When an amorphous capsule partly crystallizes: which dissolution test notices, and does bioequivalence survive?

Background and motivation

Many drug candidates dissolve too poorly to be absorbed well, and an amorphous solid dispersion (ASD), in which the drug is dispersed in a hydrophilic polymer, is one way around this. The amorphous drug has a higher free energy than its crystal and therefore a higher apparent solubility, which can raise oral bioavailability (Section 1, refs 2–6) C1. The same free energy drives the drug back to the crystal. Crystallization can start during manufacture or on storage, especially at high temperature and humidity, and it can cancel the solubility gain, so a quality-control test must be able to detect it (refs 7–11) C1·C2.

The standard quality-control tool is dissolution testing. Compendial USP methods for poorly soluble drugs are run under sink conditions: enough medium, often 500 or 900 mL and often with surfactant, to dissolve about three times the dose at the drug's solubility C4. Under such conditions an ASD never builds up much supersaturation, and the authors note that this "may have poor discriminatory power" for crystalline drug in an ASD C4. Non-sink conditions make supersaturation and its loss visible, through crystallization or through liquid–liquid phase separation into drug-rich nanodroplets (Konno 2008, ref 12; Ilevbare 2013, ref 13), but for ASDs it was not defined how far from sink, with respect to the amorphous solubility, a test should be C3·C4. A commentary from the same group (Sun 2016, ref 15) had laid out what crystallinity should do to non-sink profiles, but mostly as hypothetical cases; few experiments existed, and the effect of partial crystallinity on bioavailability and pharmacokinetics was unknown C5.

Physiologically based pharmacokinetic (PBPK) models could translate a dissolution profile into a predicted blood concentration profile, and so tell which test is clinically relevant. For ASDs their use had been limited by the difficulty of modeling supersaturation, nucleation, crystallization and re-dissolution in the gut; a few studies had predicted dose-dependent absorption of ASDs in rats (Mitra 2016, ref 16; Gao 2010, ref 17) C6.

Tacrolimus offered a convenient test case. It is a poorly soluble immunosuppressant sold as capsules containing the amorphous drug with hypromellose (HPMC) at a 1:1 weight ratio (ref 11) M1·M2. In earlier work the group had found that a marketed tacrolimus capsule crystallized within a few days in an open dish at 40 °C and 75% relative humidity (RH) (Trasi 2017, ref 11), and that amorphous tacrolimus reaches about 50 µg/mL in the USP dissolution medium I (Trasi 2017, ref 21) R20·R4. A product that crystallizes this readily allows crystals to be grown inside the formulation itself, which matters because seeds added from outside may not behave like crystals formed within the ASD (Jackson 2015, ref 18; Schram 2016, ref 19) C7.

The paper set out to do three things: measure dissolution of fresh and partly crystallized commercial tacrolimus capsules in different media and volumes; build a PBPK absorption model for tacrolimus and use the dissolution data as its input; and run virtual bioequivalence trials of the partly crystallized generic against the innovator product Prograf and against the fresh generic, to see which dissolution test predicts a pharmacokinetic difference P7·P8·P10·P12.

Background concepts

Sink index. To describe how far a dissolution test is from sink, the authors use the sink index (SI) of Sun et al. (ref 15) E1:

Here $C_s$ is the solubility of the drug in the medium, $V$ the volume of medium and Dose the amount of drug in the vessel E1. In plain terms: SI is how many doses the medium could dissolve at that solubility. Above 1 the whole dose can dissolve; below 1 it cannot, and if more drug goes into solution anyway the solution is supersaturated. The authors compute SI twice for each condition, with the crystalline solubility ($\mathrm{S}{\mathrm{I}}_{\mathrm{c}\mathrm{r}\mathrm{y}\mathrm{s}\mathrm{t}}$) and with the amorphous solubility ($\mathrm{S}{\mathrm{I}}_{\mathrm{a}\mathrm{m}\mathrm{o}\mathrm{r}\mathrm{p}\mathrm{h}}$) R4. For a 5 mg dose and a crystalline solubility of 1.8 µg/mL, 900 mL gives $\mathrm{S}{\mathrm{I}}_{\mathrm{c}\mathrm{r}\mathrm{y}\mathrm{s}\mathrm{t}}=1.8\times 900/5000=0.32$, which reproduces Table 3 R4·E1. A test can therefore be a sink for amorphous drug but non-sink for the crystal, and this is the situation in USP test I C20.

