Journal of Pharmacokineties and Biopharmaceutics, Vol. 14, No. 6, 1986

Studies on the Reliability, of a Bihyperbolic Functional Absorption Model. I. Ring-Substituted Anilines

Adela Martin-Villodre, ~ Jos6 M. Phi-Delfina, ~'3 Joaquin Moreno, 2 Dolores P6rez-Buendia, ~ Joaquln Miralles, ~ Enrique F. CoHado, 1 Elvira Sfinchez-Moyano, 1 and Alfonso del Pozo 2

Received October 28, 1985--Final May 15, 1986

The present study reviews and checks the rearranged master lines of the functional bihyperbolic absorption model proposed by Pld-Delfina and Moreno, by examining the correlations between absorption rate constants experimentally found in the small intestine and in the colon of the rat, and two types of partition constants for a series of ring-substituted anilines, of low to medium molecular weight. Evidence is given which demonstrates the reliability of the bihyperbolie equation for the small intestine data, showing the importance of the type of substitution in the absorption rate of compounds; for the colonic data, the collapsed, monohyperbolie form of this equation (i.e., the Wagner-Sedman equilibrium model) applies, independent of the nature and position of the group substituems in the aniline molecule. This means that, as the bihyperbolic model equation predicts, aqueous pore diffusion is a crucial factor, as important as membrane permeation~ in absorption in the small intestine, whereas in the colon only this latter route is operative. The perspectives opened by the application of the model to gastrointestinal absorption studies are also discussed.

KEY WORDS: anilines; absorption models; bihyperbolic model; intestinal absorption; colonic absorption; pore diffusion; membrane permeation; lipophilicky parameters.

I N T R O D U C T I O N

Correlations between gastrointestinal absorption and partition con- stants for homologous series of xenobiotics are a suitable source of informa- tion in the understanding of the passive penetration mechanisms. But it is essential to reach as exact a knowledge as possible on the nature of these relationships, which, if clearly established, could be, in addition, a very

The present paper is part of an investigative project (No. 1563/82) developed with a grant from the Comisi6n Asesora de Investigaci6n Cientffica y T6cnica (CAICYT) of the Ministry of Education and Science of Spain. The project has been developed jointly by the Depart- ments of Pharmaceutics of the Universities of Valencia and Barcelona.

Department of Pharmaceutics, Faculty of Pharmacy, Valencia, Spain. 2 Department of Pharmaceutics, Faculty of Pharmacy, Barcelona, Spain. 3 To whom correspondence should be addressed.

615

616 Martln-Villodre et al.

useful tool in conducting oral absorption design studies for new drugs and even in elucidating some features about the structural arrangement of abosorbing membranes. Unfortunately, there is no general agreement about the choice of the biophysical model which should be applied to the available data.

In a previous paper (1), a new tentative model was proposed through the fitting and interpretation of several absorption-parti t ion data. At present, the chief rearranged lines of the proposed absorption model can be summar- ized as follows:

1. The general equation which represents the correlation between absorption rate constants and partition coefficients or related constants can be expressed as:

k , = k l + k 2 = kmp~ ~- kpO_____~' (1) Q + p " Q ' + p " '

where ko represents the actual absorption rate constant experimentally determined for each compound; kl and k2 are the rate constants governing the penetration of the compounds into the lipoidal membrane and across the aqueous pores, respectively; P is the partition coefficient or related constant of each compound in vitro; and n, n', Q, and Q' are constants that depend on the technique used, easily approached in a computer through a logistic-logarithmic regression of kl or k2 versus P. This means that the correlation between ka and P is represented by the sum of two hyperbolic functions, direct for the lipidic membrane permeation (kl) and inverse for aqueous pore diffusion (k2), with two limiting asymptotic values for mem- brane (kin) and for pore (kp) routes. It could be assumed that the km value should be about 4-6 hr -~ when the rat gut in situ technique recommended here is used, provided that the tested compounds are free of vasoactivity and severe acute local toxicity. The actual kp value will depend largely on the molecular weight or size of the first element of the series; in practice, values between 0 and 8 hr -1 or somewhat larger can be expected if the rat gut in situ technique is utilized.

2. Equation (1) will be fully applicable to specialized absorption sites, such as the small intestine, provided that the series tested includes com- pounds of molecular weight low enough to pass the intestinal aqueous pores (below 200-250, depending on the features of the series). Theoretically, Eq. (1) should be applicable only to true homologous series (i.e., when a straight-chain -CH2- substituent is added to each term). If the homology is not perfect (i.e., if a branched-chain -CH2-substituted compound is included along with the former elements), the steric effects arising will exceedingly hinder the pore penetration and such element will be out of the correlation. But, since some substituents or atomic associations do

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618 Martin-Villodre et al .

not seem to have such hindering capacity, the field of application of Eq. (1) may be rather large.

