Introduction

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The small intestine is endowed with transporters that effect the penetration of drugs across the luminal (or apical) membrane into the cell against a concentration gradient (for review, see Tsuji and Tamai, 1996; Lin et al., 1999). Permeation via passive diffusion of lipophilic drugs exists and is highly correlated to the surface area of contact and the pKa that influence the degree of ionization and hence lipophilicity. The varying abundance of the villi along the intestinal length constitutes differing surface areas among the intestinal segments, being highest at the duodenum and upper jejunum and lowest toward the ileum (Magee and Dalley, 1986). Net apical to basolateral transport is additionally influenced by the presence of drug binding, metabolizing enzymes, transporters for efflux and basolateral transport, and the gastrointestinal motility that modulates drug transit time.

Several models have been developed to describe processes of intestinal absorption, metabolism, and secretion simultaneously (Yu and Amidon, 1998; Ito et al., 1999; Cong et al., 2000). A traditional, physiologically-based model (TM²), which regards the intestine as a single homogeneous compartment with all of the intestinal blood flow perfusing the tissue, has been developed to account for oral drug bioavailability (Doherty and Pang, 2000). However, this and other existing models fail to predict route-dependent intestinal metabolism, namely little metabolism occurs after systemic dosing, but notable metabolism exists following oral dosing. This led to the development of the segregated flow model (SFM) (Cong et al., 2000) that describes the majority of the intestinal blood flow to the nonabsorptive and nonmetabolizing serosal and submucosa regions, and only partial flow (Granger et al., 1980) to the absorptive and metabolizing, enterocyte region at the villus tips of the mucosa where the metabolic enzymes and the P-glycoprotein reside. The SFM was shown able to describe a greater extent of intestinal metabolism with oral over systemic dosing or the route-dependent intestinal hydrolysis of enalapril (Pang et al., 1985) and ()-6-aminocarbovir (Wen et al., 1999), glucuronidation of morphine (Doherty and Pang, 2000), and oxidation of midazolam (Paine et al., 1996, 1997; Thummel et al., 1996).

However, variation in segmental absorption was shown to exist for oxyprenolol (Godbillon et al., 1987), talinolol (Grámatte et al., 1996), amoxicillin (Barr et al., 1994), lefradafiban (Drewe et al., 2000), allopurinol (Patel and Kramer, 1986), thymidine analogs (Park and Mitra, 1992), and benzoate (Cong et al., 2001) in both human and animal studies. Undoubtedly, heterogeneity of absorptive carriers would bring about variations in absorption. Regional or segmental distribution of apical transportersthe oligopeptide transporter, PEPT1 (Fei et al., 1994), the apical bile salt transporter (Shneider et al., 1995; Aldini et al., 1996), the organic anion transporting polypeptide 3 (Walters et al., 2000), the monocarboxylic acid transporter 1 (Tamai et al., 1999; Cong et al., 2001), and the nucleoside transporter (Ngo et al., 2001)is well recognized. Heterogeneity is further known to exist for both metabolic enzymes and efflux transporters. The cytochrome P450 3A (Hoensch et al., 1976; Bonkovsky et al., 1985; Paine et al., 1996, 1997; Thummel et al., 1996; Lown et al., 1997; Li et al., 2002), sulfotransferases, glutathione S-transferases and the UDP-glucuronosyltransferases (Clifton and Kaplowitz, 1977; Pinkus et al., 1977; Schwarz and Schwenk, 1984; Koster et al., 1985; Coles et al., 2002) are higher at the proximal end than the distal intestine. The multidrug resistance-associated protein 2 for intestinal exsorption follows the distribution of the cytochrome P450s and conjugation enzymes (Gotoh et al., 2000; Mottino et al., 2000) whereas the MDR1 gene product, the 170 kD P-glycoprotein (Lown et al., 1997; Collett et al., 1999; Nakayama et al., 2000; Stephens et al., 2001) is higher in the jejunum/ileum than other parts of the intestine. The basolateral Mrp3, in contrast to multidrug resistance-associated protein 2 that is higher in jejunum and duodenum, is more prevalent in the ileum and colon (Rost et al., 2002). The manner in which heterogeneity impacts drug bioavailability is virtually unknown.