Supersaturation, seeds and desupersaturation. When an ASD dissolves faster than crystals can form, the drug concentration can rise above the crystalline solubility up to roughly the amorphous solubility, the highest concentration the amorphous drug can reach C26. Such a solution is supersaturated. If crystals are already present in the product, they act as seeds: dissolved drug can grow onto them without first having to nucleate, and the concentration falls back toward the crystalline solubility. This fall is called desupersaturation C43. The authors use an empirical crystal growth law to describe how fast seeds grow (Eq. 2, from Mullin, ref 51) E3:

Here $R_G$ is the crystal growth rate, $k_G$ a growth rate coefficient, $A$ the crystal surface area, $C_b$ the concentration of dissolved drug in the bulk solution, $C^{*}$ the solubility of the crystal and $g$ the overall growth order, typically between 1 and 2 E3. In plain terms: the more crystal surface there is and the further the solution is above the crystal's solubility, the faster the crystals grow; because $g$ is at least 1, doubling the supersaturation at least doubles the rate C52. No values of $k_G$, $A$ or $g$ are given for tacrolimus; the equation is used qualitatively E3.

Dissolution against growth. To read the shape of a dissolution profile in which drug dissolves from the ASD while seeds grow, the authors borrow a framework from Cardew and Davey (ref 52), developed for solution-mediated transformation between polymorphs (Eq. 3) E4:

Here $\tau$ is the time for the whole transformation, ${\tau }_D$ a characteristic dissolution time and ${\tau }_G$ a characteristic crystal growth time E4. In plain terms: the overall change is limited by whichever process is slower. If growth is much faster than dissolution (${\tau }_G\ll {\tau }_D$), supersaturation is consumed as soon as it forms; if dissolution is much faster (${\tau }_G\gg {\tau }_D$), supersaturation persists as long as undissolved ASD is left to replace the drug that the crystals take C53. The authors state that the model was derived for polymorphs but "can be applied" to an amorphous drug dissolving while crystals grow C53.

PBPK absorption model. GastroPlus represents the gut by the advanced compartmental absorption and transit (ACAT) model: a chain of compartments from stomach to ascending colon, in each of which drug can be unreleased, undissolved, dissolved or inside the enterocytes (Figure 1) E7·P10. Absorbed drug passes the gut wall and the liver, where CYP3A metabolizes it with Michaelis–Menten kinetics, and is then distributed by a two-compartment model with a central volume $V_c$ and transfer rate constants $k_{12}$ and $k_{21}$ E8·E9·P10. Tacrolimus binds strongly to red blood cells (blood/plasma ratio 35 in Table 1), and clinical concentrations are measured in whole blood, so the authors converted blood to plasma concentrations to fit the disposition parameters (Eq. 1) E2·P10:

Here $C_p$ is the drug concentration in plasma, $C_B$ in whole blood and $C_{RBC}$ in red blood cells, and HCT is the hematocrit, the volume fraction of red cells in blood E2. In plain terms: the blood concentration is a volume-weighted mix of plasma and red-cell concentrations, so dividing by that mix recovers the plasma value. The authors consider the conversion valid because the blood-to-plasma ratio "appears to be linear" from 0 to 50 ng/mL (ref 35) C8. The hematocrit and red-cell concentrations used are not printed E2.

Virtual bioequivalence. Two products are bioequivalent when the 90% confidence interval (CI) of the test-to-reference (T/R) ratio of the peak concentration (Cmax) and of the area under the concentration–time curve (AUC to the last time point, AUCt, and to infinity, AUC) lies within 80.00–125.00% E10. In a virtual trial the PBPK model simulates a crossover study in a population of virtual subjects whose physiological parameters vary around their means, and the same statistics are applied to the simulated data P12. Tacrolimus is a narrow therapeutic index (NTI) drug, for which a fully replicated design with reference-scaled limits is now required; the authors used the simpler two-way crossover with fixed limits, on which several generic tacrolimus capsules were approved before December 2012 C13.

