Review: storyline · equations and derivations
Following Taylor L.S., Zhang G.G.Z. (2016) Physical chemistry of supersaturated solutions and implications for oral absorption. Advanced Drug Delivery Reviews.
What this page is. Taylor and Zhang (2016) build one line of reasoning from the crystalline solubility through the amorphous solubility, liquid–liquid phase separation (LLPS), solubilization and membrane flux to the dissolution of amorphous solid dispersions (ASDs) and a set of absorption simulations, and end with "spring and plateau" as the target for enabling formulations. This page follows that line step by step; each step gives the review's argument and then what the library's papers, from 2010 to 2026, have measured since, with links to the findings. Where the review states a simulation or an interpretation, and where the library holds a measurement, is marked in each step.
Question. Against which state is supersaturation measured, and which terms of the dissolution rate can a formulation change?
The review's reasoning (2016). The review starts from the Noyes–Whitney equation with a Nernst–Brunner diffusion layer [review p. 2]:
The diffusion coefficient D and the layer thickness h are set by the molecule and the gastrointestinal tract, whereas surface area S and solubility C_s can be changed by formulation [review p. 2]. The crystalline solubility is a solid–liquid equilibrium with the supercooled liquid as standard state [review p. 3]:
A solution is supersaturated when the chemical potential of the solute exceeds that of the solute in equilibrium with the most stable crystal [review p. 3]:
The concentration ratio of Eq. 4 approximates Eq. 3 only when \gamma_D^{W(S)}/\gamma_D^{W(c)} is close to 1, which the authors expect at very low supersaturation and/or in very dilute solutions in simple media [review p. 3].
What the library shows. The reference C^{*} has to be measured in the same medium, including dissolved polymer. At 1 mg/mL, HPMC and two HPMCAS grades raised the crystalline solubility of papaverine from 12.2 to 19.0–21.9 µg/mL [hsieh2014 R4] (2014), and 0.1% SDS raised that of 11 drugs 1.2- to about 266-fold [chen2015 R1] (Crystallization from solution F19). A higher total concentration was not a higher activity: 5 µg/mL HPMCAS doubled the celecoxib solubility (1.2 → 2.4 µg/mL) without changing its membrane mass flow (0.44 µg/min) [li2016a R15] (Crystallization from solution F19). At the mg/mL levels that a dispersion releases, dissolved HPMCAS raised crystalline resveratrol from 42 to about 1230 µg/mL at 20 mg/mL, which the authors attribute mainly to a soluble drug–polymer complex [wegiel2015 R2, R3, C41] (2015), whereas with 22 µg/mL to 1 mg/mL polymer felodipine, celecoxib and lopinavir kept their crystalline solubility within about 0.84–1.43 times [konno2008a R1; xie2015 R11; xie2016a R1; li2018 R1] (Supersaturation from ASD dissolution F17).
Corrections and qualifications.
Next. This step fixes the reference against which every activity is read; it does not say how far above the crystal a non-crystalline drug can go, which is the amorphous solubility.
Pages. crystalline solubility, supersaturation, chemical potential, thermodynamic activity, activity coefficient, Noyes–Whitney equation, solid–liquid equilibrium solubility equation, activity-based supersaturation ratio, supersaturation ratio.
Question. What concentration is reached when the amorphous form, not the crystal, is in contact with the solution, and what sets its ratio to the crystalline solubility?
The review's reasoning (2016). Strictly no equilibrium with amorphous material exists, but when crystallization is slow a metastable equilibrium can be treated as a liquid–liquid equilibrium, with the amorphous drug as a supercooled liquid, also for drugs that are glasses at the temperature of interest [review p. 3]. Assuming \gamma_D^{W(c)} \cong \gamma_D^{W(a)} at these low concentrations, Eq. 2 gives the amorphous from the crystalline solubility [review p. 3]:
The chemical potential difference needs \Delta H_f and T_m, and with constant \Delta C_p is printed as [review p. 3]:
Water absorbed by the amorphous drug lowers its chemical potential, so the activity of drug in the water-saturated amorphous phase enters (Eqs. 8–9) and the amorphous solubility becomes [review pp. 3–4]:
where the water term comes from the sorption isotherm by the Gibbs–Duhem equation [review p. 4]. Amorphous phases generated in situ above the amorphous solubility give values on the line of slope 1 against prediction for 23 compounds [review p. 6, Fig. 4]. The amorphous-to-crystalline ratio grows with T_m and \Delta H_f and falls with water uptake: ibuprofen only 4 (T_m ~77 °C), atazanavir ~65 (T_m ~208 °C) [review p. 8]. Higher ionic strength lowers the amorphous solubility (ritonavir, Fig. 8), and for weak bases the un-ionized drug stays at the amorphous solubility, so the ratio "remains constant as a function of pH" [review pp. 8–9].
