Rate- and Extent-Limiting Factors of Oral Drug Absorption: Theory and Applications

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Rate- and Extent-Limiting Factors of Oral Drug Absorption: Theory and Applications KIYOHIKO SUGANO, KATSUHIDE TERADA Department of Pharmaceutics, Faculty of Pharmaceutical Sciences, Toho University, Funabashi, Chiba 274-8510, Japan Received 18 December 2014; revised 23 January 2015; accepted 23 January 2015 Published online in Wiley Online Library (wileyonlinelibrary.com). DOI 10.1002/jps.24391 ABSTRACT: The oral absorption of drugs has been represented by various concepts such as the absorption potential, the maximum absorbable dose, the biopharmaceutics classification system, and in vitro–in vivo correlation. The aim of this article is to provide an overview of the theoretical relationships between these concepts. It shows how a simple analytical solution for the fraction of a dose absorbed (Fa equation) can offer a theoretical base to tie together the various concepts, and discusses how this solution relates to the ratelimiting cases of oral drug absorption. The article introduces the Fa classification system as a framework in which all the above concepts were included, and discusses its applications for food effect prediction, active pharmaceutical ingredient form selection, formulation C 2015 Wiley Periodicals, Inc. and the American Pharmacists Association J Pharm Sci design, and biowaiver strategy.  Keywords: intestinal absorption; salt selection; bioequivalence; biopharmaceutics classification system (BCS); in silico modeling; dissolution; food effects; formulation; gastrointestinal transit; oral absorption

INTRODUCTION The theories of oral drug absorption have been actively investigated in the last three decades.1 Various concepts have been introduced to represent the oral absorption of drugs, for example, the absorption potential (AP),2 the maximum absorbable dose (MAD),3 the biopharmaceutics classification system (BCS),4 the developability classification system (DCS),5 and in vitro–in vivo correlation (IVIVC).6 These concepts originate from the same differential equations that describe the dissolution and intestinal membrane permeation of drugs. The aim of this article is to Abbreviations used: AP, absorption potential; API, active pharmaceutical ingredient; AUC, area under the curve; AUC BE, bioequivalence of AUC; BCS, biopharmaceutics classification system; BCS-BWS, BCS-based biowaiver scheme; BE, bioequivalence; COAS, computational oral absorption simulation; Cmax BE, bioequivalence of Cmax ; Cdissolv , concentration of a dissolved drug; Cdissolv,ss , concentration of a dissolved drug at the steady state; DCS, developability classification system; DF, degree of flatness; DRL, dissolution rate limited; Deff , effective diffusion coefficient; Dn, dissolution number; Dncrit , critical dissolution number; Do, dose number; Docrit , critical dose number; Dose, dose strength; EIE, equivalent-in-effect; EIP, equivalence of independent parameter; Fa, fraction of a dose absorbed; FaCS, Fa classification system; GI, gastrointestinal; IR, immediate release; IVIVC, in vitro–in vivo correlation; MAD, maximum absorbable dose; MDT, mean dissolution time; PBPK, physiologically based pharmacokinetics; PL, permeability limited; PL-E, epithelial membrane permeability limited; PL-U, unstirred water layer permeability limited; Pncrit , critical permeation number; PUWL , unstirred water layer permeability; Papp , apparent permeability; Peff , effective intestinal membrane permeability; Pep , epithelial membrane permeability of unbound drug molecules; PKs, pharmacokinetics; Pn, permeation number; S1I7, GI compartment model with one stomach compartment and seven intestinal compartments; SL, solubility–permeability limited; SL-E, solubility–epithelial membrane permeability limited; SL-U, solubility–unstirred water layer permeability limited; SMF, safe margin factor; Sblank , solubility in a blank buffer; Sdissolv , solubility in the GI tract (free and bile micelle bound drug molecules); Sn, saturation number; Tabs , transit time through the absorption site in the GI tract; UWL, unstirred water layer; V, fluid volume in the GI tract; VE, villi expansion factor; Xdissolv , dissolved amount; fu , free fraction at the surface of the intestinal epithelial membrane; in vitro T85% , time to reach 85% dissolution in an in vitro dissolution test; kabs , absorption rate coefficient; kdiss , dissolution rate coefficient; kel , elimination rate coefficient; kperm , permeation rate coefficient; rp , particle radius of a drug; T1/2 , elimination half-life. Correspondence to: Kiyohiko Sugano (Telephone: +81-47-472-1494; Fax: +8147-472-1337; E-mail: [email protected]) Journal of Pharmaceutical Sciences

 C 2015 Wiley Periodicals, Inc. and the American Pharmacists Association

provide a comprehensive overview of theoretical relationships between these concepts. A brief history in this scientific area is shown in Table 1.

DIFFERENTIAL EQUATIONS OF ORAL DRUG ABSORPTION The oral absorption of a drug can be expressed by the two differential equations that describe the dissolution and intestinal membrane permeation of a drug (except for supersaturation). The dissolution of a drug is usually expressed by the Noyes– Whitney equation introduced in 1897 (Eq. (1)).7,14 The intestinal membrane permeation of a drug is usually expressed by the first order equation (Eq. (2)). These are typically expressed as:   1 2 X dissolv dX undissolv 3 3 = −kdiss Dose X undissolv 1 − dt Sdissolv V

(1)

dX abs = kperm X dissolv dt

(2)

kdiss =

3Deff Sdissolv rp2 D

(3)

