin that will maintain Cpeak and Ctrough of 8 and 0.5 mg/L:

000183

Administration of 100 mg of gentamicin infused over 30 minutes given every 24 hours will provide Cpeak and Ctrough of approximately 8.0 and 0.5 mg/L.

 

19.

A.

000124

 

20.

C.

000028

 

6-17. References

Atkinson A, Daniels C, Dedrick R, et al. Principles of Clinical Pharmacology. Academic Press, San Diego, Calif.; 2001.

Ensom MH, Davis GA, Cropp CD, Ensom RJ. Clinical pharmacokinetics in the 21st century: Does the evidence support definitive outcomes? Clin Pharmacokinet. 1998;34:265-79.

Levy RH, Bauer LA. Basic pharmacokinetics. Ther Drug Monit. 1986;8(1):47-58.

Meibohm B, Derendorf H: Basic concepts of pharmacokinetic/pharmacodynamic (PK/PD) modelling. Int J Clin Pharmacol Ther. 1997;35:401-13.

Rolan, PE. Plasma protein binding displacement interactions: Why are they still regarded as clinically important? Br J Clin Pharmacol. 1994;37: 125-8.

Rowland M, Tozer T. Clinical Pharmacokinetics. 3rd ed. Media, Pa.: Williams & Wilkins; 1995.

Saitoh A, Jinbayashi H, Saitoh AK, et al. Parameter estimation and dosage adjustment in the treatment with vancomycin of methicillin-resistant Staphylococcus aureus ocular infections. Ophthalmologica. 1997;211(4):232-35.

Sawchuk RJ, Zaske DE, Cipolle RJ, et al. Kinetic model for gentamicin dosing with the use of individual patient parameters. Clin Pharmacol Ther. 1977;21:362-69.

Tod MM, Padoin C, Petitjean O. Individualising aminoglycoside dosage regimens after therapeutic drug monitoring: Simple or complex pharmacokinetic methods? Clin Pharmacokinet. 2001; 40:803-14.

Wilkinson, GR, Shand, DG. Commentary: A physiological approach to hepatic drug clearance. Clin Pharmacol Ther. 1975;18:377-90.