Measuring dissolution and membrane transport together: what drug-rich nanodroplets do for amorphous solid dispersions

Background and motivation

Many new drug candidates dissolve too poorly in intestinal fluid to be absorbed well. Two broad formulation answers exist. Solubilizing additives, such as surfactants, raise the total amount of drug in solution, but earlier work showed that they leave membrane transport unchanged or even lower it, because they lower the thermodynamic activity of the drug (Raina 2015, ref 4; Miller 2011, ref 5). Supersaturating formulations take the other route: they raise the concentration of free drug above its crystalline solubility. Because the driving force for passive membrane transport is the difference in chemical potential across the membrane (Cussler, ref 10), a supersaturated solution gives a higher flux, as long as the drug does not crystallize during the time it takes to be absorbed (refs 11–13). Amorphous solid dispersions (ASDs), in which the drug is dispersed in a polymer, are one of the most used ways to generate and hold supersaturation (refs 15–19).

Supersaturation has an upper limit. When the concentration of a hydrophobic drug exceeds its amorphous solubility, the solution undergoes liquid–liquid phase separation (LLPS): it splits into a water-rich phase, whose drug concentration equals the amorphous solubility, and a drug-rich phase of water-saturated amorphous drug, usually present as nanodroplets. The two phases share one thermodynamic activity and sit in metastable equilibrium until crystals nucleate, so the amorphous solubility is the highest free drug concentration the system can reach (Ilevbare and Taylor 2013, ref 23; Taylor and Zhang 2016, ref 11). Earlier in vitro work from the same group showed that, without crystallization, these nanodroplets act as a reservoir: as free drug crosses a membrane, the droplets dissolve and keep the free concentration, and therefore the flux, at its maximum until they are used up (Indulkar 2016, ref 12). It has also been suggested that drug-rich colloids reduce the diffusion barrier of the unstirred water layer at the intestinal wall (Stewart 2017, ref 27).

The tools for studying these effects had two weaknesses. Standard USP dissolution testing is a closed, one-compartment test without an absorptive sink, and it often fails to predict how supersaturating formulations behave (refs 28, 29). Removing drug through a membrane can change both dissolution and crystallization; crystallization from supersaturated solution was less extensive when an absorptive membrane was present (Bevernage 2012, ref 30; Hate 2017, ref 31). Two-compartment cells, with a donor and a receiver separated by a membrane, add that sink, but their membrane area is small. Since the mass transfer rate is proportional to membrane area, these cells transfer drug slowly; receiver concentrations are low, an unstirred water layer slows transfer further, and experiments become long. In the group's flow-through side-by-side cell, it took 16 h to follow the depletion of the drug-rich phase, much longer than the 3–4 h available for absorption in the intestine (refs 12, 13).

The group had therefore built a flow-through absorptive dissolution apparatus around a hollow-fiber membrane module (Hate 2017, ref 31). Hollow fibers give a large membrane area per volume; fluids flow continuously on both sides, which reduces the unstirred water layer; fresh receiver fluid keeps sink conditions; and an in-line probe reads the receiver concentration in real time. This paper uses that apparatus to ask how supersaturated systems that undergo LLPS behave when dissolution and absorption are coupled. The model drug is atazanavir (ATZ), a weak base that crystallizes relatively slowly and whose crystallization can be held off for more than 4 h by suitable polymers (Indulkar 2018, ref 39). The authors set out to do four things: measure transport from solutions below and above the amorphous solubility; characterize the nanodroplets by size and number; measure dissolution and absorption together for ASDs that differ in drug loading and polymer, since both control the release rate and whether nanodroplets form (Jackson 2015, ref 15; Alonzo 2011, ref 42); and compare these runs with closed-compartment dissolution.

Background concepts

Amorphous solubility and liquid–liquid phase separation. The crystalline solubility is the concentration in equilibrium with the stable crystal; for ATZ in pH 6.8, 50 mM phosphate buffer at 37 °C it is 5 µg/mL. The amorphous solubility is the concentration in equilibrium with the amorphous, water-saturated drug; it is much higher, 78 µg/mL for ATZ in the same buffer with 1 mg/mL HPMCAS. Above the amorphous solubility, adding more drug does not raise the free concentration; it only adds drug-rich nanodroplets. The authors measured the amorphous solubility by the UV-extinction method: a methanolic drug solution is added slowly to buffer, and the concentration at which light scattering at 400 nm appears is taken as the amorphous solubility and the onset of LLPS. ATZ has a pKa of 4.52 (Materials, ref 43; the Results section prints 4.42), so at pH 6.8 it is essentially unionized and both solubility values refer to the neutral drug.