2DF Peff R

(4)

kperm =

where kdiss is the dissolution rate coefficient, kperm is the permeation rate coefficient, Dose is the dose strength, Xundissolv is the undissolved amount, Xdissolv is the dissolved amount, Xabs is the absorbed amount, Sdissolv is the solubility in the intestinal fluid (free and bile micelle bound drug molecules), Deff is the effective diffusion coefficient, Peff is the effective intestinal membrane permeability (free and bile micelle bound drug Sugano and Terada, JOURNAL OF PHARMACEUTICAL SCIENCES

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Table 1. Brief History of Theoretical Biopharmaceutics Year

Events

Reference

1897 1985 1986 1993 1995 1996

Noyes–Whitney equation Absorption potential Mixed tank model Plug-low model Biopharmaceutics classification system Maximum absorbable dose Compartment absorption transit model Absorption-limiting step classification Biopharmaceutics drug disposition classification system Fa equation Developablility classification system

7 2 8 9 4 3 10 11 12

1999 2005 2009 2010

  Fa = 1 − exp −kperm Tabs = 1 − exp (−Pn)

13 5

Sequential First-Order Approximation

QUEST FOR ANSWERS: A BRIEF HISTORY

Trivial Answers Dissolution Rate-Limited Cases In the case of dissolution rate-limited (DRL) absorption, Fa can be calculated by integrating the dissolution equation. By applying Xdissolv = 0 (perfect sink condition), we obtain  32



2 = 1 − 1 − Dn 3

(5)

(6)

Permeability Limited Cases When the whole amount of a drug instantly and completely dissolves after administration in the GI tract, the dissolution process will not become the rate-limiting step. In this case, the Sugano and Terada, JOURNAL OF PHARMACEUTICAL SCIENCES

Fa = 1 −

kperm exp (−kdiss Tabs ) kperm − kdiss

−

  Pn kdiss exp (−Dn) exp −kperm Tabs = 1 − kdiss − kperm Pn − Dn

−

Dn exp (−Pn) Dn − Pn

(8)

The above three trivial answers were simply derived from the differential equations. However, the concentration gradient term [1−Xdissolv /(Sdissolv × V)] makes it difficult to solve the equations for the cases of great interest in the pharmaceutical sciences. As no trivial answer is provided for this case, pharmaceutical insights are required to solve the equations. The concept of solubility - permeability limited absorption first emerged as the AP in 1985,2 and then eventually developed to the concept of the MAD3 and BCS.4 When the dissolution rate of a drug is much faster than the permeation rate and the dose to solubility ratio (Dose/Sdissolv ) exceeds the intestinal fluid volume (V), the concentration of a dissolved drug (Cdissolv = Xdissolv /V) in the GI tract reaches close to the equilibrium solubility of the drug (Sdissolv ). In this case, Eq. (2) can be integrated by applying a constant value of Xdissolv = Sdissolv × V as:

 32

where Tabs is the transit time through the absorption site in the GI tract. Tabs can be approximated as the small intestinal transit time for many cases. We can introduce a dimensionless parameter for dissolution [dissolution number (Dn) = kdiss × Tabs ]. This equation can be approximated as a first-order process, Fa = 1 − exp (−kdiss Tabs ) = 1 − exp (−Dn)

When the oral absorption of a drug can be represented as the sequential first-order process of dissolution and permeation, the analytical solution becomes

Solubility - Permeability Limited Case

A simple analytical solution can usually be derived from a differential equation(s) by applying the initial and boundary conditions for a special (limiting) case. Historically, this approach was first applied to the dissolution and permeation equations for the three absorption limiting cases, that is, the dissolution rate, permeability, and solubility–permeability limited (SL) cases. An illustrative explanation of these limiting cases is available elsewhere in the literature.15

2 Fa = 1 − 1 − kdiss Tabs 3

(7)

This equation is often used to correlate in vitro membrane permeability values with Fa, for example, the Caco-2 cell assay,16,17 the Madin–Darby canine kidney cell assay,18 and the parallel artificial membrane permeation assay.19–21 We can also introduce a dimensionless parameter for permeation (Pn = kperm × Tabs ).

molecules), D is the true density, and rp is the particle radius of a drug. R is the radius of the gastrointestinal (GI) tract, DF is the degree of flatness, and V is the fluid volume in the GI tract. Eq. (1) is for monodispersed spherical particles smaller than 60 :m. To calculate the fraction of a dose absorbed (Fa), Eqs. (1) and (2) have to be integrated simultaneously. However, the exact analytical solution for general cases has not been discovered. The quest for the answer(s) that leads to Fa is one of the main themes of theoretical biopharmaceutics.



oral absorption of the drug becomes permeability limited (PL). The trivial answer for Eq. (2) is:

Fa =

MAD Pn kperm Sdissolv VTabs = = Dose Dose Do

(9)

Dose Sdissolv V

(10)

Do =

where Do is the dose number. This oral absorption pattern is often referred as “solubility limited” in the literature. However, to explicitly recognize the role of permeability, we refer it as “solubility - permeability limited” in this article. In the AP, kperm is represented by the lipophilicity of a drug. The maximum absorbable dose is defined as MAD = kperm × Sdissolv × V × Tabs . BCS categorizes a drug by Do and Pn. The classification boundary of DCS is based on Fa = Pn/Do (Fig. 1). Therefore, AP, MAD, BCS, and DCS are related to each other via Eq. (9). DOI 10.1002/jps.24391

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Computational Numerical Integration

Pn BCS I

BCS II

10

0.1

1

1

10 Do

BCS III

BCS IV

0.1 Figure 1. The BCS plane (Pn–Do plane) and DCS lines. The solid and gray lines corresponds to Fa = Pn/Do = 0.3 and 0.7 for SL cases.