3. If the homologous series is formed by compounds whose molecular weights are over the above range (i.e., above 200-250), Eq. (1) will collapse to the more general monohyperbolic equation:

kmp ~ go (2) Q+pn

already proposed by Wagner (2, 3) and similar in nature to others which have been postulated (4, 5). In this case, the pore route would not be available, the second terra in Eq. (1) would vanish, and the experimental data would be well fitted to Eq. (2), independent of the position of the substituents in the molecule.

4. In the nonspecialized absorption sites, such as the stomach or the colon, it is assumed that only very small pores suitable for water exchange should exist. Larger pores are virtually lacking, so that, for practical pur- poses, any homologous series should be fitted to Eq. (2), independent of the molecular weight and the position of substituents.

Consequently, it can be suggested that, for series which include only components above 250 in molecular weight in the small intestine, as well as for all series in stomach or colon, collapsed monohyperbolic correlations between ka and P according to Eq. (2) should be found, whereas for series with components below 250 in molecular weight, bihyperbolic correlations according to Eq. (1) should be obtained in the small intestine. In this latter case, the form and features of the correlation curves may be extremely variable, depending on the relative increments in lipophilicity and molecular weight of the compounds; therefore, a maximum value of ka, or a minimum, or neither, or both may be found within the series, as schematized in Fig. 1.

Although the data analyzed in our previous paper (1) strongly substanti- ated the above assumptions, additional experimental evidence would be desirable in order to check the general validity of this bihyperbolic functional absorption model. In the present paper, such evidence is given for a series of ring-substituted amines ranging from 93 to 175 in molecular weight, in specialized and nonspecialized absorption sites (small intestine and colon, respectively), through the use of two types of partition constants. Further evidence will be provided for other xenobiotic series of different characteris- tics in forthcoming papers.

MATERIALS AND M E T H O D S

Homologous Series Tested

Thirteen aromatic amines, including two condensed-ring compounds and 11 ring-substituted anilines, were used in the experiments. The complete

Bihyperbolic Functional Absorption Model 619

Table I. Equations Describing the Apparent Zeroth-Order Water Reabsorption Kinetics in the Small Intestine and Percentages Reabsorbed at a Fixed Time for Each Amine Test Solution a

V, = - K t + Vo Percentage Equation parameters of water

reabsorption No. Tested amines K(ml/min) V o (ml) r at 30 rain ~

1 Aniline 0.0963 10.87 0.992 20.2 2 2-Methylaniline 0.0950 10.76 0.994 20.9 3 4-Methylaniline 0.0828 10.65 0.997 18.3 4 2, 4-Dimethylaniline 0.1246 10.65 0.999 30.9 5 4-Ethylaniline 0.1305 10.73 0.999 31.8 6 4-Isopropylaniline 0.0916 10.70 0.999 20.5 7 1-Naphtylamine 0.0951 10.74 0.999 21.1 8 2-Naphtylamine 0.1019 10.59 0.995 24.7 9 4-Propylaniline 0.1101 10.72 0.999 25.8

10 4-Aminobiphenyl 0.0968 10.66 0.999 22.4 11 4-Tertbutylaniline 0.0795 10.65 0.996 17.3 12 4-Butylaniline 0.0947 10.58 0.993 22.6 13 4-Cyclohexylaniline 0.0916 10.50 0.990 22.5

a Experimental points were obtained at 0, 5, 15, and 25 min (means of three animals per time). b Apparent percentages, assuming an initial perfusion volume of I0 ml (6).

list o f inves t iga ted c o m p o u n d s is given in Table I. E lements subs t i tu ted in the para pos i t i on were p re fe r r ed for expe r imen ta l des ign reasons and in o rde r to ma in t a in the h o m o l o g y o f the series, a l t hough two or tho-subs t i tu ted

c o m p o u n d s were also i n c l u d e d in o rde r to check the effects o f this type o f subs t i tuen t in abso rp t ion . The amines were used as bases and were s u p p l i e d as r eac t ive -g rade p roduc t s by the manufac tu re r s ( M e r c k A. G., Janssen Co., and S igma Produc ts ) , with an act ive ma t t e r conten t o f not less than 98.5%. Desp i te the fact that mos t o f these a m i n e s - - m a i n l y because o f the i r long- t e rm risk p o t e n t i a l i t i e s - - a r e o f tox ico log ica l interest , no effects which cou ld affect the abso rp t i on ra te were no t iced dur ing the a bso rp t i on tests.

