COMMENTARIES

Correlation between Net Water Flux and AbsorptiveClearance Determined from In Situ Intestinal PerfusionStudies Does Not Necessarily Indicate a Solvent Drag Effect

ZHENG YANG, GUANFA GAN, RONALD J. SAWCHUK

Department of Pharmaceutics, University of Minnesota, 308 Harvard St. SE, Minneapolis, Minnesota 55455

Received 25 February 2006; revised 9 July 2006; accepted 31 July 2006

Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/jps.20763

ABSTRACT: Estimation of absorptive clearance (PeA) of drugs from in situ perfusionstudies, based on the disappearance of drugs from the intestinal lumen, involvescorrecting outflow perfusate drug concentration with net water flux (Jw). However, asdemonstrated through both theoretical derivations and simulations, the PeA estimatedfrom a nonlinear equation approximates a linear relationship with Jw for a lowpermeability drug, regardless of whether or not Jw has a real effect on PeA. As such, acorrelation betweenJwandPeA is lessmeaningful as an indicator of a solvent drag effect.Moreover, from the linear relationship, the slope of the Jw-PeA correlation plot (definedas the sieving coefficient) equals the ratio of outflow versus inflow perfusate drugconcentrations and can be greater than unity when more water than drug isabsorbed during perfusion studies. The intercept of the correlation plot can be belowzero if this occurs. �2006Wiley-Liss, Inc. and theAmericanPharmacistsAssociation JPharmSci

96:517–521, 2007

Keywords: intestinal absorption; transcellular transport; simulations; permeability;paracellular transport

To the Editor:

A solvent drag effect on the intestinal absorptionof drugs is commonly evaluated by correlating netwater flux (Jw) with the absorptive clearance(PeA) that is determined from in situ perfusionstudies based on the disappearance of drugsfrom the intestinal lumen.1,2 The equation

that describes such a correlation, partitioningintestinal absorption into diffusive and convectiveterms, is as follows:3,4

PeA ¼ ðPAÞdiffusion þ f � Jw ð1Þ

where (PA)diffusion is the permeability-area pro-duct that represents both transcellular and para-cellular diffusion; f is the sieving coefficientdefined as the ratio of the solute concentrationin the convective stream to that in the luminalfluid. An observed linear correlation between Jwand PeA is generally considered as water has asignificant effect on the intestinal absorption ofdrugs. Particularly, this has been observed withhydrophilic drugs where transcellular membranepermeability is low and net water flux could havea large effect on absorption. However, an estima-tion of PeA involves using Jw to correct for outflow

JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 96, NO. 3, MARCH 2007 517

Zheng Yang’s present address is Metabolism and Pharma-cokinetics, Bristol-Myers Squibb Co., Princeton, New Jersey08543.Guanfa Gan’s present address is Department of Drug

Metabolism and Pharmacokinetics, Boehringer IngelheimPharmaceuticals Inc., Ridgefield, Connecticut 06877.Correspondence to: Ronald J. Sawchuk (Telephone: 612-624-

0646; Fax: 612-624-0951; E-mail: sawch001@ umn.edu.)

Journal of Pharmaceutical Sciences, Vol. 96, 517–521 (2007)� 2006 Wiley-Liss, Inc. and the American Pharmacists Association

perfusate drug concentrations due to net waterflux. Here, the relationship between Jw and PeA,as we will demonstrate below, mathematicallyapproximates a linear relationship for a lowpermeability drug, regardless of whether or notJw has a real effect on PeA. As such, a linearcorrelation between Jw and PeA, as is oftenobserved with low permeability drugs, is lessmeaningful as an indicator of the solvent drageffect.

The intestinal PeA of a drug in an in situsingle-pass perfusion study is generally estimatedat steady state from the following equation:5

Cout

Cin¼ exp �PeA

Qin

� �ð2Þ

where Qin is the inflow perfusion flow rate; Cin

and Cout are the inflow and outflow drug concen-tration, respectively. Equation 2 assumes thatthere is no net water absorption during perfusion;that is, Qin equals Qout, where Qout is the outflowperfusion flow rate. However, in actual perfusionexperiments, net water flux often occurs, result-ing in Qout lower than Qin. A common approach todeal with this issue is to estimate the amount ofnet water flux during perfusion by employing anonabsorbable marker (e.g., PEG3350) or by thegravimetric method and then correct Cout byassuming no changes in the perfusion rate forthe calculation of the PeA. Thus, Equation 2becomes:

Cout;corrected

Cin¼ ðCout �Qout=QinÞ

Cin¼ exp �PeA

Qin

� �

ð3Þ

where Cout,corrected is outflow drug concentrationcorrected for net water absorption and equalsCout�Qout/Qin. Rearrangement of Equation 3 yields:

Cout �Qout

Cin �Qin¼ exp �PeA

Qin

� �ð4Þ

Recognizing that Qout¼Qin� Jw, where Jw is netwater flux at steady state during in situ perfusionstudies, Equation 4 becomes:

CoutðQin � JwÞCin �Qin

¼ exp �PeA

Qin

� �ð5Þ

For a hydrophilic compound, PeA is much less thanQin. Equation 5 can be approximated as follows:

CoutðQin � JwÞCin �Qin

� 1� PeA

Qinð6Þ

Rearranging Equation 6 yields:

PeA � Qin 1� Cout

Cin

� �þ Cout

CinJw ð7Þ

Equation 7 shows that PeA is linearly related toJw, when Cout is constant relative to Jw atsteady state. This is a likely situation duringin situ perfusion studies. In our own studies,7

the median value of the coefficient of variation(%CV) in Cout at steady state among differentexperiments was 2.7% (range¼ 0.8–8.6%, n¼ 27experiments, with 14 determinations in eachexperiment). On the other hand, %CV in Qout

measured by the gravimetric method had amedian value of 13% (range¼ 5–35%, n¼ 18experiments, with 14 determinations in eachexperiment). Other methods, such as the useof a nonabsorbable marker in measuring Qout,could lead to a similar degree of variability, ifnot larger.6 In our studies,7 net water fluxgenerally accounted about 10–30% of Qin (0.2mL/min) with perfused segment lengths rangingfrom 15 to 28 cm. Because of its relativelysmall value, %CV in Jw was much larger, with amedian value of 33% (range¼ 12–289%).These results demonstrate that Jw exhibitsmuch higher variability than that of Cout atsteady state during in situ perfusion studies.Therefore, it is reasonable to assume that Cout isconstant relative to Jw. As such, Jw and PeAapproximate a linear relationship as indicated inEquation 7.

To further elucidate such a linear relationshipbetween Jw and PeA for a low permeability drug,simulations were performed using the nonlinearequation (Eq. 10, see below) to generate PeA aftercorrecting Cout with Jw. The pairs of Jw and PeAwere then examined for their correlation. In thesimulations, the inflow perfusion flow rateQin wasfixed at 0.2mL/min and the inflowdrug concentra-tion Cin was fixed at 1 mg/mL. Jw (0.06 mL/min)was assumed to account for 30% of Qin. BecauseQout not Jw is a parameter that is measured fromreal experiments, three scenarios with differentvariability in Qout (i.e., %CV in Qout¼ 5, 10, and15%) were evaluated. Under each scenario, fivevirtual experiments were simulated. In eachvirtual experiment, PeA value was first randomlygenerated from the normal distribution (JMP,v.5.1, Cary, NC) based on amean value of 0.02mL/min (1/10th of Qin) and a %CV of 30%. Fromrandomly generated PeA value, Jw (0.06 mL/min)andCin (1mg/mL), steady-stateCout values in each

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of five virtual experiments were calculated usingthe equation that is rearranged from Equation 5:

Cout ¼Cin �Qin

Qin � Jwexp �PeA

Qin

� �ð8Þ

Using the calculated Cout as a mean value andassuming a CV of 3%, 10 Cout values at steadystate for each virtual experiment were randomlygenerated from the normal distribution. Tencorresponding Qout values were also randomlygenerated from the normal distribution based ona mean value of 0.14 mL/min and a CV value ofeither 5, 10, or 15%. As a result, in each virtualexperiment, there were 10 pairs of Qout and Cout,as if they were obtained from actual experiments.These values along with Qin (0.2 mL/min) and Cin

(1 mg/mL) were then used to calculate 10 pairs ofJw and PeA using the following equations.

Jw ¼ Qin �Qout ð9Þ

PeA ¼ Qin � lnCin �Qin

Cout � ðQin � JwÞ

� �ð10Þ

where Equation 10 is rearranged from Equation5. For each scenario, Jw and PeA calculatedin each virtual experiment were then pooledtogether (10 pairs per virtual experiment, 50 pairsfor each scenario) to assess the correlationbetween the two.

Table 1 lists the simulated data for in situperfusion studies. In all three scenarios, %CV insimulatedCout is much less than that in simulatedJw. Figure 1 shows correlation plots between Jwand PeA. They are linearly correlated, with acorrelation coefficient (r) ranging from 0.83 to 0.97(p< 0.05). The results demonstrate that the PeA ofa low permeability drug obtained after correctingfor Jw in the nonlinear equation (Eq. 10) exhibits alinear relationship with Jw, regardless of whetheror not Jw has a real effect on PeA. As expected, thecorrelation coefficient increased with higher %CVin Qout, as Cout became more constant in Equation7 when the variability in Qout became larger.