Approximate Fa Equation for General Cases In 2009, by applying the steady-state approximation, an approximate open analytical solution for Fa was discovered.13,22 This equation (the Fa equation, Eq. (11)) captures the essential processes of oral drug absorption (except for supersaturation). 

1 Fa = 1 − exp − 1 Do + Pn Dn ≈

1 1 + Do Dn Pn

 if Do < 1, set Do = 1.

for Fa < 0.7

(11)

By taking the limit, the Fa equation can be rearranged to Eqs. (6), (7) and (9). When comparing Eq. (11) with Eq. (7), we can define the absorption rate coefficient (kabs ) as: 1 Do 1 = + kabs kdiss kperm

(12)

Some important aspects of Fa can be directly derived by the Fa equation.

r Fa is determined by three factors, i.e., Dn, Do, and Pn. r Dn is independent from Do and Pn. r Pn and Do are conjugated as Pn/Do. r Dn or Pn/Do can be the dominant factor when one largely exceeds the other. The Fa equation enables us to predict Fa from the in vitro data available in drug discovery by a back-of-the-envelope calculation.23 The saturation number (Sn) that represents the ratio of Cdissolv at a steady state (Cdissolv,ss ) and Sdissolv can be defined as: Sn =

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1 Cdissolv,ss = Pn Sdissolv 1 + DnDo

(13)

The wide spread of personal computers after the late 1980s provided new research tools for many scientists. Computational numerical integration of differential equations (computer simulation) can provide answers to more general cases compared with analytical solutions. Computer simulation is now used in various research areas such as astronomy, meteorology, engineering, economics, and so on. Pharmaceutical sciences have been reaping many benefits from computer simulation as well. Computational oral absorption simulations (COASs)13 have been used since the mid-1980s. A simple mixed tank model and a plug flow model were first employed to represent the GI tract.8,9 The dissolution and permeation equations were numerically integrated with these models. The compartment absorption transit model was then introduced in 1996 to represent the distribution of a drug in the GI tract.10,11,24 The other multicompartment models such as the gastrointestinal transit absorption model25 and the advanced dissolution absorption and metabolism model26 were later introduced. In most cases, the stomach and the small intestine are expressed as one and seven compartments, respectively [the GI compartment model with one stomach compartment and seven intestinal compartments (S1I7) model]. In each GI compartment, the dissolution and permeation processes of a drug are simulated. The GI transit of polydispersed particles between the compartments can be simultaneously simulated.13 By using a S1I7 model, various scenarios of oral drug absorption can be simulated, such as the effects of pH change in the GI tract.27 One of the well-known disadvantages of computational simulation is that it might distract us from understanding the deep and often abstracted nature.28 Therefore, even in this age of massive computing power, analytical solutions will not lose their importance. Computer simulation and analytical solution are complementary to each other. Because of its complexity, COAS is often used as a black box. However, commercial programs have not been sophisticated enough for nonexpert users. Therefore, a simple analytical solution and/or a classification system should be used alongside with COAS to understand the essence of oral drug absorption. Commercial COAS programs are often used side by side with a physiologically based pharmacokinetics (PBPK) model.29,30 Pharmacokinetic (PK) scientists sometimes use oral absorption and formulation modules in software, whereas formulation scientists merely use the PBPK module on its own. A good collaboration between the biopharmaceutics and PK scientists is vital for an appropriate use of COAS. Even though the S1I7 models seem to provide significant advantages, a simple one compartment model is sufficient to predict Fa in many cases.31 The Fa equation and the seven compartment model give similar Fa values for nonsupersaturable cases.22 To simulate the plasma concentration–time profile of a drug, kabs can be used with a one-compartment PK model. As COAS is a relatively new research tool for pharmaceutical scientists, there is little consensus on how to write the method section in a research paper. There are many indefinite factors in in vivo GI physiology and there are significant discrepancies between in vitro and in vivo conditions. The awareness of this issue initiated an international project in Europe (OrBiTo).32 Therefore, an almost perfect prediction of PK profiles reported so far in many articles is at least questionable (many of them employ a commercial software). A good simulation practice13 Sugano and Terada, JOURNAL OF PHARMACEUTICAL SCIENCES

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Figure 2. Fa classification system and its relationship with BCS, food effect (by bile micelles), API and formulation design, and biowaiver strategy.

should be provided as a guidance for the healthy development of this emerging scientific area.

BIOPHARMACEUTICS CLASSIFICATION SYSTEM The biopharmaceutics classification system has been widely used in drug discovery and development. BCS was derived from Eqs. (1) and (2) by Amidon and coworkers4,9 in the mid-1990s. BCS classifies a drug substance by Do and Pn. A drug can be spotted on the Do–Pn plane (Fig. 1). BCS was originally introduced for biowaiver consideration. However, as a simple and basic classification system, BCS has inspired many scientists to investigate its applicability to various situations in drug discovery and development. Roughly speaking, Do = 1 and Pn = 2 (Fa = 0.85–0.9) have been used as the criteria for solubility and permeability, respectively. However, the rationale for the high/low-permeability boundary has not been rigorously established. It might have been derived from the bioequivalence (BE) criteria in the biowaiver scheme (discussed later), or indefinitely derived from the tacit knowledge among the experts.33 The biopharmaceutics drug disposition classification system suggests that the extent of metabolism can be used as a surrogate for Fa.12,34 The Developability classification system also classifies a drug by Do and Pn; however, the criteria are based on Fa = Pn/Do rather than Do = 1 and Pn = 2 (Fig. 1).5 DCS can be considered as an improved descendant of MAD that has also been widely used in drug discovery and development (cf. Pn/Do = MAD/Dose).35