Methods in detail

The study has three parts that feed into each other: making capsules with known crystallinity, dissolving them under conditions that span the sink index, and using the dissolution profiles as input to a PBPK model for virtual bioequivalence trials.

Part 1: capsules with crystals grown inside the product

Problem. To study crystallinity in a real product, the crystals should form in the formulation itself, not be added as a separate powder, and their amount must be known C7.

What they did. Generic tacrolimus capsules (Accord Healthcare, made by Intas, 5 mg, lot R13627) were stored in an open container at 40 °C and 75% RH M2·P1. X-ray powder diffraction (XRPD) of the capsule contents, using the tacrolimus monohydrate peak at 9.3° 2θ, followed crystallization; a calibration was made by adding known amounts of crystalline tacrolimus monohydrate to fresh capsule contents (R² = 0.9905) P2·R2. The limits of detection and quantification were 10% and 15% crystallinity, or 0.38% and 0.57% w/w of the contents, high because the drug is only about 4% of the capsule content weight R2·C15. After 5 weeks the contents were fully crystalline C14. These contents were then mixed geometrically with fresh contents to give 0–100% crystallinity in 10% steps and filled into size 3 gelatin capsules at 5 mg P4. The USP 37 HPLC assay of 10 pooled capsules checked that the drug had not degraded, for both the generic and Prograf (Astellas, lot 047354) P3·M1.

Why it works. The blends contain crystals formed in the formulation's own environment, next to HPMC and the other excipients, at a known fraction. How it differs. Earlier seeding studies added crystals from outside; the authors expect such seeds to differ in their properties from crystals formed within the ASD C7.

Part 2: dissolution tests spanning sink to non-sink

Problem. If the dissolution test dissolves crystals as easily as amorphous drug, it cannot see crystallinity; if it supersaturates the solution, crystals may grow and change the profile. The test conditions therefore decide what is detected C33.

What they did. The crystalline solubility of tacrolimus monohydrate was measured by the shake-flask method (300 rpm, 37 °C, 24 h, HPLC at 210 nm) in the two media of the USP monograph for tacrolimus capsules: medium I, 50 µg/mL hydroxypropyl cellulose (HPC) in water adjusted to pH 4.5, and medium II, 1.38 mg/mL sodium phosphate and 1 mg/mL sodium dodecyl sulfate (SDS) at pH 7 P5·P6. With the 5 mg dose this gave five conditions (Table 3) R4. USP tests I and II used 900 mL in USP apparatus II at 50 rpm with sinkers and 37 °C, with a single sample at 90 min (test I) or 60 min (test II), on 3 capsules per crystallinity level P7. The non-compendial tests used medium I at 450, 100 and 40 mL, sampled at 10, 20, 30, 40, 60, 90 and 120 min through 10 µm cannula filters (and 1 µm syringe filters at 40 and 100 mL), with fresh Prograf added at 100 and 40 mL P8. The apparatus, stirring and number of replicates are not restated for these low-volume tests P8·X15.

Table A. The five dissolution conditions for a 5 mg dose (from Table 3; crystalline solubility measured, amorphous solubility cited from ref 21) R4.

Why it works. In medium I all conditions are below 1 for the crystal, so a capsule that dissolves completely is always supersaturated with respect to crystalline tacrolimus C20. For amorphous drug the same medium ranges from a sink (SI 9 at 900 mL) through the point where the dose just fits the amorphous solubility (SI 1 at 100 mL) to a condition where it cannot all dissolve (SI 0.4 at 40 mL) R4. SDS raises the crystalline solubility about eight-fold, to 14.9 µg/mL, which the authors attribute to micelles, so test II is close to a sink even for the crystal (SI 2.68, "8.4 fold" more sink than test I) R4·C17·C32. How it differs. Compendial tests are single-point checks for quality control; the low-volume tests follow the whole supersaturation and desupersaturation profile C37.