Absorption Studies

Biological Technique

The s tudy was p e r f o r m e d in male Wis ta r rats weighing 200-280 g. The in situ rat gut p r e p a r a t i o n desc r ibed by Do lu i s io et al. (6) was used for smal l in tes t ine exper iments ; in o r d e r to p reven t e n t e rohe pa t i c recycl ing, the bi le duct was c a n n u l a t e d p r io r to the per fus ion . A s imi la r t echn ique was used to assess co lon ic abso rp t ion , in which a segment o f nea r ly 20 cm of gut be tween the p r o x i m a l and the d is ta l co lon was cannu la ted . The pe r fused vo lumes o f the test so lu t ions were 10 ml for the smal l in tes t ine and 5 ml for the colon. Before the tests each segment was pe r fused with 200 and 50 ml o f sa l ine , respect ively , in o rde r to r emove feces and c lean the gut lumen. Samples o f 0.20-0.40 ml were r emoved for xenob io t i c assay; the

620 Martln-Villodre et al.

sampling intervals were 5 min, for a total of 25 min for the small intestine tests and for a total of 30 min for the colon experiments. For 4-cyclohexylani- line, the samples, after the first 5 min, were taken at 3-rain intervals, both in the small intestine and the colon, since otherwise the absorption kinetics have proved to be difficult to assess, at least in most animals.

Perfusing Solutions

Two isotonic vehicle solutions were prepared, buffered to pH 6.2 (small intestine tests) and 7.5 (colon tests), by addition of 1% (v/v) S6rensen phosphate solutions; perfusion liquids of limited buffer capacity were employed in order to prevent potentially disturbing effects of phosphates in absorption. The test solutions were prepared immediately before the absorption experiments by dissolving a fixed amount of amine in the vehicle solution (w/v) according to its own solubility: 0.006% for 4-cyclohexylani- line, 0.015% for 4-aminobiphenyl, 0.020% for 2-naphthylamine, 4-propy- laniline, 4-terbutylaniline, and 4-butylaniline, and 0.050% for the remainder. After dissolving the xenobiotic, the pH of the solution was adjusted again. The above concentrations will assure the management of a solution diluted enough to avoid precipitation into the lumen during the absorption tests.

Water Reabsorption Studies

Very little reduction in volume, not exceeding 4% at 30 rain, was noted in colon experiments, so no correction factor was applied to these data (6). For the small intestine tests, however, the reduction in volume of the perfused solutions at the end of the experiment was clearly significant (up to 30% or even more) and a correction became necessary in order to accurately calculate the absorption rate constants. Since our previous experience was that markers such as phenol red or polyethyleneglycols are not entirely satisfactory, an alternative method based on the direct measure, at fixed times, of the remaining volumes of the test solutions perfused independently in selected animals was employed. Thus, the remaining volumes at 0, 5, 15, or 25 rain were recovered as completely as possible into the ileal syringe at the prescribed time and the ileal cannula was removed from its junction; the whole small intestine was then disbridled, separated from the abdominal cavity, and left hanging in a glass vessel, in which the residual gut fluid was recovered through the ileal cannula by pumping with the duodenal syringe as well as by some smooth manual pressure on the gut surface. The two remaining fractions (in syringe and residual) were then joined, centrifuged, and measured, employing, in all cases, the same calibration flask. For the zero-time samples, the residual volume recovered was diluted with 10 ml of saline, centrifuged, and measured.

Bihyperbolic Functional Absorption Model 621

Water reabsorption was characterized as an apparent zero-th-order process since the linear regression of the remaining volumes V~ versus time t,

V~ = -kot + Vo (3)

gives, in all cases, the best fit (r > 0.990), as shown in Table I. Accordingly, the actual concentrations Aa found at any time in the perfusing samples were corrected as follows:

A = AaV~/Vo (4)

with A the corrected concentration used to calculate the true absorption rate constants in the small intestine absorption tests.

Absorption Rate Constants

The absorption rate constants of the compounds, ka, were determined by least-squares regression analysis of the natural logarithms of the remain- ing xenobiotic contents A expressed as percentage of the initial xenobiotic amount (100%) versus time:

In A = -k~ t + In Ao (5)

In order to minimize the contribution of "adsorption" on the intestinal mucosa (7), only the samples taken from the perfused solutions (5 rain and later) were used for regression, since membrane adsorption effects are rapidly established.

Partition Studies

Partition coefficients

Bulk-phase partition coefficients P between two selected solvents, chloroform and n-octanol (Merck analytical grade), and an aqueous phase identical to the vehicle solutions (pH 6.2 or 7.5) were determined; phase- volume ratios were selected for each amine according to the classical approaches (8, 9) in order to minimize the standard deviation. Aliquots of the aqueous phases were removed and assayed for the amine content, and the partition coefficient was then determined.