FA CLASSIFICATION SYSTEM The Fa equation can provide a classification system for oral drug absorption (referred as the Fa classification system (FaCS) in this article). FaCS includes the concept of BCS, but it provides a more mutually exclusive and collectively exhaustive classification system for oral drug absorption (Fig. 2; Table 2). On the basis of the Fa equation, the limiting factors of oral drug absorption can be classified as:

r Dissolution rate limited (DRL) r Permeability limited (PL) r Solubility - permeability limited (SL) The basic concept of this classification system might have been implicitly suggested in the literature before the mid-1990s or earlier. In 1999, Yu11 explicitly explained this concept with the criteria shown in Table 2. Takano et al.36 experimentally confirmed this concept. Fa classification system and the criteria based on the Fa equation were introduced in 2010 and 2011, respectively.23,37 In FaCS, PL and SL can be further classified by the rate-limiting factors of intestinal membrane permeation, i.e., the unstirred water layer (UWL) and the epithelial membrane.38,39 The Peff can be expressed as: Peff =

1 PUWL

PE + VEf1u Pep

(14)

Table 2. Absorption-Limiting Steps in Oral Drug Absorption Criteria Absorption-Limiting Steps Dissolution rate limited

Permeability limited

Solubility–permeability limited

a b

Yua

FaCS

Dn < 1.1 Pn > 5.7 Pn/Do >> 1 Dn > 4.4 Pn < 5.7 Pn/Do >> 1 Dn > 4.4 Pn > 5.7 Pn/Do << 1

Dn < Pn/Do

Fa = 1−exp(−Dn)

Pn < Dnb Do < 1

Fa = 1−exp(−Pn)

Pn/Do < Dnb Do > 1

Fa = Pn/Do

Fa Equation

Ref. 11. Converted to corresponding dimensionless numbers. Further classified by the rate-limiting step of the effective permeability.

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where PE is the plica expansion factor, VE is the villi expansion factor, fu is the free fraction at the surface of the intestinal epithelial membrane, PUWL is the unstirred water layer permeability (free and bile micelle bound drug molecules), and Pep is the epithelial membrane permeability of unbound drug molecules. Taken together, FaCS classifies drug products into the five classes as shown in Figure 2.23,37 FaCS explicitly includes the basic concept of BCS (classification by Pn and Do). In addition, FaCS also explicitly includes the dissolution perspective as represented by the Dn in its classification scheme (Fig. 2; Table 2). In contrast to commonly speculated interpretation, BCS cannot determine whether Fa becomes DRL or not.5 For example, when the solubility of a drug is 0.001 mg/mL, the dose is 0.1 mg, the particle size is 20 :m, Deff is 6.6 × 10−6 cm2 /s, and Peff is 6.6 × 10−4 cm/s (corresponding to BCS class I; Dn = 0.7, Pn = 18.9, Do = 0.8), Fa becomes DRL. The third discriminate point of FaCS is related to the permeability criterion. Unlike BCS, the permeability boundary in FaCS is based on the rate-limiting factors of intestinal membrane permeation, i.e., UWL or the epithelial membrane.

FOOD EFFECT PREDICTION The Fa equation and FaCS have been applied to elucidate the food effect by bile micelles.37,40 In the DRL cases, the solubilization of a drug by bile micelles would increase the dissolution rate, leading to a positive food effect. For example, a positive food effect (2.6-fold) was observed in ivermectin.41 In the epithelial membrane permeability limited (PL-E) cases, a negative food effect can be observed. Bile micelle binding reduces the unbound drug concentration at the epithelial surface and reduces the effective permeability of a drug.42–44 In the solubility–epithelial membrane permeability limited (SL-E) cases, Fa would not be increased by bile micelles. The drug molecules bound to bile micelles cannot permeate across the epithelial cell membranes. Therefore, the flux across the epithelial membrane would not be increased (flux = Sdissolv × Peff ࣈ (Sblank /fu ) × (VE × fu × Pep ) = Sblank × VE × Pep . Solubility in a blank buffer (Sblank ) = Sdissolv × fu ). Pranlukast was suggested to be a typical example for this case.37 The solubility of pranlukast was increased by approximately ninefold in the fed-state simulated intestinal fluid compared with that in the fasted state simulated intestinal fluid.45 However, area under the curve (AUC) increased only 1.5-fold when taken with a food (cf. Fa% in the fed state is 11% at 300 mg). In the solubility–unstirred water layer permeability limited (SL-U) cases, a positive food effect would be observed as the drug molecules bound to bile micelles could permeate across UWL. Many drugs in this class show positive food effects,46 for example, griseofulvin,47 danazol,48 and atovaquone.49

ACTIVE PHARMACEUTICAL INGREDIENT FORM SELECTION AND FORMULATION DESIGN Fa classification system can be used as a guidance for active pharmaceutical ingredient (API) form selection and formulation design, which are critically important for successful drug development.5,50,51 DOI 10.1002/jps.24391

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DRL Cases In the case of DRL, particle size reduction would be effective to increase Fa. However, as the dissolution rate increases, the absorption regime changes from DRL to SL. The critical particle radius to become DRL can be calculated based on the Fa equation.23 The discriminate equation between DRL and SL is: Dn <

Pn Do

(15)

When the dimensionless numbers are broken down, this equation becomes: Sdissolv VSI 2DFPeff 3Deff Sdissolv < rp2 D Dose RSI

(16)

