Residual crystals in an amorphous dispersion: why their shape, not their weight, decides how much supersaturation is lost

Background and motivation

An amorphous solid dispersion (ASD) disperses a poorly soluble drug in a hydrophilic polymer so that, under non-sink conditions, dissolution can raise the dissolved drug concentration above the crystalline solubility. That supersaturation is the point of the formulation, but it is also a driving force for crystallization: if crystals nucleate or grow during dissolution, the extra dissolved drug is lost (Williams 2013, ref 1; Hancock and Parks 2000, ref 4; Almeida e Sousa 2015, ref 5). C1 Polymers can slow or prevent nucleation of amorphous drugs both in the solid and in supersaturated solution (Ilevbare 2013, ref 10; Trasi 2015, ref 11). C7

The difficulty the paper starts from is that real amorphous products are not always free of crystals. Water and heat during manufacture or storage can crystallize the drug; the formulation patent of the ivacaftor product Kalydeco allows up to 15% crystalline drug in the dispersion; a commercial tacrolimus product contains a low level of crystalline seeds formed during manufacture; and a lyophilized paclitaxel product was found to contain trace crystals (Zha 2014, ref 13; Trasi 2017, ref 14; Schmitt 2015, ref 15). Common methods (X-ray diffraction, thermal analysis, microscopy, Raman) struggle below about 1% crystallinity (Wanapun 2010, ref 18). The authors conclude that it "may not be possible" to always make ASDs completely free of residual crystals. C1·C7 Such seeds can remove the solubility advantage if their growth is not inhibited during dissolution (Alonzo 2012, ref 19). C8

Two gaps follow. Little work had looked at how residual crystals affect ASD dissolution, and the seeding studies that existed used crystals from conventional solvent crystallization, that is, bulk crystalline drug (Ilevbare 2013, ref 10; Alonzo 2012, ref 19). Seeds that form inside an ASD may be quite different from that bulk material, and crystals grown in different environments are known to grow at different rates (Schram 2016, ref 20; Jackson 2016, ref 21). C2 Crystallinity limits, however, are set as a weight percent, usually at the detection limit of the analytical method. C54

The paper therefore tests the hypothesis that seeds of different morphology, compared at the same initial weight percent crystallinity, affect the dissolution of an ASD differently. C9 Paclitaxel was chosen because it crystallizes as needles, and HPMCAS-MF as the polymer. Seeds were made under different conditions and added to the dissolution medium; as-received crystals served as bulk API seeds for comparison, and scanning and transmission electron microscopy (SEM, TEM) were used to understand the seed properties. P6·P9·P10·P11

Background concepts

Supersaturation. The supersaturation ratio compares the thermodynamic activity of the dissolved drug with its activity at crystalline saturation (Section 2, eq 1):

Here $a$ is the activity of the solute, $c$ the drug concentration in the supersaturated solution, ${\gamma }^{\prime }$ the activity coefficient, and the asterisk marks the values at saturation. In plain terms: S says how far the solution is above the crystalline solubility. In a simple buffer the authors take the ratio of activity coefficients as 1, so S is just the concentration divided by the crystalline solubility. E1·C10 For paclitaxel this gives S = 88 at the amorphous solubility (31.6/0.36). R2·E1

The highest supersaturation an ASD can give. When the drug concentration reaches the amorphous solubility, the drug separates as a drug-rich amorphous phase instead of rising further, provided crystals do not form first; the amorphous solubility is therefore the maximum supersaturation a solubility-enhancing formulation can create (Taylor and Zhang 2016, ref 31; Mosquera-Giraldo 2015, ref 34; Ilevbare and Taylor 2013, ref 35). C20·C34 The paper sketches this as a concentration–temperature diagram (Figure 13): above the amorphous solubility lies liquid (glass)–liquid phase separation, then a zone of primary nucleation, below the metastable boundary a zone where only secondary nucleation and crystal growth on existing crystals occur, and finally the crystalline solubility. C34

