IInn VViittrroo --IInn VViivvoo CCoorrrreellaattiioonnss

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FABAD J. Pharm. Sci., 28, 215-224, 2003 SCIENTIFIC REVIEW

IInn V Viittrroo -- IInn V Viivvoo C Coorrrreellaattiioonnss

Esra DEM‹RTÜRK*, Levent ÖNER*°

IInn VViittrroo -- IInn VViivvoo CCoorrrreellaattiioonnss

SSuummmmaarryy :: In vitro-in vivo correlation (IVIVC) is the establish- ment of a relationship between a biological property or a para- meter derived from a biological property produced by a dosage form and a physicochemical property of the same dosage form.

The most commonly used biological properties are one or more pharmacokinetic parameters, such as maximum plasma con- centration (Cmax) or area under the plasma concentration time curve (AUC), obtained following the administration of the dosa- ge form. The most commonly used physicochemical property is a dosage form’s in vitro dissolution behavior (e.g., percent of drug released under a given set of conditions). Use of a validated IVIVC greatly improves the certainty with which predictions of in vivo results from in vitro release can be made. IVIVC levels can be grouped as level A, B, C and Multiple C. Level A can be used to predict the in vivo time course from the in vitro data be- cause it represents a point-to-point relationship between the in vitro dissolution rate and the in vivo absorption rate of the dosa- ge form. Level B and C correlations, however, are used to select the appropriate excipients, optimizing manufacturing processes, for quality control purposes and for characterizing the release patterns of immediate-release (IR) and modified release products relative to the reference. The aim of the IVIVC, especially if level A correlation has been provided, is to reduce the number of bi- oequivalence studies using these data or in some cases to waive them.

K

Keeyywwoorrddss:: In vitro-in vivo correlation.

Received : 27.2.2003 Revised : 4.5.2004 Accepted : 6.10.2004

‹‹nn VViittrroo -- ‹‹nn VViivvoo KKoorreellaassyyoonn Ö

Özzeett:: : ‹n vitro-in vivo korelasyon bir dozaj fleklinin biyolojik özelli-

¤i ya da biyolojik özelli¤inden türetilen bir ölçüt ile dozaj flekline ait fizikokimyasal özellik aras›nda iliflki kurulmas›d›r. En çok kullan›- lan biyolojik özellikler, dozaj fleklinin uygulanmas›ndan sonra elde edilen maksim›m plazma konsantrasyonu (Cmax) veya e¤ri alt›nda kalan alan (AUC) gibi bir veya daha fazla farmakokinetik para- metrelerdir. En çok kullan›lan fizikokimyasal özellik dozaj formu- nun in vitro çözünme h›z› davran›fl›d›r (Örn., bir tak›m koflullar al- t›nda ilac›n yüzde çözünen miktar›). Geçerlili¤i kan›tlanm›fl bir in vitro-in vivo korelasyonun kullan›m›; in vitro çözünme h›z› bulgula- r›ndan in vivo sonuçlar›n tahmin edilmesindeki kesinli¤i büyük öl- çüde art›r›r. ‹n vitro-in vivo korelasyon düzeyleri A, B, C ve çoklu C düzeyleri olarak grupland›r›labilir. A düzeyi korelasyon dozaj flekli- nin in vitro çözünme h›z› ve in vivo absorpsiyon h›z› aras›nda nok- tasal bir iliflkiyi temsil etti¤inden tüm in vivo zaman e¤risini, in vitro verilerden tahmin etmek amac›yla kullan›labilir. B ve C düzeyi ko- relasyonlar ise formülasyon gelifltirilmesi s›ras›nda uygun yard›mc›

maddelerin seçimi, üretim ifllemlerinin optimizasyonu, kalite kontrol ve referans ürüne göre hemen sal›m sa¤layan veya de¤ifltirilmifl sa- l›m sa¤layan ürünlerin çözünme h›z› özelliklerinin incelenmesinde kullan›l›r. ‹n vitro-in vivo korelasyonun amac›, özellikle A düzeyi bir korelasyon sa¤lanm›flsa, bu verilerle biyoeflde¤erlik çal›flmalar›n›n say›s›n›n azalt›lmas› veya baz› durumlarda vazgeçilebilmesini sa¤la- makt›r.

