MARTINEZ AND AMIDONUNDERSTANDING THE FACTORS AFFECTING DRUG ABSORPTIONPHARMACOKINETICS AND PHARMACODYNAMICS
`
`PHARMACOKINETICS AND PHARMACODYNAMICS
`
`A Mechanistic Approach to Understanding
`the Factors Affecting Drug Absorption:
`A Review of Fundamentals
`
`Marilyn N. Martinez, PhD, and Gordon L. Amidon, PhD
`
`This article provides an overview of the patient-specific and
`drug-specific variables that can affect drug absorption fol-
`lowing oral product administration. The oral absorption of
`any chemical entity reflects a complex spectrum of events.
`Factors influencing product bioavailability include drug sol-
`ubility, permeability, and the rate of in vivo dissolution. In
`this regard, the Biopharmaceutics Classification System has
`proven to be an important tool for predicting compounds
`likely to be associated with bioavailability problems. It also
`helps in identifying those factors that may alter the rate and
`extent of drug absorption. Product bioavailability can also be
`markedly influenced by patient attributes such as the integ-
`
`rity of the gastrointestinal tract, physiological status, site of
`drug absorption, membrane transporters, presystemic drug
`metabolism (intrinsic variables), and extrinsic variables such
`as the effect of food or concomitant medication. Through an
`awareness of a drug’s physicochemical properties and the
`physiological processes affecting drug absorption, the skilled
`pharmaceutical scientist can develop formulations that will
`maximize product availability. By appreciating the potential
`impact of patient physiological status, phenotype, age, gen-
`der, and lifestyle, dosing regimens can be tailored to better
`meet the needs of the individual patient.
`Journal of Clinical Pharmacology, 2002;42:620-643
`©2002 the American College of Clinical Pharmacology
`
`A fundamental premise associated with the use of a
`
`therapeutic agent is that for any given patient, the
`clinical response can be predicted on the basis of the
`selected drug product, dose, and dosing regimen. This
`tenet provides the foundation for concepts of
`prescribability and switchability.1 Prescribability refers
`to an assumed relationship between a therapeutic out-
`come and the rate and extent of drug exposure. A physi-
`cian will prescribe a particular product in accordance
`with assumptions pertaining to this relationship.
`Generally, the process of drug movement from in-
`take (e.g., oral delivery systems) to its site of action can
`be schematically presented as follows (Figure 1).
`As depicted in Figure 1, the relationship between
`drug intake and a clinical response is highly complex,
`potentially affected by a host of intrinsic and extrinsic
`
`From the Office of New Animal Drug Evaluation, HFV-130, Center for Vet-
`erinary Medicine, Food and Drug Administration, Rockville, Maryland (Dr.
`Martinez) and the University of Michigan, College of Pharmacy, Ann Arbor,
`Michigan (Dr. Amidon). Submitted for publication August 15, 2001; re-
`vised version accepted February 15, 2002. Address for reprints: Marilyn N.
`Martinez, Office of New Animal Drug Evaluation, HFV-130, Center for
`Veterinary Medicine, Food and Drug Administration, 7500 Standish Place,
`Rockville, MD 20855.
`
`620 • J Clin Pharmacol 2002;42:620-643
`
`variables. Accordingly, deviations between drug re-
`sponse within or between individuals may be ascribed
`either to product bioavailability (i.e., the rate and extent
`of drug absorption), drug pharmacokinetics (which in-
`cludes the metabolism, distribution, and elimination of
`a compound), or the particular concentration-effect
`relationship.
`While product formulation can significantly affect
`processes leading to drug absorption, once in the circu-
`lation, the original formulation is generally considered
`to no longer affect the ultimate drug response. In other
`words, it is the concentration of the drug moiety, along
`with its corresponding effect, that will ultimately de-
`termine product safety and effectiveness. For this rea-
`son, once a patient is titrated to a particular product
`and dosing regimen, we assume that a comparable clin-
`ical response will be achieved if the patient elects to
`take a less expensive generic equivalent.
`The purpose of this article is to discuss basic princi-
`ples associated with the process of drug absorption.