What the library shows. Across 17 compounds, 17 of 24 measured onsets lie between 0.91 and 1.15 times the value of Eq. 11; ritonavir in water gave 37.2 µg/mL against a predicted 39.2 [ilevbare2013a R8, R13] (2013), and atazanavir 70 against 68 µg/mL [indulkar2017a R5, R6] (Amorphous solubility and LLPS F5). The water term is not small: exp[−I(a2)] was 0.27 for ritonavir and 0.22 for atazanavir [ilevbare2013a M1; indulkar2015 M2]. For telaprevir, Eq. 11 gave 245 ± 5 µg/mL with the Hoffman equation and 97 ± 8 with the crystal-to-supercooled-liquid heat capacity, against 90–92 µg/mL measured [mosqueragiraldo2015 R13] (2015) (Amorphous solubility and LLPS F7). The ratio spans from 2.2 for efavirenz [ilevbare2013a R8] to about 603 for pazopanib at pH 6.5 [sugihara2018 R4] (2018) (Amorphous solubility and LLPS F6). The ritonavir onset fell from 37.2 µg/mL in water to 18.8, 14.3 and 4.7 µg/mL in 100, 200 and 500 mM phosphate [ilevbare2013a R13] (Amorphous solubility and LLPS F9), and for clotrimazole, atazanavir and nicardipine the total LLPS concentration rose 30- to 65-fold with ionization while the un-ionized part stayed near 5.6–8.4, 57–70 and 4.5–6.8 µg/mL [indulkar2015 R9] (Amorphous solubility and LLPS F10).
Corrections and qualifications.
Next. This step gives the ceiling as a number; to use it the review must show what phase coexists with the solution at that number and why reaching it from a solution gives the same state.
Pages. amorphous solubility, amorphous solubility advantage, supercooled liquid, water sorption correction of amorphous solubility, Hoffman equation, Henderson–Hasselbalch equation, amorphous solubility advantage with water-sorption correction, amorphous–crystalline free energy difference from heat capacity, amorphous-to-crystalline solubility ratio.
Question. What phase coexists with the solution at the amorphous solubility, and what lowers that solubility once other components are present?
The review's reasoning (2016). Drug and water have a miscibility gap: between the binodal compositions x_{DW} (drug-rich) and x_{WD} (water-rich) the mixture splits into two liquids, by nucleation and growth between binodal and spinodal and spontaneously inside the spinodal (\partial^2G/\partial x^2 = 0) [review p. 4, Fig. 1]. If the drug-rich phase is below its water-plasticized T_g the process is glass–liquid phase separation (GLPS) [review p. 4]. At equilibrium the drug has the same activity in both phases [review p. 5]:
so the amorphous solubility x_{WD} is set by the activity of drug in the water-saturated drug-rich phase, the water term of Eq. 10 [review p. 5]. Equilibrating amorphous drug with water and adding drug to water until LLPS end in the same two phases; the second route is the one relevant to drug delivery [review p. 5]. A second drug that mixes into the drug-rich phase lowers the drug's activity there and hence the amorphous solubility; for ritonavir and lopinavir ideal mixing predicts that each is halved at a mole fraction of 0.5, while the diclofenac anion had no effect [review p. 9, Fig. 9]. PVP, HPMC and HPMCAS had no detectable effect on the amorphous solubility of danazol, and by NMR PVPVA and HPMCAS made up less than 7 wt.% of a drug-rich phase, "confirming" that the polymers do not mix substantially with it [review p. 9].
