Giving a dissolution test an absorptive sink: a hollow-fibre membrane apparatus and what it shows about supersaturated nevirapine

Background and motivation

Dissolution testing is the routine tool for judging oral dosage forms, and ideally it ranks formulations the way they will behave in patients (McAllister 2010; Dressman 1998; Section "Introduction"). For poorly soluble drugs, formulators use complexation, micelles, cocrystals or amorphous solid dispersions to raise the dissolved concentration above the crystalline solubility. Such solubility-enabling formulations often supersaturate in the gut and may then precipitate. The standard paddle or basket apparatus is a closed vessel: it has a fixed volume, no absorptive sink, and no biorelevant hydrodynamics, and it often fails to predict or discriminate these formulations C1. Flow-through cells, biorelevant media and multicompartment models that mimic gastric emptying address parts of the problem, but none of them removes drug the way absorption does.

Removing drug matters most for supersaturating systems. As drug crosses the gut wall, the concentration left in the lumen falls, which changes the supersaturation profile and with it both the dissolution of any remaining solid and the rate of crystallization. Bevernage et al. (2012) showed that precipitation from a supersaturated solution was less extensive when an absorptive compartment was present C3. Solubilizing additives raise the total dissolved concentration but lower the free fraction; a closed dissolution test cannot see this, whereas a membrane experiment shows it as slower transfer at the same total concentration (Dahan 2012; Miller 2011) C4. Two families of absorptive tests exist. Biphasic tests add an organic layer on top of the aqueous medium; they helped prediction when combined with a pH shift (Frank 2014) but suffer from solvent volatility, emulsions with surfactant-rich media and blocked sampling lines C5. Membrane tests separate a donor and a receiver compartment, from the dissolution/Caco-2 system of Ginski and Polli (1999) onward.

The membrane tests share one problem: the membrane area per donor volume is small. The amount transferred is flux times area, so a small area gives slow transfer, long waits for a measurable receiver signal, and little feedback of absorption on the donor concentration C2. A side-by-side diffusion cell with a few square centimetres of membrane cannot remove drug fast enough to change what happens in the donor over the hours that matter. Small receiver volumes also make it hard to keep sink conditions, and a stagnant water layer next to the membrane adds a further barrier (Indulkar 2016; Sironi 2017) C2.

Hollow-fibre membranes offer a large area per volume and allow fluid to flow on both sides, which thins the stagnant layers; they had been used to simulate intestinal absorption (Lamberti 2012; Blanquet 2004) but not to measure transport from supersaturating dosage forms C7. The authors therefore set out to build a high-surface-area, flow-through absorptive dissolution apparatus around a hollow-fibre module, compare it with a side-by-side cell, optimize it, describe it with a mass transfer model, and test it with supersaturated solutions of the weak base nevirapine that crystallize at different speeds C65·C8.

Background concepts

Supersaturation and crystalline solubility. A solution is supersaturated when its concentration exceeds the equilibrium solubility of the crystal. The paper uses the supersaturation ratio $S=C/C_s$, the measured concentration divided by the crystalline solubility E11. Nevirapine is a weak base with a pKa of 2.8 M1. It dissolves well in acid, but at pH 6.5 it is substantially un-ionized and its crystalline solubility in 50 mM phosphate buffer at 37 °C is 128 µg/mL R1·C8. Dissolving a dose in 0.1 N HCl and then doubling the volume with 0.17 M Na2HPO4 to reach pH 6.5 therefore gives a supersaturated solution; the authors aimed at 500 µg/mL, an S of 3.9 P7·R18.

Induction time. A supersaturated solution does not crystallize at once. The nucleation induction time is the delay before crystals are detected; in this paper it was taken from the rise of UV extinction at 400 nm and therefore includes the time for nuclei to grow to a detectable size P2. At 500 µg/mL nevirapine crystallized after about 5 min without polymer, after about 60 min with 0.1% PVPVA (polyvinylpyrrolidone/vinyl acetate, Kollidon VA 64) and not within 4 h with 0.05% HPMC-AS (hydroxypropyl methylcellulose acetate succinate, MF grade) R2. These three cases, fast, slow and no crystallization, carry the later comparisons.