Nucleation and growth. Crystallization has two steps. Primary nucleation creates the first crystals in a crystal-free solution; the measured induction time is the time for a critical nucleus to form plus the time for it to grow to a detectable size. E6 Crystal growth adds molecules to crystals that already exist, and secondary nucleation makes new crystals from or on existing ones. C34 A seed is a crystal already present; it bypasses nucleation entirely, which is why a polymer that blocks nucleation may still fail to protect a supersaturated solution that contains seeds. C36

How a crystal face grows, and how a polymer can stop it. In adsorption layer theory, molecules adsorb on the crystal surface, join kink sites along growth steps, and the steps sweep across the face. To start a new layer, a two-dimensional (2D) nucleus, an island one molecule thick, must form, and it is stable only above a critical radius (Burton, Cabrera and Frank 1951, ref 23; eq 2): C11

Here ${\rho }_c$ is the critical radius, $\gamma$ the edge free energy, $a$ the size of a growth unit, $k$ the Boltzmann constant and $T$ the temperature. In plain terms: the higher the supersaturation, the smaller the island that can start a new layer. E2 If polymer molecules adsorb at kink sites along a step, they pin it; the step must bulge between the pinning points, and its average speed depends on their spacing $l$ (Kubota 2001, ref 24; Kubota and Mullin 1995, ref 25; Cabrera and Vermilyea 1958, ref 26; eq 3): C11

Here $\upsilon$ is the time-averaged step velocity with adsorbed polymer and ${\upsilon }_0$ the velocity of a free, straight step (the printed equation writes the velocities with the symbol ϑ). In plain terms: polymer molecules spaced much wider than the critical nucleus hardly slow the step; as the spacing approaches the critical radius the step slows, and if the critical radius exceeds the spacing the step stops. E3 Because ${\rho }_c$ grows as supersaturation falls, the same adsorbed polymer can let a crystal grow at high supersaturation and stop it at lower supersaturation; this is the paper's central theoretical tool. E2·E3·C39

Needles and their growth area. A needle forms when the end faces grow much faster than the side faces. For a given mass, long thin needles therefore have few fast-growing ends, while short needles or more equant crystals offer more. The paper measures this as the crystal end area per gram and the aspect ratio, length divided by width. C14·C48·E5·P13

Methods in detail

The study has five parts that build on each other: a solubility and nucleation baseline; the making and characterization of four seed types; seeded growth in plain supersaturated solution, without and with HPMCAS; seeded dissolution of the ASD itself; and a calculation that compares the critical nucleus with the spacing of adsorbed polymer. All solution work used 50 mM pH 6.8 phosphate buffer (ionic strength 0.16) and, where stated, 37 °C and 300 rpm. M5·P1·P5·P7

Part 1: the solubility and nucleation baseline

Problem. To know what supersaturation the ASD can reach, and whether HPMCAS can hold it without seeds, the authors needed the crystalline and amorphous solubility and the nucleation behaviour. C12·C13

What they did. The crystalline solubility of the dihydrate (confirmed as the dihydrate by X-ray diffraction and thermogravimetry, Figures S1 and S2) was measured by stirring excess solid in buffer for 48 h at 37 °C, removing solid by ultracentrifugation at 35000 rpm and analysing the supernatant by HPLC. P1·R19·R20 The amorphous solubility was measured in buffer containing 20 µg/mL HPMCAS-MF by three methods: the concentration at which light scattering at 400 nm rose as a methanol stock was pumped in at 25 µL/min; the concentration at which the emission peak ratio of 1 µM pyrene changed; and the concentration left in solution after a drug-rich phase, created at 40 µg/mL, was pelleted by ultracentrifugation. All were run in triplicate. P2·P3·P4 For nucleation, paclitaxel was added from the methanol stock to 50 mL of buffer at 30.7 µg/mL, with or without 20 µg/mL HPMCAS, and the induction time was taken as the rise in extinction at 400 nm. P5

Why it matters. The amorphous solubility sets the supersaturation (S = 88) at which all seeded tests were run, and the nucleation test shows what HPMCAS does when no seeds are present. R2·R3