A

Annaahhttaarr kkeelliimmeelleerr:: ‹n vitro in vivo korelasyon.

IINNTTRROODDUUCCTTIIOONN

The therapeutic efficacy of pharmaceutical formulations is governed by factors related to both the in vitro dissolution characteristics of the drug and its in vivo bioavailability. This inherent interdependency within the drug-patient biosystem is the major con- cern that underlines the importance of in vitro-in vivo correlation (IVIVC) studies.

An IVIVC has been defined by the Food and Drug Administration (FDA) as "a predictive mathematical model describing the relationship between an in vitro property (usually the extent or rate of drug release) and a relevant in vivo response (e.g. plasma concentration or amount of drug absorbed)". The United States Pharmacopoeia (USP) also defines IVIVC as "the establishment of a relationship betwe-

* Hacettepe University, Faculty of Pharmacy, Department of Pharmaceutical Technology, 06100 S›hhiye, Ankara-TURKEY.

° Corresponding author e-mail: [email protected]

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en a biological property, or a parameter derived from a biological property produced by a dosage form, and a physico-chemical characteristic of the same dosage form"^1,2. Typically, the parameter derived from the biological property is AUC_0-∞ or Cmax, while the physicochemical property is the in vitro dissolution profile.

IVIVC attempts to link in vitro drug product performance to in vivo drug product biopharmaceutic- pharmacokinetic performance. For orally administe- red drugs, dissolution and intestinal permeation have long been recognized as two possible rate-limiting phenomena in the absorption process³. In general, compared to immediate-release (IR) products, an IVIVC is more readily defined for modified release dosage forms where drug release is rate limiting in the absorption process. Dissolution of a dosage form in vivo is often the rate-limiting factor determi- ning the physiological availability of the drug. It is apparent that, if a good correlation exists between an in vitro dissolution parameter and some parameter of bioavailability, then monitoring of the dissolution profile should permit the prediction of bioavailability⁴. Of particular importance, however, is that modified-release products cannot be characterized using a single-time point dissolution test which dif- fers from the IR dosage forms. Initially it was tho- ught that developing a meaningful correlation for IR dosage forms would be an easier task than for modified-release products. However, because of the natu- re of the principles upon which each type is based, it is believed that an IVIVC is more readily defined for modified-release dosage forms^5-7.

Investigating the absorption behavior of modified- release products in humans has resulted in several complicated practical problems like volunteer selection, dosing intervals, blood sampling times, drug analytical method, side effect risk and physiological effects. From the economic, technical and ethical perspectives of bioavailability studies, however, it is necessary to establish an in vitro test method that can predict the progress of drug release and the absorption of products in vivo⁸. The objectives of the

• To determine whether any correlations can be found between in vitro release data and in vivo performance;

• To determine whether differences exist between reference and test products in terms of both in vitro release and in vivo performance;

• To compare dissolution of the same product obtained using different dissolution test methods;

• To evaluate the variability of dissolution and bioavailability data between and within products⁹.

Wagner¹⁰ recommended that the most accurate manner of relating in vitro and in vivo data of the dissolution process is the correlation of ratios of half absorption times estimated from plasma concentration data with the ratios of in vitro t50% values. Sjö- vall et al.¹¹, in an IVIVC study of microencapsulated bacampicillin hydrochloride (an oral prodrug of am- picillin), evaluated the relationship between dissolution half life and each of the response variables: Plas- ma peak concentration, area under the plasma concentration time curve (AUC), urinary recovery and the results of the sensory recordings for the bitter taste of the drug. Individual linear regression analysis equations were estimated and combined in an overall estimate equation of the regression line.

E

Essttiimmaattiioonn ooff IIVVIIVVCC UUssiinngg tthhee BBiioopphhaarrmmaacceeuuttiiccaall D

Drruugg CCllaassssiiffiiccaattiioonn SSyysstteemm

IVIVC is normally expected for highly permeable drugs or drugs under dissolution rate-limiting conditions. This statement is supported by the Biophar- maceutical Classification System (BCS), which anti- cipates the successful IVIVC for highly permeable drugs. BCS is a fundamental guideline for determi- ning the conditions under which IVIVC are expected. In the BCS, a drug is classified in one of four classes based solely on its solubility and intestinal permeability¹².