What the library shows. The isolated ritonavir drug-rich phase held 94.85–95.97% drug and 4.03–5.15% water, matching the 5.21% that amorphous ritonavir sorbs at 100% RH by extrapolation [ilevbare2013a R6, E14] (2013) (Amorphous solubility and LLPS F1). Whether it is a liquid or a glass follows its wet T_g: 0.4 °C for ritonavir, about 14 °C for clotrimazole and about 51 and 52 °C for atazanavir and telaprevir [ilevbare2013a R5; indulkar2015 R22; mosqueragiraldo2015 R2]; the glassy telaprevir phase still redissolved within about 2 min on dilution [mosqueragiraldo2015 R8] (Amorphous solubility and LLPS F2). A second drug lowered the onset as the review states: with 10 µM lopinavir, paclitaxel or felodipine, ritonavir separated at about 14, 10 and 12 µg/mL instead of about 26 µg/mL, while with diclofenac it stayed at about 25 µg/mL [trasi2015a R7, R11] (2015) (Amorphous solubility and LLPS F11). For danazol, 1–1000 µg/mL PVP, HPMC or HPMC-AS left the onset at 7–9.1 µg/mL and the maximum flux unchanged [jackson2016 R8, R11] (Crystallization from solution F22). Later papers found polymers that do lower the ceiling: 300 µg/mL HPMC and PVP-VA lowered the amorphous solubility of ibuprofen from 177.1 to 96.9 and 90.7 µg/mL [ueda2020b R1, R13] (2020) (Amorphous solubility and LLPS F19); HPMCAS-HF lowered atazanavir from 81.5 to 35.5 µg/mL and clozapine from 233.0 to 95.0 µg/mL, while AS-LF moved them only to 75.8 and 219.0 µg/mL [ueda2020a R1] (Bioperformance F19); and HPMCAS and Eudragit E PO lowered dissolved enzalutamide from 42 to about 20.5–36.5 and 23.5–30.5 µg/mL [wilson2021 R8] (2021) (Crystallization from solution F19).
Corrections and qualifications.
Next. This step establishes that a drug-rich liquid or glass can coexist with a solution at a fixed activity; whether that state appears in practice depends on whether the crystal forms first.
Pages. liquid–liquid phase separation, binodal, spinodal decomposition, free energy of mixing, drug-rich phase, glass–liquid phase separation, ideal mixing, polymer partitioning into the drug-rich phase, ideal-mixing reduction of amorphous solubility.
Question. When a solution is pushed above the amorphous solubility, does it form the drug-rich phase or crystals, and how long does the two-phase state last?
The review's reasoning (2016). Between the crystalline and the amorphous solubility curves only crystals can form; above the amorphous curve either LLPS or crystallization can take place [review p. 5, Fig. 2]. Because crystal nucleation and growth have kinetic barriers, "slow crystallizers" given a rapidly generated high supersaturation split into two liquids, and the amorphous phase is a precursor expected to crystallize later, as in the "oiling out" of process chemistry [review p. 5, Fig. 3]. The drug-rich species measure 100–500 nm by DLS when formed and can grow unless additives such as polymers inhibit growth [review p. 6]. In a study of about 50 compounds, about a third crystallized within 2.5 min of solvent shift and a third had not crystallized after 1 h [review p. 6]. Light scattering at a non-absorbing wavelength, polarity probes and ultracentrifugation locate the onset, the droplets redissolve rapidly below the amorphous solubility, and agreement between methods suggests little overshoot before separation [review pp. 6–8]. Droplets coarsen and agglomerate, and their interfaces may favour heterogeneous nucleation [review pp. 13–14].