Chromatographic Partition Constants

In order to determine the chromatographic ( 1 / R s - 1) values, which are homologous to the partition coefficients for correlation purposes (10), the reversed-phase thin-layer partition technique used was the same as in a previous study (11), with the following modifications: (1) Merck's Cel- lulose F plates were used as substrate; (2) 0.1% solutions of amines in 70%

622 Martin-Villodre et al.

ethanol were spotted; and (3) development was carried out at 24~ with a mixture of S/Srensen phosphate buffers (pH 6.2 or 7.5) and acetone (6 : 4, v/v), to 8 cm above the starting line.

Analysis of the Samples

The color reaction according to the classical Bratton and Marshall diazotization and coupling technique (12), using a Perkin-Elmer Lambda 3 automatic spectrophotometer, was developed. For a reliable determina- tion, two critical modifications should be introduced to the original pro- cedure: (1) 0.5 N HC1 must be used for all the operations instead of the 0.1 N solution recommended, and (2) the readings should be made 6-8 hr after the addition of the coupling solution, depeding on the amines, at 540-570 nm. For 2-naphthylamine, 4-aminobiophenyl, 4-tertbutylaniline, and 4-cyclohexylaniline, 0.2 ml of a 5% solution of polysorbate 80 were added prior to the coupling reaction in order to improve the color development.

The described procedure is suitable for both biological and partition samples, provided that a calibration curve is developed with each determina- tion. It was observed, however, that, in presence of small quantities of chloroform and n-octanol, the color development in the 4-aminobiphenyl partition samples became too much slow; the partition coefficient of this compound was therefore assessed by ultraviolet spectrophotometry at 247 nm, a method with an excellent linearity range.

Fitting of Models to Data

Absorption-parti t ion data were treated as previously (1). Besides the bihyperbolic general equation (1) and its collapsed form [Eq. (2)], the fitting to the parabolic equation

in k~ = a + b In P + c(ln p)2 (6)

representative of other trends in model conception, was also attempted. When partition chromatographic constants were used instead of partition coefficients, the term P in the above equations was substituted by the (1 /Rf-1) parameter. The statistical criteria for assessing the goodness of fit were also the same as previously described (1).

RESULTS

Absorption Rate Constants

Absorption rate constants ka, found in the rat small intestine and in the rat colon are shown in Tables II and III, respectively; the former values

Bihyperbolic Functional Absorption Model 623

Table II. Absorption Rate Constants and Related Parameters Found in the Rat Small Intestine (Five Animals per Compound, Averaged Values)

Small intestine absorption kinetics: averaged values of parameters

No. Group Tested amine k, + s (hr -1) Ao+s (%)

1 A,B Aniline 5.645 + 0.49 76.92 + 3.42 2 B 2-Methylaniline 5.987 4- 0.31 78.88 4-11.73 3 A 4-Methylaniline 6.410 • 0.37 88.64 • 4.30 4 B 2,4-Dimethylaniline 6.307 • 0.17 74.89 + 3.92 5 A 4-Etbylaniline 7.375 • 0.31 82.49 • 5.16 6 B 4-Isopropylaniline 6.437 4- 0.52 86.82 • 4.78 7 A 1-Naphthylamine 8.239 + 0.39 84.12 4-11.55 8 A 2-Naphthylamine 8.347 + 0.29 85.63 • 1.72 9 A 4-Propylaniline 7.917 + 0.22 88.77 • 6.14

10 A 4-Aminobiphenyl 7.763 + 0.23 73.86 • 3.28 11 B 4-Tertbutylaniline 6.803 • 0.53 82.35 + 3.28 12 A 4-Butylaniline 6.590 • 0.30 78.30 • 5,34 13 A,B 4-Cyclohexylaniline 6.138+0.36 75.87+4,55

are already corrected for water reabsorption. The average k~ values, as calculated from five individual rat absorption kinetics, are shown, as well as the corresponding intercept values Ao.