The BCS defines three dimensionless numbers, dose number (D_o), dissolution number (D_n) and absorption number (A_n), to characterize drug substances.

These numbers are combinations of physicochemi-

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most fundamental view of gastrointestinal drug absorption.

First, the absorption number is the ratio of permeability (P_eff) and the gut radius (R) times the residence time (T_si) in the small intestine, which can be writ- ten as the ratio of residence time and absorption time (T_abs) (Eq. 1)¹³.

Eq. 1

Second is the dissolution number (D_n), which is the ratio of the residence time to the dissolution time (T_diss), which includes solubility (C_s), diffusivity (D), density (r) and the initial particle radius (r) of a compound (Eq. 2)¹³.

Eq. 2

Finally, there is the dose number, D_o, which is defined as the ratio of dose concentration to drug solubility, where C_sis the solubility, M is the dose and V_o is the volume of water taken with the dose, which is generally set to be 250 ml (Eq. 3)¹³.

Eq. 3

FFiigguurree 11.. The relationship between D_o, D_n and A_n and fraction dose absorbed¹³

Do = M/V^o Cs

Dn = 3D r² C^s

ρ Tsi = T^si Tdiss

An = P^eff

R xTsi = T^si Tabs

Figure 1 shows the relationship between D_oand D_n on the fraction dose absorbed (F) of the administe- red dose at a given A_n. 100% absorption can only be observed when the absorption time is shorter than the residence time. Important shifts in the curve happen around the dose number of 1 and the dissolution number of 1. In this shift area small changes in the value of D_nor D_ocan bring about important differences in the absorbed fraction. So it is important to know where a drug is located in the graph in order to overcome bioavailability problems at an early stage in the formulation development¹³.

Class I drugs such as metoprolol exhibit a high absorption number and high dissolution number. The rate-limiting step to drug absorption is drug dissolution or gastric emptying rate if dissolution is very rapid. Class II drugs such as phenytoin have a high absorption number but a low dissolution number. In vivo drug dissolution is then a rate-limiting step for absorption. For Class III drugs, permeability is the rate controlling drug absorption. Class IV drugs are low solubility and low permeability drugs. The absorption for Class II drugs is usually slower than for Class I and occurs over a longer period of time.

IVIVC is usually expected for Class I and Class II drugs (Tables 1, 2)^14,15.

Tables 1 and 2 illustrate the BCS and the expected IVIVC for immediate- and extended-release formulations.

T

Taabbllee 11.. Biopharmaceutical drug classification and expected IVIVC for immediate release drug products¹⁴

C

Cllaassss SSoolluubbiilliittyy PPeerrmmeeaabbiilliittyy IIVVIIVVCC

I High High Correlation

(if dissolution is rate-limiting step)

II Low High IVIVC expected

III High Low Little or no IVIVC

IV Low Low Little or no IVIVC

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T

Taabbllee 22.. Biopharmaceutical drug classification for extended release drug products¹⁴

Class Solubility Permeability IVIVC

IA High&Site Independent High & Site Independent IVIVC Level A expected IB High&Site Independent Dependent on site & Narrow IVIVC Level C

absorption window expected IIa Low&Site Independent High & Site Independent IVIVC Level A

expected IIb Low&Site Independent Dependent on site & Narrow Little or no IVIVC

absorption window

Va Acidic Variable Variable Little or no IVIVC Vb Basic Variable Variable IVIVC Level A expected

Class I drugs are high solubility and high permeability drugs and Class II drugs are low solubility and high permeability drugs. In Table 2, Sirisuth et al.¹⁴ suggested a new sub-classification for the drugs that have high and site independent solubility or low and site independent solubility. Drugs that have high permeability and site independent permeability are classified as Class Ia or Class IIa and drugs that have site dependent permeability and narrow absorption window are classified as Class Ib or Class IIb. Because little or no IVIVC is expected for Class III or Class IV drugs, there is no other sub-classification for these groups. Drugs that have variable solubility and variable permeability are classified as Class V. Class Va includes acidic drugs and Class Vb includes basic drugs. By the evaluation of three more properties of the drugs (site dependent or independent solubility, site dependent or independent permeability and narrow absorption window), the number of drugs which have been classified as Class I, II, III or IV decreases and the prediction of IVIVC becomes safer. Another sub-classification has also been made by Amidon¹⁶ according to the pH 1.2 and pH 6.8 solubilities of the drugs and their perme- abilities.