What the library shows. For ritonavir the drug-rich phase lies far inside the metastable zone (37.2 against 2.4 µg/mL crystalline solubility in water at 37 °C) [ilevbare2013a R8, R11] (2013) (Amorphous solubility and LLPS F3). Lifetimes without polymer run from minutes to hours: telaprevir gave birefringent particles after about 15 min, while 5 µg/mL HPMCAS-MF kept the turbid solution for hours [mosqueragiraldo2015 R1], and pazopanib held its supersaturation for 5 ± 2 min without and about 39 min with 50 µg/mL HPMC [sugihara2018 R22] (2018) (Amorphous solubility and LLPS F3). Unseeded induction times at the calculated amorphous solubility were about 2.4 min for celecoxib and 120 min for ritonavir, although their seeds grew at almost the same rate per area (6.23 and 6.14 mg min⁻¹ m⁻²), so the difference lies in nucleation [ilevbare2013c R8; ilevbare2013b R7] (Crystallization from solution F3). Fresh droplets measured 116–387 nm for three weak bases [indulkar2015 R14], and ritonavir droplets grew from about 345 to about 842 nm in 64 min [ilevbare2013a R3] (Amorphous solubility and LLPS F1). With 300 µg/mL HPMC or PVP-VA fresh ibuprofen droplets measured 268–345 nm instead of 3182–5313 nm, but over 3 h the droplet-phase drug fell from about 264 to 67 µg/mL with PVP-VA against about 260 to 183 µg/mL with HPMC [ueda2020b R5, R15] (2020) (Amorphous solubility and LLPS F22). For ritonavir the induction time was about 284 min at 17 µg/mL, below the LLPS concentration of 18.2 µg/mL, against 119.3 min at 20 µg/mL, and SDS and Tween 80 shortened it only when droplets were present [ilevbare2013d R16, R12] (Supersaturation from ASD dissolution F13).
Corrections and qualifications.
Next. This step shows that a two-phase solution can persist at a constant activity for minutes to hours; the review then needs a read-out of that activity, which is membrane flux.
Pages. metastable zone, crystallization tendency, nucleation induction time, drug-rich nanodroplets, drug-rich phase coarsening, heterogeneous nucleation, light scattering by particles, pyrene I1/I3 polarity ratio, temperature–composition phase diagram.
Question. Does membrane transport follow concentration or activity, and is there a highest flux that supersaturation can give?
The review's reasoning (2016). Dissolution-limited bioavailability is addressed by faster dissolution, solubility-limited bioavailability only by supersaturation [review p. 9]. Crystal-saturated solutions of very different concentration gave nearly constant flux, and solubility and membrane–solution partition coefficient are reciprocal, so a solubilizer does not raise flux; following Higuchi, flux is written in terms of activity [review p. 9]:
with D, h and \gamma_m constant for a given system. For danazol (crystalline solubility about 1 µg/mL) flux rose linearly to about 8 µg/mL and stayed constant above, about an order of magnitude above the crystalline flux; the plateau is the amorphous solubility, above which added drug enlarges the drug-rich phase at constant activity, and solutions made by dissolving ASDs with 90 wt.% PVP, HPMC or HPMCAS gave a flux similar to antisolvent solutions [review pp. 9–10, Fig. 10]. The authors then state that the amorphous solubility caps the supersaturation of any formulation: temperature change, antisolvent addition, pH swing, ASD and salt dissolution all gave a drug-rich phase, lipolysis may, and prodrugs and co-crystals are "unexplored potential routes"; the cap is the amorphous solubility, "or strictly speaking, the spinodal decomposition point" [review p. 10, Fig. 11]. The ratio "probably should be considered during lead optimization and candidate selection" [review p. 10].
What the library shows. The flux plateau is repeated in every drug tested: telaprevir flux rose linearly to about 0.97 µg/min at 90 µg/mL and reached only about 1.07 µg/min at 130 µg/mL [mosqueragiraldo2015 R12] (2015); ritonavir, lopinavir and paclitaxel broke at 27.3, 16.1 and 30.1 µg/mL, matching three other onset estimates [trasi2015a R1, R2]; and atazanavir rose linearly to 70 µg/mL and stayed at about 0.114–0.121 µg/min·cm² up to 200 µg/mL [indulkar2017a R10] (2017) (Amorphous solubility and LLPS F8). The cap holds for dispersions: every danazol dispersion that formed a drug-rich phase gave 7.1–9.1 µg/mL free drug by flux, like antisolvent solutions (7.2–8.2 µg/mL), whereas the 50:50 HPMCAS dispersion, which formed none, gave 5.4 ± 0.8 µg/mL [jackson2015 R9]; felodipine flux relative to the crystal was 10.5, 9.5 and 8.5 for 90:10 and 50:50 HPMC dispersions and pure amorphous drug against a predicted factor of about 9 [alonzo2011 R14]; and six marketed 5-mg tacrolimus capsules all levelled off at about 46–50 µg/mL, the amorphous solubility measured four ways [trasi2016 R10, R4] (2016) (Supersaturation from ASD dissolution F7).
Corrections and qualifications.