Flux and activity. The driving force for passive transport across a membrane is the difference in chemical potential, that is, in thermodynamic activity, not in total concentration (Cussler 2009; Twist and Zatz 1986) C6. The paper writes the flux as

In plain terms: the flux $J$ is the mass $M$ crossing unit membrane area $A$ per unit time; it grows with the solute activity $a$ and the diffusion coefficient $D$, and falls with the membrane thickness $h$ and the activity coefficient of the solute in the membrane ${\gamma }_m$ E1. Two consequences follow. The total amount transferred is flux times area, so a larger area moves more drug in the same time. And because activity, not total concentration, drives transport, a supersaturated solution gives a proportionally higher flux than a saturated one, which earlier Taylor-group work found to hold without a break at the solubility (Raina 2014; Indulkar 2016) C18.

Absorptive sink, donor and receiver. In the apparatus the formulation dissolves in a donor vessel. Its solution is pumped through the inside of the hollow fibres; fresh buffer flows past the outside and carries away drug that has crossed the membrane. That outside stream is the receiver. Because the receiver buffer is always fresh, the receiver side stays at sink, and the rate of transfer is set by the donor concentration P4·C36. The paper distinguishes dissolution only in a closed vessel (D) from dissolution-absorption with the membrane connected (D-A) P7.

Receiver peak as a measure of donor concentration. The receiver concentration is measured in-line with a flow-through UV cell, so the receiver curve is a real-time, non-cumulative record of how fast drug appears across the membrane P4·C36. Its maximum, Cmax, depends on the donor concentration at the time steady transport is reached. If Cmax is proportional to donor concentration over a wide range, a measured Cmax can be converted back into an effective donor concentration and hence an effective supersaturation, which is what the authors do C19·C49.

Overall mass transfer coefficient. The resistance to transfer from the fibre lumen to the outside is the sum of three resistances in series: the aqueous layer inside the fibre, the membrane, and the aqueous layer outside E3:

In plain terms: $K_{in}$, the overall mass transfer coefficient (cm/s), is limited by the slowest of the three steps; $k_{in}$, $k_m$ and $k_{out}$ are the coefficients of the inner layer, the membrane and the outer layer E3. Faster flow thins the two aqueous layers, so $K_{in}$ should rise with flow rate C15·C28.

Methods in detail

The study has four parts: build and benchmark the apparatus, calibrate its receiver signal, describe it with a mass transfer model, and use it on supersaturating nevirapine systems in comparison with a closed vessel.

Contribution 1: a hollow-fibre absorptive apparatus and its benchmark

Problem. Side-by-side cells transfer too little drug to couple dissolution with absorption C2. What they built. The module contains 36 polyethersulfone (PES) hollow fibres with a 10 kDa molecular weight cut-off (pore size about 2.5 nm), an internal diameter of 0.5 mm, a wall thickness of 0.2 mm and a length of 20 cm, for a stated area of 115 cm² M10. A two-channel peristaltic pump drives the donor solution through the fibre lumen and back to the donor vessel, and fresh pH 6.5 buffer from a reservoir through the shell side in the same direction (co-current); the shell outflow passes a flow-through UV cell and is collected as the receiver (Figure 1) P4. The system is held at 37 °C and washed with 50/50 methanol/water for 30 min after every run P4. A 10 µm cannula filter at the donor inlet keeps undissolved particles out of the fibres P7.

Benchmark. The comparator was a PermeGear side-by-side cell with a 7.07 cm² flat PES sheet of 6–8 kDa cut-off, with the receiver followed by a UV dip probe P3·M11. Both were run with 100 µg/mL nevirapine at pH 6.5 and 37 °C for 60 min (Table 1) R3. The text describes the comparison as made "at its crystalline solubility", but the table gives 100 µg/mL, below the measured solubility of 128 µg/mL; the table value is the one used here X1.