Löbenberg et al.¹⁷showed that a correlation can be developed for BCS Class II drug products using bi- orelevant dissolution media and that more than one dissolution time point is needed to characterize rele-

vant dissolution media (BDM) containing lecithin and sodium taurocholate in physiological amounts have been proposed to obtain a better understan- ding of the dissolution process in vivo and to predict oral drug absorption^18-20.

C

Coorrrreellaattiioonn LLeevveellss

IVIVC are categorized into levels A, B, C and Mul- tiple C by the FDA. The concept of correlation level is based upon the ability of the correlation to reflect the entire plasma drug concentration time curve that will result from administration of the given dosage form.

Level A represents a point-to-point relationship between in vitro dissolution and the in vivo input rate of the drug from the dosage form. In such a correlation, the mathematical description for the in vitro dissolution and in vivo input rate curves is the same.

Level B represents a relationship between the mean in vitro dissolution time and the mean residence time or the mean in vivo dissolution time using all of the in vitro and in vivo data. Since it does not reflect the actual in vivo plasma level curve, it is not considered to be a point-to-point correlation.

Level C represents a single point correlation between one dissolution time point (t_50%, t_90%, etc.) to one pharmacokinetic parameter such as AUC, C_max or time to reach maximum plasma concentration (T_max).

Multiple C represents the relationship between the amount dissolved at several time points of the product and one or several pharmacokinetic parameters of interest².

Level A is the most informative and useful correlation level which represents a point-to-point relationship between in vitro release and in vivo release/absorption from the dosage form that current IVIVC studies have focused on the development and validation of a Level A correlation^21,22. Level B and C

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formulation development, for example, for selecting the appropriate excipients and optimizing manufacturing processes, for quality control purposes, and for characterizing the release patterns of newly for- mulated IR and modified-release products relative to the references.

M

Meetthhooddss UUsseedd ffoorr tthhee EEvvaalluuaattiioonn ooff CCoorrrreellaattiioonn LLee-- vveellss

Principally, there are at least three correlation techniques available in the pharmaceutical sciences.

Single point, statistical moment and convolution and deconvolution techniques are discussed in terms of the advantages of each along with the resul- ting potential utility as a predictive tool for the user.

Since both the deconvolution and convolution techniques and the statistical moment calculations utili- ze all of the dissolution plasma level data available to develop the correlations, they represent a major advantage over the single point approach².

A

A.. SSiinnggllee PPooiinntt CCoorrrreellaattiioonn TTeecchhnniiqquuee

This technique represents the correlation between one dissolution time point (t_50%, t_90%, etc.) to one pharmacokinetic parameter. It is generally only useful as a guide in formulation development or as a production quality control procedure. It does not reflect the complete shape of the plasma level, which is the critical factor that defines the performance of the dosage form. Thus, this correlation technique is not predictive of actual in vivo product performance². Level C correlation can be established by this technique, but because of its obvious limitations, it has limited usefulness in predicting IVIVC.

Smolen and co-workers^23-25 pointed out that since the selection of these single correlative points is usually arbitrary, the interpretation of the results can be misleading. More preferable would be the correlation of the entire in vivo response time profile to the complete dissolution rate time curve. Such correlation can only result in developing dissolution tests that predict reliably the time course of the in vivo behavior of the drug.

B

B.. SSttaattiissttiiccaall MMoommeenntt CCoorrrreellaattiioonn TTeecchhnniiqquuee

The concept of Mean Residence Time (MRT) based on statistical moments provides one method for correlating in vivo-in vitro data. The theory of statistical moments is based on the preliminary assumpti- on that the movement of the individual drug molecules through the body compartment is governed by probability. Furthermore, the time course of drug concentrations in plasma can usually be regarded as a statistical distribution curve⁴.