Part 3: from dissolution profile to virtual bioequivalence

Problem. A difference in a dissolution profile matters only if it changes exposure in patients. A PBPK model can estimate this, but standard absorption models drive release from particle size and crystalline solubility and cannot represent a supersaturating product C11.

What they did. The model (GastroPlus V9.0) combined the ACAT absorption model with two-compartment disposition (Figure 1, Table 1) P10. Its main inputs were a molecular weight of 804.04 g/mol, logP 3.26, an effective intestinal permeability of 4.77 × 10⁻⁴ cm/s extrapolated from a preclinical assay, a blood/plasma ratio of 35 and an unbound plasma fraction of 27% P10. Of the reported protein binding values (73–99%) the authors chose the ultracentrifugation value, because ultrafiltration "may increase" nonspecific adsorption and so overestimate binding R19·C9. CYP3A metabolism in gut and liver used Vmax 0.348 mg/s and Km 3.665 mg/L from human microsomes, with Vmax scale factors optimized to 2.4 (intestine, from oral data) and 4.2 (liver, from intravenous data) P10. P-glycoprotein was left out: with its Km assumed above the 40 µM used in vitro, simulations with and without it did not differ (data not shown), so its effect "should be minimal" R18·C10. The disposition parameters were fitted to healthy-volunteer intravenous and oral blood data, converted to plasma by Eq. 1: Vc 8.361 L/kg, k12 0.317 h⁻¹, k21 0.076 h⁻¹ P10·E2. The key choice is the dosage form "CR:Dispersed", in which release in the gut follows the input dissolution profile; in this way the supersaturation and crystallization seen in vitro enter the model C11. The model assumes no further precipitation in vivo C59.

The model was checked against four published sets of blood concentrations after 5 mg oral doses in fasted healthy volunteers (Figure 5), against dose linearity of Cmax and AUC from 1 to 10 mg compared with observed data at 3, 7 and 10 mg (Figure 6, using USP I data of fresh Prograf as input), and against literature values of the fraction absorbed and bioavailability (Table 4) P11. The hepatic availability in Table 4 comes from the well-stirred relation E5:

Here $C{L}_H$ is the blood clearance (0.04 L/h/kg from an intravenous study, ref 44) and $Q_H$ the hepatic blood flow (1.2429 L/h/kg, ref 45) E5. In plain terms: the fraction of drug that escapes the liver is one minus the fraction of liver blood flow that is cleared. With these numbers $F_H=1-0.04/1.2429=0.968$, which reproduces the 96.8% in Table 4 E5·R12. Oral bioavailability is then the product $F=F_a{F}_{gut}{F}_H$ of the fractions absorbed, escaping gut metabolism and escaping the liver E6.

For the virtual trials, PK profiles were simulated for 24 virtual healthy volunteers, fasted, in a two-way crossover at 5 mg, the highest strength and the one "most vulnerable" to crystallization in the small volume of gut fluid P12·C12. Physiological parameters kept the GastroPlus default variability, and Km, Vmax and both Vmax scale factors were given a 50% coefficient of variation because microsomal CYP3A activity varies widely P12·C12. Two inputs were compared: the 900 mL USP test I data (condition 1) and the 100 mL data (condition 4) P12. Crystalline generic capsules were tested against fresh Prograf (0–100%) and against the fresh generic (10–100%), and Cmax, AUCt and AUC were analysed by average bioequivalence in Phoenix P12·E10.

Why it works. Because the release input is the measured profile, every difference between conditions, including desupersaturation, is passed to the simulated exposure, and the bioequivalence statistics translate it into a pass or fail. How it differs. Earlier PBPK work on ASDs predicted absorption in rats; here the model is used in humans to compare dissolution tests by their predicted clinical consequence C6·C64.