Activity, flux and speciation. In a supersaturating formulation, drug can be present as free unionized drug, ionized drug, drug in micelles, drug in complexes and colloidal drug species. Only free, unionized drug crosses a membrane by passive diffusion (ref 11). The total concentration, which a UV probe in a dissolution vessel reports, can therefore be a poor guide to how much drug is available for absorption. This is the reason for measuring absorption directly.

The hollow-fiber absorptive dissolution apparatus. The donor solution (50 mL) and the receiver fluid are pumped in parallel, co-current flow, both at 4 mL/min, through a cellulosic hollow-fiber membrane with 100 cm² of surface and 15 nm pores. The receiver is fresh buffer that passes the module once, so its concentration is not cumulative: at each moment it reports the drug that crossed the membrane in one pass. At these flow rates the flow in the fibers is laminar, with a parabolic velocity profile, and one pass through a single fiber takes about 10 s. The authors summarize each receiver profile by two numbers: the maximum receiver concentration, Cmax, and the area under the receiver concentration–time curve, AUC. The paper states in words how the AUC turns into an amount of drug:

In plain terms: multiplying the area under the receiver curve (µg·min/mL) by the receiver flow rate $Q$ (4 mL/min) gives the mass of drug $m_{\mathrm{t}\mathrm{r}\mathrm{a}\mathrm{n}\mathrm{s}\mathrm{f}\mathrm{e}\mathrm{r}\mathrm{r}\mathrm{e}\mathrm{d}}$ (µg) that crossed the membrane in that time. For dissolution–absorption runs the authors also count the drug released by an ASD in both compartments (Figure 9 caption):

In plain terms: the total drug dissolved at time $t$ is the drug still in the donor solution, $m_{\mathrm{d}\mathrm{o}\mathrm{n}\mathrm{o}\mathrm{r}}$, plus the drug already carried into the receiver.

Seeing nanodroplets. Three methods are used. (1) ATZ is autofluorescent. Excited at 250 nm, a solution below the amorphous solubility emits a single band at 329 nm; above it a second band appears at 369 nm, characteristic of ATZ in a drug-rich environment (Figure S1; Indulkar 2017, ref 46). The ratio of the intensities, I(369)/I(329), is about 0.58 at the amorphous solubility and rises as droplets form; its fall during an experiment shows droplets being used up. (2) Dynamic light scattering (DLS) gives the mean droplet size and the polydispersity index (PDI); the paper notes that a PDI above 0.7 means a broad size distribution. (3) Nanoparticle tracking analysis (NTA) follows the Brownian motion of individual particles under a microscope and converts it to size with the Stokes–Einstein equation, which the paper names but does not print; it also counts particles per mL. Because 1 mg/mL HPMCAS solutions gave a high background, "most likely" from small polymer aggregates, NTA was run in fluorescence mode with Nile red, a hydrophobic dye that partitions into the drug-rich droplets, so only the droplets were seen.

Drug loading notation. The ASDs were made at 10, 30 and 50 wt% drug and are written as polymer:drug ratios, 90:10, 70:30 and 50:50. The three polymers were HPMCAS (hydroxypropyl methylcellulose acetate succinate, MF grade), HPMC (hydroxypropyl methylcellulose) and PVPVA (poly(vinylpyrrolidone–vinyl acetate), Kollidon VA 64). "Diss" denotes closed-compartment dissolution and "Diss-Abs" simultaneous dissolution–absorption.

Methods in detail

The study has three parts that build on each other: solutions of known supersaturation in the absorptive apparatus; nine ASDs dissolved with and without the absorptive sink; and a set of runs that connect the ASD results to the solution results (same droplets by two routes, different doses, longer times). The method flow below summarizes them.