Next. Flux reads activity and the amorphous solubility caps it in simple buffers; the intestine and most formulations contain solubilizers, which raise the total concentration without raising the activity, so the review has to separate the two.
Pages. membrane flux, membrane transport, thermodynamic activity, solubility–permeability interplay, dissolution-rate-limited absorption, supersaturating drug delivery systems, membrane flux in terms of solute activity, supersaturation from membrane flux ratio.
Question. When micelles or other solubilizers are present, which part of the dissolved drug sets the driving force, and does the concentration ratio still measure it?
The review's reasoning (2016). Micellar solubilization is described by a micelle–water partition coefficient [review pp. 10–11]:
so the total solubility rises while the free drug in water, which alone partitions into the membrane, does not. For felodipine with Vit E TPGS the crystalline solubility rose from about 1 to 40 µg/mL and the amorphous solubility from about 10 to 177 µg/mL; the ratio fell from about 9 to about 4.5, Eq. 4 under-predicted the supersaturation in TPGS and in FaSSIF, and the maximum flux was the same as in buffer [review pp. 10–11]. A micelle–water partition coefficient that decreases as drug concentration rises is called "the most plausible explanation" [review p. 11]. This is the review's interpretation; the coefficient was not measured in the work it cites.
What the library shows. The felodipine data are those of Raina 2015: onsets 10.4, 177.3 and 214.6 µg/mL in buffer, 0.04% Vit E TPGS and FaSSIF, ratios 9.2, 4.5 and 5.0, and the buffer flux band of about 0.11–0.15 µg/min reached only at 175–200 and from 250 µg/mL [raina2015c R11, R9] (2015) (Bioperformance F4); above their critical micelle concentration six additives cut the flux of 50 µg/mL felodipine from about 0.14 to 0.010–0.12 µg/min [raina2015c R7] (Bioperformance F3). The partition coefficient was measured in 2017: for atazanavir in 3.6 mg/mL SDS, Km/w fell from about 327 to about 99 as total drug rose to 100 µg/mL and then stayed at about 90–114 up to 1450 µg/mL, and the amorphous solubility rose only half as much as predicted from the crystal (κ 0.183 against 0.351) [indulkar2017a R14, R9] (Amorphous solubility and LLPS F18). At the amorphous solubility the concentration ratio was 37.5, 35.9 and 33.0 at 1, 2 and 3.6 mg/mL SDS, while the flux-derived activity ratio was 70.0, 66.1 and 65.0, as in buffer (66.0) [indulkar2017a R13]; in five simulated media and pooled human intestinal fluid the flux-based maximum stayed at about 50–56 for atazanavir and 29–37 for posaconazole, while the concentration-based value fell to about 14 and 5 in human fluid [elkhabaz2019b R8, R9] (2019) (Amorphous solubility and LLPS F16).
Corrections and qualifications.
Next. With free and solubilized drug separated, the review can place the formulation in the intestine as a set of compartments around one aqueous phase from which drug is absorbed.
Pages. micellar solubilization, free drug concentration, bile-salt micelles, supersaturation ratio, critical micelle concentration, activity from concentration, activity-based supersaturation ratio.
Question. How do drug-rich droplets, micelles and undissolved solid in the gut lumen feed the free drug that is absorbed?
The review's reasoning (2016). The gastrointestinal tract is simplified to a central aqueous compartment in contact with the membrane, from which only the un-ionized drug is thought to be absorbed passively, surrounded by compartments (micelles, lipid vesicles, crystals, drug-rich droplets) that exchange drug with it as drug is absorbed [review pp. 11–12, Fig. 12]. Ideally an ASD dissolves rapidly and completely into a supersaturated solution in equilibrium with drug-rich nanodroplets, which exchange fast because they are pre-wetted and have a very high specific surface area [review p. 14]. For clotrimazole (amorphous solubility 7.5 µg/mL) donors of 0.5–7 µg/mL gave flux proportional to concentration that declined with time, whereas above 7.5 µg/mL 200–250 nm droplets formed and the flux stayed at its maximum for a time that "roughly correlates" with the excess over the amorphous solubility; the authors conclude that the activity in the aqueous phase is "maintained at its maximum value of 1" until the droplets are consumed [review pp. 14–15, Figs. 13–14]. The review also states that "a well-designed formulation will rely on transferring the drug into drug-rich liquid droplets and compartments such as micelles" [review pp. 12–13].