Partition Constants

Partition coefficients found in chloroform and n-octanol against aqueous buffers (means of four determinations) and reversed-phase

Table IlL Absorption Rate Constants and Related Parameters Found in the Rat Colon (Five Animals per Compound, Averaged Values)

Colonic absorption kinetics: averaged values of parameters

No. Tested amines k a + s (hr -1) Ao• (%)

1 Aniline 2.766:5 0.19 93.48 + 4.38 2 2-Methylaniline 3.805 • 0.44 93.14• 4.67 3 4-Methylaniline 3.759 + 0.44 93.41 4- 2.61 4 2,4-Dimethylaniline 3.938 + 0.30 88.27 + 9.24 5 4-Ethylaniline 4.213 + 0.45 94.13 4- 5.65 6 4-Isopropylaniline 4.306 + 0.22 91.90 • 5.73 7 1-Naphtylamine 4.284 • 0.20 89.60 • 0.67 8 2- Naphtylamine 4.318 • 0.43 91.65 • 5.92 9 4-Propylaniline 4.356 + 0,30 88.45 • 4.25

10 4-Aminobiphenyl 4.440 • 0,38 84.18 • 1. t6 11 4-Tertbutylanfline 4.406 + 0.36 87.70 • 5.47 12 4-Butylaniline 4.558 • 89.67 • 4.02 13 4-Cycylohexylaniline 4.651 + 0.30 85.06 • 3.23

Tab

le I

V.

Bu

lk-P

has

e P

arti

tion

Coe

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s an

d C

hro

mat

og

rap

hic

Par

titi

on

Co

nst

ants

Fo

un

d f

or

the

Am

ines

at

the

Tw

o S

elec

ted

pH

Val

ues

in

the

Aq

ueo

us

Ph

ases

Par

titi

on c

on

stan

t at

pH

= 6

.2

Par

titi

on

co

nst

ant

at p

H =

7.5

No.

T

este

d a

min

e P

(ch

loro

form

) P

(n-o

ctan

ol)

(1

/Rf)

-

1 P

(ch

loro

form

) P

(n-o

ctan

ol)

(1

/Rf)

-

1

1 A

nili

ne

26.3

6•

9.5

6•

0.3

39

• 2

3.9

6•

9.6

2•

0.6

46

+0

.02

2

2-M

eth

yla

nil

ine

80.7

8•

21

.46

• 0

.69

6•

92

.16

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6.2

2•

1,21

0•

3 4

-Met

hy

lan

ilin

e 79

.42•

2

2.4

9•

0.7

25

• 8

3.7

0•

24

.60

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205•

4

2,4

-Dim

eth

yla

nil

ine

182.

90 •

18.

06

45.0

4 •

1.26

1.

464

• 0.

09

186.

98 •

9.5

6 47

.81

• 1.

68

1,73

1 •

0.16

5

4-E

thyl

anil

ine

189.

89•

86

.52

• 1.

531•

19

1.08

• 9

2.3

7•

1,85

4•

6 4

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pro

py

lan

ilin

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4.34

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2

10

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• 2.

575•

32

4.36

• 2

02

.55

• 3

.42

9•

0.33

7

1-N

aph

tyla

min

e 40

4.82

• 3

8,56

19

9.54

• 6

.43

2.66

7 •

0.29

40

0.15

• 4

3.31

18

5.48

• 4

.94

2.79

6 •

0.35

8

2-N

aph

tyla

min

e 48

0.65

• 2

3.91

23

7.97

• 3

.21

2.34

2 +

0.2

0 49

6.31

• 2

6.38

24

8.45

• 3

.39

2.43

8 •

0.24

9

4-P

rop

yla

nil

ine

752.

28 +

50.

90

248.

68 •

5.7

1 3,

433

• 0.

41

981.

40 •

67.

88

253.

49 •

11

.10

3.88

8 •

0.39

10

4

-Am

ino

bip

hen

yl

928.

68 •

92,

42

449.

25 •

38.

47

4.64

8 •

0.53

13

64.8

9 •

13.4

3 72

7.02

• 5

.33

4.88

0 •

0,52

11

4

-Ter

tbu

tyla

nil

ine

949.

78 •

25.

20

270.

70 •

6.7

8 4.

354

• 0.

41

1050

.62

• 49

.76

298.

07 •

7.2

5 4,

692

• 0.

43

12

4-B

utyl

anil

ine

1640

.12•

85

2.52

• 7.

298•

2

35

0.7

4•

1110

.36•

7

.71

0•

13

4-C

yclo

hexy

lani

line

31

33.7

9•

1944

.97•

13

.566

• 45

44.7

6•

2023

.64•

14

.316

•

o

Bihyperbolic Functional Absorption Model 625

chromatographic constants (means of six chromatograms) are shown in Table IV. The values obtained at pH 6.2 were correlated with the absorption rate constants determined in the small intestine, whereas the values found at pH 7.5 were used for correlation with the colonic absorption rate con- stants.

Absorption-Partition Correlations

The colonic absorption rate constants closely correlated with partition constants through Eq. (2), as expected from the aforementioned assump- tions. The parabolic fits were also analysed. The fits and statistical para- meters associated with each model are indicated in Table V; in Fig. 2, a representative plot of ka vs. P(chloroform) is shown. The plot has been represented in linear-logarithmic scale so as to facilitate the portrayal and the visual inspection of the graph; for this reason a sigmoid curve has been obtained instead of a hyperbola (in Fig. 1 the same effect can be seen).