Contribution 1: transport from solutions below and above the amorphous solubility

Problem. Above the amorphous solubility the free drug concentration is fixed, so classical theory predicts that the flux across a membrane stops rising: in a side-by-side diffusion cell the mass transfer rate "would typically" reach a single maximum (ref 11). Whether the droplets contribute anything beyond keeping the free concentration constant could not be tested well in slow, small-area cells.

What they did. Supersaturated solutions were made by the solvent-shift method: aliquots of a 25 mg/mL methanolic ATZ stock were added to 50 mL of pH 6.8, 50 mM phosphate buffer containing 1 mg/mL pre-dissolved HPMCAS at 37 °C. Initial concentrations were 30, 50, 60, 75, 100, 150, 200, 300 and 500 µg/mL, from just above the crystalline solubility to about six times the amorphous solubility. The fluorescence ratio was measured over this range (Figure 1); DLS sized the droplets at 100–500 µg/mL (Table 1, n = 3); NTA counted them at 75, 100 and 150 µg/mL (Figure 2); above 150 µg/mL there were too many particles to track. Each solution was then pumped through the hollow-fiber module for 100 min with fresh receiver buffer at 4 mL/min, and the receiver profile was recorded in-line (Figure 3). A 30 min wash with 50% methanol after each run recovered about 5–10% of the ATZ from the apparatus. The receiver profiles were reduced to Cmax and AUC and plotted against the initial donor concentration (Figure 4), with separate straight-line fits below and above the amorphous solubility.

Why it works. The large membrane area makes transfer fast enough that the donor is depleted appreciably within 100 min, and the single-pass, non-cumulative receiver signal follows changes in the donor almost in real time. The steady state in the module is reached within 10 min. Because the 15 nm pores are far smaller than the roughly 200 nm droplets, any change in transfer above the amorphous solubility must come from what the droplets do on the donor side, not from droplets crossing the membrane.

Difference from earlier work. The earlier static and flow-through side-by-side cells (refs 12, 13) showed the reservoir effect, but slowly. Here the same question is asked over 100 min, with nine concentrations, and with droplet number measured alongside.

Contribution 2: ASDs dissolved with and without an absorptive sink

Problem. The supersaturation an ASD generates depends on drug loading and polymer. A closed dissolution test shows how fast and how high the concentration rises, but not how much of that drug can cross a membrane, and it does not let dissolution respond to absorption.

What they did. ASDs with 10, 30 and 50 wt% ATZ in HPMCAS, HPMC or PVPVA were prepared by rotary evaporation from methanol (HPMCAS, PVPVA) or 1:1 dichloromethane:methanol (HPMC) with a 45 °C water bath, dried under vacuum for at least 24 h, cryo-milled and stored at 0% RH. All nine were X-ray amorphous (Figure S2). In closed-compartment tests, powder equivalent to 200 µg/mL ATZ was suspended in 50 mL of buffer at 37 °C and stirred at 300 rpm for 120 min, with a UV dip probe in the vessel (Figure 5). In simultaneous dissolution–absorption, the same dose was suspended in the donor container of the apparatus and the flow was started; a 10 or 70 µm cannula filter kept undissolved particles out of the fibers. Donor and receiver were followed for 2 h (Figure 6). Samples were filtered (0.45 or 1 µm glass fiber) and checked for droplets by fluorescence, DLS and NTA (Table 2), and the donor of the 50:50 PVPVA ASD was examined by polarized light microscopy (Figure S3).

Why it works. Running the same ASDs in both configurations isolates the effect of the sink: any difference in the donor profile comes from the drug removed through the membrane. The AUC over 120 min (Figure 6G) puts all formulations on one scale of drug transferred.

Contribution 3: linking the ASD results to the droplets

Problem. ASD dissolution produces droplets that may differ from those made by solvent shift (size, polymer concentration), and the number of droplets depends on dose and on how much of the ASD dissolves. To attribute the ASD results to droplets, the two routes need to be compared directly.

What they did. Three sets of runs. First, a solvent-shift solution and a dissolving 90:10 HPMCAS ASD were run side by side for 240 min, with the fluorescence ratio sampled during transport (Figure 7). Second, the 90:10 HPMCAS ASD was dosed at 100, 200 and 500 µg/mL (Figure 8). Third, the three 10% loading ASDs were run for 4 h instead of 2 h (Figure S6). In addition, droplet size was followed by DLS over 105 min in a 200 µg/mL solvent-shift solution containing 1 mg/mL PVPVA (Figure S4), and the total drug released from the 50% loading ASDs was compared between closed and absorptive runs (Figure 9, Figure S5).