What the library shows. The clotrimazole data are Indulkar 2016: the steady receiver period was about 1 h at 10 µg/mL, 5 h at 15 and at least 13 h at 20 µg/mL, and 7.5 mg/mL of 150–250 µm amorphous particles gave no plateau, falling from about 0.63 to 0.42 µg/mL, below the one-phase control [indulkar2016 R6, R7] (2016) (Bioperformance F5). The effect was carried to ASD-derived droplets: 90:10 HPMCAS and HPMC atazanavir ASDs held the hollow-fibre receiver above the level of an amorphous-solubility solution for 120 min, with maxima of about 10.0 and 9.4 µg/mL [hate2018 R13] (2018). In the same module the transfer kept rising above the amorphous solubility, the AUC slope falling from 5.51 to 1.29 at 78 µg/mL without a plateau, as droplet count rose from about 2.3 × 10⁹ to 1.06 × 10¹⁰ per mL; the authors read this as a higher mass transfer coefficient and leave the mechanism untested [hate2018 E3, E4, R7, C56] (Bioperformance F15).
Corrections and qualifications.
Next. The reservoir works only if the formulation delivers the dose into the droplet state rather than into crystals, so the review turns to what happens while an ASD dissolves.
Pages. nanodroplet reservoir effect, drug-rich nanodroplets, drug-rich phase, sink conditions, membrane mass transfer coefficient, mass transferred from receiver AUC.
Question. Which processes during ASD dissolution decide whether the solution reaches the amorphous solubility and forms the reservoir, or loses its supersaturation to crystals?
The review's reasoning (2016). Copovidone and HPMC matrices tend to erode in water while HPMCAS formulations can be designed to disintegrate [review p. 12]. The driving force for dissolution of a multicomponent solid is "poorly understood": felodipine ASDs at low drug:polymer ratio dissolved rapidly under non-sink conditions and generated nanoparticles, read as the amorphous solubility being exceeded, whereas at higher ratios dissolution was slower, no nanoparticles formed and the concentration approached but did not exceed the amorphous solubility [review pp. 12–13]. For sulfathiazole–PVP the polymer dissolved faster than the drug, and the drug-enriched surface lowered the rate [review p. 13]. Water lowers the Tg of the wetted solid: amorphous nifedipine crystallized immediately in water, but not with HPMC, and water-induced amorphous–amorphous phase separation, to which PVP dispersions are susceptible, is "a precursor to crystallization" [review p. 13]. Felodipine–PVP dispersions gave high but short-lived supersaturation, so an effective crystallization inhibitor is "essential"; with one, dissolution continues until the solution splits into two liquid phases [review p. 13]. The droplets can grow, agglomerate and nucleate crystals heterogeneously, and surfactants can inhibit or promote this [review pp. 13–14].
What the library shows. The two loss routes were separated in situ: neat amorphous felodipine at 37 °C was about 54% crystalline at 1 min and dissolved no higher than the crystal (about 0.9–1.1 µg/mL), whereas amorphous indomethacin at 25 °C stayed amorphous while needles grew in the liquid [alonzo2010 R2, R1, R11] (2010), and nifedipine glass crystallized within minutes with or without dissolved polymer while its 50:50 dispersions crystallized from the solution instead [raina2014b R2, R13] (2014) (Supersaturation from ASD dissolution F1). The loading effect was named the limit of congruency: ritonavir–PVPVA tablets released about 97% at 60 min at 25% loading, about 29% at 30% and at most about 2% at 35–50% [indulkar2019a R11] (2019), and in PVPVA the limit lay between 2% and 40% for the drug forms tested to 2022 (Release mechanism and LoC F6). In 2017–2020 only release under polymer control passed the amorphous solubility and formed 190–370 nm droplets [purohit2017b R10, R11] (Release mechanism and LoC F4); droplets from a ritonavir–PVP dispersion vanished on dilution and had a Tg of about 1 °C [ilevbare2013d R1, R2] (2013) (Supersaturation from ASD dissolution F9).
Corrections and qualifications.
Next. A dispersion that reaches the ceiling and forms droplets still has to hold it while the membrane removes drug, so the review adds absorption to the picture.