Experimental analysis

Crystallization and stability of the capsules. In the open dish at 40 °C/75% RH the crystallinity of the generic contents rose from about 11.5% at day 9 to about 19.5% at day 15, about 51% at day 23 and about 105% at day 28, staying at about 103.5% at day 35 (Figure 2) R1. The authors see "a lag period before crystallization commences or becomes detectable" C14. Note by the AI writer (not discussed in the paper): no point is plotted before day 9 although the methods say samples were analysed every 3 days, and the day 9 value lies below the 15% limit of quantification, so the lag is inferred from missing points X13. The assay after 5 weeks was 99.4 ± 3.4% for the generic (fresh 100.1 ± 1.4%) and 95.7 ± 1.2% for Prograf (fresh 96.4 ± 1.8%), within the 93.0–105.0% USP limits; the authors conclude that the drug does not degrade under this stress (Table 2) R3·C16.

Main result 1: the compendial tests. Table B gives the USP results read from Figure 3.

Table B. Release of generic capsules in the compendial tests, 900 mL, mean of 3 capsules, read from Figure 3 (all values approximate) R5.

Test I lost about 35 points of release between 10% and 100% crystallinity, while test II stayed between about 77.5% and 90% at every level R5. With a specification of not less than 80% (Q), the authors expect capsules with up to 20% crystallinity to pass Stage 1 (every capsule at least 85%) and capsules with 30% crystallinity to pass Stage 2 (average at least 80%), so that "up to 30% crystallinity can pass" test I; test II is "even less discriminating" and would pass capsules with up to 80% crystalline drug C18·C19. Only 3 capsules were tested per level rather than the 6 of a Stage 1 test, and the expectation rests on the low variability and on the uniform crystallinity of the blends C18. Two readings deserve care. The 20% bar reads about 84.7%, at the Stage 1 limit rather than clearly above it X4. In test II there is no trend: 50% crystallinity reads about 80% with an error bar down to about 75%, as low as 90% crystallinity, so the "80%" figure is better read as test II being insensitive across the whole range X5.

The authors explain the difference by the sink index. SDS raises the crystalline solubility so far that test II is almost a perfect sink, and crystals then dissolve along with amorphous drug C32. Test I is a sink for amorphous drug but not for the crystal: "From a theoretical perspective, once sufficient drug has dissolved to reach the crystalline solubility, there is no driving force for further dissolution of crystals", so crystallinity lowers the extent of release C34. They also state that at 900 mL the profile rises and then reaches a sustained plateau, so that the crystals do not grow detectably, and that growth is "most likely poisoned" by HPMC in the capsule and HPC in the medium, polymers being better growth inhibitors at low supersaturation (ref 49) C35·C36·R21. Note by the AI writer (not discussed in the paper): Figure 3 shows only the 90-minute (or 60-minute) point, so the plateau at 900 mL is not shown in the paper X9.

Main result 2: the 100 mL test. At 100 mL the amorphous sink index is 1 R4. Table C summarizes the profiles of Figure 4b.

Table C. Release (% of the 5 mg dose; 100% = 50 µg/mL) in 100 mL of medium I, selected samples read from Figure 4b (all values approximate; the Prograf point at 10 min is hidden among other markers) R7.

Every level of crystallinity gives a profile of its own: the highest reading falls stepwise from about 98% for the fresh generic to about 76.5% (10%), 67% (20%), 55.5% (30%), 50.5% (40%), 37% (70%), 25% (80%) and about 10% (100%), and every generic profile then declines R7. The fresh generic peaks at about 49 µg/mL, at the cited amorphous solubility, within 20–30 min and falls to about 20 µg/mL by 120 min R7·C26. Prograf rises more slowly, reaches about 93.5% at 90 min and does not fall; the generic reaches its maximum in 10–20 min, Prograf in about 90 min R7·R9·C24. The authors judge this condition to "appear to have the best ability to discriminate drug crystallinity in all the dissolution tests evaluated" C39.

