Residual crystals, fluid volume and absorption: testing amorphous tacrolimus capsules with an absorptive sink

Background and motivation

Amorphous solid dispersions (ASDs) raise the oral bioavailability of poorly soluble drugs because the amorphous drug dissolves to concentrations well above its crystalline solubility. The resulting supersaturated solution is metastable: drug can crystallize out of it, and a polymer in the formulation usually serves as a crystallization inhibitor that should keep the supersaturation through the absorption window C6. A second risk sits in the solid itself. Amorphous drug can crystallize during storage, especially at high humidity where absorbed water lowers the glass transition temperature and raises molecular mobility, and some crystallinity can be left behind by manufacture (incomplete amorphization, an unsuitable process temperature, slow solvent removal) C7. Such residual crystals can seed further crystallization when the product dissolves; how much they lower the supersaturation is expected to depend on the origin, shape and surface of the seeds and on additives, and in vivo studies have found variable effects of residual crystallinity on absorption (Section 1, refs 10, 14, 26–29) C7.

Testing such products raises a practical problem. Compendial dissolution tests use a large volume, usually 900 mL, to keep sink conditions; this is good for batch control of simple products but cannot show supersaturation or the crystallization that follows, so non-sink conditions have gained attention (Sun et al. 2016, ref 10) C5. The fluid volume in the gut, however, is small and variable. MRI studies report fasted stomach volumes of 18–54 mL, small-intestinal volumes of 30–420 mL with an average of about 100 mL in the fasted state, and fluid that sits in separate pockets with median volumes of 4–12 mL R21. Because membrane flux depends on the free drug concentration, a change in luminal volume changes the concentration and so the absorption rate C4.

Tacrolimus (TAC), an immunosuppressant with a narrow therapeutic index and large intersubject variability, is marketed as amorphous capsules: the brand Prograf and several generics in 0.5, 1 and 5 mg strengths C8. Earlier work from the same group (Trasi et al. 2017, ref 22) found that one generic, made for Accord Healthcare, crystallized during open-dish storage under stress, whereas Prograf did not R3. A follow-up (Purohit et al. 2018, ref 27) showed in closed non-sink dissolution that crystalline drug lowered the level and duration of supersaturation R6. What was missing was the absorption side. The group had built a high-surface-area hollow fibre apparatus that measures dissolution and membrane transport at the same time (Hate et al. 2017, ref 31), and argued that non-sink dissolution should ideally be coupled to such an absorptive compartment, because the sink itself changes the concentration-time profile C9.

This paper puts these threads together. The authors stored generic capsule contents until 20, 50 or 100% of the drug was crystalline, dissolved them with Prograf, the fresh generic and a crystalline suspension in 240, 100 and 40 mL next to the absorptive membrane, and compared the absorbed amounts, including a "virtual" bioequivalence test on the in vitro data P1·P4·P9. Their stated hypothesis was that a lower volume would give higher supersaturation and faster absorption, but would also amplify crystallinity-induced desupersaturation, "potentially lowering the drug available for absorption" C10. They then ran supersaturated solutions without seeds and with seeds, and built a simple model of absorption against crystal growth to explain when the seeds matter P5·P6·P10.

Background concepts

Crystalline and amorphous solubility. The crystalline (equilibrium) solubility $C^{*}$ of tacrolimus in the dissolution medium, 5 mM phosphate buffer at pH 4.5 containing 50 µg/mL hydroxypropyl cellulose (HPC), was measured here as 2.5 ± 0.4 µg/mL at 37 °C M1·M8. The amorphous solubility, the highest free drug concentration that the amorphous solid can produce, had been reported as about 50 µg/mL M1. Above the amorphous solubility a drug-rich liquid phase would separate (liquid–liquid phase separation, LLPS), but for these tacrolimus products LLPS is not observed: the solid simply stops dissolving at the amorphous solubility C16·R5. The window between 2.5 and about 50 µg/mL is therefore the range in which a dissolved amorphous product is supersaturated and can crystallize.