`Special attention will be given to the use of the
`Biopharmaceutics Classification System (BCS) as a
`predictive tool for identifying compounds whose ab-
`sorption characteristics may be sensitive to intrinsic
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`
`UNDERSTANDING THE FACTORS AFFECTING DRUG ABSORPTION
`
`ORAL DRUG INTAKE
`
`Drug Disintegration and Dissolution
`Loss via Luminal Degradation
`
`Diffusion through Gastrointestinal Fluids
`
`Membrane Permeation
`
`Uptake into Blood or Lymph
`
`Drug in Systemic Circulation
`
`Loss via Mucosal Metabolism
`
`Loss via Hepatic Metabolism
`
`Bound Drug Unbound Drug
`
` Clearance
`
`Bound Tissue Drug
`Concentrations
`
`Free Tissue Drug
`Concentrations
`
` Active Site Concentrations
`
`EFFECT
`
`Figure 1. Schematic diagram of the relationship between an oral
`dose of a drug product and its ultimate effect.
`
`(physiological) and extrinsic (e.g., food and formula-
`tion) variables. Accordingly, this review focuses on
`those factors that can affect drug dissolution, aqueous
`solubility, membrane permeability, and presystemic
`drug metabolism.
`
`WHAT IS THE BCS?
`
`One of the most significant prognostic tools created to
`facilitate product development in recent years has been
`the BCS.2 By knowing the solubility and permeability
`characteristics of specific compounds, we improve our
`ability to predict those variables (such as formulation,
`food, dosing regimen, and disease) that will alter oral
`drug absorption.
`Currently, all pharmaceutical compounds are
`grouped into one of the following categories:
`
`Class I—high solubility, high permeability: generally very
`well-absorbed compounds
`Class II—low solubility, high permeability: exhibit disso-
`lution rate-limited absorption
`Class III—high solubility, low permeability: exhibit per-
`meability rate-limited absorption
`
`Class IV—low solubility, low permeability: very poor oral
`bioavailability
`
`Solubility is calculated on the basis of the largest
`strength manufactured. It is defined as the minimum
`solubility of drug across a pH range of 1 to 8 and at a
`temperature of 37 ± 0.5°C. High-solubility drugs are
`those with a ratio of dose to solubility volume that is
`less than or equal to 250 ml. Permeability (Peff, ex-
`pressed in units of 104 cm per second) is defined as the
`effective human jejunal wall permeability of a drug.
`High-permeability drugs are generally those with an
`extent of absorption greater than or equal to 90% and
`are not generally associated with any documented in-
`stability in the gastrointestinal tract.
`It is interesting to note that for certain compounds,
`Peff is not necessarily constant. For example, nonlinear
`changes in Peff were observed with increasing doses of
`the surface-active molecule, fluvastatin. This nonlin-
`ear increase in Peff was attributed to its effects on mem-
`brane surface tension and to a possible decrease in
`poly-glycoprotein (P-gp) activity associated with an in-
`crease in intestinal membrane fluidity.3
`The application of this system to nonhuman species
`may require adjustment of these classification parame-
`ters based on physiological differences in gastric vol-
`ume and the pH of the gastrointestinal (GI) fluids. Ac-
`cordingly, at this time, we cannot be certain that the
`BCS classification of a compound remains constant
`across all species. This question is currently being ex-
`plored by the Food and Drug Administration’s (FDA’s)
`Center for Veterinary Medicine.
`By understanding the relationship between a drug’s
`absorption, solubility, and dissolution characteristics,
`it is possible to define situations when in vitro dissolu-
`tion data can provide a surrogate for in vivo
`bioequivalence assessments. The use of this surrogate
`relies on the validity of three fundamental assump-
`tions. First, it must be assumed that a comparison of
`product in vitro dissolution performance accurately re-
`flects relative differences in product in vivo dissolu-
`tion behavior. Second, we must assume that if two
`products present with equivalent in vivo dissolution
`profiles under all luminal conditions, they will present
`equivalent drug concentrations at absorptive mem-
`brane surfaces. Third, for comparable dissolution pro-
`files to ensure comparable in vivo absorption, the rate
`and extent of drug presented to absorptive membrane
`surfaces must determine the absorption characteristics
`of that drug product.
