Reduced-Resistances Model for Enhanced Drug Permeation via a Solubilizing Receiver Medium: A Mechanistic Study with Hollow Fiber Membranes
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Reduced-Resistances Model for Enhanced Drug Permeation via a Solubilizing Receiver Medium: A Mechanistic Study with Hollow Fiber Membranes
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Molecular Pharmaceutics

Cite this: Mol. Pharmaceutics 2026, 23, 3, 2036–2049
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https://doi.org/10.1021/acs.molpharmaceut.5c01771
Published February 12, 2026

Copyright © 2026 The Authors. Published by American Chemical Society. This publication is licensed under

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Abstract

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A solubilizing receiver medium has been documented to increase drug flux in vitro, but the mechanisms underlying this effect remain poorly understood. This study investigated these mechanisms and established a mathematical model to describe the increase in apparent permeability. Flow rate experiments were performed to quantify the individual boundary layer and membrane resistances associated with diffusion. The impact of nine solubilizing receiver additives, including surfactants, cyclodextrins, and bovine serum albumin, on the flux of griseofulvin was investigated. The increase in apparent permeability followed the rank-order, though not the magnitude, of the solubility enhancement in the receiver (Spearman’s ρ = 0.93, p < 0.001, n = 20). The mechanistic model, termed the reduced-resistances model, demonstrates that a solubilizing receiver reduces diffusional resistance in the membrane and in the receiver-side boundary layer. At high ratios of receiver to donor solubility, a hyperbolic relationship was observed where diffusion through the donor-side boundary layer becomes rate-limiting. Additional drug cocktail permeability studies with antipyrine, phenytoin, and meloxicam confirmed the broader applicability of this model. These findings provide a framework for informed receiver selection in permeability assays and underscore the importance of considering the receiver medium when comparing results across experiments.

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Introduction

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The hollow fiber membrane (HFM) has emerged as an attractive in vitro method for elucidating drug product performance. HFM provides a substantially greater surface area-to-volume ratio than conventional planar membranes, thereby mitigating the limitations associated with very low permeation rates. (1) The flow-through setup allows for continuous replenishment of both donor and receiver media, and thus loss of transmembrane sink due to accumulation of drug on the receiver side is unlikely. (2) The apparatus consists of a bundle of hollow porous tubes inside an outer shell, allowing separate solutions to flow axially both inside (lumen side) and outside (shell side) of the hollow fibers. In the context of drug permeation studies, donor solution typically flows on the lumen side, while receiver media flows cocurrently on the outside. The module’s geometry promotes a laminar flow pattern, (3) thereby establishing a well-defined environment at the fluid-membrane interface. Under these conditions, the concentration boundary layer thickness can be reliably modulated by controlled changes in flow rate. (4) However, HFM’s high sensitivity to flow conditions and the potential for pressure-driven convective flux complicate analysis. (5) HFM has been applied successfully to study the dissolution-permeation behavior of amorphous solid dispersions, (6) biopharmaceutics risk, (7) and the effects of micellization on drug permeation. (8) The impact of receiver media composition on drug permeation, however, merits further investigation.
Solubilizing additives are commonly included in the receiver medium in permeability studies to maintain sink conditions, improve mass balance, or prevent precipitation of drug on the receiver side. (9−11) The maintenance of a permeative sink in vitro is crucial for predicting the bioperformance of formulations containing highly permeable drugs. (5) This is particularly relevant where a considerable mass of drug is expected to permeate into a limited receiver volume over the time course studied. (12) Jacobsen et al. (13) explored the impact of three different surfactants in the receiver medium, namely sodium lauryl sulfate (SLS), polysorbate 80 (PS80), and D-α-tocopheryl polyethylene glycol 1000 succinate (TPGS) in a two-compartment 96-well plate dissolution-permeation setup. Addition of surfactant to the receiver increased the flux from crystalline tadalafil. The magnitude of flux increase followed the same rank-order as the solubility ratio (i.e., the equilibrium solubility of the drug in the receiver medium compared to the donor medium), though the flux enhancement was far more modest than the solubility ratio. Narula et al. (14) included bovine serum albumin (BSA) in the receiver when studying amorphous formulations of atazanavir and lopinavir in a vertical Franz diffusion cell. Both drugs demonstrated similar fold increases in solubility of 3.4 and 3.8 respectively in the presence of 3% BSA. However, the fold increase in the permeability of the free drug was 2.5 for atazanavir and 15.7 for lopinavir through the modified parallel artificial membrane permeability assay (PAMPA) membrane. This was ascribed to the greater hydrophobicity of lopinavir allowing for more effective partitioning into the BSA-containing media. Further examples, including those which document enhanced permeability in flow-through and ex-vivo setups, are outlined in a recent review by Sitovs and Mohylyuk. (15)
In drug solutions below saturation where the donor and receiver media are identical, the concentration gradient adequately captures the driving force for diffusion per Fick’s Laws. However, if the drug is more soluble in the receiver than the donor, the solute has a lower chemical potential in the receiver and the absolute concentration gradient no longer solely determines the flux. In these cases, diffusion is driven by the gradient in chemical potential rather than absolute concentration. (16,17) This distinction becomes especially evident in biphasic dissolutions, where the drug may have a much higher solubility in the organic phase than the aqueous phase. (18) Asymmetrical membrane transport models, which describe diffusion in the context of different media on either side of a membrane, commonly account for solubilizing additives by dividing the receiver concentration by a receiver-donor solubility ratio. (14,19,20) Partition- or solubility-based coefficients have also been incorporated into mathematical models that describe the permeability advantage of supersaturating formulations, where chemical potential is increased on the donor side. (21) These coefficients thus serve as experimentally accessible surrogates for the change in chemical potential across a membrane.
Beyond the effects of the receiver on the driving force for diffusion, solubilizing additives may additionally modulate permeability through other mechanisms. The donor-side free fraction of drug (i.e., the portion of drug in solution which is not part of a colloid or aggregate) has been demonstrated to be a key predictor of flux as it is molecularly dissolved drug which is most available for permeation. (16,22) The impact of free fraction on the receiver side is less studied, but additives which reduce the free fraction are assumed to increase flux. Particle drifting, (23) which describes the reduction in the apparent thickness of the concentration boundary layer due to the presence of nonabsorptive species, has also been proposed as a mechanism for flux enhancement in the context of solubilizing receivers. It is theorized that drug-binding colloidal moieties such as BSA can enter the receiver-side concentration boundary layer and reduce its apparent thickness. (14) Further considerations when predicting the impact of receiver on permeability include the effects of additives on drug recovery, capillary pressure in a porous membrane, or their potential to reverse permeate onto the donor side.
The present study interrogates receiver-mediated flux enhancement by examining the effect of nine different receiver additives, including surfactants, cyclodextrins, and BSA, on the flux of the model drug, griseofulvin (GRS), in HFM. A “reduced-resistances” mathematical model to describe the increase in apparent permeability was developed by extending a previous framework proposed by Dahuron. (4) The broader applicability of this model was studied through a series of drug cocktail permeation studies consisting of the freely water-soluble drug antipyrine (APY), and the poorly water-soluble drugs phenytoin (PHT) and meloxicam (MLX). This work advances the mechanistic understanding of the impact of receiver media on flux and supports the design of more predictive and reproducible approaches to in vitro permeability testing.