Supersaturation ratio. The paper measures supersaturation as the ratio of concentration to crystalline solubility:

In plain terms: $S$ tells how many times the solution exceeds what the crystal can hold; with $C^{*}$ = 2.5 µg/mL, 50 µg/mL is $S$ = 20 and about 21 µg/mL is $S$ ≈ 8 E2·R7.

Sink index. Whether a given volume can dissolve the whole dose is expressed by the sink index, defined here with respect to the amorphous solubility $C_s$:

In plain terms: $SI$ compares how much drug the volume $V$ can hold at the amorphous solubility with the dose. For 5 mg tacrolimus, 240, 100 and 40 mL give SI = 2.4, 1 and 0.4, which the authors label sink, at-sink and non-sink E1·R7. All three are non-sink for the crystalline form, so crystalline drug in the capsule cannot dissolve once the solution reaches the crystalline solubility unless the sink index with respect to that solubility reaches 1 C32.

Table A. The three test volumes and what they mean for a 5 mg dose (values as printed, p.5, p.10–11, p.16) R7·R21·C11.

Absorptive dissolution. In the apparatus the dissolution vessel (the donor) is pumped through the lumen of cellulosic hollow fibres with 100 cm² of membrane and 15 nm pores, while a receiver fluid flows co-currently outside the fibres; both flows run at 2 mL/min P4. Drug that crosses the membrane is carried away by the receiver stream, so the membrane acts as a continuous sink. The receiver concentration, read continuously by an in-line UV flow-through probe, is a measure of the absorption rate rather than a cumulative amount; the donor is sampled for HPLC P4·C13. The area under the receiver curve (AUC) is used as the measure of how much was absorbed C23.

Desupersaturation and crystal growth. Desupersaturation is the loss of dissolved drug from a supersaturated solution. When crystals are already present, as with residual crystallinity, the loss is taken to occur mainly by growth of those seeds rather than by new nucleation; the authors make this explicit, "assuming minimal secondary nucleation" C42. Growth rates are commonly described by a power of the excess concentration, with an exponent (the growth order) near 2 when an adsorbed polymer makes the integration of molecules into the crystal surface rate-limiting (refs 39, 40) C44.

Virtual bioequivalence. Regulatory bioequivalence (BE) requires the 90% confidence interval of the test-to-reference ratio (T/R) of AUC to lie within 80–125%. The authors apply this rule to the in vitro receiver AUC, comparing the generics with Prograf (inter-product) and the stressed generics with the fresh generic (intra-product), but judge only the mean ratio, because their confidence intervals reflect the error of triplicate experiments rather than variability between subjects P9·C26.

Methods in detail

The study has three parts: making samples with graded crystallinity, testing them in the absorptive apparatus at three volumes, and separating the two processes that remove drug from solution with supersaturated and seeded solutions plus a simple model.

Contribution 1: generic samples with graded crystallinity

Problem. To study residual crystallinity, the authors needed the same product with known fractions of crystalline drug. The generic (Accord) crystallizes under stress, whereas Prograf does not R3.

What they did. The contents of five generic capsules were pooled and mixed, to have enough material and an even distribution of crystals, and stored in an open container at 40 °C and 75% relative humidity (RH) for 2–5 weeks P1. Crystallinity was followed by powder X-ray diffraction (PXRD) between 9.5 and 11.5° 2θ, using a calibration made by adding known amounts of crystalline tacrolimus monohydrate to fresh generic powder; crystallinity was taken from the ratio of peak areas between 10–10.5° and 9.5–10.8° as in ref 22 P2. The calibration had R² = 0.9808, a detection limit of about 1% and a quantification limit of about 5% R2. Samples were removed when they reached 20, 50 and 100% crystallinity and kept at room temperature until tested; an earlier study had found no chemical degradation at these conditions R2·R3. In Figure 1, Prograf and the fresh generic show flat traces, while the stressed samples show the crystalline peaks near 10.5 and 11.4° 2θ, growing with crystallinity R1.

For scanning electron microscopy (SEM), the most crystallized generic was washed with 10 mL water for about 5 min to remove the soluble excipients, filtered and dried, which left tacrolimus crystals mixed with croscarmellose sodium P3. Figure 2 shows that the crystals grown in the product are plate-like and smaller than 1 µm, while the as-received crystalline drug forms larger plates of somewhat similar shape R4. These sub-micron plates are the seeds that the rest of the paper is about.