Level B correlation is based on correlating mean time parameters that characterize the in vitro and in vivo time courses. If a good correlation exits between the MRT for in vitro dissolution and MRT for a suitable in vivo disposition parameter, then the relatively simple procedure of monitoring the dissolution profile should allow the prediction of in vivo availability. By definition, MRT is the average time a drug molecule spends in the introduced kinetic spa- ce. It depends on the site of input and the site of elimination²⁶.

The traditional area under the plasma concentration time curve (AUC) is one of the most basic parameters necessary for pharmacokinetic data analysis and is well used as a measure of drug disposition.

MRT is the time when 63.2% of an intravenous dose has been eliminated. This concept is similar to the biologic half life, the time required for 50% of a dose to be eliminated. MRT may be calculated as the ratio of the area under the first moment curve (AUMC) to the AUC, where AUMC is the area under the curve observed for the product of time and concentration versus time^27-29. The true MRT of a drug in the body may be calculated only when the actual time course of the amount of drug in the body is known and is independent of the details of trans- port within the body³⁰.

Many of the applications of statistical moment theory have stemmed from a desire to characterize drug absorption in a noncompartmental fashion.

These methods are also applicable to nonparenteral routes of drug administration other than the oral ro-

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ute. Cutler³¹first proposed mean absorption time as a novel method to characterize the rate of drug absorption in bioavailability studies. Riegelman and Collier³²extended this theory by virtue of the addi- tivity of various transit times, including the mean absorption time (MAT), which summarizes the mean time for drug molecules to remain unabsorbed.

MAT = MRT_iv– MRT_ni Eq. 4

MAT is simply the difference in MRT following intravenous administration (MRT_iv) and another no- ninstantaneous administration (MRT_ni). In the same manner, the mean dissolution time (MDT) of a solid dosage form may be determined by the difference in MAT for solid dosage form and a solution of the drug substance^27,33,34.

There are some limitations to pharmacokinetic data treatment using statistical moment theory. These relationships become more complex when a distribution component or a two compartment model is necessary to describe the data, and elimination must be assumed to occur only from the central compartment. A rigorous experimental design must be used to provide sufficient sampling during the absorption phase and more importantly, during the terminal elimination phase. Recognition of these limitations may preclude any inaccuracies in determination of various pharmacokinetic parameters based on statistical moment theory^27,35. Among others, noncompartmental analysis methods based on statistical moment theory are becoming increasingly popular for rapid data analysis by investigators³⁶.

C

C.. DDeeccoonnvvoolluuttiioonn aanndd CCoonnvvoolluuttiioonn CCoorrrreellaattiioonn T

Teecchhnniiqquuee

This is another technique that has been used to cal- culate the in vivo dissolution rate of oral solid dosage forms. Model dependent deconvolution methods are based on mass balance. The approximate equation used in absorption analysis for the two-compartment model was first published by Loo and Riegel- man in 1968³⁷. Wagner published an exact Loo-Ri-

1983³⁸. This is a general equation for absorption analysis of one- to three- compartment models.

Convolution is a model independent method based on the superposition principle. If a linear relationship exists between the rate of drug release or dissolution in the gastrointestinal tract, F(t), and the re- sulting systemic drug level C(t), that relationship can be expressed as a convolution:

Eq. 5

where C_δ(t) is the systemic drug concentration resul- ting from the instantaneous introduction of a unit amount of dissolved drug into the gastrointestinal tract. In practical terms, C(t) and C_δ(t) represent the drug concentrations following oral administration of a solid dosage form and an aqueous solution, res- pectively. If these parameters are known, the in vivo release profile of the solid dosage form may be determined by deconvolution.

The following is obtained upon taking the derivati- ve of C(t) with respect to time:

Eq. 6

For the case where C_δ(0) = 0, Eq. 6 simplifies to

Eq. 7

The drug concentration at a sampling site following administration of an impulse dose DI can often be well described by a sum of exponentials (39-43):

Eq. 8

The calculation of the drug absorption rate by this method requires the characteristic response parameters. The most ideal instance is the case in which the iv administration data are available and can be fitted C(t) = DIC(t) =

∑

_i=1ⁿ aie^-αit , αi > 0

C(t) = Cδ (t)F(t) C(t) = Cδ (t)F(t) + Cδ(0)

0 tF(u)du C(t) = Cδ (t)F(t) = Cδ

0 t

(u)F(t-u)du

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(Ae^-αt+ Be^-βt, for a monoexponential function, B=0).