Optimization. With a 50 mL donor, flow rates from 0.5 to 9 mL/min were tried. Co-current flow at similar rates in both channels gave the least flow disturbance and bubble formation, and 2 mL/min became the operating rate; the transmembrane pressure gradient was removed so that no convective flow crossed the membrane P4·R10. The optimization data themselves are not shown.

Contribution 2: closing the mass balance and calibrating the receiver signal

Because the receiver is measured as a flowing stream, the amount transferred is the area under the receiver curve times the receiver flow rate:

In plain terms: integrating the receiver concentration over time and multiplying by the volume flow $Q_{out}$ of the receiver stream gives the mass $M_{total}$ that has crossed the membrane E10. To check that no drug is lost, a run with 5 mg of nevirapine in the donor was stopped after 60 min, the module and tubing were washed with solvent, and the drug in donor, receiver and wash was measured (Table 2, two trials) P5·R5.

For the calibration, donor solutions from about 30 to 800 µg/mL, below and above the crystalline solubility, were run for 60 min, and the receiver Cmax and the area under the receiver curve over 60 min (AUC0-60) were recorded (Figure 3) P6·R6. How the supersaturated calibration solutions were prepared is not stated P6.

Contribution 3: a mass transfer model of the module

The model follows hollow-fibre extraction theory (D'Elia 1986; Prasad and Sirkar 1989, 1992). It assumes steady state, no drug adsorption onto the membrane once steady state is reached, and uniform pores and wetting C9. A balance over a short length $dz$ of the fibres reads

In plain terms: at steady state, what the lumen stream (flow rate $Q_{in}$) loses in concentration $c_{in}^z$ over $dz$ equals what crosses the walls of $N$ fibres of internal diameter $d_{in}$, driven by the difference between the lumen concentration and the wall concentration $c_{in}^{z*}$ E2. Because the membrane is hydrophilic and wetted by water on both sides, there is no partitioning and $c_{in}^{z*}$ equals the shell concentration $c_{out}^z$; fresh buffer enters the shell at zero concentration C10. A balance over the whole module then gives the receiver concentration

In plain terms: the receiver stream carries exactly what the donor stream lost, scaled by the ratio of the two flow rates E5. The donor vessel of volume $V_{in}$ receives back the depleted stream:

In plain terms: the donor concentration $c_{in}^0$ falls at a rate set by how much the recirculated stream loses in one pass (its exit concentration is $c_{in}^L$), divided by the donor volume; a larger donor volume depletes more slowly E7·C44. Combining these with the single-pass solution (Eq. 6) and integrating over time gives

In plain terms: without crystallization the donor concentration falls exponentially with time; the rate constant depends on the flow rates, the donor volume, the membrane area $A=\pi d_{in}NL$ (with fibre length $L$) and the single unknown, $K_{in}$ E8·E12. The paper prints the same result also in exponential form as Eq. 9 E9.

The authors did not compute $K_{in}$ from first principles. They fitted Eq. 9 to runs at similar operating conditions with initial donor concentrations above and below the solubility, obtaining a mean of $(9.07\pm 1.06)\times {10}^{-5}$ cm/s, and attribute the scatter to imprecise flow readings, to which the model is "very sensitive" R12·C12. They also fitted $K_{in}$ at 0.5, 2, 3 and 4 mL/min (Figure 6) R14.

Two quick checks by the AI writer use only printed values. First, the fibre dimensions give $A=\pi \times 0.05\mathrm{c}\mathrm{m}\times 36\times 20\mathrm{c}\mathrm{m}=113.1$ cm², close to the stated 115 cm², and the same dimensions reproduce the 1.41 cm³ lumen volume of Table 1 E12·X10. Second, Eq. 8 with the mean $K_{in}$, 115 cm², 2 mL/min in both channels and a 50 mL donor predicts that 42.8% of the drug leaves the donor in 60 min, against 41.5% transferred in Table 1 (the flow rate of that run is not stated in the table) E8·R3.