The two products differ in how they are made. Prograf is described as an ASD made by solvent impregnation of the drug into the polymer (ref 38), whereas reverse engineering in ref 22 concluded that the generic is mainly amorphous drug deposited as a thin layer on excipients and physically mixed with the polymer M2·M3·C33. Both capsules contain about 5 mg hydroxypropyl methylcellulose (HPMC) M2·M3.

Contribution 2: dissolution and absorption at three volumes

What they did. Each sample was added to the donor vessel: the contents of one Prograf or fresh generic capsule, or 132 mg of the pooled stressed powder (the powder mass of one generic capsule), each holding 5 mg tacrolimus; a suspension of crystalline monohydrate served as control P4·M3. The medium was the pH 4.5 phosphate buffer with HPC, at 37 °C M8·P4. Donor samples were filtered through 1 µm glass fibre filters and assayed by HPLC at 210 nm on a C8 column; the withdrawn volume was replaced with buffer, and a 10 µm cannula filter kept particles out of the fibre module P4·P7. Every formulation was run in triplicate at 240, 100 and 40 mL for 2 h P4.

Read-outs. Three quantities come out of each run. The donor concentration shows how much has dissolved and remains in solution; the receiver concentration shows the absorption rate; and the total amount of drug in donor plus receiver, calculated over time, shows whether drug leaves solution by crystallization, since a fall after the maximum cannot be explained by absorption P8·C19. The receiver AUC over 0–120 min feeds the virtual BE comparison P9.

Why it differs from earlier work. Earlier tests on the same products (refs 22, 27, 30) were closed vessels without a membrane. Here drug is removed continuously, which keeps the donor supersaturation lower than in a closed vessel; the authors see this as closer to the competition that happens in the gut C9·C31.

Contribution 3: separating absorption from crystal growth

Absorption without seeds. To isolate the membrane, the authors dissolved 5 mg tacrolimus at once by adding a methanolic stock (at most 250 µL methanol) to 100 mL (S 20) or 240 mL (S 8) and followed donor and receiver for 4 h P5. They state that no crystallization occurred, which they attribute to HPMC inhibiting nucleation (ref 22), so the donor decline reflects absorption alone C28. The donor concentration change across the hollow fibre is written as their eq 2 (from ref 31):

In plain terms: $C_{in}(0)$ is the initial donor concentration, $Q_{in}$ and $Q_{out}$ are the flow rates inside and outside the fibres, $V_{in}$ is the donor volume, $K_{in}$ the mass transfer coefficient of the membrane and $A$ its area. $Z$ is negative, so the donor concentration decays exponentially, and the absorption rate is proportional to the concentration present E3. Non-linear fitting of the Figure 8 profiles gave $K_{in}$ = 1.09×10⁻⁴ cm/s R16.

Crystal growth with seeds. Seeds were made by equilibrating one capsule of the fully crystallized generic in 100 mL medium overnight. Methanolic tacrolimus (10 mg/mL stock, final methanol 0.2–0.5 v/v%) was then added to reach the chosen concentration, and the concentration was followed by UV P6. The desupersaturation rate was the slope of concentration against time over the first part of the curve, stated as "~40 min" in the methods and "the initial 60 min" in the results P6·X5. Their eq 3 describes growth on the seeds:

In plain terms: the rate of drug loss grows as a power $n$ (the growth order) of the excess concentration above the crystalline solubility; $k_g$ is the growth rate constant and $A$ is here the crystal surface area, which is assumed constant and folded into the constant E4·C42. Taking logarithms, the slope of $\log (dC/dt)$ against $\log (S-1)$ gives $n$ and the intercept gives the constant E5. Figure 11 shows five seeded levels on such a plot; the printed fit is $y=1.677x-3.136$ with R² = 0.9896, so $n$ ≈ 1.7, and the constant is given as 1.17×10⁻⁴ cm/s R18.