Difference from earlier work. Earlier studies attributed higher diffusive flux from some ASDs to nanodroplets (refs 15, 42). Here the droplet route is checked against a solvent-shift control in the same apparatus, and the size of the reservoir is varied through the dose.

Experimental analysis

Experimental setup in brief. All work was done in pH 6.8, 50 mM phosphate buffer at 37 °C. The solution series and the amorphous solubility used 1 mg/mL pre-dissolved HPMCAS; the ASDs were dissolved in plain buffer. The paper states replicate numbers only for the DLS sizes in Table 1 (n = 3, standard deviations); the other figures show error bars without saying how many runs they represent or what kind of error they are.

Table A. Solvent-shift ATZ solutions: droplet detection and membrane transfer. DLS sizes from Table 1 (mean with SD in parentheses, n = 3; PDI 0.08–0.15); all other values read from Figures 1, 2A and 4 (approximate). Amorphous solubility 78 µg/mL.

Main result 1: above the amorphous solubility, droplets of constant size form in growing numbers. Below 78 µg/mL the solutions were clear and the fluorescence ratio stayed near 0.3. At 75 µg/mL it reached about 0.58, the value the authors give for the amorphous solubility, and above that it rose steadily to about 2.1 at 500 µg/mL, while the solutions turned turbid (Figure 1). The droplet size did not change: 204–226 nm from 100 to 500 µg/mL, with low PDI (0.08–0.15), while the DLS derived count rate rose from 28633 to 342132 kcps (Table 1). Same size and more signal means more droplets, which the authors found "intuitive" and then "confirmed" with NTA: about 2.3, 5.4 and 10.6 × 10⁹ droplets per mL at 75, 100 and 150 µg/mL, roughly doubling at each step (Figure 2). Droplets were already counted at 75 µg/mL, which the Figure 2 caption places "at" the amorphous solubility, although the text gives the amorphous solubility as 78 (± 5) µg/mL.Card note X2: the paper gives 78 µg/mL in the text but about 75 µg/mL in the Table 2 footnote, and the reference lines drawn in its figures vary between about 81 and 94 µg/mL depending on the polymer.

Main result 2: transfer keeps rising above the amorphous solubility, at a lower slope. All receiver profiles rose to a steady state within 10 min, reached Cmax and then declined over 100 min, which the authors attribute to the donor being depleted (Figure 3). Below the amorphous solubility, Cmax and AUC rose with concentration, "as expected" for a higher driving force. Above it, they did not level off. Figure 4 shows two regimes, each fitted with a straight line:

In plain terms: $C_d$ is the initial donor concentration and $C_{\mathrm{a}\mathrm{m}}$ the amorphous solubility, both in µg/mL. Below the amorphous solubility, each extra 1 µg/mL in the donor raises the receiver peak by about 0.07 µg/mL; above it, by much less, but still by a positive amount. The paper prints the first intercept as "1,56" with a decimal comma.Card note X7: the printed upper equation does not reproduce its own points. It gives 7.81 µg/mL at 100 and 11.81 µg/mL at 500 µg/mL, whereas the plotted Cmax values are about 8.5 and 13.8; a straight line through the plotted points rises by about 0.013 µg/mL per µg/mL. The slope is printed to one significant figure. The slope break itself is clear in the points. The AUC follows the same pattern:

In plain terms: below the amorphous solubility, the area under the receiver curve grows by 5.51 µg·min/mL per µg/mL of donor; above it, by 1.29, a little over a quarter of the slope below. These two printed equations do reproduce the plotted AUC points (card records E3, E4). The authors read the change in proportionality as a change in the mass transfer coefficient: "This shows that there is a difference in the mass transfer coefficient in the presence of drug-rich nanodroplets". In the Discussion they argue that, because the free drug concentration and the driving force are constant above the amorphous solubility, "logically, the observed behavior results from the increase in the number of amorphous droplets". The droplets themselves cannot pass the 15 nm pores, and since they are more than two orders of magnitude larger than dissolved molecules, their own contribution to diffusivity is "expected to be negligible".