Pages. limit of congruency, congruent release, polymer-controlled release, matrix crystallization, solution crystallization, plasticization by water, drug-rich nanodroplets, surface-normalized release rate.
Question. How does removal of drug by the membrane change the activity in the central compartment, and for which drugs does activity matter?
The review's reasoning (2016). Membrane flux links all earlier processes to passive absorption and is set by the activity of the drug in the central compartment, which, not the total concentration, should be measured or estimated [review p. 14]. For BCS class IV drugs slow permeation is likely rate-determining and activity "may not be the most critical parameter"; for BCS class II drugs a higher activity by supersaturation drives transport [review p. 14]. Removal from the central compartment may be fast compared with entry by dissolution, so that the effective activity is lowered and, in the extreme, absorption is dissolution-rate-limited; a reservoir with a low barrier for entering the central compartment overcomes this [review p. 14]. In the simulations the activity with and without absorption is compared for a slowly dissolving ASD (Fig. 18) [review pp. 16–17]. This is the review's argument and simulation; it reports no measurement with a sink.
What the library shows. Measurements with an absorptive sink came from 2017. With 0.05% HPMC-AS a nevirapine tablet donor stayed at about 525 µg/mL for 270 min in a closed vessel but fell to about 253 µg/mL with absorption, and with 0.1% PVPVA the total drug stayed at about 44–49 mg with absorption while the dissolved drug of the closed vessel fell to about 26 mg [hate2017 R15, R7, R17] (2017); 50% atazanavir ASDs released about 6200, 6300 and 5000 µg at 120 min with a sink against about 4200, 4600 and 3600 µg without (HPMCAS, HPMC, PVPVA) [hate2018 R18] (2018) (Bioperformance F14). A sink also raised atazanavir release from SBA-15 at 240 min from about 46.5 to 89.5% [hate2020a R20] (2020) (Overview F14). These measure the review's point, and add that removal also raises the release of slow dispersions.
Corrections and qualifications.
Next. With supply, removal and crystallization each given a rate, the review can compare whole scenarios by the fraction of the dose absorbed in a finite residence time.
Pages. absorptive sink, absorptive dissolution testing, non-sink dissolution, dissolution-rate-limited absorption, desupersaturation, hollow-fibre donor depletion.
Question. Which dissolution and phase behaviour gives the largest fraction of a high dose-number drug absorbed, and what should an enabling formulation aim for?
The review's reasoning (2016): a simulation. The assumptions are a crystalline solubility of 1 µg/mL and an amorphous solubility of 10 µg/mL (activity 1 for the amorphous and 0.1 for the crystalline phase); a 5 mg dose; a central compartment of 100 mL, after a human study [109]; passive absorption only; and a flux chosen for high permeability, absorption being limited by free drug [review p. 15]. The simulations "do not contain sufficient parameters to represent the complex biological situation" and serve to compare scenarios [review p. 15]:
Shortening the residence time from 8 h to 4 h lowers every case (Table 1; introduced on p. 18 of the review, and placed on p. 2 of the extracted text) [review p. 18]:
| Case | % absorbed, 8 h | % absorbed, 4 h |
|---|---|---|
| 1 | 100 | 65 |
| 2a | 23 | 17 |
| 2b | 46 | 27 |
| 2c | 71 | 52 |
| 3 | 30 | 11 |
| 4 | 13 | 6 |
From Case 1 the authors define "spring and plateau": fast dissolution to the LLPS/GLPS concentration, the thermodynamic limit, held by replenishment from the drug-rich phase with crystallization inhibited; they "believe that this should be the goal of every enabling formulation with high dose number", rather than the "spring and parachute" of Case 2c [review pp. 16, 18]. They add that the 8 h window is "somewhat long", that constant permeability "is unlikely to be valid for a majority of compounds", and that in the stomach enteric polymers (HPMCAS, Eudragit L 100-55) do not dissolve while PVP, HPMC and Eudragit E PO begin to, so fasted and fed states differ [review p. 18].
What the library shows.
Corrections and qualifications.
Next. The chain ends here; the points along it that the library has not tested are listed below.
Pages. nanodroplet reservoir effect, crystallization inhibition, crystal seeding, food effect, oral bioavailability, in vitro–in vivo correlation, power-law crystal growth rate, non-compartmental AUC.