The model. With these constants, eqs 2 and 3 were used to compute both rates as a function of $S$ at the initial time point, with $C^{*}$ = 2.5 µg/mL (Figure 12) P10·R19. Because absorption scales with the first power of concentration and growth with a power above one, the two curves must cross at some supersaturation; the schematic Figure 10 summarizes this as $dC/dt\propto S$ for absorption and $dC/dt\propto (S-1{)}^n$ for crystallization E7·C43.

Note by the AI writer (not discussed in the paper). Several printed quantities in this part do not fit together. The rate unit in Figures 9B and 11 (per second) does not match the slopes of the Figure 9A curves, which agree with the plotted values only if read per minute X1. The Figure 11 abscissa, labelled log (S − 1), has values (about 1.26–1.68) that fit ${\log }_{10}(C-C^{*})$ for 20–50 µg/mL rather than ${\log }_{10}(S-1)$ X2. The intercept −3.136 corresponds to 7.31×10⁻⁴, not to the stated 1.17×10⁻⁴, and the unit cm/s is not that of $k_{g}A$ in eq 3 X3·E5. Finally, eq 2 with the printed $K_{in}$, area and flow rates gives absorption rates about 8 to 47 times lower than the Figure 12 line for the actual test volumes X4·E3. The qualitative shape of the model is not affected, but its numbers should not be reused.

Experimental analysis

Release and absorption fall with crystallinity

At 240 mL (Figure 3), Prograf released slowly and steadily, from about 5.2 µg/mL in the donor at 10 min to about 15.5 µg/mL at 120 min, so that release was "nearly complete" after 2 h R8. The fresh generic released within 20 min, peaked at about 14.9 µg/mL at 40 min and then declined slowly as drug crossed the membrane; its peak stayed below the theoretical 21 µg/mL, which the authors attribute to simultaneous absorption R8·C14. The 20% sample behaved like the fresh generic (peak about 15.6 µg/mL). The 50% sample reached only about 7.3 µg/mL; the text gives "~9 µg/mL", but the plotted maximum is about 7 R8·X6. The 100% sample stayed at about 2.8 µg/mL, close to the crystalline suspension (about 2.6 µg/mL) R8.

At 100 mL (Figure 4) the same order held at higher concentrations: fresh and 20% peaked at about 40.3 and 38.3 µg/mL at 20 min, Prograf rose slowly to about 29.9 µg/mL at 80 min, and the 50% and 100% samples peaked at about 15.2 and 4.8 µg/mL R9. Here the authors could not distinguish the 20% sample from the fresh generic within experimental error, and they note that absorption kept the donor from reaching the theoretical 50 µg/mL, "This observation highlights how absorption can decrease the extent of supersaturation achieved in the donor compartment" C15.

At 40 mL (Figure 5), the fresh generic dissolved fast to about 53 µg/mL, close to the amorphous solubility, and then fell gradually in both compartments, to about 23.6 µg/mL in the donor at 120 min R10. The 50% sample dissolved to about 26 µg/mL, "approximately half of the amorphous solubility", and the 100% sample to about 9.4 µg/mL, above the crystalline solubility, which the authors read as "either residual amorphous content or a defective crystal structure" R10·C18.

Table B. Receiver AUC0-120 in µg/mL·min, read from Figure 7A, C, E (approximate) R12.

Table B condenses this into the receiver AUC. At every volume the AUC falls with crystallinity, and Prograf is below the fresh generic because it releases more slowly R12·C24. The authors' explanation is simple: the amorphous fraction dissolves rapidly to a supersaturated solution, after which the crystalline fraction cannot dissolve, so "the maximum solution concentration generated is dependent on the amorphous content" and on how fast the crystals grow; lower supersaturation then means lower membrane transport C36·C37.