The absorption rate constants found in the small intestine should be distributed, in accordance with the above assumptions, into two groups, A and B (Table II), before fitting to Eq. (1). This division is also convenient for fitting to Eq. (6) in order to compare results. Computer evidence shows

Table V. Analysis of the Colonic Absorption-Partit ion Data Found for the Tested Amines According to the Selected Model Equations

Equation parameters Weighted Partition Model sum of constants equations Symbol Value squares r AIC test

P(chloroform) Parabolic (Eq. 6)

Hyperbolic (Eq. 2)

P(n-octanol) Parabolic (Eq. 6)

Hyperbolic (Eq. 2)

1 / R / - 1 Parabolic chromatography (Eq. 6)

Hyperbolic (Eq. 2)

a 0.2602 b 0.3279 0.1778 0.969 -16.449 c -0.0214

km 4.5886 n 0.8063 0.0681 0,988 -28.928 Q 8.3301

a 0.6248 b 0.2687 0,3767 0.933 -6,693 c -0.0202

k~ 4.5056 n 0.9681 0.0878 0.985 -25,623 O 5.2101

a 1,2445 b 0.2710 0.2532 0.959 -12.817 c -0.0646

k,. 4.5619 n 1.6506 0.0648 0,989 -29.572 Q 0,3049

626 Martin-Villodre et ai.

i

c 8

g

o_ g -6

4

3 - -

2

1

J o ~ I I I I 1 10 100 1000 10000

Parh t~on c o e f f i c i e n t ( c h l o r o f o r m )

Fig. 2. Plot of colonic absorption rate constant vs. chloroform partition coefficient for the tested amines, according to Eq. 2. Equation parameters are given in Table V.

that groups A and B are separate sets of data, as well as that the first component (aniline) and the last component (4-cyclohexylaniline, for which the pore route should be hardly operative) are common to the two series; for group B the fitting to Eq. (1) is not advisable, since it is made up of by six compounds (the same as the number of equation parameters), apart from other reasons which will be discussed later. The fits and statistical figures obtained for group A are shown in Table VI. Figure 3 is a representa- tive plot showing the bihyperbolic fit found for chromatographic partition data, drawn as indicated above; in this case, two sigmoid curves have been obtained instead of the corresponding hyperbolas, so that the summation of kl and k2 yields the theoretical ka value for each compound.

DISCUSSION

Partition Constants

A point of outstanding interest is to assure that partition phenomena are effectively maintained. The presence of five straight-chain true homologous compounds in the tested series demonstrates that this condition is quite fulfilled for bulk-phase partition coefficients (Table VII). The P values and a log P structural parameters are, on the other hand, in close

Bihyperbolic Functional Absorption Model 627

Table V1. Analysis of the Intestinal Absorption-Partition Data Obtained for the Amines of Group A, According to the Selected Model Equations

Equation parameters Weighted Partition Model sum of constant equation S y m b o l V a l u e squares r AIC test

P(chloroform) Parabolic (Eq. 6)

Bihyperbolic (Eq. 1)

P(n-octanol) Parabolic (Eq. 6)

Bihyperbolic (Eq. 1)

1 / Rf - 1 Parabolic chromatography (Eq. 6)

Bihyperbolic (gq. 1)

a -0.0054 b 0.7014 1.0189 0.932 +6.169 c -0.0590

k m 5.9804 kp 5.3996 n 1.2498 n' 2.1291 0.0373 0.998 -17.591 Q 1.215 x 103 Q' 2.286 x 106

a 0.8410 b 0.4825 0.7661 0.949 +3.602 c -0.0470

k m 6.3231 kp 5.8296 n 1.3188 n' 2.4129 0.3312 0.979 +2.055 Q 1.153 • 103 Q' 2.676 x 106

a 1.9888 b 0.1813 0.9499 0.937 +5.537 c -0.0986

k m 5.8074 kp 5.5632 n 2.1341 n' 2.2669 0.1828 0.988 -3.296 Q 3.1492 Q' 24.1201

agreement with those reported in the specialized li terature (8, 13). As far

as chromatographic par t i t ion constants are concerned, it becomes apparen t through the compar i son of the results with those found for other solutes (14) that the inc idence of adsorp t ion forces in migra t ion varying with p H value canno t be discarded; no twi ths tanding , the ARm increments are reason-

ably cons tan t (Table VII) and, for practical purposes , the relative par t i t ion behavior of the ani l ines is ma in t a ined for each par t icular system, so that the ( 1 / R s- - 1 ) values are complete ly reliable for correla t ion purposes (Tables V and VI). Al though some authors have criticized the chromatographic

methods (3, 15), adduc ing that the par t i t ion constants they afford have a l imited value range, we believe that, if sui table impregna t ing phases and

developing fluids are avai lable, the va luable range of the result ing constants could be as large as that offered by the part i t ion coefficients, with some

628

10

Martln-Villodre et ai.