Their reading follows the two cases of Sun et al. (Figure 8) C41. Prograf behaves like Case 1, an ASD without crystals that does not crystallize during the test C41. The partly crystallized generic behaves like Case 2: once the concentration exceeds the crystalline solubility (about 1.8 µg/mL), the crystals "are not expected to contribute significantly" to the dissolved drug, so the dissolvable dose and the peak fall in proportion to crystallinity, and the steep decline shows that "the crystal seeds are able to grow rapidly at these dissolution conditions" C42·C43. At SI 1 all amorphous drug can dissolve and the supersaturation is the highest possible, "the highest possible driving force for crystal growth" C40. The fresh generic, with no detectable crystallinity, is "thought to contain a low level of crystalline seeds" (ref 11); "it can be inferred" that they grow slowly at first because their surface area is small, and since the fresh capsules release more than 95%, the seeds are assumed to be below 5% of the drug C44·C45·C46.

Note by the AI writer (not discussed in the paper): the proportional picture does not hold exactly. The 10% capsules peaked at about 76.5%, well below 90%, and nominally 100% crystalline contents released about 10% at 10 min (about 5 µg/mL), more than twice the 1.8 µg/mL crystalline solubility of raw tacrolimus monohydrate; the same excess appears in every condition (about 58% at 900 mL, about 3.2 µg/mL) X6·R5·R7·R4. The crystals formed in the aged capsules therefore dissolve to a higher level than the raw monohydrate, or some amorphous drug remains below the XRPD limit; the paper does not say which X6·R2.

Main result 3: 450 and 40 mL. At 450 mL (amorphous SI 4.5) release rose to plateaus that fell with crystallinity, about 81% (10%), 78% (20%), 50.5% (50%) and 33.5% (100%) at 120 min; only 30% and 40% declined late, from about 68% to 55% and from about 56% to 47.5% between 60 and 120 min (Figure 4a) R6. The authors read the low-crystallinity plateau as "indicating that insufficient crystal surface area is present to observe crystal growth", and the late decline as "additional crystallization of tacrolimus during the dissolution experiments" C38·C22. No fresh generic or Prograf curve is shown at 450 mL, although the caption of Figure 4 names Prograf X11.

Table D. Release (% of the 5 mg dose; 40% = 50 µg/mL) in 40 mL of medium I, selected samples read from Figure 4c (all values approximate) R8.

At 40 mL (amorphous SI 0.4) the dose cannot all dissolve even as amorphous drug R4. Prograf held about 43–45% for 2 h, about 54–56 µg/mL; the fresh generic stayed at about 37.5–39% (about 47–49 µg/mL) from 20 to 60 min and then fell to about 15%; with crystallinity the plateau shortened and the decline started earlier (Table D) R8·C25·C50. The authors write that "at least 60% of the drug remains undissolved at maximum release", which matches the postulate that ASDs with a high drug-to-polymer ratio, here 1:1, release incompletely when the medium is non-sink for amorphous drug (ref 15; similar behavior for felodipine–HPMC and felodipine–PVP ASDs, ref 50) C47·C48·R22. That figure holds for the generic capsules; Prograf reached about 45%, and its 54–56 µg/mL lie somewhat above the ~50 µg/mL cited as the amorphous solubility X7. Compared with 100 mL, the plateau lasts longer at 40 mL and the 10% capsules reach a higher concentration (about 50 against 38 µg/mL), which the authors explain by undissolved amorphous drug replacing the drug that the crystals take: "This is again a result of the balance between the crystal growth and dissolution processes" C49. For the fresh generic the maximum was about the same in both volumes (about 48.5 and 49 µg/mL), so only the longer plateau applies to it X8.

The authors read all three volumes through the Cardew–Davey time scales: at 450 mL the system is dissolution dominated for 0–30 min, balanced for 30–90 min (the plateau) and growth dominated for 90–120 min; at 100 mL the generic switches from dissolution to growth control after 20 min; at 40 mL "the results suggest" dissolution control for 0–10 min, balance for 10–60 min and growth control, or exhaustion of undissolved drug, for 60–120 min C54. Halving the volume from 900 to 450 mL doubles the possible supersaturation, which "is the likely reason" that crystal growth appears at 450 mL but not at 900 mL C55.

Main result 4: the PBPK model. Table E compares simulated and observed values.

Table E. Model verification in fasted healthy volunteers; Figure 5 peaks read from the plot (approximate), other values as printed R10·R11·R12.