In this communication, we examined, in theoretical models, the influence of apical transporter and cellular metabolic heterogeneities, drug partitioning, and gastrointestinal transit on the area under the concentration-time curves after oral (AUC_po) and intravenous (AUC_iv) dosing for estimation of the clearance (CL_iv) and bioavailability (F) for a compound that is removed solely by the intestine by secretion and metabolism. We further tested the hypothesis that heterogeneity in transporter and metabolic functions, together with gastrointestinal transit and drug partitioning properties, affect the extent of metabolite formation after oral and intravenous drug dosing.

	Materials and Methods

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Physiologically Based Intestinal Models. The schematic depictions of the segmental traditional model (STM; Fig. 1) and the segmental segregated flow model (SSFM; Fig. 2) are shown. These theoretical models are extensions of the published TM and the SFM (Cong et al., 2000) that only contained nonsegmented compartments. The two previous models are physiologically-based models, and the difference between the models is division of the intestinal tissue into the serosal (nonabsorptive and nonmetabolizing) and enterocyte (absorptive and metabolizing) regions and partitioning of flow for the SFM. With only a fraction (f_Q) of the total intestinal flow (Q_int) perfusing the enterocyte region, less drug is exposed to metabolic enzymes with intravenous administration.

View larger version (36K): [in this window] [in a new window]   Fig. 1.   Schematic presentation of the STM for intestinal absorption, metabolism, and secretion of substrates given orally or intravenously; the conditions considered mimic the recirculating perfused small intestine preparation with additional (parallel) clearances (CLo) occurring within the central or reservoir compartment. The intestine is divided into three equal segments receiving parallel flow. Refer to text for details.

View larger version (39K): [in this window] [in a new window]   Fig. 2.   Schematic presentation of the SSFM for intestinal absorption, metabolism, and secretion of substrates given orally or intravenously; the conditions considered mimic the recirculating perfused small intestine preparation with additional (parallel) clearances occurring within the central or reservoir compartment. The intestine is divided into three equal segments receiving parallel flow. Only a fraction (fQ) of the segmental intestinal flow goes to the enterocyte layer, and the remaining flow enters the nonabsorptive, nonmetabolizing serosal region. Refer to text for details.

Simulations. For the present models, the unbound fraction is assumed to be unity, and linear or first-order conditions prevail. The mass balance equations for the above schemes for the STM (eqs. 1 to 15, Appendix) and SSFM (eqs. 16 to 36) were written for simulation of data. Simulation was performed with volumes and flow rates shown in Table 1. The values have been chosen previously to describe glucuronidation of morphine and benzoate absorption in the vascularly perfused, recirculating rat small intestine preparation (Doherty and Pang, 2000; Cong et al., 2001). For values pertaining to the simulation on other species, the volume and flow values will need to be scaled-up or scaled-down. For the SSFM, the segmental enterocyte region was assumed to receive 10% of the intestinal flow to that segment (or f_Q Q_int/3, in which f_Q = 0.1), whereas the segmental serosal region receives 90% of the intestinal flow to the segment [(1 f_Q) Q_int/3].