Theoretical

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Figure 1 summarizes the modeling workflow associated with this study. The approach combines the frameworks of Dahuron (4) and Kedem and Katchalsky (24) to account for both a solubilizing receiver medium and advection (the bulk flow of fluid from one side of the membrane to the other). The inclusion of advection was necessary as the pressure difference during the flow rate experiments resulted in volume shifts (Figure 2).

Figure 1

Figure 1. Overview of modeling workflow.

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Figure 2

Figure 2. Diagram of the HFM setup showing the volumetric flow rate (Q), concentrations (C), and volumes (V) associated with the donor (blue) and receiver (orange) circuits. The donor circuit is recycled, while the receiver circuit is single-pass to provide a constant physical sink.

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Overall flux is the sum of both diffusion and advection: (24)
J=Jdiff+Jadv
(1)
where J is the overall flux, Jdiff is the diffusional flux, and Jadv is the advective flux. Jadv is defined as the product of the volumetric flow rate across the membrane, Q, and concentration, C, divided by the membrane area, A:
Jadv=Q·CA
(2)
Unlike Kedem and Katchalsky, (24) where C represents the average concentration in the membrane, C here represents the drug concentration on the side which is losing volume. Q can be determined by measuring the final donor and receiver volumes and comparing these with the volumes expected without advection.
Diffusion across a membrane where the donor and receiver media are the same can be described in terms of Fick’s first law:
Jdiff=PappΔC
(3)
where Jdiff is the diffusional flux, Papp is the apparent permeability, and ΔC is the transmembrane concentration difference. In the case of HFM with a recycled donor solution and a single-pass receiver solution, let Cd(in) and Cd(out) be the concentrations at the inlet and outlet of the donor side, and Cr(in) and Cr(out) be the concentrations at the inlet and outlet of the receiver side. The concentration on the donor side is assumed as Cd(0) = Cd(in) = Cd(out) where Cd(0) is the initial donor concentration over the time course. This assumption is standard in the definition of Papp as Cd ≫ Cr(out). The concentration on the receiver side is assumed to vary linearly along the length of the fiber, such that Cr(in) = 0 and Cr(out) is constant at steady state over the time-course studied. As such, the concentration of fluid is taken to be the average of Cr(in) and Cr(out), which is Cr(out)2. Let Qd→r be the volumetric advective flow rate from the donor side to the receiver side. The updated equation for J is
J={Papp(Cd(0)−Cr(out)2)+Sd→r·Cd(0)AQd→r,ifQd→r≥0Papp(Cd(0)−Cr(out)2)+Sr→d·Cr(out)2AQd→r,ifQd→r≤0
(4)
where S denotes direction-specific sieving coefficients associated with advection. Taking the case of Qd→r ≥ 0, Papp can be calculated as follows:
Papp=J−Sd→r·Cd(0)AQd→rCd(0)−Cr(out)2
(5)
Under the current experimental conditions, Cr(out) is not measured directly. The receiver medium is collected in a vessel and samples are taken. As such, during the early stages of the experiment the concentration in the receiver vessel is less than the Cr(out) reached at steady state. The concentration in the receiver vessel approaches Cr(out) over time. The final measured receiver concentration is therefore assumed to be Cr(out). As Cd(0) ≫ Cr(out), Cr(out) is assumed to be 0 for the purposes of calculating Papp. Cr(out) is therefore only used to estimate receiver-to-donor advection. Assuming S = 1 from the pore size of the membrane, (3) the equation for Papp simplifies to
Papp=J−Cd(0)AQd→rCd(0)
(6)
The reciprocal of Papp is termed the resistance, R, and can be expressed as the sum of three resistances in series:
1Papp=1Pd+1Pm+1Pr
(7)
R=Rd+Rm+Rr
(8)
where Pd, Pm, and Pr are the individual donor-side, membrane, and receiver-side permeabilities, and Rd, Rm, and Rr are the corresponding resistances. Rd and Rr arise as a result of concentration boundary layers on either side of the membrane. Increasing the axial fluid velocity reduces these resistances by altering the hydrodynamics and thickness in this region. The relationship between resistance and reciprocal axial velocity is described by the following relationships:
1Pd∝1vdn,n∈(0,1)
(9)
1Pr∝1vrn,n∈(0,1)
(10)
where vd and vr are the donor and receiver axial velocities and n is the exponent which provides the best fit. As velocity increases, the associated resistance approaches zero (limv→∞⁡1v=0) and transport is limited only by the other two resistances:
limvd→∞⁡1Papp=1Pm+1Pr
(11)
limvr→∞⁡1Papp=1Pm+1Pd
(12)
Therefore, by plotting R versus 1vdn, the y-intercept represents the sum of the membrane and receiver-side resistances. Similarly, the y-intercept of a plot of R versus 1vrn represents the sum of donor and membrane resistances.
If the drug is more soluble in the receiver medium than the donor medium, a partition coefficient, H, can be defined as follows:
H=Sr*Sd*
(13)
where Sd* and Sr* are the thermodynamic equilibrium solubilities in the donor and receiver media, respectively. Under the reduced-resistances model, H influences Papp by reducing Rr as follows:
1Papp=1Pd+1Pm+1HPr
(14)
Similarly, if the receiver medium fills the pores of the membrane, solubility-mediated reductions in membrane resistance may also be observed:
1Papp=1Pd+1HPm+1HPr
(15)
Assuming the latter case, at high H, Rm and Rr approach zero and flux is limited only by Rd. Thus, the relationship between Papp and H is described by a right rectangular hyperbola which approaches Pd as H →∞. Papp is therefore increased in the presence of a solubilizing receiver by the following relationship:
Papp=11Pd+1HPm+1HPr
(16)
Pd is not modified by H as diffusion through the donor-side concentration boundary layer it is not influenced by solubilizing additives on the receiver side. Although validated using HFM, the above relationship is expected to be apparatus-independent.

Materials and Methods

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Materials

Antipyrine, bovine serum albumin (heat shock fraction), cetyltrimethylammonium bromide, D-α-tocopherol polyethylene glycol 1000 succinate, phenolphthalein (0.5% w/w in 1:1 ethanol: water), polyoxyethylene (10) lauryl ether, polyoxyethylene (23) lauryl ether (Brij L23), sodium carbonate, sodium lauryl sulfate, sodium phosphate monobasic dihydrate, and γ-cyclodextrin were purchased from Sigma-Aldrich (St Louis, MO, USA). Hydroxypropyl-β-cyclodextrin (Kleptose HPB Oral grade) was purchased from Roquette Pharmaceutical Ltd. (Lestrem, France). Griseofulvin was purchased from Alfa Aesar (Ward Hill, MA, USA). Phenytoin was purchased from AK Scientific, Inc. (Union City, CA, USA). Meloxicam was purchased from AmBeed (Arlington, IL, USA). Polysorbate 80 was purchased from Spectrum Chemical (New Brunswick, NJ, USA). MidiKros modified poly(ether sulfone) (mPES) HFM modules with an effective length of 20 cm and a MWCO of 10 kDa were purchased from Repligen (Marlborough, MA, USA).

