Non-Effective Improvement of Absorption for Some Nanoparticle Formulations Explained by Permeability under Non-Sink Conditions

We evaluated the in vitro permeability of nanoparticle formulations of high and low lipophilic compounds under non-sink conditions, wherein compounds are not completely dissolved. The permeability of the highly lipophilic compound, griseofulvin, was improved by about 30% due to nanonization under non-sink conditions. Moreover, this permeability was about 50% higher than that under sink conditions. On the other hand, for the low lipophilic compound, hydrocortisone, there was no difference in permeability between micro-and nano-sized compounds under non-sink conditions. The nanonization of highly lipophilic compounds improves the permeability of the unstirred water layer (UWL), which in turn improves overall permeability. On the other hand, because the rate-limiting step in permeation for the low lipophilic compounds is the diffusion of the compounds in the membrane, the improvement of UWL permeability by nanonization does not improve the overall permeability. Based on this mechanism, nanoparticle formulations are not effective for low lipophilic compounds. To accurately predict the absorption of nanoparticle formulations, it is necessary to consider their permeability under non-sink conditions which reflect in vivo conditions.


Introduction
In recent years, due to the broadening of pharmaceutical targets and the desire for better medicinal efficacy, the chemical structures of drug candidates have become much more complicated [1]. As a result, a lot of drug candidates have the problem of low absorption, caused by poor solubility [1][2][3]. To overcome this issue, various formulation technologies have been developed to improve absorption, such as nanoparticle formulations, amorphous solid dispersions (ASDs) and the use of solubilizing additives [4][5][6]. Among these, nanoparticle formulations have successfully improved the absorption of various pharmaceutical compounds, and several, such as Rapamune ® , Emed ® , Tricor ® , MEGACE ® ES, have already been launched as pharmaceuticals.
In pharmaceutical development, the practice of predicting in vivo absorption with in vitro tools is essential for optimizing formulations and designing manufacturing processes [3,[7][8][9][10][11][12][13]. However, it is difficult to predict the absorption of nanoparticle formulations using the existing in vitro tools [14]. Though nanoparticle formulations successfully increased the absorption of some compounds by more than ten-fold, they have been unable to increase that of other compounds [15]. The mechanism by which nanoparticle formulations improve absorption can be explained by solubility, dissolution rate and permeability [15][16][17]. The relationship between solubility and particle size is described by the Ostwald-Freundlich equation. Based on this equation, the solubility of small-molecule compounds is calculated to improve by about 10% to 15% when the particle size of the un-milled compounds decreases to 100 nm [16,18]. As many studies have shown that nanoparticle formulations can more than double the absorption of some compounds, we do not think that solubility contributes to the absorption of nanoparticle formulations [15]. The relationship between dissolution rate and particle size is described by the Noyes-Whitney equation [15,16]. For some poorly water-soluble compounds, the rate-limiting step in the absorption is in the dissolution process. It has been reported that nanoparticle formulations improve the absorption of fenofibrate and ritonavir by improving the dissolution rate [19,20]. Recently, it was reported that nanoparticle formulations could also affect permeability [17]. The nanoparticle-improved permeability of poorly water-soluble compounds, namely aprepitant and fenofibrate, has been observed in both in vivo and in vitro models [21,22]. Though these studies suggested that the improved overall permeability was caused by the improved permeability of the unstirred water layer (UWL), the detailed mechanism has not been elucidated.
In this study, we elucidate the mechanism by which nanoparticle formulations are able to improve permeability. The permeation process in passive diffusion is composed of two continuous processes: diffusion of compounds in the UWL, and in the membrane [23,24]. Membrane permeability (P m(app) ) is not affected by the undissolved compounds. On the other hand, our previous study clarified that UWL permeability (P UWL(app) ) is affected by them [25]. The undissolved compounds can enter the UWL, resulting in the reduction of the apparent UWL thickness (h UWL(app) ) and the improvement of P UWL(app) . The effectiveness of P UWL(app) improvement will depend on the particle size of the compounds. The nanosized compounds may improve P UWL(app) much more than the micro-sized compounds. In addition, P m(app) depends on the lipophilicity of the compounds [26]. Therefore, for highly lipophilic compounds, the rate-limiting step in permeation is the diffusion of the compounds in the UWL, and for low lipophilic compounds it is the diffusion of the compounds in the membrane. Thus, nanoparticle formulations may improve the absorption of highly lipophilic compounds, but not low lipophilic compounds. To confirm the improvement of permeability by nanoparticle formulations experimentally, we had to measure permeability under non-sink conditions, wherein compounds are not dissolved completely. However, the conventional Caco-2 and parallel artificial membrane permeability assay (PAMPA) only measures drug permeability under sink conditions, where they are fully dissolved. Thus, the P UWL(app) of nanoparticle formulations has never been reported.
In this study, we prepared nanosuspensions of a highly lipophilic compound, griseofulvin (MW = 352.77 and Log P = 2.18), and a low lipophilic compound, hydrocortisone (MW = 362.46 and Log P = 1.55), by wet milling (Figure 1) [27,28]. We measured the permeability of the un-milled samples and the nanosuspensions under non-sink conditions using the in vitro tool Pion MicroFlux™ (Billerica, MA, USA), which has a permeation compartment similar to that of PAMPA. The purpose of this study was to elucidate the mechanism by which nanoparticle formulations improve permeability by reducing the h UWL(app) and improving the P UWL(app) . In addition, we aimed to reveal that the improvement of permeability depends on the lipophilicity of the compounds.