The simulated blood profile follows the shape of the four observed 5 mg data sets, with a peak near 1.5 h and similar late concentrations (about 1 ng/mL at 72 h), and the authors state that the model "accurately" predicts the observed concentrations R10·C27. The simulated Cmax and AUC rise linearly with dose and are "consistent with those observed", and the simulated bioavailability (20.2%) lies inside the literature range (14.4–25%) R11·R12·C28. Note by the AI writer: the simulated slopes are about 1.44 times (Cmax) and 1.42 times (AUC) the observed ones, and the simulated peak lies above all four observed peaks, so the model over-predicts absolute exposure by about 40% in the dose-linearity data X3. The Cmax axis of Figure 6a is labelled ng/mL, but its values (0.005–0.066) only match Figure 5 if read as µg/mL X2.

Main result 5: virtual bioequivalence. Table F lists the AUC ratios read from Figure 7.

Table F. Point estimates of the AUC test-to-reference ratio (%) in the virtual trials, read from Figures 7a–7d (all values approximate); a level fails when the 90% CI of AUC, AUCt or Cmax leaves 80–125% R13·R14·R15·R16.

With the 100 mL data as input, the generic fails against Prograf from 20% crystallinity (AUC ratio about 70%, CI about 67–80%) and against the fresh generic from 10% (about 79.5%, CI about 73–88%) R13·R14·R17. With the 900 mL data it fails against both only from 40% (about 69% and 74.5%) R15·R16·R17. The fresh generic itself passes against Prograf with both inputs (AUC ratio about 109% with 100 mL data, about 92% with 900 mL data) R13·R15. The results section states the thresholds as "20% or above", "10% or above" and "40% or above"; the discussion writes "greater than 20%" and "greater than 40%", and the figures agree with the results wording R17·X1. Some levels sit right at the limit: the 10% capsule against Prograf with 100 mL data has its lowest CI bound at about 80%, and the 30% capsule with 900 mL data likewise X14. Note by the AI writer (not discussed in the paper): with 100 mL input the 30% capsules give lower ratios (about 43%) than the 40–60% capsules (about 48–51%), mirroring their 100 mL profiles, which converge to about 26–29.5% by 120 min R13·R7.

Discussion

What the authors conclude. In their conclusion the authors write that the virtual trials "suggest that compendial dissolution measurements may not be sufficiently discriminatory against the tolerable level of crystallinity in a formulation to be bioequivalent", that such tests "may underestimate the impact of crystallinity on BE between fresh and aged formulations", and that tests in lower volumes "may provide more appropriate input data into PBPK models" C62·C63. In the abstract the PBPK approach "can be used to assess the impact of partial drug crystallinity in the formulated product and to guide the development of appropriate dissolution methods" C64. They add that a dissolution method for supersaturating products "must be able to differentiate formulations with varying levels of crystallinity", and that "future studies are now warranted" to find which tests discriminate in a clinically relevant way C61·C65.

Where the approach applies. The study covers one generic product of one drug, an amorphous tacrolimus–HPMC capsule with a 1:1 drug-to-polymer ratio, at one dose strength, in one non-compendial medium (medium I at pH 4.5 with HPC) M2·P8·P12. The crystals were grown inside the product under one stress condition P1. The logic, however, is general: a test detects crystallinity only if crystals cannot dissolve along with the amorphous drug (SI below 1 for the crystal), and it detects seed growth only if it lets the solution supersaturate strongly (amorphous SI near or below 1) C33·C40. Within this study the most sensitive condition was the one at which the dose just fits the amorphous solubility, where all amorphous drug can dissolve and the supersaturation is highest C39·C40.

The model assumptions. The PBPK model assumes no precipitation in vivo, which the authors call "a fair assumption" because fresh products hold supersaturation for about 1 h in the non-sink tests and absorption is mostly over within 1 h (Tmax about 1 h) C59. They also note that integrating in vitro release and precipitation with PBPK "remains a challenge" and that GastroPlus offers "very limited modeling options" for in vivo supersaturation and precipitation C60. In effect, the test medium decides how much desupersaturation enters the model: the 100 mL profiles carry it, the single-point 900 mL data do not C11·P12.