General Procedure for HFM Studies

The current study adapts the HFM methods previously developed by Patel et al. (8) and Adhikari et al. (25) Three sets of experiments were performed as described below, namely flow rate experiments (with GRS), screening of receiver media (with GRS), and drug cocktail permeation experiments (with APY, PHT, and MLX). The chemical structures of all receiver media additives and drugs are depicted in Figure 3. Receiver media additives were selected on the basis of their prior use in permeability studies, or through their use in compendial dissolution methods. Two concentrations for each additive were identified in the same manner. GRS was selected as an initial model compound as it has a Log P and melting point similar to drugs used in permeability studies with solubility-enhancing receivers, as identified by Sitovs and Mohylyuk. (15) Additionally, its diffusion in HFM has been characterized previously by Patel et al. (8) MLX and PHT were included in the drug cocktail as two poorly water-soluble drugs with different levels of solubility enhancement in surfactant- and cyclodextrin-containing media. Conversely, APY was included as an FDA-recommended model BCS Class I drug for permeability studies (26) which is freely soluble in all receiver conditions studied with the cocktail.

Figure 3

Figure 3. Structures of all drugs (blue) and receiver media additives (orange) used in the present study. The higher and lower strength of each receiver media additive is shown below each structure, in % w/v. An additional strength of SLS, 0.01%, which is below the critical micelle concentration, was studied. The visualization of BSA was generated using the Mol* viewer based on coordinates from the Protein Data Bank (PDB ID: 3V03). (27−29)

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Preparation of Donor and Receiver Media

Sodium phosphate buffer was prepared by dissolving 50 mM of sodium phosphate monobasic dihydrate in Milli-Q water, adjusting the pH to 6.8 with 1 M aqueous sodium hydroxide solution, and made up to the final volume. pH 6.8 was selected given its widespread use in compendial dissolution testing and physiological relevance to intestinal conditions. GRS donor solution was prepared by dissolving 7 mg L–1 of GRS in this buffer. Drug cocktail donor solution contained 10 mg L–1 each of APY, PHT, and MLX in buffer. The drugs were left to dissolve for 24 h in both cases. Receiver solution was prepared by dissolving the receiver media additive in sodium phosphate buffer before making up to the final volume.

Quantification of Drugs

All drugs were quantified using Ultra-Performance Liquid Chromatography (UPLC) (Acquity H-Class, Waters Corporation, Milford, MA, USA) with photodiode array detection (210–400 nm), employing a ZORBAX SB-C18 column (150 mm × 4.6 mm, 5 μm; Agilent Technologies, Savage, MD, USA). The flow rate was 1 mL min–1, and the injection volume was 10 μL. Both the column and samples were maintained at 37 °C.
The mobile phase for GRS was an isocratic mixture of 60% aqueous ortho-phosphoric acid (0.3% v/v) and 40% acetonitrile. GRS was detected at a wavelength of 292 nm with a retention time of 7.1 min. The total run time for GRS was 10 min. The calibration range for GRS was 0.156 mg L–1 to 10 mg L–1 (R2 = 0.9993, LOD = 0.0283 mg L–1, LOQ 0.0857 mg L–1).
APY, PHT, and MLX were quantified concurrently using a single gradient method. The aqueous solvent was 0.3% v/v aqueous ortho-phosphoric acid, and the organic solvent was acetonitrile. For the first minute, a ratio of 80% aqueous and 20% organic solvent was used. The proportion of organic solvent increased linearly from 20% to 60% between minutes 1 and 10, and was maintained at this level between minutes 10 and 12. The proportion of organic solvent decreased linearly back to the initial 20% between minutes 12 and 13, and was kept at this level for 5 min to re-equilibrate the column. The total run time was 18 min. APY, PHT, and MLX were detected at 220, 220, and 364 nm, with retention times of 3.9, 7.9, and 10.4 min, respectively. The calibration range for APY was 0.625 mg L–1 to 20 mg L–1 (R2> 0.9999, LOD = 0.103 mg L–1, LOQ 0.313 mg L–1). The calibration range for PHT was 0.3125 mg L–1 to 20 mg L–1 (R2> 0.9999, LOD = 0.007 mg L–1, LOQ 0.022 mg L–1). The calibration range for MLX was 0.15625 mg L–1 to 20 mg L–1 (R2> 0.9999, LOD = 0.023 mg L–1, LOQ 0.0709 mg L–1).

Equilibrium Solubility Measurements

The equilibrium solubility of GRS in all additives and strengths not previously reported by Patel et al. (8) were determined. Further solubility measurements for GRS were taken in 10%, 2.5%, and 0.5% w/v of each of the cyclodextrins to construct a phase solubility curve. The equilibrium solubilities of MLX and PHT were determined in blank buffer, 2% SLS, 2% PS80, and 1% γCD, unless previously reported by Patel et al. (8) Excess drug was added to 5 mL of media in triplicate scintillation vials and placed in a shaking water bath at 37 °C for 72 h. The undissolved drug was removed by filtering through a 0.45μm polyvinylidene membrane filter unit, and the first milliliter was discarded. The samples containing BSA were diluted 1:4 with acetonitrile and centrifuged at 15,000g (Beckman Coulter Microfuge 20R) for 10 min. The supernatant was then further diluted using the mobile phase. All other samples were diluted directly using an appropriate dilution factor with mobile phase and analyzed by UPLC. APY solubility exceeded 1 g mL–1 in all relevant media and was therefore not quantitatively determined.

HFM Setup

The setup for the experiments is illustrated in Figure 2. Unless otherwise stated, all HFM studies in this paper adhere to the following procedure. 500 mL of donor solution was stirred at 75 rpm in the USP II apparatus at 37 °C. A multichannel peristaltic pump (Cole Parmer, Vernon Hills, IL, USA) calibrated to a given flow rate pumped the donor solution through the hollow fibers of the HFM membrane and then recycled the donor solution back into the original vessel. Concurrently, receiver media at 37 °C was pumped from a beaker to a USP II receiver vessel via the receiver side of the HFM by a calibrated multichannel peristaltic pump. One mL samples were removed without replacement from both donor and receiver vessels every 20 min for analysis by UPLC. BSA-containing samples were prepared as described for the solubility study, while all other samples were analyzed undiluted. The total run time was 2 h. The final volume in the donor and receiver chambers was measured using a graduated cylinder. All studies were performed in triplicate with permeation in three different HFM membranes running simultaneously.

Flow Rate Experiments

Flow rate experiments were performed to support later modeling efforts, where the sensitivity of Papp to fluid velocity was used to determine the permeability in each of the boundary layers and the membrane itself. Receiver flow rates of 1, 2, 3, 4, and 5 mL min–1 were investigated at a fixed donor flow rate of 2 mL min–1. Similarly, donor flow rates of 1, 2, 3, 4, and 5 mL min–1 were studied while the receiver flow rate was kept fixed at 2 mL min–1. Samples were taken every 30 min over 3 h for the experiment with a donor flow rate of 1 mL min–1 due to low flux.