Part 2: four seed types with the same chemistry and different shapes

Problem. To test morphology at equal mass, the authors needed seeds of one solid form but different size, shape and history. C9

What they did. Methanol stock was added to 15 mL of buffer to give 5.8 µg/mL (S = 16) or 28.8 µg/mL (S = 80), and the crystals grew for 5.5 h so that all seeds had a common history. Half of each batch was then broken with a probe sonicator (40% amplitude, 4 s on and 2 s off, 10 min, on ice). This gave four seed types: S16, S80, S16 w/ s and S80 w/ s (Table 2). As-received crystals, slurried in buffer for 5.5 h to wet them, served as bulk API seeds ("seeds from bottle"). P6 SEM of 100 crystals per sample gave length (c) and width (b) distributions; assuming cuboid crystals, the crystal end area per gram was estimated from these dimensions; and the mean aspect ratio was calculated. TEM and SEM were used to image the tips of S16 and S80. P10·P13·P14·C18 The formula for end area per gram, and the crystal density it needs, are not printed. E4

Part 3: seeded growth in plain supersaturated solution

Problem. Before adding the complication of a dissolving ASD, the authors wanted to see how the four seed types grow at the highest supersaturation an ASD can produce. C20

What they did. The seed suspension was diluted to 18 wt% seeds relative to the paclitaxel that would be added, in a final 15 mL; HPMCAS was added before supersaturation was created (33 µg/mL in the methods; the results and figure captions give 31.6 µg/mL) or left out; after 2 min of stirring at 37 °C the methanol stock was added to 31.6 µg/mL (S = 88), and the dissolved concentration was followed with an in situ UV probe at 230 nm, minus the 400 nm extinction to correct for scattering by the seeds. P7·X1 After growth without polymer the crystals were sized again by SEM (labelled -2), and after growth with HPMCAS they were imaged by TEM (labelled -3), where 20 widths of the thin "fingers" at the crystal ends were measured per sample. P10·P11

How it differs from earlier work. The seeds come from controlled antisolvent crystallization in the same buffer, at known supersaturation, and are compared at equal mass with and without sonication, instead of using bulk crystalline API as the only seed. C2·P6

Part 4: seeded dissolution of the ASD

Problem. The real question is what seeds do to the supersaturation that a dissolving ASD produces. C9

What they did. A 49/51 (wt%) paclitaxel–HPMCAS-MF dispersion was made as a thin, clear film by rotary evaporation from tetrahydrofuran (water bath 45 °C) on the wall of a 20 mL vial; the drug in the film was enough to reach the amorphous solubility in 15 mL if it all dissolved. P8·R21 Without seeds, 15 mL of buffer already saturated with crystalline paclitaxel was added; with seeds, 15 mL of seed suspension was added, each suspension diluted with saturated buffer so that all seed types carried the same mass (Figure 2). The dissolved concentration was followed by UV (230 nm minus 400 nm) for 16 h, and at the end the residual concentration was measured by HPLC after filtration through a 0.45 µm glass fibre filter. P9 The temperature and stirring of these runs and the basis of the 18 wt% are not stated in the dissolution method. X9·X10

Part 5: comparing the critical nucleus with the polymer spacing

Problem. Eq. 2 needs the crystal–water edge energy of paclitaxel, which could not be determined experimentally. C37

What they did. The authors used literature interfacial tension values for three compounds spanning a range of log P as stand-ins: methylene iodide (log P 1.6), octane (5.15) and felodipine (3.4). The growth-unit area, 2.64 nm², was taken from the length and width of a paclitaxel molecule in the crystal structure RIGKUP. With T = 310 K and ln S = 4.47 they calculated ρc at S = 88 (Table 3) and then plotted ρc against S together with the measured finger widths at the residual supersaturation reached after 16 h (Figure 14). P12·P15·R15·R16·R17

Why it works, in the authors' logic. If the finger widths mark the spacing of adsorbed HPMCAS, then eq 3 says growth can continue while ρc is smaller than that spacing and should stop when supersaturation has fallen far enough for ρc to reach it. C27·C39