`Lobenberg and Amidon4 have summarized the rela-
`tionships between dose, dissolution characteristics,
`drug solubility, and drug absorption properties. These
`relationships can be described as follows:
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`MARTINEZ AND AMIDON
`
`1. Absorption number (An) = (Peff/R) • <Tsi>,
`where R is the gut radius and <Tsi> the residence time
`of the drug within the intestine.
`2. Dissolution number (Dn) = (3D/r2) • (Cs/ρ) • <Tsi>,
`where D is the diffusivity of the dissolved drug, ρ is the
`density of the dissolved drug, Cs is the drug solubility,
`and r is the initial radius of the drug particle.
`M / V
`,
`3. Ratio of dose to dissolved drug (D0) =
`0
`C
`where M is the dose of the drug and V0 is the volume of
`fluid consumed with the dose.
`The fraction of drug absorbed is closely related to the
`drug’s effective permeability across mucosal cells.4 If
`the Peff of a drug is less than 2 • 10–4 cm/s, then drug ab-
`sorption will be incomplete, whereas complete absorp-
`tion can be expected for substances whose Peff exceeds
`this value. For poorly soluble drugs, critical variables
`include the volume of the intestinal fluids, GI pH, and
`GI transit time (where adequate time is needed to dis-
`solve poorly soluble materials). For these lipophilic
`compounds, food and bile salts may increase drug
`solubility.
`Class I compounds are highly permeable and readily
`go into solution (Dn > 1). In this case, the fraction ab-
`sorbed (F) can be expressed as follows:
`
`s
`
`F = 1 –exp(–2An).
`
`For these agents, as “An” increases, the fraction of
`drug absorbed increases, with 90% absorption (highly
`permeable compounds) occurring when An = 1.15. Re-
`ferring back to the equation for An, we see that F can be
`affected by a change in the compound’s membrane per-
`meability, the gut radius of the host, or the intestinal
`transit time. Based on these factors alone, it is evident
`that differences in GI physiology due to factors such as
`disease, age, or animal species can alter the value of An
`and, therefore, the fraction of drug absorbed.
`For Class II drugs (high permeability, low solubility),
`Dn < 1. In these cases, the relationship between D0 and
`Dn is critical for determining the fraction of drug ab-
`sorbed, and the rate of drug dissolution tends to be the
`rate-limiting step. Accordingly, anything that increases
`the rate and extent of in vivo dissolution will also in-
`crease the bioavailability of that compound.
`
`SOLUBILITY
`
`Aqueous solubility can be estimated by determining
`the ability of a drug to partition from lipid to aqueous
`environments. This partitioning behavior is often a
`function of solvent pH due to the latter’s effects on drug
`
`622 • J Clin Pharmacol 2002;42:620-643
`
`ionization. In general, ionized drugs tend to exhibit far
`greater aqueous solubility than the un-ionized counter-
`part. Consequently, the rate of solute dissolution in
`aqueous media can be markedly affected by the pH of
`that solvent.
`To examine the effect of pH on drug ionization, one
`can use a rearrangement of the Henderson-Hasselback
`equation:5
`
`Weak acid: % un-ionized = 100/(1 + antilog (pH-pKa)).
`Weak base: % un-ionized = 100/(1 + antilog (pKa-pH)).