A smaller volume gives more absorption

The same table shows the second main result. The AUC of the fresh generic rose from about 362 at 240 mL to about 682 at 100 mL and about 992 µg/mL·min at 40 mL, and every formulation followed this trend, while the crystalline suspension stayed at about 87 µg/mL·min at all volumes R12·C24. Figure 13 shows the receiver profiles of the fresh generic: a plateau near 3.3–3.4 µg/mL at 240 mL, a peak of about 7.2 µg/mL at 100 mL and about 10.5 µg/mL at 40 mL R20. The constant suspension acts as an internal control: when the dissolved concentration is pinned at the crystalline solubility, the volume does not matter; when the amorphous drug supersaturates, a smaller volume gives a higher concentration and so a faster flux. The authors call the higher AUC at the lowest volume "somewhat counterintuitive" and suggest that such differences "could translate to in vivo scenarios" and contribute to the high inter-subject variability of tacrolimus products C51.

Crystallization during the test happens only in 40 mL

Figure 6 adds up donor and receiver to give the total dissolved drug. At 240 and 100 mL it stayed essentially flat for all four generic samples, at about 4 mg for the fresh generic and the 20% sample R11. The totals below 5 mg are attributed to drug adsorbed on the membrane, solution held in the tubing and variation of drug content between capsules C21. At 40 mL the picture changed, as Table C shows.

Table C. Total dissolved drug (mg) at 40 mL, read from Figure 6C (approximate) R11·C20.

The donor curves at 40 mL tell the same story: the 20% sample began to fall after 30 min and ended at about 9.2 µg/mL at 120 min, against about 23.6 µg/mL for the fresh generic R10·C17. The authors read the falling totals as "indicating that additional crystallization was occurring in the dissolution medium" C20. The fresh generic never crystallized at any volume. The authors give two reasons: both products contain about 5 mg HPMC, and tacrolimus without seeds stays supersaturated for up to 3 h and, with HPMC, for more than 6–8 h (ref 30), "This explains why there was no crystallization of the fresh generic formulation" C22·R5; and, in the Discussion, the lower supersaturation left by simultaneous absorption, which differs from the crystallization seen in a closed vessel in ref 27 C35·R6.

Virtual bioequivalence depends on the volume

Table D. Mean T/R of receiver AUC in percent, read from Figure 7B, D, F (approximate) R13.

Judged on the mean ratio against 80–125%, the fresh generic exceeded the upper limit versus Prograf at 240 mL, because it released faster, and fell within the limits at 100 and 40 mL R13·C25. The 20% sample was within the limits versus both references at 240 and 100 mL; at 40 mL it fell to about 72% of the fresh generic, and the authors also call it not bioequivalent to Prograf there, although that bar sits at about 81% R13·C25·X9. The 50% and 100% samples were far below 80% at every volume, as they were in an in vivo study in dogs (ref 28) R13·R22·C40. The authors conclude that "the dissolution volume can have significant impact on the bioequivalence outcomes", especially for amorphous formulations with residual crystallinity, and stress that confidence intervals, which would be critical in an in vivo study, were not considered C41·C26.

Note by the AI writer (not discussed in the paper). In Figure 7D (100 mL) the 50% and 100% bars referenced to Prograf (about 30 and 13) are lower than those referenced to the fresh generic (about 38 and 17), although Prograf's AUC is the lower of the two in Figure 7C; from the plotted means they would be about 46 and 20 X8. The text also cites "Figure 7a and 7b" for the 100 and 240 mL AUCs, which by the legend are panels 7C and 7A X7. Neither point changes the not-bioequivalent outcome.

Supersaturated solutions: faster absorption at higher S

Without seeds (Figure 8), the solution at S 20 in 100 mL fell from about 53 to about 34 µg/mL over 4 h, while the solution at S 8 in 240 mL fell from about 24.7 to about 20 µg/mL R14. The receiver peaked at about 8.2 µg/mL from the smaller volume and about 4.3 µg/mL from the larger, and the AUC over 0–240 min was about 1460 against about 925 µg/mL·min, "It is clear that a higher amount of drug was absorbed when a lower volume was used" R14·R15·C28. Over 0–120 min the AUCs were 871 ± 60 and 488 ± 37 µg/mL·min; the authors compare them with 682 ± 54 and 362 ± 38 for the fresh generic and find they "corresponded closely", suggesting little effect of excipients R15·C29. The solution values are about 28% and 35% higher, and the solutions start fully dissolved, so this agreement is loose X10. The first donor points of Figure 8 (about 53 and 24.7 µg/mL) also lie above the nominal 50 and about 21 µg/mL X12.