Sdissolv can be cancelled out from both sides of Eq. (16), suggesting that the discrimination boundary between DRL and SL does not depend on the solubility of a drug (for Do > 1). Even though it is counterintuitive, this can be interpreted as follows; when Sdissolv is low, the dissolution rate becomes slow, and at the same time, the ceiling of Cdissolv (i.e., Sdissolv ) becomes low. On the contrary, when the solubility is high, the dissolution rate becomes fast and the ceiling of Cdissolv becomes high. Therefore, the tendency of Cdissolv to reach Sdissolv does not depend on Sdissolv (cf. the Sn does not depend on Sdissolv as well). By solving this equation for rp , we obtain23  rp >

3Deff DoseRSI 2DFPeff VSI

(17)

By using a conventional milling method, the mean particle size can be reduced to 10 :m or less. Therefore, according to Eq. (17), even for relatively high Peff cases (e.g., 5 ×10−4 cm/s), when the dose is more than 20 mg, Fa becomes SL. SL-E Cases Theoretically, the free drug concentration at the epithelial membrane surface should be increased to achieve an increase in Fa for the SL-E cases. Supersaturable API forms and formulation technologies would be effective in this case. Supersaturable API crystalline forms are salts,52 cocrystals,53 and anhydrates.54,55 Solid dispersions and some of digestible selfemulsifying drug delivery systems can also be employed to increase the free drug concentration at the epithelial membrane surface.56–58 It should be noted that an in vitro permeability assay often underestimates the permeability of a highly lipophilic drug (the octanol water distribution coefficient > 1.5).59,60 This could result in misclassification of permeability (i.e., a BCS class II drug can be falsely classified as a BCS class IV drug). As the physicochemical principles of solubility and passive membrane permeability suggest,61,62 a genuine low-solubility/lowpermeability drug rarely exists. SL-U Cases In addition to the solubilization technologies for the SL-E cases, formulation technologies that increase the apparent solubility would be effective for the SL-U cases, such as cyclodextrin.63 Interestingly, particle size reduction has been shown to be effective in increasing Fa for the SL-U cases.64,65 The particle Sugano and Terada, JOURNAL OF PHARMACEUTICAL SCIENCES

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drifting effect has been hypothesized to explain this phenomenon.66 It is well known that small particles can drift into the UWL.67,68 In this case, the apparent thickness of UWL can be reduced.

BIOEQUIVALENCE Problem Statement The equivalence of the PKs between two drug products containing the same drug molecule is called “BE”. Clinical BE is defined as “20% acceptance range (80%–125%) for the 90% confidence interval of the ratio between test and reference least square means after log transformation of the PK parameters of interest, Cmax , and AUC.”69 If it is possible to allow waivers of clinical BE studies based on the in vitro data (“biowaiver”), it would be beneficial for both drug developers and patients. However, an in vitro dissolution test is not an all-round tool and only reflects a certain dimension of complicated in vivo situations. Therefore, the problem statement for a biowaiver scheme is “when and under what conditions can waivers of clinical studies be allowed?”4 BCS-Based Biowaiver Scheme The BCS-based biowaiver scheme (BCS-BWS) for oral immediate-release (IR) dosage has been employed by US FDA, EMA, WHO, and many other regulatory agents. There are many excellent review articles regarding BCS-BWS.33 The rationale to allow biowaivers for BCS Class I drugs was described as, “When the in vivo dissolution of an IR oral dosage form is rapid in relation to gastric emptying, the rate and extent of drug absorption is likely to be independent of drug dissolution. Therefore, similar to oral solutions, demonstration of in vivo bioequivalence may not be necessary as long as the inactive ingredients used in the dosage form do not significantly affect the absorption of the active ingredient. Thus, for BCS Class I (high solubility- high permeability) drug substances, demonstration of rapid in vitro dissolution using the recommended test methods would provide sufficient assurance of rapid in vivo dissolution, thereby ensuring human in vivo bioequivalence.”33 In BCS-BWS, the criterion for solubility is based on the solubility of an API in the plain buffers of the entire pH range in the GI tract (e.g., pH 1.2–7.4). The criterion for permeability is based on the permeability value for nearly complete absorption (e.g., Fa > 0.85–0.90) (there are some variations in each regulatory guideline). Discussion Based on FaCS In this section, a biowaiver strategy is discussed based on FaCS. As described above, the dissolution criteria in BCS-BWS is based on the ratio of the dissolution rate and the gastric emptying rate. However, the gastric-emptying rate largely depends on the phase of the migrating motor complexes, which are the waves of the GI walls that sweep through the stomach and the intestine in a regular cycle during a fasting state.70 In addition, the gastric emptying half time can be as short as 4 min in a fasted state.71,72 Furthermore, the solubility of a drug in Sugano and Terada, JOURNAL OF PHARMACEUTICAL SCIENCES

the small intestine was suggested to be sufficient to justify biowaiver.73,74 Therefore, in the following discussion, the gastric emptying is assumed instant. The following discussion is not intended to suggest any change of the current regulatory biowaiver guidelines. A biowaiver strategy is not only used for a regulatory purpose but also used for routine formulation researches. An in vitro dissolution test is routinely used as a surrogate of in vivo oral absorption in drug development. Fa Congruent Condition On the basis of the Fa equation, the congruence of Fa can be written as: Fa (Dn1 , Do1 , Pn1 ) = Fa (Dn2 , Do2 , Pn2 )

(18)

where the subscript number indicates each formulation (e.g., 1, reference formulation; 2, test formulation). For BE, Fa should be equivalent at any time point (cf. Fa is essentially a function of time even though it usually refers to the total absorbed amount at an infinite time after dosing). Usually, the equivalence of Fa is judged by the representative parameters for the rate and extent of Fa. Cmax1 (Dn1 , Do1 , Pn1 ) = Cmax2 (Dn2 , Do2 , Pn2 )