Contribution 4: supersaturating systems with and without an absorptive sink

Samples. Three nevirapine samples were tested: a crystalline suspension (excess powder in the pH 6.5 medium), the drug powder, and a commercial 200 mg tablet (Camber; excipients include microcrystalline cellulose, croscarmellose sodium, corn starch, povidone, sodium starch glycolate, colloidal silicone dioxide (as printed) and magnesium stearate) P7·M4. Powder and tablet were dissolved in 0.1 N HCl at 37 °C for 30 min and then shifted to pH 6.5 with an equal volume of 0.17 M Na2HPO4. The final volume was 100 mL for suspension and powder and 400 mL for the tablet, so that 200 mg dissolves in the acid and the same supersaturation results after the shift P7. For the polymer arms, 0.05% HPMC-AS was dissolved in the Na2HPO4 solution beforehand; because that solution is then mixed 1:1 with the acid, the final polymer concentration in the donor may be half the stated value, and the basis of the percentage is not given P7·X13. The donor was stirred at 300 rpm, sampled by hand through 0.45 µm glass fibre filters and analysed by UV for 4 h; the absorption runs used 2 mL/min P7.

Closed versus absorptive. The same pH-shift runs were done in a closed vessel for the tablets with and without HPMC-AS (Figure 7) R15. A separate comparison used a solution of 500 µg/mL nevirapine made from a methanolic stock in pH 6.5 buffer with 0.1% PVPVA, followed for 120 min with and without absorption at 4 mL/min (Figure 8) P8. The donor volume of that experiment is not printed; the plotted amounts imply about 100 mL X14.

Supersaturation ratios. Three values of S are compared in Table 3: the theoretical S from the dose and volume, the maximum S in the donor from the donor concentration just after the pH shift, and the S "observed at t_max in receiver", obtained by converting receiver Cmax into a donor concentration with the Figure 3 correlation R18·E13. The equation of that correlation is not printed E13.

Experimental analysis

The hollow fibre transfers far more drug

From the 100 µg/mL solution, 41.5% of the drug crossed the hollow-fibre membrane in 60 min, against 1.50% in the side-by-side cell (Table 1) R3. The authors call this a "considerably faster" transfer and, in the abstract, 30 times higher C14. Table A sets out what differs between the two set-ups.

Table A. Flat-sheet side-by-side cell against hollow-fibre module, nevirapine at pH 6.5 and 37 °C (from Table 1) R3.

The ratio of the two percentages is 27.7, which the abstract rounds to 30; because the donor volumes also differ, the ratio of absolute masses is about 46 X2. The authors attribute the gain "primarily" to the large ratio of membrane area to donor volume, and also to the thinner membrane, the continuous flow that reduces the unstirred water layer, and the fresh buffer that keeps the receiver at sink C35. These factors were not separated experimentally, so the 30-fold figure describes the apparatus as a whole under the Table 1 conditions, not the effect of area alone X2. During optimization, transfer rose with flow rate up to an optimum and then fell; the authors explain the rise by thinner aqueous boundary layers and better sink, and the fall by too short a residence time in the module R10·C15.

The receiver signal: shape, mass balance and calibration

At 2 mL/min the receiver concentration rose for about 15 min to its maximum (about 17.7 µg/mL in the run of Figure 2) and then fell slowly, to about 12.6 µg/mL at 60 min R4. The authors attribute the initial rise to the membrane taking up drug until steady state, and the slow decline to the shrinking driving force as the donor is depleted ("can be attributed") C16. The donor concentration of the Figure 2 run is not stated X11.

The mass balance closed: 2.09 and 1.78 mg remained in the donor, 1.89 and 2.14 mg reached the receiver, and 0.99 and 1.07 mg were recovered in the solvent wash, for totals of 4.97 and 4.99 mg of the 5 mg added (Table 2) R5·C17. Note by the AI writer (not discussed in the paper): about 20% of the dose, and about a third of the drug that left the donor, was held in the module and tubing and came out only in the wash. The model assumes no adsorption once steady state is reached, so in short runs the donor loses more drug than the receiver gains X12·C9. Using Eq. 10 with the plotted AUC0-60 at 100 µg/mL (about 830 µg/mL·min) and 2 mL/min gives about 1.7 mg, slightly below the 1.89 to 2.14 mg found in the receiver E10·R6·X11.