Z" I ..~ 8

t~

o 6

t~

g

o t~

_Q t~

c 2

E

~--kp /

~" / kl k2 \~,/ / \

/ /

/ /

/ /

/ /

/

0.1 1

km---:

\ \

\ \

\ \

\ \

\

10

Chromatographm partition constant

Fig. 3. Plot of absorption rate constants found in the small intestine vs. chromatographic reversed-phase partition constants for amines of group A (Table II), according to Eq. (1). Equation parameters are shown in Table VI.

Table VII. Partition Parameters for True Homologous Compounds, Showing the Additivity of the Incremental values A log P and ARm [A log (1 /Rf) - 1 ], Thus Indicating the Outstanding

Predominance of Partition Phenomena in the Assessment of the Constants

Regression versus the number of straight-chain carbon atom (N):

log P = A log P- N + log Po ~ R,~ = ARm" N + R,~ b Equation parameters experimental

A log P or ARm Partition A log P for next

pH constant (ARm) Intercept c r bomologs

6.2

7.5

P(chloroform) 0.456 26.30 0.997 0.448 • 0.12 P ( n - o c t a n o l ) 0 .494 8.51 0.998 0.488 • 0.09 (1 / Ry) - t 0 .334 0.34 0 .999 0.333 • 0.01

P(chloroform) 0.505 23.99 0.995 0.498 • 0.16 P(n-octanol) 0.514 8.51 0.997 0 . 5 1 6 • (1 /Rf) - 1 0.266 0.63 0.997 0 . 2 6 9 •

For partition coefficients. b For chromatographic partition constants. c Theoretical values of P or ( 1 / R y - 1) for aniline, the first, nonsubstituted element of the series.

Bihyperbolic Functional Absorption Model 629

practical advantages: rapidity, ease of handling, and, sometimes, a superior degree of accuracy, especially when the tested series includes highly hydro- philic or highly lipophilic compounds, for which the partition coefficients are difficult to assess almost in all recommended solvents (8).

Adsorption to the Mueosae

Adsorption effects of amines are significantly different in the two absorption sites tested, as observed with other basic compounds (16). The amounts lost by adsorption ranged from 11 to 26% in the small intestine and from 6 to 16% in the colon. Although some of the xenobiotic loss is attributable to a dilution effect (see the Vo values in Table I), it can be assumed that the greater loss values in the small intestine probably reflect the greater mucosal surface area available in this highly specialized absorp-. tion site.

Absorption Models

From the experimental data it becomes evident that, from a biophysical modelling viewpoint, the absorption behavior of the tested amines in the small intestine and in the colon is quite different.

Absorption in the small intestine

Since the molecular weight of the amines is below 200, the bihyperbolic noncollapsed model [Eq. (1)] should be applied to the absorption-partition data and, as pointed out above (see Tables II and VI), these must be distributed in two sets, A and B. Although it may be somewhat surprising, 4-aminobiphenyl and the naphthylamines are included in group A along with the true homologs (Fig. 3). Some of the described features had already been documented in the specialized literature (1, 17, 18); this situation is therefore not new in this type of study, but it can be substantiated, in light of the bihyperbolic model, as due to the fact that neither benzene nor the condensed-ring substituents impair pore penetration more than do their corresponding number of straight-chain substituents, whereas branched- chain and ortho-methyl groups have much larger hindering capacity. The highly lipophilic 4-cyclohexylaniline also fits within this group of nine compounds. These data exhibit a very good fit to Eq. (1) (three degrees of freedom), as is concluded from the statistical figures shown in Table VI.

Group B, made up of six elements, which include ortho- and branched- chain substituted and other types of compounds, is clearly nonnatural and, because of its heterogeneity, cannot be considered as a homologous series; moreover, the nonexistence of degrees of freedom makes it statistically inadvisable to fit these data to Eq. (1). But, if the membrane hyperbola obtained for group A is applied to these elements (r = 0.995 for their k~

630 Martln-Villodre e t a l .

values) and the pore hyperbola is then calculated from the differences (ka - k~) (which leads to r = 0.990 for k2 values), the impaired pore penetra- tion due to the branched-chain and the ortho substitution can be easily substantiated, as shown in Fig. 4.