(19)

AUC1 (Dn1 , Do1 , Pn1 ) = AUC2 (Dn2 , Do2 , Pn2 )

(20)

There are two types of conditions to satisfy these equations: the equivalence of independent parameter (EIP) and equivalent-in-effect (EIE) conditions. When Dn, Do, and Pn of two formulations are identical, it is obvious that Cmax and AUC become equivalent (Fig. 3a). Dn1 = Dn2 , Do1 = Do2 , Pn1 = Pn2

(21)

We can also define the EIE condition in which AUC and Cmax become insensitive to the independent parameters. In a certain range, even when the independent parameters differed (i.e., Dn1 ࣔ Dn2 , Do1 ࣔ Do2 , and/or Pn1 ࣔ Pn2 ), it could result in the bioequivalence of Cmax (Cmax BE) and AUC (AUC BE). For example, when Dn >> Pn, Do <1, and Pn > 2, AUC becomes insensitive to the differences of these parameters within this range (Fig. 3b). Dn1 , Dn2 > Dncrit ; Do1 , Do2 < Docrit ; Pn1 , Pn2 > Pncrit

(22)

where the subscript “crit” indicates the critical values to satisfy the EIE conditions. Discriminate Points in FaCS for Bioequivalence In FaCS, each discriminate point determines whether an EIE condition is applicable or not. Dn Discriminate Point. The first discriminate point in FaCS is Dn versus Pn/Do (Fig. 2; Table 2). We can define the critical dissolution number (Dncrit ) as the lowest Dn value that provides the Cmax and AUC ratios of more than 0.8 against a solution formulation.75 The worst-case scenario within this range is that one of the two formulations shows instant dissolution, whereas the other shows slowest dissolution in this range. When both DOI 10.1002/jps.24391

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(a) Formulation 1

Fa

Formulation 2

Dn1

Pn1

Dn2

Do1

Pn2 Do2

1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

7

(b) Insensitive

0

1

2

3

4

5

Pn Figure 3. An illustration of (a) EIP and (b) EIE conditions for biowaiver.

Dn1 and Dn2 are larger than Dncrit , the dissolution rate does not affect the bioequivalence of AUC and Cmax even when Dn1 ࣔ Dn2 (Dn1 and Dn2 become “EIE”). When Dn1 and/or Dn2 are smaller than Dncrit , AUC and/or Cmax become sensitive to Dn. In this case, the EIP, that is, Dn1 = Dn2, has to be proved. For the Cmax BE, Dncrit can be roughly calculated as: Dncrit >

1 Do Pn

+

T1/2

×4

(23)

ln2 ×Tabs

The elimination half-life (T1/2 ) was included as it affects Cmax [cf. Cmax ∝ ≈ 1/(1 + kel /kabs ); kel is the elimination rate coefficient; for kabs , see Eq. (12)]. The multiplying number of four is originated from the 80% threshold of BE. For the AUC BE of a low-permeability drug, Dncrit can be roughly calculated to be 5 as: 1 kperm (Tabs − MDT) =1− > 0.8 kperm Tabs Dncrit

(24)

where MDT is the mean dissolution time. The Tabs –MDT term suggests that MDT reduces the time available for drug absorption. Numerical integration can be used to calculate Dncrit more accurately. Figure 4a shows the relationship among Pn, elimination T1/2 , and Dncrit obtained by numerically solving three first-order equations (with kdiss , kperm , and kel ) that are sequentially connected (simulated for Tabs = 3.5 h; Do < 1). Figure 4a suggests that in the case of short half-life drugs (<120 min.), the dissolution rate criteria for a highpermeability drug should be larger than that for a lowpermeability drug because of the sensitivity of Cmax to Dncrit .75,76 Figure 4b is the cross-section of Figure 4a at T1/2 = 60 min. The Dncrit lines for Cmax and AUC show different trends. For Cmax BE, as the permeability of a drug becomes higher, a faster dissolution is required (Table 3). This might be one of the reasons for that some of the BCS class I drugs failed to show Cmax BE even when they complied with the rapid dissolution criteria.77 Several low-permeability drugs show clinical BE even when the dissolution profiles significantly differed among the formulations, for example, cimetidine,78 fexofenadine,79 and so on. The Cmax of a high-permeability and short half-life drug can be sensitive to the dissolution profile, for example, ibuprofen.80 In the Do > 1 cases, the Dncrit plane shifts lower, suggesting that AUC and Cmax become less sensitive to the dissolution DOI 10.1002/jps.24391