Experimental analysis

The baseline: S = 88, and HPMCAS blocks nucleation

The crystalline dihydrate dissolved to 0.36 ± 0.01 µg/mL. The three amorphous-solubility methods gave 31.5 ± 0.8 (light scattering), 30.9 ± 1.8 (pyrene fluorescence) and 32.3 ± 0.4 µg/mL (ultracentrifugation), which the authors call good agreement; the average, about 31.6 µg/mL, is about 88 times the crystalline solubility (Table 1). R1·R2·C12 Without polymer, unseeded paclitaxel at this level crystallized within 6 min; with 20 µg/mL HPMCAS the solution stayed supersaturated for more than 16 h, so HPMCAS is a "highly effective" nucleation inhibitor for paclitaxel (Section 5.2). R3·C13 The methods give 30.7 µg/mL for this test, which is S ≈85 rather than the stated 88; the difference is small but worth knowing. X2

The seeds: two kinds of long needle, and two kinds of short fragment

All four seed types were needles (Figure 3). The unsonicated seeds were long and thin; sonication broke them into fragments almost all shorter than 2 µm. R4·R5 By length, S80 had relatively more short crystals than S16, which the authors explain by classical nucleation theory: at higher supersaturation the nucleation barrier is lower, more nuclei form, and the crystals end up smaller ("can be readily explained"). R5·C16 By width, the authors see no significant difference among S16, S80 and S80 w/ s, while S16 w/ s became narrower (Figure 4); no statistical test is given. C17·X9 Table A collects the measures that the argument rests on.

Table A. Seed properties before growth, read from Figures 4, 5 and 8 (approximate; 100 crystals per sample; end area estimated for cuboid crystals). R5·R6·R9

S16 and S80 thus have the same end area per gram, and sonication raised it about 7–9-fold. The text says "about 7–8 fold" and, later, about 7 times for S80 w/ s; the plotted bars give about 8.8 for the S16 pair and about 7.4 for the S80 pair. R6·C19·X13 The tips also differ (Figure 16): S16 needles end in narrow, smooth, pointed tips, S80 needles in flat, rough-edged ends. R18

Growth without polymer: more ends, faster early loss, and fine crystals from long needles

With 18 wt% seeds at S = 88 and no polymer, the dissolved concentration fell at once for every seed type (Figure 6). R7 Table B shows the course over the 10 min recorded.

Table B. Apparent paclitaxel concentration (µg/mL) without polymer, start 31.6 µg/mL, 18 wt% seeds, read from Figure 6 (approximate; n not stated). R7·X9

The sonicated seeds removed supersaturation fastest at first, which the authors attribute to the larger area of growth sites at their many ends ("presumably"). R7·C21 S80 and S16 have the same end area but did not behave alike: S80 was the slowest seed type throughout, while S16 started slower than the sonicated seeds, crossed below them after about 5–6 min and ended lowest. The authors read this as "perhaps suggesting" events other than growth at the needle ends. R7·C22 Note by the AI writer (not discussed in the paper): unseeded paclitaxel at this supersaturation crystallizes within 6 min, and Figure 6 has no unseeded control, so primary nucleation may contribute to the second half of these curves. X14

Size distributions after growth (Figure 7) and the aspect ratios (Figure 8) help explain the S16 result. The aspect ratio rose for S80 (about 20.1 to 23.2), S16 w/ s (about 7.3 to 14.7) and S80 w/ s (about 4.7 to 13.7) but fell for S16 (about 23.6 to 17.7). R9·C24 S16 did not shift to longer crystals; instead the share of crystals under 2 µm rose from about 38 to about 53 of 100. The sonicated seeds clearly grew longer (to about 12–13 µm at most), and S16 w/ s also widened; the authors call the widths of the others comparable before and after, although the S80 and S80 w/ s histograms also shift somewhat wider. R8·C23·X12 SEM after growth (Figure 15) shows small needle-like crystals on the surfaces of larger ones. The authors interpret the fall in S16 aspect ratio, and the smaller increase for S80, as secondary nucleation producing fine low-aspect-ratio crystals, and argue that these new crystals add growth sites that "can further accelerate" desupersaturation; in the sonicated seeds secondary nucleation also happened, but growth at their many ends dominated. R10·C43·C44 The discussion cites Figure 7 for these aspect ratios; they are in Figure 8. X6