`
`Weakly basic drugs tend to have a slower dissolution
`rate at higher pH (when more drug exists in its un-
`ionized form), whereas weakly acidic drugs dissolve
`faster at higher pH (when more drug exists in its ion-
`ized form). Examples of the relationship between the
`percentage of drug in its un-ionized form as a function
`of drug pKa and pH are found in Figures 2 and 3. For
`this reason, by increasing the proportion of drug exist-
`ing in its un-ionized state, meals that elevate gastric pH
`can decrease the dissolution of a weak base. For exam-
`ple, weak bases such as indinavir (with pKa of 3.7 and
`5.9) are expected to precipitate when gastric pH is ele-
`vated during a meal, resulting in a significant reduction
`in AUC and Cmax values in fed versus fasted human sub-
`jects.6 Conversely, the same meal can increase the dis-
`solution rate of a weak acid by increasing the propor-
`tion of drug existing in its ionized state, thereby making
`it more water soluble.7
`By definition, solubility is the extent to which mole-
`cules from a solid are removed from its surface by a sol-
`vent. While solubility may be expressed in many ways,
`some generalizations can be made:8
`
`Very soluble: Less than 1 part solvent needed to dissolve 1
`part solute
`Freely soluble: From 1 to 10 parts solvent needed to dis-
`solve 1 part solute
`Soluble: From 10 to 30 parts solvent needed to dissolve 1
`part solute
`Sparingly soluble: From 30 to 100 parts solvent needed to
`dissolve 1 part solute
`Slightly soluble: From 100 to 1000 parts solvent needed to
`dissolve 1 part solute
`Very slightly soluble: From 1000 to 10,000 parts solvent
`needed to dissolve 1 part solute
`Practically insoluble: More than 10,000 parts solvent
`needed to dissolve 1 part solute
`
`A compound’s aqueous solubility, as measured by its
`propensity to distribute between octanol and water, is a
`function of its ability to form hydrogen bonds with the
`water molecule. Generally, aqueous solubility is di-
`rectly proportional to the number of hydrogen bonds
`that can be formed with water.9 As discussed later,
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`UNDERSTANDING THE FACTORS AFFECTING DRUG ABSORPTION
`
`percent drug
`unionized
`
`100
`
`80
`
`60
`
`40
`
`20
`
`0
`
`pKa = 2
`pKa = 4
`pKa = 6
`pKa = 8
`
`0
`
`1
`
`2
`
`3
`
`4
`pH of solution
`
`5
`
`6
`
`7
`
`8
`
`Figure 2. Relationship between percentage of drug un-ionized, and
`pH and pKa of weak acids.
`
`percent drug
`unionized
`
`100
`
`80
`
`60
`
`40
`
`20
`
`0
`
`pKa = 2
`pKa = 4
`pKa = 6
`pKa = 8
`
`0
`
`1
`
`2
`
`4
`3
`pH of solution
`
`5
`
`6
`
`7
`
`8
`
`Figure 3. Relationship between percentage of drug un-ionized, and
`pH and pKa of weak bases.
`
`while very high aqueous solubility is beneficial for
`drug dissolution in aqueous media, these same com-
`pounds often exhibit low permeability due to their
`high polarity and poor lipophilicity.
`Although lipid/water partitioning is often used to
`describe drug solubility, there is some evidence that
`solubility may better be described by the compound’s
`dynamic energy properties.10 The solubility parameter
`of any compound can be described in terms of the en-
`ergy required to fragment a molecule into its constitu-
`ent atoms (its cohesive energy). When described in
`terms of the square root of its cohesive energy density
`(energy of vaporization per unit volume), the solubility
`parameter will lie on a scale from 10 (nonpolar) to 48
`(water). For two materials to be miscible, their solubil-
`ity parameters must be similar.
`When comparing the percent absorbed versus log P
`(octanol/water partition coefficient), the percent ab-
`sorbed versus the solubility parameter, and the percent
`absorbed versus the number of hydrogen bond accep-
`tors, it was noted that a high level of negative correla-
`
`tion was observed for the latter two relationships. Con-
`versely, a large degree of scatter was observed in the re-
`lationship between permeability and log P. It was also
`noted that highly permeable compounds tend to have
`solubility parameter values almost identical to that of
`biological membranes (solubility parameter values of
`20-26 MPa1/2). Accordingly, thermodynamic consider-
`ations rather than physicochemical interactions10 may
`serve as the best predictors of a compound’s membrane
`permeability.