rate. Therefore, it is safe (conservative) to use Figure 4a for the Do > 1 cases as well. Some of the transporter and paracellular substrates are mainly absorbed from the upper small intestine. In this case, Tabs can be shorter than 3.5 h, so that a larger kdiss should be used as the dissolution rate criteria for AUC BE (cf. kdiss = Dn/Tabs ). A similar approach can be applied to take the gastric emptying rate into account. The dissolution rate should be approximately fourfold faster than the gastric-emptying rate for Cmax BE of a short half-life drug. When using the gastric-emptying half-life of 10 min, in vivo T85% should be shorter than 5 min (Dncrit > 84). Do Discriminate Point. The discriminate point next to Dn > Dncrit is the Do discriminate point (Fig. 2). We can define the critical dose number (Docrit ) as the highest Do value that provides a sink condition in vivo. Docrit < 1 is used in the BCS-BWS guidelines. To ensure a sink condition, it might be safer to use Docrit < 0.3 as the EIE condition. Thirty percent of the saturated solubility is often used as a criterion for a sink condition. When Do > Docrit , Do1 = Do2 is required to prove the BE (together with Pn1 = Pn2 as the oral absorption becomes SL in this case). Pn Discriminate Point. The discriminate point next to Do < Docrit is the Pn discriminate point (Fig. 2). We can define the critical permeation number (Pncrit ) as the lowest Pn value that provides the Cmax and AUC ratios of more than 0.8 against the theoretically highest permeability case of Pn = 20. Pn = 20 is calculated based on the highest permeability value observed in humans (Peff = 10 × 10−4 cm/s for glucose) and adjusted for the average molecular weight of modern drugs (400).81 Figure 5 shows the relationship between Pncrit and T1/2 . For drugs with T1/2 > 600 min, Pncrit is approximately 2, whereas for drugs with T1/2 less than approximately 600 min, Pncrit is larger than 2. When Pn < Pncrit , Pn1 = Pn2 is required to prove the BE. Proofs for EIP and EIE Conditions The strategies to prove the EIP and EIE conditions are summarized in Table 4 (conditions A–G). The EIP and EIE conditions discussed above are for in vivo, but not for in vitro. Therefore, a justification is required when using in vitro data to prove in vivo conditions, for example, IVIVC and a safe margin. Sugano and Terada, JOURNAL OF PHARMACEUTICAL SCIENCES

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Figure 4. The relationship among Dncrit , Pn, and T1/2 . (a) Dncrit plane satisfying both AUC BE and Cmax BE. (b) Cross-section at T1/2 = 60 min. The AUC and Cmax lines satisfy the equivalence of AUC and Cmax , respectively. The Dcrit values for Pn > 2 (Fa > 0.85–0.90) and T1/2 < 10 h become higher than that for the Pn < 2 cases. Table 3. Dissolution Criteria for Biowaiver T85% (min)a

Dncrit Pn

T1/2

AUC

Cmax

BEb

Dncrit × 3c

FaCS Based

Current BCS-BWS

0.2 0.2 2 2 20 20

60 600 60 600 60 600

4.7 4.7 3.0 3.0 1.7 1.7

2.5 4.3 2.9 2.6 9.2 2.3

4.7 4.7 3.0 3.0 9.2 2.3

14 14 9.0 9.0 28 6.8

28 28 45 45 14 59

15d 15d 30 30 30 30

a

85% dissolution time. Take the larger Dncrit . SMF = 3 was used as an example. d EMA and WHO guidelines. b c

r The constituents of the intestinal fluid in vivo such as bile

A. Dn > Dncrit

micelles usually increase the solubility of a drug.

The conditions of a compendium in vitro dissolution test could be dissimilar with those in vivo dissolution. Therefore, an appropriate safe margin should be applied when using an in vitro dissolution test as a surrogate for in vivo dissolution. Usually, the dissolution rate criterion is described by the time to reach 85% dissolution in an in vitro dissolution test (in vitro T85% ). In vivo Dncrit can be converted to in vitro T85% as: In vitro T85% = −

Tabs ln (1 − 0.85) Dnctir × SMF

supersaturated solubility. Therefore, the equilibrium solubility of an API in plain buffers should be smaller than the apparent solubility of a drug in vivo from a drug product. Consequently, in vivo Do < Docrit can be proved by using in vitro data (in vivo Do < in vitro Do < Docrit ).

(25)

where SMF is the safe margin factor. For AUC BE of a lowpermeability drug, Dncrit > 5 is required. When applying SMF = 3, in vitro T85% becomes approximately 30 min (Table 3). For a high-permeability drug with T1/2 = 60 min, in vitro T85% should be set 15 min for Cmax BE (Table 3). B. Do < Docrit The following three reasons would justify the use of the in vitro equilibrium solubility of an API in plain buffers to prove Do < Docrit of a drug product in vivo. Sugano and Terada, JOURNAL OF PHARMACEUTICAL SCIENCES

r The excipients increase the solubility of a drug. r The equilibrium solubility of a drug is smaller than the

C. Pn > Pncrit In the T1/2 more than approximately 600 min range, Fa > 0.85–0.90 (Pn > 2) would be appropriate to justify biowaiver (Fig. 5). However, in the T1/2 less than approximately 600 min range, it does not guarantee Cmax BE. When Pn < Pncrit , a proof for Pn1 = Pn2 in vivo is required [see sections (F) or (G) below]. When using a clinical Fa value for the permeability criterion, no safety margin would be required. However, when an in vitro permeability assay is used as a surrogate, an appropriate safe margin would be required. D. Dn1 = Dn2 DOI 10.1002/jps.24391

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E. Do1 = Do2

10 9

Pn crit for 80% C max or AUC

9

The apparent solubility of a drug can be increased by the excipients in the drug product. Therefore, the solubility of an API cannot be used to prove Do1 = Do2 of drug products. A dissolution test with a sink condition cannot be used to prove Do1 = Do2 . A nonsink dissolution test with biorelevant media may be used to prove Do1 = Do2 , especially for supersaturable APIs and formulations.52

8 7 6

(b)

(a1)

5 F. PUWL1 = PUWL2

UWL line

4 3

(c2)

(a2)

2 1

(c1)

AUC = 80% line (Fa= 0.8)

0 60

600 EliminationT1/2 (min)

6000

The permeability of a drug can be affected by the excipients in the drug product. However, it is highly likely that most of the excipients have little or no effect on PUWL (diffusion through a water layer). It would be difficult to judge the rate-limiting step in permeability from the in vivo Fa data, as Fa > 0.98 (Pn > 4) is required to be UWL limited. In an in vitro assay such as Caco-2, the apparent permeability (Papp ) should be more than 50 × 10−6 cm/s to ensure UWL-limited permeation. Therefore, a sufficient agitation is necessary for an in vitro assay. G. Pep1 = Pep2

Figure 5. The relationship between Pncrit and T1/2 . When Pn is above the Pncrit line [(a1) and (a2) areas], Pn satisfies EIE for both AUC and Cmax . Fa > 0.85–0.90 data can be used in the T1/2 more than approximately 600 min range. When Pn is below the Pncrit line, EIP should be proved. PUWL1 = PUWL2 is required in the (b) area and Pep1 = Pep2 is required in the (c1) and (c2) areas. Fa < 0.8 can be used to prove that the permeability is limited by the epithelial membrane, whereas the other approach is required to diagnose the rate-limiting step for the Fa > 0.8 cases [the (b) and (c2) areas].