Growth with HPMCAS: dendritic tips

Seeds grown at S = 88 in the presence of HPMCAS looked different (Figure 9): the needle ends split into bundles of thin, parallel fingers, a dendritic growth, and the many fine crystals produced when these dendrites broke made size distributions impossible. R11·C25 The authors explain the dendrites by HPMCAS adsorbing on the seeds and pinning the steps, so that crystal can grow only between the adsorption sites, as in the Kubota–Mullin model ("can be explained"), and they take the width of each finger as the distance between neighbouring adsorption sites. C26·C27 From 20 measurements per sample, the mean widths were about 16.8 nm (S16-3), 16.0 nm (S80-3), 10.5 nm (S16 w/ s-3) and 14.3 nm (S80 w/ s-3) (Figure 10). The text summarizes this as 10 to 16 nm in the results and about 10–20 nm in the discussion. R12·C28·X3 The same breakage of dendrites means that the effect of HPMCAS on secondary nucleation could not be judged. C45

Seeded ASD dissolution: the seed type decides what is left

Without seeds the ASD dissolved to about 31 µg/mL, the amorphous solubility, within about 1.5 h and showed no desupersaturation over 16 h (Figure 11), in line with HPMCAS inhibiting nucleation. R13·C29 With 18 wt% seeds, every run still first reached about 32–33 µg/mL within about 2–4 h, which the authors read as dissolution being much faster than growth, "quite a remarkable observation" given the seed load. R13·C31·C47 Desupersaturation followed, by crystal growth: HPMCAS cannot completely block growth, although the loss is far slower than without polymer, hours instead of minutes. C30·R7·R13 The sonicated seeds gave similar profiles that were fast at first and then slowed; S16, S80 and bulk API gave a steadier slope, S80 faster than S16 and bulk API. C31 Table C lists values read at 8 and 16 h and the HPLC values measured at 16 h (Figure 12).

Table C. Paclitaxel concentration (µg/mL) during dissolution of the 49/51 paclitaxel–HPMCAS ASD with 18 wt% seeds: UV apparent concentration read from Figure 11 and residual concentration by HPLC read from Figure 12 (all approximate). R13·R14

By HPLC, bulk API and S16 left about 25 and 19 µg/mL ("considerable residual supersaturation"), while S80, S16 w/ s and S80 w/ s left about 10, 8 and 9 µg/mL. R14·C32 All are far above the crystalline solubility, which the authors take to mean that HPMCAS is "a very effective crystal growth inhibitor at somewhat lower supersaturations". C33 The UV and HPLC numbers do not agree for the seeded runs: the UV readings at 16 h are about 2–10 µg/mL higher, and the two methods rank S16 and bulk API in opposite order. The unseeded run agrees. The paper does not discuss the difference; the HPLC values, measured on filtered samples, are the ones the authors quote. X4

Critical nucleus against polymer spacing

With the three stand-in interfacial tensions (4.16, 5.08 and 3.90 × 10⁻²⁰ J/nm²), eq 2 gives ρc = 5.7, 7.0 and 5.4 nm at S = 88, "5~7 nm" in the text, smaller than every measured finger width. R15·C38 On that basis the authors conclude that HPMCAS cannot prevent growth at the amorphous solubility because the critical nucleus is very small, which "presumably" results from the very high supersaturation; the polymer still poisons the interface, giving much slower growth and very thin crystals. C38 Table D shows the comparison made in Figure 14 at the supersaturation left after 16 h.