Seeded solutions: faster desupersaturation at higher S

With seeds (Figure 9), a solution started at 50 µg/mL fell from about 48.5 to about 30 µg/mL in 50 min and to about 21 µg/mL by 235 min, while one started at 20 µg/mL (first point about 24.5) fell only to about 22 µg/mL at 50 min and about 19 µg/mL at 240 min R17. The plotted desupersaturation rates were about 0.39 and 0.075, "much greater for the higher supersaturation" R17·C30. Over five levels the log-log plot gave the growth order of about 1.7, which the authors find "in good agreement" with the value near 2 expected when an adsorbed polymer makes growth integration-controlled R18·C44.

Table E. Model constants as printed (p.19, p.27) R16·R18·M1.

The model: who wins at which supersaturation

Figure 12 plots both rates against S from 2 to 24. Absorption rises linearly, from about 0.0078 to about 0.094 µg/mL/s; crystal growth rises faster, from about 0.0005 to about 0.115 µg/mL/s, and the two curves cross near S 18.5 R19. The authors read this as absorption "clearly" rate-controlling at low supersaturation and crystal growth predominant at higher supersaturation, with both rates falling as the concentration drops over time C45. They use it to explain the experiments: the larger volumes generate a lower maximum supersaturation, and the membrane keeps lowering it, which "prevented additional crystal growth"; the polymer also "clearly contributed" by poisoning the crystal surface; at 40 mL the high supersaturation lies in the growth-dominated regime, which "explains the rapid solution crystallization" of the stressed samples C46·C47·C48.

Note by the AI writer (not discussed in the paper). The data do not follow the crossover exactly. At 40 mL the 50% sample lost dissolved drug in the first 20 min although its donor peak was about 26 µg/mL (S about 10), below the crossover, whereas the 20% sample at 100 mL peaked at about 38 µg/mL (S about 15) without losing drug R10·R11·R9·X16. The 50% sample carries more seeds, and the model holds the crystal area constant, so the threshold supersaturation should depend on how much crystal is present. Together with the reproduction problems of the model constants X3·X4, this makes S 18.5 a property of this simulation, not a general limit.

Discussion

The authors' argument links the three sets of experiments into one causal chain, which can be drawn as follows C36·C43·C46·C48.

What decides the switch. In this picture, how high the supersaturation goes, which depends on dose, volume and amorphous solubility, decides whether residual crystals merely dilute the dose or actively drain the solution C49. The authors' general statement is that "crystal seeds can have different impacts on absorption depending on the supersaturation profile generated following dissolution, which in turn depends on the volume of dissolution medium available", and that these relationships "will vary as a function of factors such as drug and formulation" but matter for "what specification should be placed on residual crystalline content" C49. In the conclusions this becomes stronger: "Our findings clearly demonstrate that crystallization kinetics dominate drug concentration depletion in a seeded environment if supersaturation is significantly high, irrespective of a high absorption rate and the presence of an inhibitory polymer" C2.

What it means for testing. The authors draw three practical points. First, an absorptive compartment is "particularly crucial" for supersaturating formulations, because it captures the competition between membrane transfer and crystallization and removes drug from the dissolving compartment C31. Second, "non-sink conditions can potentially provide more discrimination between formulations with small amounts of residual crystallinity", here shown by the 20% sample, which differed from the fresh generic only at 40 mL, but such results should be set against the minimum and maximum fluid volumes expected in vivo C39·C38. Third, "the risk presented by residual crystallinity needs to be evaluated in the context of the dosing conditions, specifically, the volume available for dissolution" C52.

Brand versus generic. The slower release of Prograf at every volume is traced to its manufacture as a solvent-impregnated ASD, against the generic's surface-deposited amorphous drug, which dissolves fast but crystallizes under stress C33. In vitro this gave Prograf a lower AUC and a later peak, and the fresh generic exceeded the upper BE limit at 240 mL; the authors note that in dogs Prograf's Tmax was about twice the generic's and its AUC trended lower (ref 28) C34·R22.