Table B. The nine ASDs in closed-compartment dissolution (Figure 5) and in simultaneous dissolution–absorption (Figure 6A–F); 200 µg/mL dose, 37 °C. All concentrations read from the figures (approximate). Droplet sizes from Table 2. Donor values above the amorphous solubility are apparent UV values that include scattering by droplets.

Main result 3: only the 10% loading ASDs pass the amorphous solubility. In the closed vessel, the 90:10 HPMCAS and HPMC ASDs dissolved within minutes to apparent concentrations of about 240–250 µg/mL, above the 200 µg/mL dose. The authors point out that above the amorphous solubility the UV reading is not quantitative, because droplets absorb and scatter light (ref 47). Fluorescence (I(369)/I(329) of 1.17–1.30) and DLS (294–326 nm) showed nanodroplets, slightly larger than those made by solvent shift with 1 mg/mL of the same polymer (221 and 311 nm; Table 2). The 30 and 50% loading ASDs of these polymers dissolved more slowly and formed no nanodroplets. The authors describe this as "consistent with the observation that the maximum concentration did not exceed the amorphous solubility" and note that slower release and a lower maximum at higher loading have been seen before and are, "in some instances", thought to come from a drug-rich layer at the ASD surface (refs 16, 40–42, 48).Card note X8: in Figure 5A the 70:30 HPMCAS curve ends at about 99 µg/mL and the 50:50 curve at about 84 µg/mL, above the dashed line at about 83 µg/mL; in Figure 5B the 30 and 50% HPMC curves reach about 88–92 µg/mL against a line at about 87. The absence of LLPS at these loadings therefore rests on the absence of droplets rather than on the UV values.

PVPVA behaved differently. The 30 and 50% PVPVA ASDs dissolved at a moderate and slow rate without LLPS, but the 70:30 and 90:10 ASDs settled above 78 µg/mL. The authors measured the amorphous solubility with 1.8 mg/mL dissolved PVPVA and found 94 (± 4) µg/mL, which explains the plateau. (Note by the AI writer: 1.8 mg/mL is the polymer concentration of a fully dissolved 10% loading ASD at this dose; the paper does not give the reason for this level.) The 90:10 PVPVA ASD dissolved immediately to slightly above this value, yet filtered samples showed no 369 nm band and no particles in DLS (ratio 0.26). Unfiltered samples gave a ratio of 0.89, which indicates a drug-rich environment. "Most likely", the droplets formed in the boundary layer agglomerated rapidly and were held back by the filter. In a 200 µg/mL solvent-shift solution with 1 mg/mL PVPVA, DLS indeed showed droplets of about 245 nm growing to about 700 nm at 75 min and about 10 µm at 105 min (Figure S4), whereas HPMCAS and HPMC droplets stayed small.

Table C. Drug transferred in 120 min of simultaneous dissolution–absorption. AUC read from Figure 6G (approximate); the 70:30 ASDs are not shown in that panel. The last column is the AI writer's arithmetic using the paper's own relation (AUC × receiver flow rate); the dose in the donor was 10,000 µg.

Main result 4: the droplet-forming ASDs transfer the most; the crystallizing ASD the least. With the absorptive sink, the donor concentration of the 90:10 cellulose ASDs did not plateau as in the closed vessel; it fell from about 195–200 µg/mL to about 127 µg/mL over 2 h. The authors attribute this decline to absorption, "which reduced the number of nanodroplets present in the donor compartment". Their receivers peaked at about 10.0 (HPMCAS) and 9.4 µg/mL (HPMC), values that "correlated well" with solvent-shift solutions of comparable concentration, and stayed above the receiver level of a solution at the amorphous solubility for the whole 120 min. The authors attribute this "in part" to the droplets replenishing absorbed drug. The 70:30 HPMCAS ASD stayed slightly below the amorphous solubility, so there was no LLPS; its donor stayed nearly constant after 30 min, which "indicates" replenishment by the residual ASD, and its receiver plateaued at about 6.0 µg/mL. The 50:50 HPMCAS ASD approached the amorphous solubility only after about 100 min, and HPMC gave similar profiles. The 90:10 PVPVA ASD held the receiver nearly constant at about 8.8 µg/mL, which the authors read as a reservoir provided by the agglomerates ("Most likely … micron-sized species"). The 50:50 PVPVA ASD released drug gradually until, from about 80 min, both donor and receiver concentrations fell: the donor had crystallized, which polarized light microscopy of a sample taken at 100 min showed as birefringent particles (Figure S3).