Across donor concentrations from about 30 to about 800 µg/mL, both Cmax and AUC0-60 rose on straight lines, with no discontinuity at the crystalline solubility (Figure 3) R6·C18. Cmax went from about 5 µg/mL at 30 µg/mL to about 26 at the solubility, about 101 at 500 and about 175 µg/mL at 800 µg/mL R6. This is what Eq. 1 predicts for a membrane that responds to activity, and it matches earlier findings (Raina 2014; Indulkar 2016) C18. The authors conclude that the line "can serve as a calibration set to determine the degree of saturation or supersaturation in an unknown system" C19.

The model: exponential depletion and a flow-dependent coefficient

Figure 5 shows $\ln (c(t)/c(0))$ of a donor falling on a straight line from about −0.12 at 20 min to about −0.95 at 240 min, with $R^2=0.9885$, which the authors take as "confidence" that the mass balance model describes the observations R13·C27. The data set is described only as "a sample data set"; its points match the powder + HPMC-AS run of Figure 4a with time counted from the pH shift X6. Figure 6 shows fitted $K_{in}$ rising from about $4.9\times {10}^{-5}$ cm/s at 0.5 mL/min to about $1.54\times {10}^{-4}$ cm/s at 4 mL/min, with $R^2=0.9799$ for a straight line, as expected for a mass transfer unit whose boundary layers thin with flow (D'Elia 1986) R14·C28.

The authors then predicted the powder + HPMC-AS donor and receiver curves with $K_{in}=1.08\times {10}^{-4}$ cm/s, plotting the prediction only after steady state, and report "good agreement" R11·C29. The predicted donor curve runs from about 491 µg/mL at 30 min to about 144 µg/mL at 270 min, and the receiver curve from about 118 µg/mL at about 60 min to about 40 µg/mL at 270 min R11. Eq. 9 with the printed inputs (100 mL donor, 2 mL/min in both channels, 115 cm², $K_{in}=1.08\times {10}^{-4}$ cm/s) reproduces the end point, 139 µg/mL E9. The model is valid only at steady state and only when nothing crystallizes; crystallizing systems would need crystallization kinetics, which the authors leave for later C30.

Note by the AI writer (not discussed in the paper): the agreement is approximate. The measured donor ends at about 184 µg/mL, about 22% above the model, and the measured receiver at about 45 µg/mL against about 40 X7·R7·R8. The slope of Figure 5 (about −0.0038 per min) corresponds through Eq. 8 to $K_{in}$ of about $6.9\times {10}^{-5}$ cm/s, lower than both the mean fitted value and the $1.08\times {10}^{-4}$ cm/s used for the prediction; the paper does not say whether that value was fitted to this run X7·X8.

Without polymer: crystallization cuts the effective supersaturation

In the acid stage the tablet dissolved completely, reaching about 990 µg/mL by 15 min (Figure 4a) R7·C23. Right after the pH shift the powder donor held about 475 µg/mL and the tablet donor about 500 µg/mL R7. Both fell quickly: the powder to about 300 µg/mL at 40 min and about 180 µg/mL at 60 min, the tablet to about 285 µg/mL at 45 min and about 205 µg/mL at 60 min, and both reached about 100 µg/mL from about 165–210 min onward R7. Crystals were seen in the powder donor under polarized light R9. The authors attribute the fall to crystallization "with some contribution from simultaneous absorption" ("can likely be attributed") C21. The suspension donor stayed at about 130 to 138 µg/mL throughout, close to the solubility R7·C20.