The values of A, B, α and β from the iv data can be directly used as the parameters. If data on iv administration are not available, data on an oral solution may be used to obtain the characteristic response function, which might be a triexponential function, assuming that the absorption from the oral solution follows first order kinetics (Ae^-αt+ Be^-βt + Ce^γt, A+B+C=0). However, the rate profile obtained by this procedure is applicable only for the analysis of in vivo dissolution kinetics for the test sample.

A deconvolution-based IVIVC model is typically established using a two-stage approach, i.e., deconvolution calculation to estimate the time course of in vivo absorption and/or release followed by comparison with in vitro fraction released. An alternative modeling approach based on convolution can be utilized to directly predict the time course of plasma concentrations using Eq. 5 in a single step. The IVIVC is assessed and validated by statistically com- paring the predicted with the observed plasma levels. This convolution based modeling focuses on the ability to predict measured quantities rather than on indirectly estimated "in vivo" fraction absorbed and/or released. Thus, the results are more readily evaluated in terms of the effect of in vitro release on in vivo performances, e.g., AUC, C_max and duration above minimum effective concentrations⁴⁴.

Vaughan and Leach⁴⁵also utilized the numerical deconvolution method for absorption rate calculations and the prediction of plasma drug profiles from in vitro dissolution data. Banakar and Block⁴⁶, however, criticized the deconvolution mathematical predictive technique used by Smolen and others^23,24as too complicated and expensive because it requires speci- al computers equipped with Fourier transform capa- bilities. Instead, a simpler method based on statistical moment theory can be recommended³⁵.

D

Deevveellooppiinngg aanndd EEvvaalluuaattiinngg tthhee PPrreeddiiccttaabbiilliittyy ooff tthhee C

Coorrrreellaattiioonn

An IVIVC should be evaluated to demonstrate that predictability of in vivo performance of a drug pro-

duct from its in vitro dissolution characteristics is maintained over a range of in vitro dissolution rates and manufacturing changes. If in vitro dissolution is shown to be independent of dissolution conditions and if the in vitro dissolution profile is shown to be equal to the in vivo absorption or in vivo dissolution profile, then the results for a single formulation may be sufficient. In all other instances where an IVIVC model is presented, results from a single formulation should be considered insufficient. Such methods include USP apparatus I (basket) or II (paddle) in a buffered aqueous dissolution media with or without the use of surfactants. The dissolution profiles of at least 12 individual dosage units from each lot should be determined. The coefficient of variation (CV) for mean dissolution profiles of a single batch should be less than 10%⁴⁷.

Bioavailability studies for IVIVC development should be performed with enough subjects to characterize the performance of the drug product under study. In prior acceptable data sets, the number of subjects has ranged from 6 to 36. Although crosso- ver studies are preferred, parallel studies or crosso- ver study analyses may be acceptable. The reference product in developing an IVIVC may be an intravenous solution, an aqueous oral solution or an IR product under fasting conditions^48,49.

Taraszka and Delor⁵⁰studied the in vivo behavior of three sulfamethazine tablet formulations having fast (T_50% ~ 1.5 min), medium (T_50% ~ 15-20 min) and slow (T_50%~ 40-50 min) in vitro dissolution rates. A significant (at the 95% confidence interval) statistical difference existed for areas under the blood level curves and for maximum blood concentrations of sulfamethazine, when the fast dissolving formulation was compared to the slow dissolving formulation. The fast dissolving formulation gave the largest AUC and C_maxof sulfamethazine. Kent et al.⁵¹first determined the bioavailability parameters for different capsule formulations of tiopinac and then modified the in vitro dissolution condition to correlate the dissolution rate of the drug to the in vivo absorption characteristics. The bioavailability of 15 prepa- rations of commercial uncoated diazepam tablets

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were compared by Ogata et al.⁵²to their dissolution rates as determined by six methods. Statistical analysis of the data showed significant differences in the rate of bioavailability but not in the amount of drug available. Another interesting finding was re- ported by Proost et al.⁵³in a study of the dissolution and bioavailability characteristics of several formulations of diazepam tablets. A correlation of the in vitro and in vivo data was possible only when an in vitro method with a relatively high stirring rate, which is less discriminating, was used. The results were explained by assuming that disintegration of the tablets in the gastrointestinal tract is enhanced by mechanical factors caused by the gastric and intestinal motilities. Accordingly, the absorption of the drug products whose disintegration depends strongly on mechanical factors can be markedly fas- ter than would be predicted from dissolution data obtained with low stirring rates^54,55.