Figure 6G ranks the formulations (Table C). The authors write that the HPMCAS and HPMC 10% ASDs "clearly showed higher amounts of drug transferred as compared to other formulations", that 50:50 PVPVA transferred the least because it crystallized, and that integrating the receiver profile reveals effects of dissolution rate, droplets and crystallization that are "less readily discernable from the dissolution profiles".Card note X6: the Figure 6G caption says "amount of drug transferred", but the axis shows AUC in µg/mL·min; the amount is the plotted value times 4 mL/min, as in the last column of Table C.

Main result 5: ASD-derived and solvent-shift droplets behave alike, and more droplets sustain transfer longer. Over 240 min, the receiver profiles of a solvent-shift solution and of the dissolving 90:10 HPMCAS ASD overlapped for the first hour, both peaking at about 10.7 µg/mL; later the ASD curve ran slightly higher (about 9.9 against 9.3 µg/mL at 100 min, about 7.9 against 7.4 at 240 min; Figure 7a). The fluorescence ratio fell the same way for both: about 1.2 for the first hour, about 0.75 at 150 min, and about 0.45 at 210 min, crossing the amorphous-solubility level near 180 min (Figure 7b). The authors take this as the gradual depletion of droplets as free drug crosses the membrane and droplets dissolve to hold the amorphous solubility, "irrespective of the route of supersaturation", and conclude that the larger ASD-derived droplets did not give "significant differences" in absorption. In the dose series (Figure 8), the receiver maximum of the 90:10 HPMCAS ASD rose from about 9.2 to 10.0 to 12.2 µg/mL at 100, 200 and 500 µg/mL, and the receiver at 120 min from about 6.1 to 8.5 to 10.3 µg/mL. The 100 µg/mL dose, only slightly above the amorphous solubility, gave a "much steeper decline". Although free drug should be the same at all three doses, the transfer was higher and more sustained at higher dose; the authors attribute this to "a greater number of drug-rich nanodroplets", and suggest that Cmax "can potentially be dependent on the number of nanodroplets flowing through the membrane module".Card note X5: the Discussion cites Figure 6 for this dose series; the data are in Figure 8.

Table D. Total drug released from the 50% loading ASDs (dose 10,000 µg), read from Figures 9 and S5 (approximate). With absorption, total = drug in the donor + drug transferred.

Main result 6: the absorptive sink speeds up release from slow ASDs and changes their ranking. For all three 50% loading ASDs, more drug was released when absorption ran at the same time (Figure 9, Table D). For HPMCAS the curves overlapped up to about 40 min and then diverged; for HPMC the closed test was ahead for the first 50 min or so; for PVPVA the absorptive run was ahead throughout. The authors conclude that the absorption compartment "clearly influenced" the dissolution rate of the slow-releasing formulations: removing drug lowered the donor concentration, which "promoted greater ASD dissolution relative to the closed compartment system, better reflecting the environment expected in vivo". The ranking changed as well: in the closed vessel HPMC released the most, followed by HPMCAS and PVPVA, whereas with the sink all three released at a similar rate over the first 60 min (Figure S5).

Controls and longer runs. The solvent-shift solutions serve as the control for the ASD runs: they give droplets of known amount without any undissolved solid, and the ASD results line up with them (Main result 5). The 4 h runs of the 10% loading ASDs separate droplets from agglomerates (Figure S6). For the HPMCAS and HPMC ASDs the donor fell to the amorphous solubility after about 200 min, "indicating depletion of the drug-rich phase", and until then the receiver stayed above the amorphous-solubility level. The 90:10 PVPVA ASD held about 100 µg/mL in the donor and about 9.3 µg/mL in the receiver for the first 110–120 min, then fell to about 4.4 µg/mL by 240 min. The authors "speculate" that fewer agglomerates were left to replenish absorbed drug at the same rate, and conclude that, although all three ASDs reached similar free drug concentrations, nanodroplets gave a longer reservoir effect and a higher AUC than agglomerated amorphous solid.