The receiver curves of powder and tablet peaked at about 81 and 79 µg/mL at about 39 min, roughly 9 min after the shift, and then fell to about 19 and 25 µg/mL at the end of the run (Figure 4b) R8. The suspension gave no peak but a plateau of about 24 to 27 µg/mL, matching the Cmax of a saturated solution in Figure 3; the authors take this as confirming that the receiver profile reflects the donor concentration and that crystalline dissolution is fast relative to transfer ("Clearly") R8·C38·C39. They also note that this reservoir effect would be harder to see in a side-by-side cell C40. The text states that the powder and tablet Cmax were "approximately 4 times" that of the suspension, whereas the plotted peaks and Table 3 give about 3 times C22·X3.

The authors read the profiles as follows. Crystallization brought the donor to the solubility, where it "showed a constant value for a certain period of time" because the crystals acted as a reservoir, and then fell below the solubility once all crystals had redissolved into the depleting donor ("indicating") C42·C43. About 50 min were needed to reach the solubility after the shift C43. In the plotted points the donor declines steadily from about 140–150 µg/mL at 90 min to about 100 µg/mL, without a distinct plateau at the solubility, so the reservoir stage is an interpretation rather than a resolved feature X16. The tablet took longer than the powder to approach the solubility, which the authors explain with Eq. 7: the tablet donor volume was four times larger, so transfer depleted it more slowly ("can be explained") C44.

With HPMC-AS: supersaturation is kept, and the receiver reports it

With 0.05% HPMC-AS no crystals were seen in the donors for up to 160 min, and for the powder no crystallization was seen for 4 h R9·C46. The powder + HPMC-AS donor fell gradually from about 478 µg/mL at 30 min to about 184 µg/mL at 270 min, and the tablet + HPMC-AS donor from about 517 to about 253 µg/mL R7. The receiver peaks were higher than without polymer: about 119 µg/mL at about 48 min for the powder and about 122 µg/mL at about 70 min for the tablet R8. The authors attribute the higher Cmax to "sustained supersaturation" C24.

Table B. Theoretical and observed supersaturation ratios; "Polymer" is 0.05% HPMC-AS; the number of replicates is not stated (from Table 3) R18·X17.

Table B carries the paper's central quantitative result. Without polymer the receiver-derived S, 2.8 and 2.9, is clearly below the donor maximum of 3.8, because crystallization in the donor begins before steady transport is reached R18·C48. With HPMC-AS the receiver-derived S, 4.10 and 4.0, agrees with the donor maximum, 3.9 and 4.07, which the authors call "good agreement" R18·C50. They propose that the receiver-derived value, which reflects the donor about 10 to 15 min after the pH change, "can be considered as the maximum effective supersaturation observed for a formulation" and used to discriminate formulations C49.

Note by the AI writer (not discussed in the paper): for powder + HPMC-AS the receiver-derived S (4.10) is higher than the donor S measured near t_max (about 420 µg/mL at 40–50 min, an S of about 3.3) and higher than the donor maximum. Converting the plotted peaks with the plotted calibration slope (about 0.20) gives about 3.1 for the powder and about 4.6 for powder + HPMC-AS, not 2.8 and 4.10. The calibration equation is not printed, so these conversions cannot be checked exactly; the receiver-derived S is best read as uncertain by roughly 10 to 15% X9.

The tablet + HPMC-AS donor stayed above the powder + HPMC-AS donor throughout, for example about 420 against 296 µg/mL at 150 min R7. The authors attribute this "slight difference" to more drug in the tablet ("can be attributed"), since tablet content can vary while the powder was weighed C25. Note by the AI writer: the donor maxima differ little (S 4.07 against 3.9), whereas the tablet donor volume was four times larger, which by Eq. 7 slows depletion; the authors use this volume argument themselves for the no-polymer case X18·C44. For the tablet with HPMC-AS the discussion states that crystallization was inhibited for "only 120 min", and the authors speculate that undissolved excipient particles such as microcrystalline cellulose "may have played a role" C47. The paper does not say which run this refers to; in Figure 4a the absorptive tablet + HPMC-AS donor steps down from about 420 to about 352 µg/mL between 165 and 180 min, while the closed run in Figure 7 stays constant X4.