Screening of Receiver Media

HFM Studies with Receiver Media Additives

HFM studies were performed as described above with a 2 mL min–1 flow rate for both donor and receiver. Two strengths were studied for each of the nine solubilizing additives as receiver media. An additional experiment was performed with 0.01% SLS to confirm whether a reduction in receiver-side capillary pressure without an appreciable solubility gain would affect drug flux. Receiver media additives did not interfere with drug quantification.
Drug cocktail permeability studies were performed using an APY-PHT-MLX cocktail with four different receiver compositions, namely buffer, SLS 2%, PS80 2%, and γCD 1%. The concentration of each drug was 10 mg L–1.

Dynamic Light Scattering

Dynamic Light Scattering (DLS) was performed to determine the hydrodynamic diameter of drug-loaded micelles at the studied strengths of each surfactant. Drug-loaded samples were obtained from the equilibrium solubility study. Triplicate measurements were carried out using a Zetasizer Nano ZSP (Malvern Instruments; Westborough, MA, USA) with polystyrene cuvettes. Each sample was analyzed at 37 °C, following a 120-s equilibration period. The refractive index of the dispersant was set to 1.330, and the viscosity was set to 0.6864 cP.

Assessment of Back-Diffusion

Aliquots of donor solution after each GRS HFM experiment were retained to evaluate the back-diffusion of receiver media additives.
Previous work by Patel et al. (8) confirmed the concentration of SLS in the donor aliquot to be below 125 μg mL–1 over 5 h with a donor volume of 900 mL and a receiver SLS concentration of 2% w/v. In the present study, DLS was performed to detect the presence of surfactant micelles, where an increase in the intensity of scattered light in the size range associated with a particular surfactant would indicate back-diffusion. The procedure for DLS was the same as described for micelle size determination.
Cyclodextrin concentration was determined spectrophotometrically with the decolorization of phenolphthalein by adapting previously described methods. (30,31) An aqueous stock solution of 0.002% w/w phenolphthalein was prepared in 50 mM sodium carbonate. 200 μL of cyclodextrin standard solutions were added to 1 mL of phenolphthalein stock solution in a polystyrene cuvette. The cuvette was agitated and absorbance was measured immediately at 550 nm using a spectrophotometer (VWR UV-1600 PC, Avantor). A calibration curve was constructed on the percentage decrease in absorption which was then used to determine the unknown cyclodextrin concentration in the donor aliquots. Linearity was observed in the calibration curve between 0–250 mg L–1 for HPβCD (R2 = 0.9912) and between 1.25–5 g L–1 for γCD (R2 = 0.9966).
The Bradford assay was used to quantify BSA in the donor solution. One mL of diluted Bradford reagent concentrate (Bio-Rad) was added to 20 μL of BSA standard solutions in Eppendorf tubes and vortexed for 10 s. One mL of this was then transferred to a polystyrene cuvette and allowed to develop for 5 min. Absorbance was measured at 595 nm. The calibration range was 8–1000 μg mL–1 (R2 = 0.9960). Unknown BSA concentrations were determined from the resulting calibration curve.

Simulation of Effect of SLS Concentration on Papp

To illustrate the practical application of the mathematical framework, the theoretical impact of receiver-side SLS concentrations between 0–2% w/v (0–69.36 mM) on Papp was simulated for the four drugs in the current study. The experimentally determined Papp for GRS diffusing into buffer with donor and receiver flow rates of 2 mL min–1 was used as the Papp for all drugs at 0% SLS. This reflects experimental observations demonstrating the similarity of Papp across drugs for HFM. (7,25) Given the low critical micelle concentration of SLS in buffered media (1.99 mM in 50 mM phosphate buffer (32)), H was assumed to vary linearly between 0 and 2% w/v SLS. Accordingly, the value for H at a given SLS concentration was calculated as
H=1+CSLS·(HSLS2%−1)2
(17)
where CSLS is the concentration of SLS expressed in % w/v, and HSLS 2% denotes the H value corresponding with 2% w/v SLS. The reduced-resistances model, which describes Papp as a function of H, was then applied to all model drugs:
Papp=1Rd+Rm+RrH
(18)
where the experimentally determined Rd, Rm, and Rr for GRS were assumed to be constant across drugs.

Results and Discussion

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GRS Flow Rate Experiments

The Papp values obtained from the flow rate experiments based on receiver-side data are shown in Figure 4. Donor-side data, and the deconvolution of diffusion and advection, is detailed in Tables S1 and S2. Advection contributed significantly to total mass transfer in cases where the donor flow rate was greater than the receiver flow rate. This is because the drug concentration of the donor solution was far greater than that of the receiver solution. In contrast, the contribution of advection when the receiver flow rate exceeded the donor flow rate was relatively small despite the volume shifts being larger. This can again be attributed to the steep concentration gradient. The most pronounced changes in Papp were seen as the receiver flow rate was varied between 1 and 3 mL min–1, with negligible gains made between 3 mL min–1 and 5 mL min–1 indicating an upper limit to Papp. GRS concentration in the receiver vessel at the final time point decreased with increasing Qr, despite an increasing Papp, indicating enhanced convective removal of drug from the outer surface of the membrane and the maintenance of a low receiver-side drug concentration. These results corroborate previous HFM studies which demonstrate that flux varies with flow rate. (5) Recovery of drug from the apparatus was favorable across flow rates (≈ 84% - 100%) and changes in mass balance were not attributable to any one variable.

Figure 4

Figure 4. Top row: Wilson plot showing the scaling of overall diffusional resistance, R, with either donor-side (A) or receiver-side axial velocity (B) to the power of −n. Error bars represent SEM (n = 3), propagated through the reciprocal transformation. Bottom row: Variations in Papp with donor-side (C) and receiver-side (D) volumetric flow rate, along with the theoretical plateaus derived from the intercepts of plots A and B. Error bars represent SEM (n = 3). The shaded region of the dotted line represents the standard error of the y-intercepts. All plots were derived using concentrations sampled from the receiver vessel.