Discussion

How the authors connect the findings. The argument runs in four steps. Free, unionized drug is what crosses the membrane, and above the amorphous solubility its activity is fixed. Yet in this apparatus transfer kept rising with the amount of drug present as droplets, and the droplets themselves cannot cross. The authors therefore infer that the droplets raise the mass transfer coefficient, while also replenishing free drug as it is absorbed. Whether an ASD gets this benefit depends on whether it dissolves fast enough to pass the amorphous solubility, which in turn depends on drug loading and polymer.

The 10% PVPVA ASD sits between the two branches: it dissolves fast, but PVPVA raises the amorphous solubility to 94 µg/mL and the droplets agglomerate, so the reservoir is made of larger amorphous particles. Over 2 h it transferred "nearly the same amount" as the cellulose ASDs; over 4 h it ran short after about 150 min. The authors' summary of the whole chain is hedged: formulations that undergo LLPS "may enhance absorption behavior not only by providing a reservoir and replenishing drug lost due to absorption, but also by contributing to enhancements in the mass transfer coefficients".

What raises transfer above the amorphous solubility: three untested explanations. The authors do not settle the mechanism; they offer three possibilities and say that a systematic study "is required".

• Convection in the boundary layer. In laminar flow through a tube the velocity is highest in the center and zero at the wall, with a matching concentration profile. "Possibly", nanoparticles moving by Brownian motion in the aqueous boundary layer cause nanoscale convection that steepens the concentration gradient at the membrane, an effect described for nanofluids (refs 51, 52).
• Dissolution-limited absorption. "Alternatively, there could be some extent of dissolution rate limited absorption": if free drug near the membrane is removed faster than droplets can resupply it, more droplets, with more total surface, would keep the local free concentration higher.
• Size-dependent solubility. The solubility of a particle rises exponentially as its radius shrinks, noticeably at the nanometre scale (ref 53; the paper states this relation in words and does not print an equation). Droplets of about 200 nm should dissolve very fast and shrink as they do (refs 54, 55); near a few nanometres they "may lead to higher free drug concentrations". With a single-pass residence time of about 10 s in one fiber, "it is plausible" that the apparatus captures this effect.

None of these was measured: free drug in the donor during transport, the concentration gradient in the boundary layer and droplet size during dissolution in the fibers are all inferred.

Where the approach applies. The authors argue that the apparatus resembles the intestine in its tubular geometry and large absorptive area, and that, "if this occurs in vivo", it is "clearly important" to assess colloidal species in vitro when choosing a formulation; they cite one in vivo study suggesting colloids help absorption (Wilson 2018, ref 56). They also note that its in vivo relevance "needs further investigation". The data cover one drug, one buffer at pH 6.8, one membrane type and three polymers.

What it suggests for formulation. The authors state three practical points: low drug loading ASDs that exceed the amorphous solubility give an absorption advantage; absorption profiles "did not always concur" with conclusions drawn from dissolution profiles alone; and an absorptive compartment gives "a more meaningful comparison between different formulations" and a more realistic dissolution rate for slowly dissolving ASDs.

Note by the AI writer (not discussed in the paper): for atazanavir at a 200 µg/mL dose, only the 10% loading ASDs passed the amorphous solubility, so the window of loadings that produce droplets was narrow here. A closed-vessel UV value above the amorphous solubility mixes droplets and free drug, and here it even exceeded the dose; it is not a measure of absorbable drug. And a polymer ranking obtained in a closed vessel for slowly dissolving ASDs (HPMC first) disappeared once a sink was present, which argues for checking such rankings with absorption before choosing a polymer.

Limitations

Limitations stated by the authors. The authors state that UV concentrations above the amorphous solubility are not quantitative because droplets absorb and scatter light. They do not resolve the mechanism of the transfer increase above the amorphous solubility and call for a systematic study of colloids, flow and the boundary-layer gradient, and for work on droplet dissolution. They describe the in vivo relevance of the higher mass transfer coefficient as needing "further investigation". Their account of the 10% PVPVA ASD rests on agglomerates that could not be detected after filtering ("Most likely"), and of its 4 h behaviour on a reduced amount of agglomerates ("We speculate"). They report that about 5–10% of the drug was recovered from the methanol wash after each run, that is, held in the apparatus.