Preparation of Microparticles and a Nanosuspension for Griseofulvin
Two sizes of griseofulvin microparticle were prepared. The purchased griseofulvin was the smaller microparticle (S-microparticle griseofulvin). The larger microparticle (Lmicroparticle griseofulvin) was prepared by recrystallization. The griseofulvin was dissolved in methanol at 70 °C. The solution was cooled to room temperature. The obtained microparticles were isolated by filtration and allowed to dry under the vacuum.
A nanosuspension of griseofulvin (nanosuspension griseofulvin) was prepared by wet milling as described in the previous report [29]. 570 mg of griseofulvin was milled in 5.1 mL of 1.33% PVP K30/0.066% AOT using 24 g of Nikkato YTT 0.8 mm zirconia beads. The milling was performed by a magnetic stirrer at 700 rpm for 30 min and repeated four times. The interval time was 15 min. The zirconia beads were removed using a TERUMO

Preparation of Microparticles and a Nanosuspension for Griseofulvin
Two sizes of griseofulvin microparticle were prepared. The purchased griseofulvin was the smaller microparticle (S-microparticle griseofulvin). The larger microparticle (L-microparticle griseofulvin) was prepared by recrystallization. The griseofulvin was dissolved in methanol at 70 • C. The solution was cooled to room temperature. The obtained microparticles were isolated by filtration and allowed to dry under the vacuum.
A nanosuspension of griseofulvin (nanosuspension griseofulvin) was prepared by wet milling as described in the previous report [29]. 570 mg of griseofulvin was milled in 5.1 mL of 1.33% PVP K30/0.066% AOT using 24 g of Nikkato YTT 0.8 mm zirconia beads. The milling was performed by a magnetic stirrer at 700 rpm for 30 min and repeated four times. The interval time was 15 min. The zirconia beads were removed using a TERUMO needle syringe (27 gauge) with an inner diameter smaller than the zirconia beads.

Preparation of a Microparticle and a Nanosuspension for Hydrocortisone
The purchased hydrocortisone was used as the microparticle sample (microparticle hydrocortisone). A nanosuspension of hydrocortisone (nanosuspension hydrocortisone) was prepared by wet milling according to a previous report [30,31]. 0.2% PVP K30/0.05% SLS was used as the milling solvent, and the other conditions were the same as those applied to the griseofulvin.

X-ray Powder Diffraction (XRPD)
X-ray powder diffraction (XRPD) patterns in the range of 3 • to 35 • (2θ) were obtained using a Malvern Panalytical Empyrean powder X-ray diffractometer with Cu Kα radiation in transmission mode. A tube voltage of 45 kV and amperage of 40 mA were used. The nanosuspensions separated by centrifuging and the microparticle samples were used to measure the XRPD patterns.

Particle Size Measurement
The particle size distributions of the nanosuspensions were measured by Malvern Instruments Zetasizer Pro dynamic light scattering (DLS). Before the measurements, the nanosuspensions were diluted to the appropriate concentration using water to prevent multiple scattering. We visually confirmed that the nanosuspensions were dispersed in the water during the measurements. All the measurements were performed in triplicate.
The particle size distributions of the microparticle samples were measured by a Malvern Instruments Mastersizer 3000 laser diffraction size analyzer. Before the measurements, the microparticle samples were suspended in the saturated heptane solution of the compound containing 0.2% sorbitan monooleate which was used to keep the microparticle samples dispersed during the measurements. And, to prevent bubbles in the test samples caused by sorbitan monooleate, heptane was chosen as the solvent instead of water. All the measurements were performed in triplicate.
The morphologies of the nanosuspensions and microparticle samples were visualized using JEOL JSM-IT500HR scanning electron microscopy (SEM). Before the measurement, the mounted samples were coated with platinum under vacuum. We measured different points in more than three images to confirm that the pictured image reflected the whole sample and was not biased in terms of particle size and shape.