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	Results

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Homogeneous DistributionsEffect of k_ai and CL_int,seci on CL_iv, F, and Metabolite Formation at CL_int,mi of 0.1 ml/min. Contrary to previous theories on the lack of influence of the absorption rate constant on the intestinal clearance, CL_iv bore an inverse relation to the k_ai and was influenced positively by the secretory intrinsic clearance, CL_int,seci (Fig. 3) for both STM (A and B) and SSFM (C and D). A higher CL_GITi brought about higher CL_iv for both STM and SSFM. When drug displays rapid partitioning (CL_d1 = CL_d2 = 10 ml/min; Fig. 3, B and D), values of CL_iv were much higher than comparable values at CL_d1 and CL_d2 of 0.9 ml/min (cf. Fig. 3, B versus A and D versus C). Bioavailability, F, increased with increases in k_ai but decreased with CL_int,seci (Fig. 4), and high CL_GITi led to lower F for both models. Higher values of F were observed for the STM versus the SSFM (cf. Fig. 4, A and B versus C and D). For drug displaying rapid partitioning (CL_d1 = CL_d2 = 10 ml/min, Fig. 4, B and D), values of F were higher than comparable values at CL_d1 and CL_d2 of 0.9 ml/min (cf. Fig. 4, B versus A and D versus C). It was interesting to note that higher values for the k_ai tended to diffuse the effects of secretion (CL_int,seci) on F. The patterns of metabolite formation were similar for the STM and SSFM. The extents of metabolite formation for both values of CL_d1 and CL_d2 (0.09 and 10 ml/min) were generally similar and were lower with higher values of CL_GITi. Metabolite formation decreased with CL_int,seci, and the amount of metabolite formed was greater for oral than for intravenous administration (cf. Fig. 5, A and B for STM and C and D for SSFM).

View larger version (25K): [in this window] [in a new window]   Fig. 3.   Effect of kai and CLint,seci of each segment on the clearance (CLiv) of drugs for the STM (A and B) and SSFM (C and D), for different values of CLGITi (0.01 and 0.1 ml/min) and CLd1 and CLd2 (0.9 ml/min for A and C; 10 ml/min for B and D). The metabolic intrinsic clearance, CLint,mi, was kept at 0.1 ml/min for all simulations. The parameters were identical among the three segmental regions.

View larger version (22K): [in this window] [in a new window]   Fig. 4.   Effect of kai and CLint,seci of each segment on the availability (F) of drugs for the STM (A and B) and SSFM (C and D), for different values of CLGITi (0.01 and 0.1 ml/min) and CLd1 and CLd2 (0.9 ml/min for A and C; 10 ml/min for B and D). The metabolic intrinsic clearance, CLint,mi, was kept at 0.1 ml/min for all simulations. The parameters were identical among the three segmental regions.

View larger version (29K): [in this window] [in a new window]   Fig. 5.   Effect of kai and CLint,seci of each segment on the cumulative amount of metabolite formed after oral (Metabolitepo) and intravenous (Metaboliteiv) dosing for the STM (A and B) and SSFM (C and D), for CLGITi at 0.01 and 0.1 ml/min, and CLd1 and CLd2 (0.9 ml/min). The metabolic intrinsic clearance, CLint,mi, was kept at 0.1 ml/min for all simulations. All of the segmental parameters were identical among the three intestinal regions. These observed trends (A, B, C, and D) were similar for CLd1 and CLd2 at 10 ml/min.

Homogeneous DistributionsEffect of CL_int,mi and CL_int,seci on CL_iv, F, and Metabolite Formation at k_ai of 3 ml/min. CL_iv rose positively with higher values of CL_int,mi, CL_int,seci, and CL_GITi (Fig. 6) for both STM (A and B) and SSFM (C and D). Higher values of CL_GITi, CL_d1, and CL_d2 brought about higher CL_iv for both STM and SSFM (cf. Fig. 6, B versus A for STM and D versus C for SSFM). Bioavailability, F, decreased with increasing values of the metabolic intrinsic clearance and CL_GITi for both models (Fig. 7). Values of F were generally higher for the STM in relation to those for the SSFM (cf. A and B versus C and D). The patterns of metabolite formation were similar for the STM and SSFM and were similar for both CL_d1 and CL_d2 values chosen. Metabolite formation for oral dosing exceeded that for intravenous administration (Fig. 8, compare A and B for STM and C and D for SSFM), and was decreased by CL_int,seci and CL_GITi.