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Figure 4 shows the deconvolution of Rd, Rm, and Rr, from flow rate data by means of a Wilson plot, and the resulting plateau in Papp with increasing fluid velocities. (33) In the case of variations in vd, n = 1 provided the best fit for the data, indicating a linear dependence of Rd on vd–1 within the vd range studied. The Lévêque solution for developing laminar flow through a cylindrical pipe suggests that Rd scales with vd−1/3. (4) This relationship yields an R2 of 0.88 for the current data and was therefore not preferred. Furthermore, the Rd intercept value associated with the Lévêque-derived fit is almost zero. This is physically implausible as it suggests Papp is not a function of Rm and Rr. Although the Lévêque-type relationship has been demonstrated previously for donor-side flow in HFM for a range of experimental conditions, (4) this is not universally observed and deviations from ideal laminar flow can produce an apparent linear dependence. Pulsatile flow from the peristaltic pump, the texture of the membrane surface, entrance effects, and nonspecific binding to the mPES membrane may influence the scaling of concentration boundary layer thickness with axial velocity. Alternative explanations, including turbulent flow patterns or approximation of plug flow, are less likely in the studied flow rate range and experimental setup.
Rr also appeared to scale best with vr–n when n = 1 (R2 = 0.99). Although the R2 was consistently high for all exponents studied, n = 1 was the only exponent to produce a physically meaningful Rr intercept. For this flow pattern, a single theoretical solution is less obvious and values of n of ≈ 1 have been previously reported for variations with vr in HFM. Yang and Cussler (34) fitted an exponent of 0.93 for absorption of carbon dioxide into laminar water flow on the receiver side, which may be due to secondary flow patterns. Dahuron (4) reported a linear dependence of mass transfer on receiver-side flow rate for the extraction of a range of small organic molecules and proteins from a solution flowing inside into stripping solution flowing in the same direction on the receiver side. The value of the exponent was attributed to channeling of fluid around the fiber, a process also likely in the current study given the random arrangement of fibers and visible presence of fiber curvature and contact. Wickramasinghe et al. (35) similarly favored channeling to explain a linear dependence between the mass transfer of dissolved oxygen in HFM and vr. The results from the flow rate experiments highlight the need for geometry-specific correlations in HFM.
Solving for the individual resistances at Qd = Qr = 2 mL min–1, Rr emerges as the dominant barrier to mass transport, accounting for 53.98 ± 2.95% of total resistance, followed by Rd (27.72 ± 6.25%) and Rm (18.30 ± 6.92%). The procedure for uncertainty estimation is described in the Supporting Information. The low standard errors of the y-intercepts in Figure 4 indicate a relatively precise estimate of the limiting resistances. It is unsurprising that Rr is greater than Rd. The concentration boundary layer on the receiver side is likely to be thicker than the concentration boundary layer on the donor side due to the slower velocity of the receiver medium (vd = 0.47 cm s–1 and vr = 0.38 cm s–1).
Assuming a diffusivity of 8 × 10–6 cm2 s–1 for GRS and using the point estimates for resistance detailed above, the donor-side boundary layer thickness was calculated to be 623.3 μm, while the corresponding receiver-side value was 1214 μm. Large boundary layer thicknesses for diffusion in HFM were also calculated by Patel et al., (8) who noted that the donor-side thickness was physically inconsistent with the fiber geometry given the internal diameter of 500 μm. In the current study, the large thickness similarly cannot reflect the physical reality of the boundary layer. Rather, the donor boundary layer thickness likely captures additional resistances, such as concentration polarization, nonspecific binding to the apparatus, or inefficient mixing of the donor solution. On the receiver side, tight packing of the fibers may hinder convective removal, thereby increasing the apparent boundary layer thickness. These fitted thicknesses therefore do not undermine the validity of the analysis, but instead serve as a lumped parameter that captures the total resistance to diffusion.
The relatively low contribution of Rm is also in line with theoretical expectations. Previous investigations with HFM have demonstrated that the relative contribution of Rm is diminished in the presence of poorly solubilizing donor and receiver media. (4,36,37) In the extraction of p-nitrophenol from an aqueous donor into an amyl acetate receiver (H = 80), the relative contribution of Rd, Rm, and Rr were 93%, 5% and 2% respectively. (4) Given that GRS is practically insoluble in aqueous solution, significant resistances from aqueous concentration boundary layers on either side of the membrane are to be expected. Assuming the membrane does not swell and the thickness remains constant at 200 μm, the effective diffusivity of GRS in the membrane is calculated as 3.89 × 10–6 cm2 s–1. (38) Unlike the boundary layer thicknesses, the effective diffusivity, Deff, value is physically plausible and indicates that the diffusivity of GRS in the membrane is approximately half that observed in solution. Deff of a porous membrane may be obtained by multiplying the diffusivity in the bulk fluid, D, by the ratio of the porosity, ϵ, to the tortuosity, τ. (39,40) The experimentally observed reduction could be explained by reasonable combinations of ϵ and τ (such as 0.7 and 1.5 respectively).

Characterization of Receiver Media Additives

Solubility

The solubility of GRS in the nine media studied is shown in Figure 5A. The ionic surfactants SLS and CTAB resulted in the greatest solubility enhancement. In most cases, an increase in the additive concentration led to an approximately proportionate increase in the solubility ratio. Both HPβCD and γCD displayed AL-type phase solubility profiles (Figure S1), with γCD complex being more stable. This observation is in line with previous studies of GRS complexation with CDs. (41,42)

Figure 5

Figure 5. (A) Bar plot comparing the thermodynamic equilibrium solubility of GRS in various receiver media at low and high concentrations. The concentrations are available in Figure 3. The horizontal dashed line represents the buffer solubility (10.27 ± 0.14 mg L–1). B. Bar plot comparing Papp values obtained from GRS permeation studies, illustrating the influence of a solubilizing receiver. The horizontal dashed line represents the buffer Papp (3.56 ± 0.22 × 10–5 cm s–1). Error bars and shaded regions represent SEM in both cases (n = 3). Both plots were derived using data sampled from the receiver vessel.

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The solubility of PHT and MLX in buffer, SLS 2%, PS80 2%, and γCD 1% are displayed in Figure 6. While PHT was extensively solubilized by micelles, their impact on the solubility of MLX were modest. γCD did not appear to be an effective solubilizer in either case. The solubility of APY was confirmed to be in excess of 1 g mL–1 in all cases and therefore not quantitatively determined.

Figure 6

Figure 6. Scatter plot showing the variation in Papp with solubility for MLX and PHT. Note that the equilibrium buffer solubility of MLX (272.68 ± 3.87 mg L–1) was higher than that of PHT (29.33 ± 0.61 mg L–1) which is relevant for the calculation of H. Only variations in Papp are shown for APY as solubility exceeded 1 g mL–1 in all media. Error bars represent SEM (n = 3)

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DLS

DLS data is presented in Table 1, with hydrodynamic diameters ranging from ∼ 4 nm in the case of SLS to ∼ 13 nm for TPGS. These values exceed the nominal pore size of the membrane, 2.5 nm, though the model of Patel et al. (8) suggests that a low level of transmembrane diffusion of micelles is possible. The membrane is structurally asymmetric and selective on the donor side only. It is therefore plausible for even the larger micelles to occupy the pores radially (i.e., the full length of the pores).
Table 1. Micelle Size Data Obtained from DLS
Additive% w/vDiameter (nm) (mean ± SEM, n = 3)
SLS14.82 (±0.31)
23.87 (±0.30)
CTAB16.48 (±0.02)
26.13 (±0.10)
PS80112.05 (±0.17)
212.06 (±0.21)
TPGS0.113.08 (±0.16)
0.212.41 (±0.35)
P10LE17.97 (±0.30)
28.90 (±0.45)
P23LE110.07 (±0.17)
29.03 (±0.12)