Table D. Values read from Figure 14 (approximate); the residual supersaturation is the HPLC residual concentration divided by the crystalline solubility. R17·R12

The authors' reading is that growth slows as the spacing approaches ρc and stops when they are equal; for S16 w/ s and S80 w/ s the spacing is "similar" to ρc at the 16 h supersaturation, which they say explains the near-zero growth rate at that time, and they present Figure 14 as "the theoretical underpinning" for residual supersaturation seen earlier in seeded systems (Lu 2017, ref 38). C39·C40·C41 Note by the AI writer (not discussed in the paper): the S16 w/ s point lies close to the curve, but the S80 w/ s spacing is still about 1.7 times ρc, and by eq 3 that leaves about 40% of the free step speed. X5 The curve's γ is not stated; its readings match eq 2 with the mean of the three Table 3 values. X8

Discussion

The authors' chain of reasoning

The discussion (Section 6) ties the results into one picture. The overall dissolution profile of an ASD depends on the interplay of the dissolution rate and the crystallization kinetics. C35 HPMCAS removes primary nucleation from the picture, so an unseeded paclitaxel–HPMCAS ASD holds S = 88 for hours; once seeds are present, what remains is a race between dissolution and growth on the seeds. C36·C46 The authors assume that the polymer also suppresses secondary nucleation, citing a suggestion in the literature ("Assuming"), and that dissolution is much faster than growth because the amorphous solubility is still reached. C46·C47 The seeds then decide the outcome through their growth area and tip structure, while HPMCAS decides how far growth can go through the spacing of its adsorption sites.

Within this chain the authors make three more specific arguments. First, sonication multiplies the needle ends: the roughly 7-fold larger end area of S80 w/ s seeds "leads to" faster growth without polymer and a steeper desupersaturation slope during ASD dissolution. C49 Second, S16 w/ s seeds, which also became narrower when sonicated, grew wider as well as longer, and this "most likely explains" why they caused the most rapid and extensive desupersaturation. C50 Third, the supersaturation at which seeds form changes them: S16 and S80 have similar end areas and size distributions but different growth kinetics, and the pointed, smooth S16 tips versus the flat, rough S80 tips "most likely" reflect different growth mechanisms that give different numbers of active sites for growth and polymer adsorption, in line with AFM work showing that seeds grown in different environments differ in interface structure (Schram 2016, ref 20). C51·C52·C53

What the authors take from it for formulation

The authors' central message is stated strongly: "Our study clearly demonstrates that for ASD performance, the mass of crystal seeds is not the relevant parameter", rather the available growth area and interface structure of the seeds (abstract), or the growth areas and their growth rates (discussion). C5 In assessing residual crystals, crystal morphology and growth area, interface structure and the effectiveness of additives in poisoning growth "need to be taken into account". C6 Crystallinity limits set as a weight percent, usually at the detection limit of the method, are called "arbitrary": percent crystallinity "per se is not a predictive indicator", and the number of growth sites matters more, although it is hard to assess. C54 With 18 wt% seeds, depending on the seeds, the ASD showed either virtually no effect or significant desupersaturation, and high-aspect-ratio crystals in an ASD are "likely" less harmful per unit weight than more equant ones, all other factors being equal. C55·C56 The authors also turn to modelling: physiologically based pharmacokinetic (PBPK) absorption models usually assume that the concentration returns to the crystalline solubility after crystallization, which they say is "clearly not supported" by experiment or theory, so improved models are needed. C42 They close with a call for more work to set appropriate limits on crystal content in amorphous formulations. C57

Note by the AI writer (not discussed in the paper): for a drug that crystallizes as needles, any process step that breaks crystals, such as milling, high-shear granulation or compression, could turn a harmless trace of long needles into many growth ends; reporting habit and size alongside percent crystallinity would make this visible. A nucleation test alone also overstates how well a polymer protects supersaturation once crystals are present: here HPMCAS held an unseeded solution at S = 88 for more than 16 h but could not stop seeded growth at the same supersaturation. R3·R13