In all three scenarios, the slope of the regressionline (i.e., the sieving coefficient in Eq. 1) wassignificantly greater than unity (p< 0.05). Thiscan be readily explained throughEquation 7, sincethe slope in Equation 7 is equal to Cout/Cin andsimulated Cout (Tab. 1) was indeed larger than Cin

(1 mg/mL). This concentrating effect for a hydro-philic drug occurs when more water is absorbedduring perfusion than the hydrophilic drug. It hasbeen suggested that intestinalwater absorption as

high as �50% occurs transcellularly via theintestinal brush borderNaþ-glucose cotransporter(SGLT1) also known as water pump.7,8 The waterpump has a high selectivity for water (channelradius <4 A)9 such that solvent drag for ordinarydrug molecules cannot occur. As an example,mannitol (MW¼ 182) is not transported by thewater pump.9 Consistent with this, in our in situperfusion studies with lobucavir and ganciclovir(MW for both compounds¼�250),10 we found thatCout was significantly higher than Cin, indicatingmore water is absorbed than drug duringthe perfusion. Moreover, a slope of greater thanunity in the correlation plots of Jw and PeA hasbeen observed with carbamazepine epoxide1 andcarbovir.2

For the same reason (Cout greater than Cin), theintercept of the correlation plot from simulationswas negative and significantly different from zero(p< 0.05). As shown in Equation 7, the interceptequalsQin*(1�Cout/Cin) and can be negative ifCout

is greater than Cin. This differs from Equation 1,since the intercept in Equation 1 cannot benegative as it represents the transcellular mem-brane permeability-area product.

Table 1. Simulated Data for In Situ PerfusionStudiesa

Experiment No.Cout

(mg/mL)Qout

(mL/min)Jw

(mL/min)

CV in Qout¼ 5%1 1.31 (2.1%) 0.14 (6.7%) 0.06 (16%)2 1.33 (4.3%) 0.14 (4.7%) 0.06 (11%)3 1.37 (3.6%) 0.14 (3.9%) 0.06 (9.7%)4 1.28 (3.3%) 0.14 (4.7%) 0.06 (11%)5 1.32 (3.0%) 0.14 (3.8%) 0.06 (8.0%)

CV in Qout¼ 10%1 1.31 (2.1%) 0.14 (9.4%) 0.06 (20%)2 1.33 (4.3%) 0.14 (11%) 0.06 (24%)3 1.37 (3.6%) 0.14 (9.8%) 0.06 (23%)4 1.28 (3.3%) 0.15 (10%) 0.05 (27%)5 1.32 (3.0%) 0.14 (9.8%) 0.06 (25%)

CV in Qout¼ 15%1 1.31 (2.1%) 0.14 (11%) 0.06 (27%)2 1.33 (4.3%) 0.14 (20%) 0.06 (46%)3 1.37 (3.6%) 0.13 (20%) 0.07 (37%)4 1.28 (3.3%) 0.14 (13%) 0.06 (31%)5 1.32 (3.0%) 0.15 (11%) 0.05 (29%)

aData are expressed as mean (%CV), with 10 simulatedvalues in each experiment.Qin andCin used in simulationswere0.2 mL/min and 1 mg/mL, respectively. Net water flux wasassumed to be 30% ofQin. PeA values used in simulations were0.016�0.0052 mL/min (n¼ 5 experiments).

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Previously, we developed an intestinal drugabsorption model to account for net water fluxduring in situ perfusion studies.7 Thus, the effectof net water flux on the luminal drug concentra-tion, the driving force for membrane permeation,is considered in the model. In this case, the PeA isestimated by the following equation:7

PeA ¼ QavelnCin �Qin

CoutðQin � JwÞ

� �ð11Þ

where Qave is a logarithmic average of Qin andQout and equals (Qin�Qout)/ln(Qin/Qout). Similar tothe deviations above, for a less permeable com-pound, Equation 11 becomes:

CoutðQin � JwÞCin �Qin

� 1� PeA

Qaveð12Þ

Since net water flux during in situ perfusionstudies typically accounts for 10–30% of theinflow perfusion rate, Qave can be approximatedby Qin, with an error less than 20%. Thus, whenthe PeA is estimated from Equation 11, itapproximates a linear relationship with Jw,which can be demonstrated through simulations(data not shown).

In summary, a linear correlation between Jwand PeA determined from in situ perfusion studiesbased on drug disappearance from the intestinallumen does not necessarily indicate a solvent drageffect. Rather, it may result from the fact that thePeA obtained after correcting Jw mathematicallyapproximates a linear relationship with Jw for alow permeability drug, regardless of whether ornot Jw has a real effect on PeA.

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Figure 1. Correlation plots between Jw and PeAbased on simulated data. %CV in Qout was 5% (a); 10%(b), and 15% (c), respectively.

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JOURNAL OF PHARMACEUTICAL SCIENCES, VOL. 96, NO. 3, MARCH 2007 DOI 10.1002/jps

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