`
`IN VIVO DRUG ABSORPTION
`
`Efforts are currently under way to identify molecular
`quantitative structure-bioavailability relationships
`(QSBR) that predict drug bioavailability.11 Factors that
`negatively influence bioavailability include the num-
`ber of hydrogen bond donors, the presence of heavy at-
`oms, and the inclusion of fragments such as tetrazole,
`4-animopyridine, and benzoquinone. Factors that tend
`to enhance drug bioavailability include the presence of
`hydrogen acceptors, low molecular weight, and the
`presence of fragments such as azide, salicylic acid, and
`amides.
`To understand reasons for these structure-
`bioavailability relationships, it is important to recog-
`nize the complex series of events that occur during the
`process of drug absorption. Molecular movement
`across lipid bilayers, such as those existing within bio-
`logical membranes, is extremely complex due to the re-
`gional differences in membrane polarity, hydrophobicity,
`and density. Generally, the bilayer can be divided into
`four distinct regions.12 These include the following:
`
`1. The first (outermost) region contains a high proportion
`of water molecules and may be the region responsible
`for interactions with other membranes and proteins.
`2. The second region has the highest molecular density
`of all four regions (contains the polar headgroups),
`contains little or no water, and exerts the greatest
`barrier to solute diffusion (due to its density
`characteristics).
`3. The third region contains the highest density of
`nonpolar tails. This region serves as the primary bar-
`rier to membrane penetration and is primarily respon-
`sible for the limitations in molecular size and shape
`associated with membrane transport.
`4. The fourth region is the most hydrophobic region of
`the membrane, serving as a hydrophobic barrier in
`membrane transport.
`
`Owing to this membrane structure, it is evident that drug
`permeability is not a simply two-step process of
`solubilization and diffusion but rather represents a
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`MARTINEZ AND AMIDON
`
`spectrum of complex molecular events. Accordingly,
`intestinal permeability reflects a multifunctional inter-
`action of factors such as molecular size (negatively cor-
`related), lipophilicity (positively correlated), polar van
`der Walls surface area (negatively correlated), and the
`molecular flexibility (intramolecular hydrogen bond
`formation).13
`In addition to cellular membrane barriers to drug
`diffusion, significant impedance is also effected by the
`components of the gastric and intestinal mucous
`layer.14 In examining the relative contribution of these
`various components, it was noted that lipid constitu-
`ents such as phosphatidyl choline, cholesterol, and
`linoleic acid significantly retard the diffusion of small
`lipophilic molecules such as propranolol and hydro-
`cortisone. Conversely, small hydrophilic molecules
`such as mannitol appear to freely diffuse through this
`lipoid barrier. Mucous gel-forming components, such
`as mucin and DNA, exert far less negative effects on the
`diffusion of lipophilic molecules. However, they may
`serve to block the diffusion of peptides and proteins.
`Molecular flexibility and the corresponding ability
`to undergo conformation changes can significantly af-
`fect the polar surface area of a molecule. The polar sur-
`face area and nonpolar surface area are powerful pre-
`dictors of intestinal permeability, being respectively
`inversely and directly related to membrane permeabil-
`ity.15 However, any particular set of descriptors may not
`adequately predict membrane permeability across
`nonhomologous compounds.9 Another important vari-
`able is the strength of the hydrogen bonds formed be-
`tween the molecules of water and solute.15 It is gener-
`ally assumed that these bonds must be broken
`(desolvation) before the solute can traverse the biologi-
`cal membrane. Which of these factors play the domi-
`nant role in determining drug permeability may vary
`across homologous drug series.
`Despite these complexities, certain generalizations
`can be made with regard to drug absorption processes.
`For example, the vast majority of orally administered
`drugs are absorbed via passive transcellular transport.15
`This necessitates that the drug traverse through a
`highly lipophilic membrane. Accordingly, diffusion
`processes are governed by Fick’s laws of diffusion and
`therefore influenced by the compound’s lipophilicity.
`This ability to diffuse through lipids has been found to
`be highly correlated with the ability of a drug to parti-
`tion between water and an organic solvent such as
`octanol. In fact, when expressed as log P0 (based on par-
`titioning between n-octanol and water), the optimal
`partition coefficient for a drug generally falls within the
`range of 2 to 7.5 Nevertheless, exceptions do occur, and
`while transcellular transport generally occurs when
`
`624 • J Clin Pharmacol 2002;42:620-643
`
`the compound is un-ionized, recently, several ionized
`molecules have been shown to be absorbed via
`transcellular processes.16,17 This finding reinforces ear-
`lier statements regarding the degree of scatter associ-
`ated with the relationship between log P and drug
`absorption.