Fluid volume and variability. Since supersaturation of tacrolimus depends on the luminal volume, and the volume varies with what is drunk, gastric emptying, transit and osmotically driven water absorption, the authors suggest fluid volume "could be a critical factor to evaluate" for amorphous formulations and a contributor to the known variability of tacrolimus exposure C50·C51.

Note by the AI writer (not discussed in the paper). The absorptive sink works in both directions for risk assessment. It lowers the supersaturation that a closed vessel would build up, and so can make a product look more robust; but the absorption rate here is a property of the hollow fibre module (100 cm², 2 mL/min), not of a human gut. The 20% sample passing at 240 and 100 mL and failing at 40 mL is therefore best read as a ranking under defined conditions rather than a prediction of clinical bioequivalence.

Limitations

Limitations stated by the authors

The authors state that the confidence intervals of the virtual BE come from the experimental error of triplicate runs and "does not represent the inter-subject variability observed in in vivo BE study", that they therefore judged only the mean T/R, and that intra-subject variability in vivo "is likely to lead to larger C.I. values" C26. They note that the totals of dissolved drug stayed below 5 mg because of membrane adsorption, tubing hold-up and capsule variability C21. They describe the absorption-growth relationships as "non-trivial to deconvolute" and dependent on drug and formulation C49, and their model simulates only the initial time point, since the absorption rate of eq 2 depends on time C45. The desupersaturation analysis assumes "minimal secondary nucleation" and a constant crystal surface area C42·E4.

The AI writer's own judgement

The dissolution-absorption data are the strong part of the paper: triplicate runs at three volumes show the same crystallinity order in donor, receiver and AUC, and the crystalline suspension gives a clean internal control for the volume effect R8·R9·R10·R12. The weaker part is the quantitative model behind the conclusion that seeds matter "only at high supersaturations". The rate units of Figures 9B and 11 do not match the curves they come from X1; the Figure 11 abscissa fits ${\log }_{10}(C-C^{*})$ rather than its label X2; the growth constant does not follow from the printed intercept and carries a unit that does not fit eq 3 X3; and the absorption line of Figure 12 cannot be reproduced from eq 2 with the printed constants for any of the test volumes, the volume used being unstated X4. The location of the crossover (S ≈ 18.5) is therefore not reproducible, and the 50% sample at 40 mL lost dissolved drug below it X16.

Several other points limit the reading. Crystallinity levels are targets; the measured crystallinity of each test sample is not reported, and the "100%" sample still dissolved to about four times the crystalline solubility X13. The polymer content of the solvent-shift and seeded solutions is not stated, although HPMC is invoked to explain the absence of nucleation X11. The absorption-sink explanation for why the fresh generic did not crystallize was not tested against the same volume without a membrane, and HPMC with slow nucleation is offered as a second explanation X15. The claim that the polymer "clearly contributed" to preventing desupersaturation has no polymer-free comparison X14. One BE panel contradicts its own AUC data, and the 20%-versus-Prograf failure at 40 mL sits on the 80% line X8·X9. All numbers are read from plots, since no tables or replicate values are printed X6·X7. Finally, the study covers one drug, one generic, one medium (pH 4.5 with HPC) and one membrane.

Conclusion

The paper shows, for commercial tacrolimus capsules, that residual crystallinity lowers both the concentration reached and the amount absorbed in an absorptive dissolution test, and that the size of the effect depends on the volume: a smaller volume raises supersaturation and absorption for every amorphous sample, and the residual crystals actively consumed the dissolved drug only in 40 mL, where they also turned the 20% sample from bioequivalent to not bioequivalent with the fresh generic in vitro R11·R12·R13·C20·C25. Supersaturated solutions and seeded solutions confirm that both absorption and crystal growth speed up with supersaturation, growth with an order of about 1.7, and a simple rate model places the switch from absorption-led to growth-led depletion at high supersaturation, although its constants cannot be reproduced from the printed values R15·R17·R18·R19·X3·X4. For formulation work the message is the authors' own: judge residual crystallinity "in the context of the dosing conditions", and test supersaturating products with an absorptive sink at the volumes they will meet C52·C31.