Closed and absorptive vessels: tablets with and without HPMC-AS

Figure 7 compares the tablet runs in a closed vessel (D) with the absorptive runs (D-A, the same data as Figure 4a). Table C lists representative values.

Table C. Tablet donor concentration (µg/mL) in a closed vessel (D) and with absorption (D-A), read from Figs. 7 and 4a, approximate R15·R7.

Without polymer both vessels crystallized; the closed vessel reached the crystalline solubility at 140–160 min and the absorptive one at 120 min R15·C52. The authors explain the earlier arrival by two routes of depletion in the absorptive vessel, transport and crystallization, against one in the closed vessel C52. That the two profiles are otherwise similar "can be rationalized" by the high driving force for nucleation right after the pH shift: crystallization "commences before substantial mass transport can occur", so absorption cannot lower the supersaturation in time C51. With HPMC-AS the closed donor stayed at about 520 to 555 µg/mL for the whole run, while the absorptive donor halved R15·R7. From this the authors conclude that dissolution tests "may overestimate the extent of supersaturation at any given time point" and that an absorptive compartment "is likely to be beneficial" for estimating the concentration driving force for absorption C53·C54.

Note by the AI writer: the authors also describe the paired tablet profiles as "fairly similar" with and without HPMC-AS and conclude that, for these two extremes, the absorptive compartment "did not appear" to change the phase behaviour C31·C32. That holds for the crystallization outcome without polymer, not for the concentrations with HPMC-AS, which differ by a factor of about two at 270 min X5.

With PVPVA: absorption prevents crystallization

The third case is a solution that crystallizes on an intermediate timescale: 500 µg/mL nevirapine with 0.1% PVPVA, whose induction time in the inhibition test was about 60 min (Figure 8) R2·C13. Table D lists the readings.

Table D. Donor concentration and total drug in solution (donor plus receiver with absorption; donor only without), 0.1% PVPVA, 4 mL/min, read from Fig. 8, approximate R16·R17.

With absorption the donor concentration fell steadily, but the total amount of drug in donor and receiver stayed at about 44 to 49 mg for 120 min, which the authors read as no drug lost to crystallization R17·C33. Without absorption the donor stayed near its starting level for an hour and then dropped, and the total fell after 60 min to about 26 mg at 120 min, "indicating that crystallization of the drug has occurred" R16·R17·C33. The authors conclude that the closed compartment "overestimates the risk for crystallization" for systems that crystallize on a slower timescale, and rationalize the result by the depletion of the donor, which reduces supersaturation "and in turn the driving force for nucleation and growth" C55·C57. This agrees with the earlier observation of Bevernage et al. (2012) C57.

Note by the AI writer: this experiment differs from the others in medium (buffer with a methanolic stock instead of the pH-shift medium), flow rate (4 instead of 2 mL/min) and unstated donor volume, and its replicates are not stated X14·X15·X17. The absence of crystallization is inferred from a constant total amount; nucleation itself was not measured C57.

Discussion

The paper's argument links the three crystallization speeds to one mechanism, the race between nucleation and depletion. The authors set it out across the Results and Discussion; the chain below follows their wording.

In the authors' reading, the absorptive compartment changes what a dissolution test reports in two ways. It changes the concentration-time profile that a formulation actually delivers, so a closed vessel "may overestimate the extent of supersaturation at any given time point" C53. And, when nucleation is slow, it can change the outcome itself, so the closed vessel "overestimates the risk for crystallization" C55. The case without polymer marks the limit: when the induction time is a few minutes, crystallization starts before absorption has removed much drug C51. The receiver signal adds a third use: through the calibration line, it gives an effective supersaturation that separates a crystallizing formulation from a stabilized one even when both start at the same S C49·C50.