`In addition to passive mechanisms, active transport
`is important to the absorption of several compounds.
`Both active and passive transport mechanisms may oc-
`cur simultaneously for the same molecule. Which of
`these mechanisms has the dominant role tends to be
`compound specific and may not be well predicted by
`in vitro systems.15 Nevertheless, it must be remem-
`bered that even active transport mechanisms require
`that the drug penetrate the intestinal cells via the
`transcellular route.
`The rate of passive diffusion of any molecule,
`whether it be absorbed via transport between mucosal
`cells or through the mucosal membrane, can be de-
`scribed by the following equation:18
`
`dM
`dt
`
`=
`
`A
`m
`
`•
`
`D
`m
`λ
`
`•
`
`C
`
`membrane
`
`•
`
`C
`
`lumen
`
`+
`
`•
`
`J
`
`fluid
`
`+
`
`K
`C
`
`m
`
`lumen
`
`•
`
`A
`
`p
`
`D
`λ
`
`q
`a
`
`aq
`
`J
`max
`+
`C
`lumen
`
`)(1 α ,
`−
`•
`
`+
`
`
`
`where
`dM/dt
`
`Daq
`
`aq
`
`λ
`Jfluid
`α
`
`K
`
`Dm
`
`Jmax
`
`Km
`
`= the effective rate of passive drug
`absorption (concentration/time).
`= the diffusion coefficient of the
`compound in water.
`= the aqueous diffusion distance.
`= the fluid flow between epithelial cells.
`= the ratio of the water flow relative to the
`solute flux, both under the influence of
`the existing pressure gradient, and is
`dependent on molecular size, volume,
`charge, and hydration number. It may
`also be influenced by the dynamic
`width of the tight junction.
`= the partition coefficient describing the
`relative tendency of the substance to
`dissolve in the membrane phase (Cmembrane)
`as compared to the surrounding aqueous
`phase (Clumen).
`= the diffusion coefficient of the
`compound within the membrane, which
`is dependent on factors such as drug
`lipophilicity, hydrogen bonding
`capacity, polar surface area of the
`molecular, molecular volume, and
`shape.
`= the maximal transport capacity of the
`carrier-mediated process.
`= the substrate specificity of the
`membrane transporter (the Michaelis
`constant).
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`UNDERSTANDING THE FACTORS AFFECTING DRUG ABSORPTION
`
`where dm/dt is the dissolution rate, expressed as the
`change in the amount of drug dissolved (m) per unit
`time (t); D is the diffusion coefficient; S is the surface
`area; h is the thickness of the diffusion film adjacent to
`the dissolving surface; Cs is the saturation solubility of
`the drug molecule; Ct is the concentration of the dis-
`solved solute; and V is the volume of the dissolution
`medium.
`Upon integration, this equation can be expressed as
`follows:25
`
`−
`
`exp(
`
`−
`
`Kt
`
`))
`
`C V
`
`
`
`s (1
`
`m =
`
`and
`
`K = S • D/h.
`
`The viscosity of the GI contents,23,26 as described by
`the following equation, can affect D, the diffusion
`coefficient:
`
`D = (KbT)/(6πR0η),
`
`
`where D is the diffusivity of a compound, Kb is the
`Bolzmann constant, T is the temperature, R0 is the sol-
`ute radius, and η is the viscosity of the diffusion
`medium.