Summary for Biowaiver Strategy

An IVIVC strategy can be applied to prove Dn1 = Dn2 .82 In IVIVC, in vitro dissolution profiles have to be proved to correlate with those in vivo. When Dn << Pn/Do, Fa becomes sensitive only to Dn and insensitive to Do and Pn. As Pn and Do become EIE in this case, the last piece to prove the Fa congruent conditions is Dn1 = Dn2 (so that EIP of Dn). Usually, for a controlled-release formulation, high-solubility/ highpermeability drugs (Pn > 2 and Do < 1, therefore, Pn/Do > 2) is selected to ensure a good absorption from the whole GI tract.83 By applying the 80% dominancy rule, Dn < 0.4 is sufficient for Fa to be DRL. Dn = 0.4 corresponds to ca. 50% release at 5 h.

All in all, the discussion based on the Fa equation and FaCS suggested that a drug product with a high permeability (Pn > 2), low solubility to dose ratio (Do < 0.3), and long elimination T1/2 (>10 h) would be most suitable for biowaiver with the data of in vitro T85% < 30 min, in vitro Do < 0.3 and Fa > 0.85–0.9 (Table 5). Therefore, the discussion based on FaCS basically supports the biowaiver for BCS Class I drugs except for the short elimination T1/2 cases. In the FaCS-based discussion, Pn plays two distinct roles: (1) the determination of dissolution criteria (with T1/2 ), and (2) the proof of Pn equivalence. The FaCS-based discussion would provide some hints about what should be carried out to improve biowaiver strategy and in vitro tests in the future.85

In contract to PUWL , it is well known that Pep can be altered by some excipients,84 especially for transporter and paracellular substrates. Once these excipients are excluded from the formulation, Pep1 = Pep2 could be anticipated.

Table 4. Equivalent-in-Effect and EIP Conditions Suggested by FaCS Conditions Equivalent-in-effect (EIE) (A) Dn > Dncrit (B) Do < 0.3 (C) Pn > Pncrit Equivalence of independent parameter (EIP) (D) Dn1 = Dn2 (E) Do1 = Do2 (F) PUWL1 = PUWL1 (G) Pep1 = Pep2

Measures

Criteria

In vitro dissolution test In vitro solubility test Clinical Fa data In vitro permeability test

In vitro Dn > Dncrit × SMFa In vitro Do = Dose/(Sblank × V) < 0.3 Fa > Fa (Pncrit )b Pn (from in vitro Papp )c > Pncrit × SMF

IVIVC Not known In vitro permeability Excipient restriction

IVIVC criteria Not known PUWL d < VE × fu × Papp × SMF No excipient affecting Pep

a

SMF depends on the predictability of an in vitro test. Fa = 0.85 and 0.90 corresponds to Pn = 1.9 and 2.3, respectively. Pn calculated from Papp by Eqs. 4 and 14. d PUWL estimated from Deff (Ref. 36). b c

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Table 5. Biowaiver Strategy Type of Equivalencea Dn EIE (A) EIE (A) EIE (A) EIE (A) EIE (A) EIP (D)

Do EIE (B) EIE (B) EIE (B) EIP (E) EIP (E) EIEg

Pn EIE (C) EIP (F) EIP (G) EIP (F) EIP (G) EIEg

FaCS

BCSb

Comments

+ PL-Ue PL-Ef SL-U SL-E DRL

I I III II IV N/A

Most suitable for biowaiver Likely to be PUWL1 = PUWL2 Excipient restriction for Pep1 = Pep2 Challenge to prove Do1 = Do2 Least suitable for biowaiver IVIVC to prove Dn1 = Dn2

PL-Uc

PL-Ed

a See test and Table 4 for the annotation of each alphabet. The color filling indicates the levels of challenge to prove the BE conditions; green, OK for biowaiver; yellow, almost OK; orange, needs more scientific evidence; red, significant challenge required. b BCS classes approximately corresponding to each biowaiver strategy. c Area (a1) in Figure 5. d Area (a2) in Figure 5. e Area (b) in Figure 5. f Areas (c1) and (c2) in Figure 5. g Derived from Dn << Pn/Do. N/A, not applicable.

CONCLUSION The theoretical investigations discussed here can significantly contribute to a better understanding of oral drug absorption. They can provide guidance for API form selection, formulation design, and biowaiver strategy. Although it is likely that computational simulations will be used more widely in the future, analytical solutions and classification systems will continue to provide a way to understand the fundamentals of oral drug absorption.

ACKNOWLEDGMENTS The authors greatly appreciate Prof. Gordon Amidon, Prof. Shinji Yamashita, Dr. Ryusuke Takano, and Ms. Asami Ono for their kind suggestions and discussions. The authors also greatly appreciate the reviewers for their kind suggestions to improve the manuscript.

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DOI 10.1002/jps.24391