Permeability Testing

Figure 5B shows permeability data for GRS based on receiver-side concentration measurements. The ionic surfactants resulted in the greatest enhancement in Papp, with the cyclodextrins showing only minimal enhancement. The increase in Papp tended to follow the rank-order, but not the magnitude, of H. Spearman rank-order correlation coefficients (ρ) indicate a strong positive relationship between H and Papp when calculated based on both donor (ρ = 0.82, p < 0.001, n = 20) and receiver (ρ = 0.93, p < 0.001, n = 20) data. An equivalent plot for the donor data is provided in Figure S2. The Papp values obtained for experiments with solubilizing additives were generally consistent with the receiver data. The Papp associated with the buffer case, however, is almost double the Papp associated with the receiver data, thereby distorting fold enhancement calculations (Figure S2). This was likely due to greater nonspecific binding in the absence of any solubilizer. An additional experiment with SLS in the receiver at the submicellar concentration of 0.01% w/v was performed to determine whether a reduction in pore capillary pressure, without a significant increase in solubility, would impact Papp. The observed value was 3.40 ± 0.04 × 10–5 cm s–1, which was not different from the buffer Papp. Additionally, submicellar SLS did not increase the average recovery of drug from the setup when compared to the buffer case (Table S2).
Figure 6 shows permeability data for APY, PHT, and MLX. For MLX, Papp generally increased with solubility, with the exception of γCD 1% w/v. A similar relationship was observed for PHT, where the plateau effect is evident with the two micellar receiver media. The anomalous results observed in both cases may be due to back-diffusion of the drug-γCD inclusion complex. In contrast, APY was very soluble (>1 g mL–1) in all media studied and therefore no flux enhancement was anticipated. This was confirmed experimentally, with no additive having an appreciable effect on flux. The drug cocktail permeation study demonstrates that the choice of receiver medium can alter the rank-order of drug permeability. For example, with buffer in the receiver the rank-order of Papp was APY > PHT > GRS > MLX, while in the presence of SLS 2% this changes to GRS > PHT > MLX > APY. As such, permeability analyses performed with different receiver media may be incomparable.
Figure 7 data shows a clear right rectangular hyperbolic relationship between permeability enhancement and H, aligning closely with the theoretical dependence described by the reduced-resistances model. Following an initial stage of rapid permeability gains, the curve approaches a horizontal asymptote which represents a theoretical limit to receiver-mediated flux enhancement. This is mathematically analogous to Michaelis–Menten enzyme kinetics, which shows a similar hyperbolic relationship. It has been proposed previously that this limiting value is either (Rd + Rm)−1, where the receiver solution cannot infiltrate the membrane, or Pd, where receiver solution can fill the membrane pores and therefore reduce Rm with increasing H. (4)

Figure 7

Figure 7. Plot of Papp ratio versus solubility ratio for GRS. Error bars represent SEM (n = 3), with error being propagated to account for the calculation of a ratio. The shaded region on the two theoretical curves reflect the standard error of the y-intercept on the relevant Wilson plots.

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Theoretical curves using estimations of Rd, Rm, and Rr from the flow rate experiments are shown on the plot above. The orange curve, where permeation is limited only by Rd and Papp → Pd, shows convincing agreement with experimental data, despite an under-prediction of the asymptote. The orange curve approaches a Papp ratio of 3.60, while the most effective solubilizer (SLS 2% w/w) is associated with a ratio of 4.14. This ∼ 15% deviation is likely due to experimental noise, particularly in the deconvolution of advection and diffusion, and of the individual resistances from R. Alternative explanations for this underprediction, such as receiver-mediated reductions in donor-side resistance, are possible but are considered less likely given the strong alignment of theoretical and experimental Papp ratios. Although reverse permeation of most solubilizing additives was negligible, the structural asymmetry of the membrane may have permitted the entry of micelles from the receiver side into the pores, facilitating solubility-related reductions in Rm. The green curve represents the case where only Rr is reduced, and this was not supported by the experimental data.
Dahuron (4) indicates that complete reduction in Rm is achieved when the pores are completely filled with the receiver-side medium. Such a situation, however, is incompatible with the physical setup. The lack of back-diffusion and narrow pore size on the donor-side of the membrane would suggest that micelles cannot be distributed radially along the entire length of the pore. The lower diffusivity and resulting thicker concentration boundary layer further hinders micelle ingress into the membrane, along with potential transmural and capillary pressure constraints. It is possible that the model’s indication of a complete reduction in Rm actually reflects only a partial reduction, with the membrane’s contribution to the total resistance having been underestimated from flow rate experiments. In any case, the experimental data supports a model of resistance reductions limited by a theoretical maximum.

Back-Diffusion

Table 2 indicates minimal back-diffusion of surfactants at lower strengths. At higher strengths, however, light scattering in the micellar region was detected for CTAB, TPGS, P10LE, and P23LE. Given that the size of the micelles as measured by DLS in all cases exceeds the pore size of the membrane, it is possible that diffusion occurred only due to surfactant monomers. Patel et al. (8) found that a model where micelle-bound drug diffuses through HFM at a rate five times lower than that of free drug successfully described the permeation of micellar solutions of GRS. In the same study, however, SLS was undetectable in the receiver solution by refractive index HPLC. Given the absence of detectable back-diffusion at lower strengths for all surfactants, and considering that the receiver-side surfactant concentration was far in excess of the critical micelle concentration, it is reasonable to assume that even in cases where the donor solution did scatter light in the micellar region that the overall level of back-diffusion of surfactants was modest. No reverse-permeation of BSA was detectable by the Bradford assay, which is unsurprising in view of the pore size of the membrane.
Table 2. Back-Diffusion of Receiver Media Additives over Two Hoursa
AdditiveLow StrengthHigh Strength
Surfactants
SLSNot detectedNot detected
CTABNot detectedDetected
PS80Not detectedNot detected
TPGSNot detectedDetected
P10LENot detectedDetected
P23LENot detectedDetected
Cyclodextrins
HPβCD8.24 ± 1.18%7.27 ± 0.07%
γCD13.01 ± 2.32%10.96 ± 1.24%
BSA
BSABelow LODBelow LOD
a

The presence of surfactant micelles in the donor media was detected by DLS. Cyclodextrins were quantified via a phenolphthalein inclusion complexation assay. BSA was quantified by the Bradford assay.

Considerable back-diffusion of cyclodextrins was observed, with γCD showing greater reverse permeation than HPβCD. In a previous investigation of the effect of receiver-side HPβCD reported by Nunes et al., (43) glucose was added to the donor solution to maintain osmotic balance. No additional bulk movement of water from donor to receiver was observed in the current study. This provides further evidence that cyclodextrins diffuse freely through the membrane thereby reducing any osmotic pressure difference.
Reverse-permeation of receiver media additives introduces experimental artifacts and is therefore undesirable. The overall effect is likely a reduction in the Papp due to a reduction in the concentration of solubilizing additives in the receiver and the back-diffusion of additive-drug complexes. Even low levels of reverse-permeation may significantly interfere with dissolution-permeation experiments where very low concentrations of additives can alter dissolution behavior. As such, these results indicate that cyclodextrins are not preferred as receiver media additives in the context of HFM.