Limitations

Limitations stated by the authors. The authors note that the effect of HPMCAS on secondary nucleation could not be evaluated, because fines from broken dendrites cannot be told apart from secondary nuclei, and that the analysis of the seeded ASD profiles therefore assumes suppression. C45·C46 They describe reaching the amorphous solubility with 18 wt% seeds as an observation that "needs to be further considered". C47 The crystal–water interfacial tension of paclitaxel could not be measured, so literature values for other compounds were used in eq 2. C37 The setting of crystallinity limits is described as an area that "deserves more investigation". C57

The AI writer's own judgement (1): the size and consistency of the evidence. The central contrast is large: at equal seed mass, sonicated seeds left about 8–9 µg/mL and long S16 needles about 19 µg/mL by HPLC, and the sonicated seeds also removed supersaturation fastest in plain solution. R14·R7 But replicate numbers and the meaning of the error bars are not stated for the growth, dissolution and imaging data, and "no significant difference" in width is claimed without a test. X9 The UV and HPLC concentrations disagree at 16 h by up to about 10 µg/mL and rank S16 and bulk API in opposite order, with no explanation. X4 The aspect-ratio ranking does not hold everywhere: S80 seeds, with an aspect ratio of about 20 and the same end area as S16, left about 10 µg/mL in the ASD, close to the sonicated seeds, while without polymer they were the slowest seed type, and the reversal between the two tests is not discussed. X11 The bulk API was not sized at all, so it cannot be placed on the end-area scale. X17

The AI writer's own judgement (2): the nucleus–spacing argument. The critical radius rests on interfacial tensions of methylene iodide, octane and felodipine, not paclitaxel, and with the units printed in Table 3 (γ in J/nm², a in nm²) eq 2 gives a dimensionless number rather than nanometres; the printed ρc values are reproduced only by reading that number as nm, so they are best treated as order-of-magnitude estimates. X7·E2 The spacing of adsorbed polymer is inferred from the width of dendrite fingers, and the adsorption itself was not measured. C27·C4 The claim that growth stops when ρc reaches the spacing fits the S16 w/ s point but not clearly the S80 w/ s point. X5

The AI writer's own judgement (3): conditions and set-up. Some conditions are stated inconsistently: the HPMCAS concentration in the seeded-growth assay is 33 µg/mL in the methods but 31.6 µg/mL in the text and captions, and the growth is described once as at S = 80 and elsewhere at S = 88; the induction test was run at 30.7 µg/mL (S ≈85) but described as at S = 88. X1·X2 How the seed mass was set is not described, and for S16 the 18 wt% target is at the edge of what the 5.8 µg/mL generation step can yield. X10 No desupersaturation curves of seeded growth with HPMCAS are shown, so in the polymer case growth and dissolution are never separated. X15 All seeds were suspended in the medium rather than formed inside the dispersion, and the work covers one drug, one polymer, one drug loading and one seed load; the authors' statement about crystals "present in an ASD" goes beyond that set-up. P9·C56

Conclusion

The paper makes three contributions. First, it shows, for paclitaxel and HPMCAS, that seeds of the same drug at the same 18 wt% can leave anywhere from about 8 to about 25 µg/mL in solution after 16 h of ASD dissolution, depending on how they were made. R14 Second, it links that spread to measurable seed properties: sonication multiplies the end area per gram about 7–9-fold and makes the seeds much more damaging, and seeds grown at higher supersaturation have rougher tips and, with HPMCAS, behave more like the sonicated ones. R6·R18·C5·C52 Third, it explains why HPMCAS, an excellent nucleation inhibitor, only slows growth: at S = 88 the 2D critical nucleus, about 5–7 nm, is smaller than the 10–16 nm spacing of adsorbed polymer, and growth should stop only when supersaturation has fallen far enough for the two to meet. R3·R15·R12·C38·C39

The authors' practical message is that residual crystallinity should be judged by the growth area, interface structure and origin of the crystals and by the supersaturation the formulation generates, not by weight percent alone. C60·C54 The evidence is clearest for sonicated versus unsonicated needles; the S16–S80 comparison and the nucleus–spacing rule are suggestive rather than tested, and crystals formed inside an ASD remain to be studied. X11·X5·P9