The first element in the correlation development is vi- sual inspection of the average in vitro dissolution rate and average in vivo absorption rate for each tested formulation. The second step involves fitting the data to an adequate correlation model. Either the two stage approach or the single stage approach can be utilized.

In the single stage approach, the plasma concentrations are directly estimated from the in vitro dissolution data. The input rate is modeled as a linear function of the in vitro cumulative amount dissolved. In the two stage approach, the in vivo percent absorbed is calculated by means of deconvolution and then corre- lated with the percent dissolved in vitro using a simple linear model with intercept (a) and slope (b):

absorbed%_invivo= a + b* dissolved%_invitro Eq. 9

A slope closer to 1 indicates a 1:1 correlation, and a negative intercept implies that the in vivo process lags behind the in vitro dissolution. A positive intercept has no clear physiological meaning. It can be a result of relatively high variability or curvature at the early time points.

Generally, IVIVC validation can be assessed by mo-

profiles from in vitro dissolution data using the developed IVIVC. Two criteria are required for the validation process: internal and external criteria. Inter- nal validation is defined as predictability of data used for model development and is recommended for all IVIVC analysis. External validation is based on how well the IVIVC predicts additional test data.

It provides a more comprehensive evaluation of the predictability than the internal one. This approach should be used when internal predictability is not conclusive, only two formulations with different release rates are available to develop the model, the correlation is being developed for a narrow therapeutic drug, and one desires a more comprehensive validation of the model¹.

IVIVC model predictability can be calculated by the percent C_maxand AUC prediction errors as shown in Eq 10-11.

Eq. 10

Eq. 11

Percent prediction error (PE%) of 10% or less for Cmax and AUC establishes the predictability of the IVIVC. In addition, the PE% for each formulation should not exceed 15%. If these criteria are not met, that is, if the internal predictability of the IVIVC is inconclusive, evaluation of external predictability of the IVIVC should be performed as a final determination of the ability of the IVIVC to be used as a surro- gate for bioequivalence. This involves using the IVIVC to predict the in vivo performance for a formulation with known bioavailability that was not used in developing the IVIVC model. With the ex- ception of narrow therapeutic index drugs, the external predictability step in the IVIVC evaluation process may be omitted if the evaluation of internal predictability indicates acceptable PE%⁵⁶.

C

COONNCCLLUUSSIIOONN

In the last few years, the usefulness of IVIVC has been recognized by investigators, in that it added time PE%AUC = AUC^obs - AUCpred

AUCobs

x 100 PE%Cmax = Cmax^obs - Cmaxpred

Cmaxobs

x 100

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mization. Formulation optimization may require al- tering formulation composition, manufacturing, and changing equipment and batch sizes. In the past, when these types of changes were applied to a formulation, bioavailability studies would also have to be performed in many instances to ensure that the

"new" formulation was to be found statistically similar in in vivo behavior as the "old" formulation. The evaluation of the concept of IVIVC from theory to practice is necessary to minimize the need for additional bioavailability studies as part of the formulation design. The present benefits of IVIVC can only be considered as preliminary. Further investigation is needed to establish the in vitro dissolution test as a guide to predict the drug absorption.

R

REEFFEERREENNCCEESS

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4. Lawrence HB, Umesh VB. Further considerations in correlating in vitro–in vivo data employing mean-time concept based on statistical moments, Drug Dev. Ind.

Pharm., 14(15-17), 2143-2150, 1988.

5. Dey M, Enever R, Marino M, Michelucci J, Smith D, Warner R, Weierstall R. Sustained release etodolac bioavailability and dose proportionality: correlation between in vivo and in vitro performance, Int. J. Pharm., 49, 121-128, 1989.

6. Hwang SS, Bayne W, Theeuwes F. In vivo evaluation of controlled release products, J. Pharm. Sci., 82(11), 1145-1150, 1993.

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