`As seen in the latter equation, increasing the surface
`area of a particle (S) can enhance its dissolution rate. S
`can be increased by micronization, a process some-
`times applied to poorly water-soluble compounds.24
`Also to be considered are particle size and density,
`which both inversely affect the dissolution rate.27 Parti-
`cle shape is also important in determining the dissolu-
`tion behavior of a drug, and for many crystalline forms
`(particularly shapes of needles and platelets), shape
`and consequently dissolution behavior may change
`markedly as the particle dissolves.28,29
`Particle properties can also affect the rate of GI tran-
`sit, the latter being highly dependent on such proper-
`ties as size, shape, and density. For example, in swine,
`about 30% to 40% of ingested food materials pass into
`the duodenum within 15 minutes in an adult pig. How-
`ever, large particles (10 mm in diameter) are retained
`within the stomach of swine for several days, with resi-
`dence time increasing with particle density and
`length.30
`A problem with the Noynes-Whitney equation is
`that there is an inherent assumption that S remains
`constant over time. Unfortunately, this assumption is
`incorrect, and the S of powders and immediate-release
`preparations tends to decrease as dissolution pro-
`
`λ
`
`= the thickness of the rate-limiting
`diffusion barrier.
`Am and Ap = the available surface areas for
`transcellular and paracellular
`transport, respectively.
`
`Thus, for passive diffusion, whether a drug is absorbed
`via paracellular or transcellular mechanisms is deter-
`mined by both physicochemical and physiological
`factors.
`Paracellular diffusion involves both diffusion and a
`convective volume flow through water-filled
`intercellular channels whose diameter is approxi-
`mately 3 to 10 Å in humans.18 Accordingly, the size and
`number of paracellular spaces influence the intestinal
`absorption of most hydrophilic compounds. This, in
`turn, is affected by the mucosal surface area and by cel-
`lular density.19 Therefore, it is not surprising that the
`bioavailability of small hydrophilic compounds tends
`to be greater in species such as dogs, in which both pore
`diameter and surface area tend to exceed that in hu-
`mans.20 In humans, the small intestinal surface area for
`paracellular absorption is approximately 0.01% of the
`total membrane surface area. For this reason, unless the
`molecule is extremely small (e.g., < 200 Da),
`paracellular transport will have a minor role in drug ab-
`sorption.15
`With permeability-limited absorption, we can ex-
`pect that although the fraction of dose absorbed re-
`mains unchanged, the absolute amount of drug ab-
`sorbed will increase as dose increases (assuming linear
`kinetics). Conversely, for solubility-limited com-
`pounds, increasing the dose will have no effect on the
`absolute amount of drug absorbed. Consequently, in
`these cases, the fraction of dose absorbed will decrease
`as dose is increased.21 Moreover, permeability is not
`necessarily constant throughout the GI tract. While for
`some compounds, drug absorption appears to be site
`independent,22 for others, it is site dependent.23 When
`drug absorption is site dependent, the availability of
`dissolved drug at the absorption site can be the
`rate-limiting factor in product bioavailability.
`
`PRODUCT DISSOLUTION
`
`Drug absorption depends on delivery of the drug parti-
`cles to its site of absorption. The Noynes-Whitney
`equation describes the variables that can affect drug
`dissolution:24,25
`
`(C
`
`−
`Cs
`
`t
`
`),
`
`••
`
`D S
`V h
`
`=
`
`dm
`dt
`
`PHARMACOKINETICS AND PHARMACODYNAMICS
`
`625
`
`RBP_TEVA05017868
`
`TEVA EXHIBIT 1035
`TEVA PHARMACEUTICALS USA, INC. V. MONOSOL RX, LLC
`
`

`
`MARTINEZ AND AMIDON
`
`drug absorbed. In this situation, fraction of drug ab-
`sorbed can only be improved by enhancing drug
`solubility (e.g., via the inclusion of surfactants in the
`product formulation). Conversely, particle size exerts
`its greatest effect when solubility is not a problem. In
`these cases, a significant improvement in the fraction of
`drug absorbed can be achieved by increasing surface
`area (i.e., decreasing particle size).