Permeability Measurement by MicroFlux™
The microparticle samples were suspended in 1.33% PVP K30/0.066% AOT for griseofulvin and 0.2% PVP K30/0.05% SLS for hydrocortisone. The test sample suspensions in the donor chamber were prepared by diluting the suspensions to a pH 6.5 phosphate buffer. The sample dose amounts of the test sample suspensions were set at 200 µg/mL for griseofulvin and 2000 µg/mL for hydrocortisone to achieve the non-sink conditions. These test sample suspensions were stirred well by the rotation stirrers at 37 • C before the permeability measurements.
The permeability was measured by a Pion MicroFlux™. The measurement conditions were the same as those in our previous study [25]. A polyvinylidene fluoride (PVDF) membrane filter of 0.45 µm pore size with 25 µL of GIT lipids solution was used as a membrane compartment. After 20 mL of ASB was added in each acceptor chamber, 20 mL of the test sample suspension (4 mg of griseofulvin or 40 mg of hydrocortisone) was added in the donor chamber. During the measurement, the solutions in the donor and acceptor chambers were stirred by cross-bar magnetic stirrers at 150 rpm, and were maintained at 37 • C. All permeability measurements were performed in triplicate.
At 0, 30, 60, 120, 240 and 360 min, 100 µL of the acceptor chamber solution was withdrawn and diluted 2-fold. At 0, 120 and 360 min, 1000 µL of the donor chamber solution was withdrawn and filtered through a Cytiva Whatman ® Anotop ® 10 glass microfiber membrane filter of 0.02 µm pose size (Little Chalfont, UK). To measure the exact concentration in the donor chamber containing the nanosuspensions, the filtration method was applied according to a previous report [32]. Then, 100 µL of the filtered solution was diluted 2-fold. The sample concentration was determined by ultra-high-performance liquid chromatography (UHPLC). From the obtained concentration-time profiles in the acceptor chambers, the flux (J), which means the mass transfer through the membrane, was calculated by Equation (1): where dm/dt is the total amount of material crossing the membrane per unit time, A is the area of the membrane (1.54 cm 2 ), V is the volume of the acceptor chamber (20 mL), and dC(t)/dt is the slope of the concentration-time profiles in the acceptor chambers. To compensate for the concentration decrease in the donor chamber, and the lag times in the permeation, the initial fluxes from 30 min to 120 min were used to calculate dC(t)/dt. As ASB can keep the acceptor chambers under sink condition during measurement, the flux is described by Equation (2): where P app is the apparent permeability of the compounds and C D (t) is the concentration of the dissolved compounds in the donor chambers. C D (t) at 0 min (=C D (0)) was used to calculate P app by Equation (2).

UHPLC Analysis
The concentrations of griseofulvin and hydrocortisone were determined using a Waters Acquity UPLC H-Class system and an Acquity UPLC ® BEH Shield RP18 1.7 µm, 2.1 × 50 mm column. 0.05%TFA/water (v/v) and 0.05%TFA/MeCN (v/v) were used as gradient mobile phase A and gradient mobile phase B respectively. At a flow rate of 1.0 mL/min, the gradient program was initially set as 5% B, and increased to 100% B over 2 min. The column temperature was controlled at 35 • C. The injection volume and ultraviolet (UV) wavelength for griseofulvin were 5 µL and 240 nm, respectively. The injection volume and UV wavelength for hydrocortisone were 1 µL and 254 nm, respectively.

Characterization of Microparticles and Nanosuspensions
The particle size distributions of the nanosuspensions and microparticle samples for griseofulvin and hydrocortisone are shown in Figure 2. The particle size distribution parameters are summarized in Table 1. Three sizes of test samples were prepared for griseofulvin. The median diameter of the nanosuspension griseofulvin was 0.30 µm, the median diameter of the S-microparticle griseofulvin was 13 µm, and the median diameter of the L-microparticle griseofulvin was 34 µm. Two sizes of hydrocortisone test samples were prepared. The median diameter of the nanosuspension hydrocortisone was 0.25 µm, and the median diameter of the microparticle hydrocortisone was 6.1 µm. In addition, the SEM images of the particles for each sample were consistent with the results of the particle size measurement (Figure 3).
The XRPD patterns of the griseofulvin and hydrocortisone samples are shown in Figure 4. For both griseofulvin and hydrocortisone, the nanosuspensions and the microparticle samples showed the same diffraction pattern, and the positions of the diffraction peaks were not changed by wet milling. The results confirmed that they had the same crystalline form and that wet milling did not cause any polymorphic transition.  The results were transformed to volume distribution. The PSD parameters for each sample are sum marized in Table 1. The PSD of the nanosuspensions was measured by dynamic light scattering where water was used as the solvent. The PSD of the microparticle samples was measured by laser diffraction size analyzer, where the saturated heptane solution of the compound containing 0.2% sorbitan monooleate was used as the solvent.  The results were transformed to volume distribution. The PSD parameters for each sample are summarized in Table 1. The PSD of the nanosuspensions was measured by dynamic light scattering, where water was used as the solvent. The PSD of the microparticle samples was measured by laser diffraction size analyzer, where the saturated heptane solution of the compound containing 0.2% sorbitan monooleate was used as the solvent.