View larger version (17K): [in this window] [in a new window]   Fig. 6.   Effect of CLint,mi and CLint,seci of each segment on the clearance (CLiv) of drugs for the STM (A and B) and SSFM (C and D), for different values of CLGITi (0.01 and 0.1 ml/min) and CLd1 and CLd2 (0.9 ml/min for A and C; 10 ml/min for B and D). kai was kept at 3 ml/min for all simulations. The parameters were identical among the three segmental regions.

View larger version (18K): [in this window] [in a new window]   Fig. 7.   Effect of the CLint,mi and CLint,seci of each segment on the bioavailability (F) of drugs for the STM (A and B) and SSFM (C and D), for different values of CLGITi (0.01 and 0.1 ml/min) and CLd1 and CLd2 (0.9 ml/min for A and C; 10 ml/min for B and D). kai was kept at 3 ml/min for all simulations. The parameters were identical among the three segmental regions

View larger version (23K): [in this window] [in a new window]   Fig. 8.   Effect of the CLint,mi and CLint,seci of each segment on the cumulative amount of metabolite formed after oral (Metabolitepo) and intravenous (Metaboliteiv) dosing for the STM (A and B) and SSFM (C and D), for CLGITi at 0.01 and 0.1 ml/min, and CLd1 and CLd2 (0.9 ml/min). kai was kept at 3 ml/min for all simulations. All of the segmental parameters were identical among the three intestinal regions. These observed trends (A, B, C, and D) were similar for CLd1 and CLd2 at 10 ml/min.

Heterogeneous Distributions of k_ai, CL_d1, CL_d2, CL_GITi, CL_int,mi, and CL_int,seci on CL_iv, F, and Metabolite Formation. The distributions of the segmental intrinsic clearances for secretion and metabolism and the absorption rate constant strongly influenced CL_iv, F, M_po and M_iv for the STM (Table 2 for CL_d1 = CL_d2 = 0.9 ml/min and Table 3 for CL_d1 = CL_d2 = 10 ml/min) and the SSFM (Table 4 for CL_d1 = CL_d2 = 0.9 ml/min and Table 5 for CL_d1 = CL_d2 = 10 ml/min). The CL_iv and F values were generally lower for the SSFM compared with the STM, although the patterns on metabolite formation remained similar. The lowest F occurred for case 24 (Tables 2 to 5) when k_ai and CL_int,mi were decreasing along the length of the intestine, whereas the CL_int,seci increased along the length of the intestine (Fig. 9, left panel). Low values of F persisted for other cases (19 to 27) in which CL_int,mi was decreasing along the length of the intestine, even when k_ai and CL_int,seci displayed varying distributions (homogeneous, increasing or decreasing gradient). The highest F was observed for case 16 (Tables 2 to 5) when the metabolic and secretory intrinsic clearances (ascending from segment 1 to segment 3) were staggered in an opposite configuration to k_ai (descending from segment 1 to segment 3) (Fig. 9, right panel). Similar patterns of F prevailed for cases 10 to 18 in which CL_int,mi displayed an increasing, segmental gradient, even when k_ai and CL_int,seci exhibited varying distributions (homogeneous, increasing or decreasing gradient). The F values were intermediate when CL_int,mi was homogeneously distributed among segmental regions (cases 1 to 9). These trends were similar at CL_GITi of 0.01 ml/min (Tables 2 and 4) and at CL_GITi of 0.1 ml/min (Tables 3 and 5). The F values, however, did not directly reflect CL_iv, which was lowest for case 25 and highest for case 7 (see Tables 2 to 5). The same comment applied to metabolite formation after oral dosing; these values do not correlate with F, although case 24 consistently provided the lowest metabolite formation (% dose) after oral dosing.

View larger version (31K): [in this window] [in a new window]   Fig. 9.   Segmental distributions (designated as segments 1, 2, and 3) of CLint,mi, kai, and CLint,seci for lowest F (left panel, case 24) and highest F (right panel, case 16). The difference existed in the descending versus ascending distributions of the segmental metabolic intrinsic clearance.