Colonic Absorption According to the assumptions stated above, the collapsed

monohyperbolic absorption model [Eq. (2)] should apply to the colonic absorption-partition data, regardless of the nature and position of the substituents in the aniline molecule. This is actually the case, as can be seen in Table V and in Fig. 2. This constitutes a further functional demonstration of the assumption that, in contrast to what occurs in the small intestine, pores with a diameter large enough to allow xenobiotics to penetrate are virtually lacking in the colonic mucosa, as would occur in the stomach (1). Unfortunately, there are no morphological studies which could confirm these assumptions, since biological structures of diameter below 10 A are in general below the discriminative power of micrographic methods (19).

10

2 Jz

r g 6 {3

2

g �9 - - 4

S_ g

~3

2

C

Group A

km ~ - - - - - - , ,

�9 --kp ~ ~

L_

\ / - / % k 1 [ c o m m o n )

\ . ~/ \

\ / \ "X \

/ " \ \ t / k 2 [group A) / \ ,

/ \ \

/ B)-\. X / / k 2 [group \

10 100 1000 1 0 0 0 0

Parhhon coeff~ctent (chloroform)

Fig. 4. Plot of absorption rate constants determined in the small intestine vs. chloroform partition coefficients for ( O ) Amines belonging to group A (Table II), according to Eq. (1). ( 0 ) Elements of group B fitted according to the kp and k I values found for the former group. Note the flatter k 2 hyperbola for the elements of group B, indicating impaired pore penetration as compared with group A compounds. (Q) Compounds common to both groups.

Bihyperbolic Functional Absorption Model 631

Perhaps future developments in this field could clarify this intriguing point, thus elucidating whether or not functional absorption studies such as the one reported here are reliable in predicting structural features of biological absorbent membranes.

Another point of interest concerning colonic absorption of anilines lies in the unusually high values of k~ which have been found, which represent absorption half-lives ranging from 9 to 15 min. This is undoubtedly related to ionization effects and to the intrinsic lipophilicity of the nonionized molecules and can illustrate the extensive yielding potentialities of colonic absorption for basic drugs of similar characteristics, thus confirming some recent observations in the rat (16, 20) and in humans (21), and validating the rat gut experimental model described here as a valuable tool for exploring gastrointestinal drug absorption potentialities.

Comparison between Models

As assessed in Tables V and VI, the parabolic correlations according to Eq. (6) yield much worse fits than does Eq. (1) or its collapsed form, Eq. (2). But, besides pure mathematical criteria, some biophysical or merely biological arguments could be adduced to explain the suitability of these compartmental models as compared with the probabilistic, parabolic-type approaches in interpreting the absorption dynamics. First, parabolic correla- tions do not have a clear physiological meaning, whereas Eq. (1) does: the km and kp values are encompassed within the law of mass action, whereas the remaining constants are only introduced in order to extrapolate the in

vitro partition values to the in vivo partition conditions. Second, it can be assumed, without transgressing any fundamental biological principle, that the colon (or the stomach) and the small intestine membranes may differ in the mean diameter of their aqueous pores (i.e., as a result of some evolutionary process leading to specialization). But it is difficult to assume that a single absorption site (such as the small intestine) could sometimes act as a homogeneous barrier (as occurs with series above 250 in molecular weight) and in other cases as a heterogeneous barrier (with series below 200 in molecular weight). For these reasons and keeping accumulated experience in mind, we believe that the probabilistic approaches, which have demonstrated their empirical usefulness in other fields of the phar- maceutical sciences (22-24), should be considered inapplicable to gastro- intestinal absorption studies.

Absorption Design Implications

If the behavior outlined here is representative of a general situation, then the incidence of the above criteria in the preclinical absorption studies

632 Martin-Villodre et al.

of new drugs might be worthy of consideration. From the analysis of the molecular weight characteristics and chemical features of a group of drug candidates, the presumed behavior of the series in specialized or nonspecial- ized absorption sites can be anticipated and a limited number of compounds could be selected and tested for absorption-partition correlations according to the simple models described here. The resulting curves, if properly analyzed, will indicate the components toward which attention should be directed. It should be borne in mind, however that by using these techniques, the intrinsic absorption constants (i.e., the absorption potential) rather than the actual rates of bioavailability after oral administration are determined. Dissolution and other important limiting factors should be predicted by single in vitro parallel tests (25), as well as the possible first-pass effects by means of more sophisticated procedures (26, 27). In most cases, however, through the analysis of the curves, the above influences can be anticipated. In forthcoming papers, these and other selected topics will be analyzed in more detail.

ACKNOWLEDGMENTS

We are indebted to Drs. Rosendo Obach Vidal and Vicente G. Casab6 A16s for their most helpful contribution to this paper.

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