`The FDA’s Center for Drug Evaluation and Research
`(CDER) has written a guidance that provides for the
`waiver of in vivo bioequivalence study requirements
`for high-solubility/high-permeability drug products
`based on in vitro dissolution data. The scientific and
`regulatory considerations that must be applied to these
`procedures are described in the CDER guidance titled
`Waiver of In Vivo Bioavailability and Bioequivalence
`Studies for Immediate-Release Solid Oral Dosage
`Forms Based on a Biopharmaceutics Classification
`System (August 2000). For Class I compounds, the
`bioequivalence of generic or revised versions of mar-
`keted drug products can be confirmed if the sponsor can
`demonstrate that gastric emptying is the rate-limiting
`step in product absorption.
`To be granted a waiver of in vivo bioequivalence
`study requirements, the CDER recommends that in vi-
`tro dissolution tests be conducted under the following
`conditions:
`• The test apparatus is USP Apparatus I at 100 rpm or
`Apparatus II at 50 rpm. Testing is conducted in 900 ml
`of each of the following dissolution media: (1) 0.1 N
`HCl or Simulated Gastric Fluid USP without enzymes,
`(2) a pH 4.5 buffer, and (3) a pH 6.8 buffer or Simulated
`Intestinal Fluid USP without enzymes.
`• For each formulation, a minimum of 12 dosage units is
`evaluated to support a biowaiver request. Samples
`should be collected at time intervals adequate for char-
`acterizing the dissolution profile of the drug product.
`When comparing the test and reference formulations,
`the respective dissolution profiles should be compared
`using the similarity factor (f2), where
`
` 
`
`,
`
`•
`
`100
`
`−
`.
`0 5
`
` 
`
`−
`R T
`t
`t
`
`(
`
`2
`
`)
`
`t
`
`+
`
`
`
`1( /
`
`n
`
`)
`
` 
`
`1
`
` 
`
`=
`
`•
`
`50
`
`log
`
`f
`
`2
`
`n
`
`∑
`
`=
`
`1
`
`where Rt is the percent dissolved of the reference prod-
`uct, Tt is the percent dissolved of the test product, and n
`is the number of units tested.
`
`• Two dissolution profiles are considered similar when
`the f2 value is ≥ 50. To allow the use of mean data, the
`
`ceeds.25 In vivo, many of these parameters are also in-
`fluenced by the conditions of the GI tract, which will
`vary over time.31 For this reason, these equations, while
`providing insights into the parameters that can affect
`drug dissolution, should not be blindly applied to pre-
`dict in vivo dissolution rate.
`It should be noted that because the Noynes-Whitney
`equations are unable to adequately model either
`S-shaped data or data with a steep initial slope, the
`more general Weibull distribution has been used to de-
`scribe dissolution profiles.25 The Weibull distribution
`can be described as follows:
`M = 1 – exp(–αtβ),
`
`where M is the accumulated fraction of material in so-
`lution at time t, α is a scale parameter, and β is a shape
`parameter, where β = 1 indicates an exponential rela-
`tionship, β > 1 indicates an S-shaped relationship, and
`β < 1 indicates an exponential relationship with a steep
`slope.
`The rate of product dissolution may or may not in-
`fluence the resulting plasma concentration-time pro-
`file. For example, Class I compounds (highly soluble,
`highly permeable) may exhibit marked difference in
`the in vitro dissolution profiles without any resulting
`differences detected in product bioavailability.32-34 In
`these instances, gastric emptying is slower than prod-
`uct dissolution. Accordingly, it is the rate of gastric
`emptying rather than product performance that is the
`rate-limiting step in determining the bioavailability
`characteristics of that formulation. Similarly, highly
`soluble, poorly permeable compounds (Class III) dis-
`solve rapidly. However, in these cases, it is not the rate
`of drug dissolution that is usually rate limiting but
`rather the rate of permeation across biological mem-
`branes. Therefore, we can again assume that so long as
`dissolution is faster than the rate of gastric emptying,
`product dissolution will not determine product
`bioavailability. In the case of Class III compounds, so
`long as absorption occurs via linear processes, the ab-
`solute amount of drug absorbed may be increased by
`increasing the dose.21
`On the other hand, for high-permeability, low-
`solubility compounds (Class II), the rate and extent of
`product dissolution will have a significant role in de-
`fining the resulting blood concentration-time profile.27
`This may be attributable to problems associated with
`either particle size (termed dissolution-lim