Simulation of the Effect of SLS Concentration on Papp

To illustrate the impact of additive concentration on the receiver side, simulated calculations were performed showing the dependence of Papp on SLS concentration (Figure 8). The four dotted lines show the theoretical increase in Papp at four theoretical HSLS 2%, ranging from 1 to 1000. With the exception of HSLS 2% = 1, each curve follows a rectangular hyperbola. Simulations of the reduced-resistances model generally agree with observed values. For example, the reduced-resistances model anticipated APY and MLX would not be markedly sensitive to 2% SLS in the receiver, while GRS and PHT would be. Importantly, the rank-order Papp at 2% SLS followed the rank-order of HSLS 2%.Aplateau was predicted for GRS (HSLS 2% = 161) and PHT (HSLS 2% = 146), although Papp was overpredicted in the case of PHT and under-predicted for GRS. Two characteristics of HFM impact the degree of agreement between predicted and observed values. First, HFM is generally highly permeable. (25) A high permeability of 3.56 ± 0.22 × 10–5 cm s–1 was similarly observed here, such that even reduced-resistances due to receiver solubilization had a modest although clearly observable effect. Second, HFM permeation has an appreciable variability between studies (even conducted on the same day) that is often unexplained. This is seen for other permeation setups such as cell culture. Papp in the absence of SLS varied approximately 2-fold, which is reflective of interoccasional variation and not true differences in drug Papp. (44) The framework described here can be extended to other receiver-side additives where a linear relationship between additive concentration and solubilization capacity is expected. Where such linearity cannot be assumed predictions may still be generated following experimental determination of H.

Figure 8

Figure 8. Simulated effect of increasing receiver-side concentrations of SLS on Papp at four levels of HSLS 2%. Additionally shown are experimentally measured Papp values for GRS, APY, PHT, and MLX at various SLS concentrations.

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Limitations

Although these results provide evidence for a relationship between the solubility ratio and flux enhancement, it is important to acknowledge several limitations. First, the geometry and experimental setup of the HFM may introduce random effects. For example, random packing of the fibers may result in channeling or local concentration differences between apparatuses. The true surface area may also deviate up to 10% from the nominal surface area. Second, the disagreement between donor data and receiver data complicates interpretation of the results. Although the Papp values for the additives were generally consistent, the Papp for diffusion into receiver-side buffer based on donor data was almost double the value obtained based on receiver data, thereby distorting flux ratio calculations. This would suggest nonspecific binding to the apparatus in the absence of additives which is not accounted for by the current mathematical model. Finally, the method used to deconvolute the individual resistances makes a number of assumptions which may not reflect the physical situation. For example, assuming a sieving coefficient of 1 may not be valid as the literature suggests the permeation of low molecular weight solutes is still influenced by pore diameter. (45) Despite these limitations, the results from this study clearly demonstrate a relationship between H and flux, thereby enhancing the design and interpretation of in vitro permeability experiments.

Impact on Permeability Testing

Receiver media additives have been described previously in the literature as “sink-forming reagents.” (9) While sink is well-defined by regulatory agencies in the context of dissolution as being 3 to 10 times the saturation volume, (46,47) the same guidance does not exist for permeability studies. The infinite sink assumption states that Cr ≈ 0 (or that Cd ≫ Cr) for all t but Rr is not eliminated. (48) Thus, receiver media additives should not be thought of simply as sink-forming reagents as they have been shown to increase flux beyond what would be expected simply due to maintaining low molecularly dissolved drug concentrations in the receiver or improved recovery. This is relevant even for systems which yield high Papp, such as HFM. Given the focus on developing poorly soluble but highly permeable drug candidates, (49,50) improving the efficiency of absorptive membranes for in vitro testing is advantageous. (51) Previous permeability experiments have largely separated the “sink-forming” properties of the receiver from physical methods of reducing the unstirred water layer. Avdeef et al. (52) employed a double sink in a 96-well plate PAMPA setup, where vigorous stirring was combined with two sources of chemical sink: a pH gradient for acidic drugs and surfactants for lipophilic bases. The calculation of the concentration boundary layer thickness was derived only from the stirring data, and did not consider the potential effects of the chemical sink on resistance in this region. As this chemical sink affects Rr differently across drugs with different values for H, the receiver medium must be considered when comparing permeability data across studies.
Narula et al. (14) describe the potential for a receiver-side particle drifting effect, (23) where the presence of a solubilizing additive thins the receiver-side concentration boundary layer. As resistance in this layer, Rr, is the reciprocal of Pr, it is directly proportional to the boundary layer thickness. Thus, the particle drifting effect also describes the increase in Papp via a reduction in Rr. Under the reduced-resistances model, it is instead H that reduces Rr directly. H acts as a surrogate for the reduced chemical potential of the diffusing drug in the receiver, and no change to the boundary layer thickness is made. Both models predict a hyperbolic relationship between Papp and receiver-side additive concentration, though they differ in mechanistic interpretation. Under the particle drifting framework, increasing additive concentration increases drift of colloids toward the membrane interface, thus thinning the boundary layer. Under the reduced-resistances model, the same increase in concentration raises H which then reduces Rr. The particle drifting effect provides a hydrodynamic interpretation of Papp enhancement, while the reduced-resistances model is a thermodynamic interpretation. Given that the results from the current study were consistent with the thermodynamic interpretation, and that colloids tend to have a lower diffusivity and thicker concentration boundary layers than molecularly dissolved drug, the reduced-resistances model was the preferred mechanistic explanation.
The observation that the receiver modulates flux presents both opportunities and challenges. The HFM system, which has a large surface area and a hydrophilic membrane, is primarily used as an absorptive sink in dissolution-permeation. The reduced-resistances framework, however, is expected to be independent of the membrane chosen or the experimental setup, provided the drug does not accumulate in the membrane and transport is diffusional. The receiver medium may therefore be tailored in biorelevant setups to better simulate in vivo conditions. If the systemic circulation is considered the ultimate source of sink for transcellular intestinal absorption, a continuously flowing receiver medium containing a biorelevant albumin concentration of 3.5–5% may better reflect in vivo conditions. (53) Saha and Kou (54) established that a receiver with 4% BSA can change the predicted BCS classification for highly lipophilic drugs. The investigations by Saha and Kou, (54) Avdeef et al. (52) and Narula et al. (14) differ from the current setup in that none incorporate a true physical sink with replenishment of receiver. The results in this study corroborate previous findings that both chemical and physical mechanisms contribute to in vivo sink, but that the chemical sink is particularly crucial for drugs that are preferentially solubilized in the receiver medium. This further raises the question of whether the receiver medium should mimic the interstitial fluid of the lamina propria, which has a low protein content and flows slowly, or the plasma, which may provide a more effective physical and chemical sink. (55) Further work is thus warranted to identify a biorelevant receiver and thereby more accurately predict in vivo disposition, though low concentration BSA appears to be a rational starting point.
The results suggest that the most effective solubilizer which does not reverse permeate should be selected where a high flux is desirable in order to obtain a detectable drug concentration in the receiver (such as in high-throughput permeability screening). An effective sink has been demonstrated to be essential in discriminating between dissolution and permeation rate-limited absorption. (7) However, other considerations outlined by Sitovs and Mohylyuk (15) apply. Ionic surfactants, though solubilizing, may form salts (56) or negatively impact cell viability. (57) Where high throughput is required, multiple sources of chemical sink may be necessary to ensure saturation volume requirements are met for a wide range of drugs. (52) The concept of sink is poorly defined in any case for supersaturating formulations. (58) Thus, while this paper demonstrates the importance of the solubility ratio in the design of in vitro permeability experiments, it remains only one part of the wider optimization problem and must be considered in light of the many other constraints of the in vitro approach.