What it suggests for formulation. Note by the AI writer (not discussed in the paper): for this capsule, a batch with 20–30% crystallinity would meet the USP test I specification but is predicted by the 100 mL-based model to fail bioequivalence against Prograf, so a crystallinity limit set from the compendial test would be too lenient C18·R17. Prograf and the generic list the same excipients and drug-to-polymer ratio, yet Prograf held supersaturation for 2 h while the fresh generic lost it within about an hour; how the product was made, or seeds below the XRPD detection limit, may matter as much as the composition M1·M2·R7·R8.

Limitations

Limitations stated by the authors. The bioequivalence results are simulations; a human study in healthy volunteers was under way, and its outcome "will provide greater insight into which dissolution volume provides in vivo relevant information" C58. The model assumes no in vivo precipitation, and current software handles supersaturation and precipitation only in a limited way C59·C60. The USP tests were run on 3 rather than 6 capsules per level C18. Pharmacopeial methods are single-point tests "not designed to capture the potential phase transformations" of supersaturating dosage forms C37. The virtual trials used a two-way crossover design, whereas NTI drugs now require a fully replicated design C13.

The AI writer's own judgement (1): the model and its inputs. The model over-predicts dose-normalized Cmax and AUC by about 40% against the observed dose-linearity data, so its T/R ratios are comparisons inside a model that is not calibrated for absolute exposure X3. More important for reproducing the thresholds, the paper does not show the 900 mL profiles used as input for Figures 7c and 7d, although USP test I was run as a single 90-minute point, and it does not say how the falling 100 mL profiles were entered into a release input that only accumulates X10. The input for Figure 5 is not stated either; its simulated 5 mg peak (about 28.7 ng/mL) differs from the about 32.5 ng/mL implied by the Figure 6a slope X10. Several model settings in Table 1 (a diffusion coefficient of 0.4 cm²/s, regional "Perm." values up to 12.47, "adjusted plasma 6.7678") have no stated units or explanation X12.

The AI writer's own judgement (2): the thresholds and the mechanism. The crystallinity thresholds come from one simulated trial of 24 subjects, and some levels lie exactly at the 80% limit, so each threshold is uncertain by about one 10% step X14. Several statements in the discussion are stronger than the plotted data: the Stage 1 pass at 20% crystallinity, the 80% limit in test II, the "at least 60%" undissolved at 40 mL (which excludes Prograf), the higher maximum at 40 mL (true for the 10% capsules only) and the 900 mL plateau (not plotted) X4·X5·X7·X8·X9. The mechanism itself, seeds growing faster at higher supersaturation and polymers poisoning growth at 900 mL, is read from concentration profiles; no solid-state analysis of the undissolved material during dissolution was made, and the presence of seeds in the fresh generic is inferred C36·C43·X16. Finally, the crystalline material of the aged capsules dissolves above the solubility of raw tacrolimus monohydrate, which the proportional dose-reduction argument does not cover X6. None of this changes the central contrast: the compendial tests barely register crystallinity, and the 100 mL test separates every level R5·R7.

Conclusion

The paper makes three contributions. First, it produced commercial amorphous capsules with known amounts of crystals grown inside the product and showed that the two USP dissolution tests barely register them: test I would pass up to 30% crystallinity and the surfactant-containing test II up to 80% C18·C19·R5. Second, it showed that tests in less medium, especially 100 mL where the dose just fits the amorphous solubility, separate every crystallinity level, and read the profiles as seed growth driven by supersaturation C39·C40·C43·R7. Third, it fed these profiles into a PBPK model and found, in virtual trials, that bioequivalence against Prograf is lost from 20% crystallinity with 100 mL data but only from 40% with compendial data R17·C29.

Under the conditions of the study, one generic product, simulated rather than measured pharmacokinetics and a model that assumes no gut precipitation, the result is a warning about compendial tests rather than a validated limit. The authors' own wording is that compendial tests "may not be sufficiently discriminatory" and "may underestimate" the effect of crystallinity, and that the human study under way would decide which dissolution volume is clinically relevant C62·C58.