The AI writer's own judgement (1): what is measured and what is inferred. The rise of Cmax and AUC above the amorphous solubility is measured directly, at five concentrations, in two quantities. The reading of that rise as a higher mass transfer coefficient tied to droplet number is an inference. Free drug in the donor during transport was never measured; the claim that it equals the amorphous solubility at every dose is assumed from the phase behaviour. Droplets were counted only up to 150 µg/mL, while the transfer data reach 500 µg/mL; above 150 µg/mL the number is inferred from the fluorescence ratio and the DLS count rate. The correlation with droplet number is therefore direct only from 75 to 150 µg/mL.

The AI writer's own judgement (2): numbers that need care. Several printed values do not fit together. The upper Cmax fit in Figure 4 does not reproduce its own points, and the drawn fit lines above the amorphous solubility do not follow the printed equations, although the printed AUC equations do match the points. The text gives the HPMC solvent-shift droplets as 350 nm, Table 2 as 311 nm. The pKa of ATZ is printed as 4.52 and as 4.42. Figure 6G is labelled as an amount but plots AUC. The amorphous-solubility lines drawn in the figures vary with the polymer, and no amorphous solubility with HPMC is reported. Replicate numbers and error types are not stated outside Table 1, and no statistical test is reported; the 10% PVPVA ASD is described as transferring "nearly the same amount" as the cellulose ASDs and as "not significant" in the SI, while the same section of the main text says the cellulose ASDs "clearly showed higher amounts" (AUC about 985 against about 1170–1220 µg·min/mL).

The AI writer's own judgement (3): absolute amounts. Using the paper's own relation (amount = AUC × 4 mL/min) gives amounts that the donor cannot always supply. For the 30 µg/mL solution, an AUC of about 350 µg·min/mL over 100 min corresponds to about 1400 µg, about 93% of the 1500 µg in the 50 mL donor, yet the receiver concentration fell only from about 3.9 to about 2.9 µg/mL, which implies that most of the drug was still in the donor. For the 100 µg/mL dose of the 90:10 HPMCAS ASD, the drug transferred (about 3800 µg) plus the drug left in the donor at 120 min (about 2350 µg) exceeds the 5000 µg dose. The donor concentrations of the solution runs are not reported, so the reason cannot be traced. Cmax and AUC are best read as relative measures within this apparatus; the absorptive totals in Figure 9, which rest on the same relation, share this uncertainty. The comparison between solvent-shift and ASD runs also carries a difference in polymer concentration: 1 mg/mL HPMCAS in the solutions, against 1.8, about 0.47 and 0.2 mg/mL polymer for fully dissolved 10, 30 and 50% loading ASDs.

Conclusion

The paper makes three contributions. First, it shows in a fast hollow-fiber apparatus that membrane transfer of atazanavir keeps rising above the amorphous solubility as drug-rich nanodroplets of constant size, about 200 nm, increase in number, although the free drug concentration is fixed; the authors read this as a higher mass transfer coefficient and leave its mechanism open. Second, it compares nine ASDs with and without an absorptive sink: only the 10% loading ASDs passed the amorphous solubility, the HPMCAS and HPMC ones formed nanodroplets and transferred the most drug, PVPVA formed agglomerates that sustained transfer over 2 h but not over 4 h, and the crystallizing 50:50 PVPVA ASD transferred the least. Third, it shows that ASD-derived droplets behave like solvent-shift droplets, that a larger dose sustains transfer longer, and that the sink speeds up release from slowly dissolving ASDs and changes their ranking by polymer. The authors' own summary is that the absorptive dissolution testing apparatus "is an efficient tool" for understanding the dissolution and absorption of enabling formulations such as ASDs.

The results hold for one weakly basic drug at pH 6.8 and 37 °C in one apparatus. What a reader can take forward is the comparison itself: for a supersaturating formulation, the amount of drug that crosses a membrane, measured while the formulation dissolves, separates formulations that a closed dissolution test ranks differently or cannot separate at all.