The authors see the approach as flexible. Hollow fibres come in several materials and areas, so the absorption rate can be tuned; highly lipophilic drugs "may pose challenges", such as adsorption and low concentrations, which "should be solvable" through membrane choice, sensitive analytics or solubilizing additives in the receiver C58. They expect it to be "of greatest relevance" for drugs with solubility-limited absorption, such as BCS class II compounds, and plan to test other drugs, membranes and biorelevant media C59·C60. The commercial nevirapine tablet behaved like the powder without polymer, which the authors take to mean that its excipients do not slow crystallization; nevirapine is nonetheless well absorbed from it (Lamson 1999) C45.

Note by the AI writer (not discussed in the paper): for formulation work, the PVPVA result is the most useful one. A polymer that only delays nucleation by about an hour in a closed vessel behaved as a full inhibitor once absorption removed drug, so ranking inhibitors by closed-vessel induction times alone may undervalue them. Conversely, when a formulation crystallizes within minutes of the pH shift, an absorptive sink does not rescue it. Comparisons between formulations in this kind of apparatus also need matched donor volume and flow rate, because Eq. 7 makes the depletion rate inversely proportional to donor volume, and the powder (100 mL) and tablet (400 mL) arms differed here E7·X18.

Limitations

Limits the authors state

The model holds only for steady state and only when no crystallization occurs; predicting crystallizing formulations would require crystallization kinetics, which is "beyond the scope of the current study" C30. The standard deviation of $K_{in}$ is attributed to imprecise flow measurement with the rotameter, and the model "was found to be very sensitive to the fluid velocity" C12. The cause of the tablet + HPMC-AS crystallization "was not investigated further" C47. Highly lipophilic drugs "may pose challenges" C58. Above all, "the in vivo relevance of the formulation performance observed in the apparatus requires further evaluation" C63.

The AI writer's own judgement

The transfer gain, the closed mass balance, the linear calibration and the large contrasts between closed and absorptive vessels are direct measurements and hold up R3·R5·R6·R15·R17. Several points weaken the quantitative conclusions:

• Replicate numbers are stated only for the solubility, Figure 2 and Table 2; the dissolution-absorption runs, Table 3 and the induction times show error bars or ± values without n X17.
• The receiver-derived supersaturation depends on a calibration whose equation is not printed and cannot be reproduced from the plots; for powder + HPMC-AS it exceeds the donor values X9.
• The model curve ends about 22% below the measured donor at 270 min, and the $K_{in}$ used for it is neither the mean fitted value nor the Figure 6 value at 2 mL/min X7·X8. Figure 5, offered as a test of the model, uses the same run X6.
• About 20% of a 5 mg dose stays in the module after 60 min, which the model does not include X12.
• The text and figures disagree in places: the Table 1 concentration (100 µg/mL, not the solubility), the "approximately 4 times" Cmax ratio (about 3 in the data), and the timing of crystallization with HPMC-AS (160 min, 4 h or 120 min) X1·X3·X4.
• The PVPVA comparison used a different medium, twice the flow rate and an unstated donor volume, and the induction-time medium is not stated; the claim that depletion lowers the nucleation driving force rests on a constant total amount, not on a measurement of nucleation X14·X15·C57.
• One drug, one membrane material and non-biorelevant buffers were used, and no in vivo comparison was made C63.

Conclusion

The paper makes three contributions. First, it shows that a hollow-fibre module with 115 cm² of membrane and flow on both sides transfers drug fast enough to couple dissolution and absorption over hours: 41.5% of a solution in 60 min, against 1.50% in a side-by-side cell R3·C60. Second, it shows that the receiver peak is a linear read-out of donor concentration across the crystalline solubility, so the apparatus reports an effective supersaturation: 2.8 to 2.9 when nevirapine crystallizes after a pH shift, against 4.0 to 4.1 when HPMC-AS keeps it in solution R6·R18·C49·C50. Third, it shows that an absorptive sink matters most when nucleation is slow: a PVPVA-inhibited solution that crystallized in a closed vessel after an hour stayed in solution for 2 h when drug was removed through the membrane R17·C33·C55. A simple steady-state model with one fitted coefficient describes the depletion when nothing crystallizes ("good agreement") C29·C62. The authors present the work as a proof of concept, with in vivo relevance still to be established C60·C63.