Griseofulvin
The griseofulvin time-concentration profiles in the acceptor chambers and the donor chambers, respectively, are shown in Figure 5. The Papp of each sample was calculated by

Griseofulvin
The griseofulvin time-concentration profiles in the acceptor chambers and the donor chambers, respectively, are shown in Figure 5. The Papp of each sample was calculated by

Griseofulvin
The griseofulvin time-concentration profiles in the acceptor chambers and the donor chambers, respectively, are shown in Figure 5. The P app of each sample was calculated by Equations (1) and (2) as shown in Figure 6. The samples in the donor chambers were visually confirmed to be suspensions, meaning that they were under non-sink conditions. Based on the concentrations in the donor chambers, we confirmed that the solubility of the griseofulvin was constant, independent of the particle size, and that solubility was not improved by nanonization. In addition, the compounds in the donor chambers were kept in saturation during the measurements. We also confirmed by DLS that the particle size distributions of the nanosuspensions did not change during the measurements. The P app of the nanosuspension griseofulvin was about 30% higher than that of the S-microparticle griseofulvin. On the other hand, the P app of the S-microparticle griseofulvin and the Lmicroparticle griseofulvin were the same. The XRPD patterns of the griseofulvin and hydrocortisone samples are shown in Figure 4. For both griseofulvin and hydrocortisone, the nanosuspensions and the microparticle samples showed the same diffraction pattern, and the positions of the diffraction peaks were not changed by wet milling. The results confirmed that they had the same crystalline form and that wet milling did not cause any polymorphic transition. Equations (1) and (2) as shown in Figure 6. The samples in the donor chambers were visually confirmed to be suspensions, meaning that they were under non-sink conditions. Based on the concentrations in the donor chambers, we confirmed that the solubility of the griseofulvin was constant, independent of the particle size, and that solubility was not improved by nanonization. In addition, the compounds in the donor chambers were kept in saturation during the measurements. We also confirmed by DLS that the particle size distributions of the nanosuspensions did not change during the measurements. The Papp of the nanosuspension griseofulvin was about 30% higher than that of the S-microparticle griseofulvin. On the other hand, the Papp of the S-microparticle griseofulvin and the Lmicroparticle griseofulvin were the same.
(a) acceptor chamber (b) donor chamber   Equations (1) and (2) as shown in Figure 6. The samples in the donor chambers were visually confirmed to be suspensions, meaning that they were under non-sink conditions. Based on the concentrations in the donor chambers, we confirmed that the solubility of the griseofulvin was constant, independent of the particle size, and that solubility was not improved by nanonization. In addition, the compounds in the donor chambers were kept in saturation during the measurements. We also confirmed by DLS that the particle size distributions of the nanosuspensions did not change during the measurements. The Papp of the nanosuspension griseofulvin was about 30% higher than that of the S-microparticle griseofulvin. On the other hand, the Papp of the S-microparticle griseofulvin and the Lmicroparticle griseofulvin were the same.

Hydrocortisone
The hydrocortisone time-concentration profiles in the acceptor chambers and donor chambers are shown in Figure 7. The P app of each sample was calculated by Equations (1) and (2) as shown in Figure 8. The non-sink condition of the donor chamber samples, the saturation of the compounds in the donor chambers, and the consistent particle size distributions of the nanosuspensions during the measurements were confirmed for both hydrocortisone samples as well as for the griseofulvin. The solubility of the hydrocortisone was not improved by nanonization. The P app of the nanosuspension hydrocortisone was almost the same as that of the microparticle hydrocortisone. Therefore, the nanoparticle formulation did not improve the permeability of the hydrocortisone.