	Discussion

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It is well recognized that drug absorption is the net result of complex interactions of apical to basolateral transport, metabolism and exsorption/efflux in the intestine for which much heterogeneity exists. In addition to the named segmental differences in surface area, flow, absorptive carriers, metabolic enzymes, and efflux transporters, bile acids are known to affect the permeability of intestinal mucosa, the solubilization of drug and/or suppression of thermodynamic activity after its involvement in the micellar complex (Emori et al., 1995). It is surmised that the influence of bile acid is greater at the sphincter of Oddi and the proximal duodenum. Hence, segmental differences in drug absorption are not unexpected outcomes.

To date, none of the proposed models (Yu and Amidon, 1998; Ito et al., 1999; Lin et al., 1999; Cong et al., 2000) is able to describe heterogeneous events in any cohesive fashion. The development of the STM and SSFM therefore provides the first theoretical models that provide predictive information on the impact of intestinal heterogeneities on drug absorption. Analogous to that shown previously for TM and SFM (Cong et al., 2000), differences exist between the STM and SSFM due to the segregation of flow for the segments of SSFM. However, common conclusions may be made for both models. Because of drug secretion, reabsorption with k_ai affects not only CL_iv and F but also metabolite formation (Figs. 3 to 5). The absorption rate constant decreases CL_iv but increases F and metabolite formation due to recycling of drug back to the circulation. The k_ai neutralizes some of the effects of drug secretion, and when k_ai is large, secretion effects become minimal. The gastrointestinal transit time, denoted by CL_GITi, effectively removes drug from the lumen and precludes absorption. Increases in CL_GITi bring about increases in CL_iv but decrease F, whereas rapid drug partitioning further brings about higher CL_iv and F (Figs. 3 to 8; Tables 2 to 5). The metabolic and secretory intrinsic clearances affect CL_iv and F for the STM to a much greater degree than for the SSFM (Figs. 3 and 4 and Figs. 6 and 7; cf. A and B versus C and D). Both metabolic and secretory intrinsic clearances increase CL_iv but decrease F.

The presence of secretion also affects metabolite formation, and a greater CL_int,seci results in lowered metabolite formation. A similar observation was made for a theoretical examination on the time course of metabolite production in Caco-2 cells (D. Tam and K. S. Pang, unpublished data) even though metabolite formation eventually equals the dose in this stagnant system. By contrast, metabolite formation is reduced by rapid gastrointestinal transit. Metabolite formation for oral dosing is usually greater than that with intravenous dosing (Figs. 5 and 8 and Tables 2 to 5). However, when k_ai is very low (<0.01 min¹) and CL_GITi (>0.1 ml/min) is high, metabolite formation after intravenous dosing can exceed that for oral dosing (unpublished simulations).

Heterogeneity in metabolic intrinsic clearance among the intestinal segments strongly impacts F. Lower values of F existed when the gradient of metabolic activities was more proximal and dwindles toward the ileum (Fig. 9, left panel). Alternately, higher F values were observed when the segmental, metabolic intrinsic clearance was increasing toward the ileum (Fig. 9, right panel). These comments hold true regardless of the distributions (homogeneous, increasing or decreasing gradient) of k_ai and CL_int,seci. Metabolite formation was influenced by all of the heterogeneities, and no succinct pattern was readily identified.

The present simulation study with two theoretical models, the STM and SSFM, revealed possible interactions of the absorption rate constant, metabolic and secretory intrinsic clearances, flow, and gastrointestinal transit on drugs of varying tissue-partitioning characteristics. Although the present exploration of the theoretical models presented only a limited scope of the influence of the various segmental variables on drug bioavailability and metabolite formation, important observations nonetheless arose. The study showed that the absorption rate constant, in contrast to cases where secretion is nonexistent, strongly affected the clearance and bioavailability. Segmental metabolic heterogeneity was another important factor that influences CL_iv and F.