Future Directions

While this paper establishes the reduced-resistances framework as the preferred mechanistic interpretation for receiver-mediated permeability enhancement, its generalizability remains insufficiently explored. The applicability of H for describing changes in the Papp of ionizable drugs under transmembrane pH gradients must be experimentally verified. This is particularly crucial for weakly acidic drugs where pH can act as the primary source of chemical sink. (52) Future investigations should also confirm the validity of this model in a range of artificial and biological membranes. Promisingly, results from Caco-2 studies show a plateau in Papp with increasing receiver-side BSA. (54) The model may need to be modified in the case of membranes which are likely to retain drug, such as PAMPA. Finally, the impact of altering donor-side conditions is a clear area requiring further evaluation. Micellar donors have previously been examined in the context of HFM. (8) Extending this evaluation to biorelevant media and formulations which alter the chemical potential gradient, such as amorphous solid dispersions, will be necessary to develop a unified mechanistic understanding of membrane permeability enhancement.

Conclusions

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This work interrogated the impact of a solubilizing receiver medium on Papp of drug solutions in HFM. A clear relationship emerged showing that the increase in Papp generally follows the rank-order of the solubility ratio, but not its magnitude. The reduced-resistances model explained this effect through a hyperbolic relationship between the solubility ratio and permeability. At large H, diffusion is limited only by Rd and Papp becomes very permissive. Results from a multidrug permeation study with APY, PHT, and MLX corroborated this relationship and indicated that the rank-order permeability can be altered by the receiver medium. Cyclodextrins showed extensive reverse permeation, thereby limiting their value as solubilizing additives when used with porous membranes. This study advances understanding of permeability testing by supporting the rational selection of receiver media and thus enhancing the robustness of in vitro permeability data. The development of biorelevant receiver media merits further investigation.

Supporting Information

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The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.molpharmaceut.5c01771.

  • Phase solubility profiles for GRS in the presence of γCD and HPβCD (Figure S1); permeability and recovery data for GRS at different flow rate combinations using both donor and receiver-side data (Table S1–S2); Papp, solubility, and recovery of GRS in different media (Table S3); bar plot comparing Papp values obtained from GRS permeation studies based on donor-side sampling (Figure S2); Papp and solubility for APY, PHT, and MLX in various media (Table S4); description of SEM propagation (PDF)

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Author Information

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  • Corresponding Author
  • Authors
    • Jack D. Murray - School of Pharmacy, University College Cork, Cork T12 K8AF, Ireland;  Orcidhttps://orcid.org/0000-0002-8168-1586
    • Roshni P. Patel - School of Pharmacy, University of Maryland, Baltimore, Maryland 21201, United States
    • Harriet Bennett-Lenane - School of Pharmacy, University College Cork, Cork T12 K8AF, Ireland
    • Patrick J. O’Dwyer - School of Pharmacy, University College Cork, Cork T12 K8AF, Ireland;  Orcidhttps://orcid.org/0000-0002-5350-8364
    • Brendan T. Griffin - School of Pharmacy, University College Cork, Cork T12 K8AF, Ireland;  Orcidhttps://orcid.org/0000-0001-5433-8398
  • Notes
    The authors declare no competing financial interest.

Acknowledgments

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J.D.M. is funded by the Taighde Éireann – Research Ireland Government of Ireland Postgraduate Scholarship Programme Grant GOIPG/2022/1580. J.D.M. received a scholarship from the Fulbright Commission in Ireland to support research conducted at the University of Maryland School of Pharmacy.

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  • Abstract

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    Figure 1

    Figure 1. Overview of modeling workflow.

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    Figure 2

    Figure 2. Diagram of the HFM setup showing the volumetric flow rate (Q), concentrations (C), and volumes (V) associated with the donor (blue) and receiver (orange) circuits. The donor circuit is recycled, while the receiver circuit is single-pass to provide a constant physical sink.

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    Figure 3

    Figure 3. Structures of all drugs (blue) and receiver media additives (orange) used in the present study. The higher and lower strength of each receiver media additive is shown below each structure, in % w/v. An additional strength of SLS, 0.01%, which is below the critical micelle concentration, was studied. The visualization of BSA was generated using the Mol* viewer based on coordinates from the Protein Data Bank (PDB ID: 3V03). (27−29)

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    Figure 4

    Figure 4. Top row: Wilson plot showing the scaling of overall diffusional resistance, R, with either donor-side (A) or receiver-side axial velocity (B) to the power of −n. Error bars represent SEM (n = 3), propagated through the reciprocal transformation. Bottom row: Variations in Papp with donor-side (C) and receiver-side (D) volumetric flow rate, along with the theoretical plateaus derived from the intercepts of plots A and B. Error bars represent SEM (n = 3). The shaded region of the dotted line represents the standard error of the y-intercepts. All plots were derived using concentrations sampled from the receiver vessel.

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    Figure 5

    Figure 5. (A) Bar plot comparing the thermodynamic equilibrium solubility of GRS in various receiver media at low and high concentrations. The concentrations are available in Figure 3. The horizontal dashed line represents the buffer solubility (10.27 ± 0.14 mg L–1). B. Bar plot comparing Papp values obtained from GRS permeation studies, illustrating the influence of a solubilizing receiver. The horizontal dashed line represents the buffer Papp (3.56 ± 0.22 × 10–5 cm s–1). Error bars and shaded regions represent SEM in both cases (n = 3). Both plots were derived using data sampled from the receiver vessel.

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    Figure 6

    Figure 6. Scatter plot showing the variation in Papp with solubility for MLX and PHT. Note that the equilibrium buffer solubility of MLX (272.68 ± 3.87 mg L–1) was higher than that of PHT (29.33 ± 0.61 mg L–1) which is relevant for the calculation of H. Only variations in Papp are shown for APY as solubility exceeded 1 g mL–1 in all media. Error bars represent SEM (n = 3)

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    Figure 7

    Figure 7. Plot of Papp ratio versus solubility ratio for GRS. Error bars represent SEM (n = 3), with error being propagated to account for the calculation of a ratio. The shaded region on the two theoretical curves reflect the standard error of the y-intercept on the relevant Wilson plots.

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    Figure 8

    Figure 8. Simulated effect of increasing receiver-side concentrations of SLS on Papp at four levels of HSLS 2%. Additionally shown are experimentally measured Papp values for GRS, APY, PHT, and MLX at various SLS concentrations.

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  • Supporting Information

    Supporting Information

    The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.molpharmaceut.5c01771.

    • Phase solubility profiles for GRS in the presence of γCD and HPβCD (Figure S1); permeability and recovery data for GRS at different flow rate combinations using both donor and receiver-side data (Table S1–S2); Papp, solubility, and recovery of GRS in different media (Table S3); bar plot comparing Papp values obtained from GRS permeation studies based on donor-side sampling (Figure S2); Papp and solubility for APY, PHT, and MLX in various media (Table S4); description of SEM propagation (PDF)


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