Hydrocortisone
The hydrocortisone time-concentration profiles in the acceptor chambers and donor chambers are shown in Figure 7. The Papp of each sample was calculated by Equations (1) and (2) as shown in Figure 8. The non-sink condition of the donor chamber samples, the saturation of the compounds in the donor chambers, and the consistent particle size distributions of the nanosuspensions during the measurements were confirmed for both hydrocortisone samples as well as for the griseofulvin. The solubility of the hydrocortisone was not improved by nanonization. The Papp of the nanosuspension hydrocortisone was almost the same as that of the microparticle hydrocortisone. Therefore, the nanoparticle formulation did not improve the permeability of the hydrocortisone.

Calculation of Pm(app) and PUWL(app)
As the griseofulvin and the hydrocortisone were neutral compounds, the molecules in the donor compartment were unionized free compounds or undissolved compounds. In this condition, the intrinsic membrane permeability was equal to the Pm(app).

Hydrocortisone
The hydrocortisone time-concentration profiles in the acceptor chambers and chambers are shown in Figure 7. The Papp of each sample was calculated by Equat and (2) as shown in Figure 8. The non-sink condition of the donor chamber samp saturation of the compounds in the donor chambers, and the consistent particle s tributions of the nanosuspensions during the measurements were confirmed for b drocortisone samples as well as for the griseofulvin. The solubility of the hydroco was not improved by nanonization. The Papp of the nanosuspension hydrocortiso almost the same as that of the microparticle hydrocortisone. Therefore, the nano formulation did not improve the permeability of the hydrocortisone.   As the griseofulvin and the hydrocortisone were neutral compounds, the mo in the donor compartment were unionized free compounds or undissolved comp In this condition, the intrinsic membrane permeability was equal to the Pm(app).

Calculation of P m(app) and P UWL(app)
As the griseofulvin and the hydrocortisone were neutral compounds, the molecules in the donor compartment were unionized free compounds or undissolved compounds. In this condition, the intrinsic membrane permeability was equal to the P m(app) .
The P UWL(app) of the griseofulvin was theoretically calculated by the following equation [25]: In our previous study, the P m(app) of the griseofulvin was 0.0284 cm/min [25]. P m(app) does not depend on the sink/non-sink conditions or the particle size of compounds. By substituting the measured P app in Equation (3), the P UWL(app) of the griseofulvin for each test sample was calculated as shown in Table 2. The P UWL(app) of the nanosuspension griseofulvin was almost twice as fast as that of the S-microparticle griseofulvin. As the P m(app) of hydrocortisone has never been reported, we theoretically calculated the impact of the P UWL(app) on the P app of the hydrocortisone using the h UWL(app) under nonsink conditions. Both the P app of the nanosuspension hydrocortisone and the microparticle hydrocortisone were 0.00239 cm/min. According to Fick's first law, P UWL(app) is calculated using the apparent aqueous diffusivity (D aq(app) ) and the h UWL(app) as follows: D aq(app) can be empirically estimated using the following equation [33] (p. 381): The D aq(app) of the hydrocortisone was calculated to be 5.12 × 10 −6 cm 2 /s by Equation (5). The h UWL(app) under sink conditions was reported to be about 100 µm [23]. Therefore, we assumed that the h UWL(app) under non-sink conditions was less than 100 µm. When the h UWL(app) was from 1 µm to 100 µm, the P UWL(app) of the hydrocortisone was calculated as shown in Table 3. The calculated P m(app) was much smaller than the calculated P UWL(app) in both conditions. Therefore, the diffusion of the compounds in the membrane was the rate-limiting step in the permeation of the hydrocortisone.

Discussion
These results demonstrate the mechanism we proposed in the introduction to explain how nanoparticle formulations improve permeability. The highly lipophilic compound, griseofulvin, had high permeability, and nanonization increased its P app by about 30%. On the other hand, the low lipophilic compound, hydrocortisone, had low permeability and nanonization did not change its P app . In this section, we discuss the importance of permeability under non-sink conditions in predicting the absorption of nanoparticle formulations. We also discuss whether nanoparticle formulations can improve the permeability of small molecule compounds which have various lipophilicities.
To assess the impact of permeability under non-sink conditions, we compared it with that under sink conditions. The P app of griseofulvin under sink conditions was 0.0148 cm/min in our previous study [25]. Therefore, the nanoparticle formulation of griseofulvin improved permeability by about 50% under non-sink conditions compared to that under sink conditions. (Figure 9) This effect under non-sink conditions has a significant impact on the absorption of nanoparticle formulations.
Pharmaceutics 2022, 14, x FOR PEER REVIEW ability under non-sink conditions in predicting the absorption of nanoparticle fo tions. We also discuss whether nanoparticle formulations can improve the perm of small molecule compounds which have various lipophilicities.
To assess the impact of permeability under non-sink conditions, we compared that under sink conditions. The Papp of griseofulvin under sink conditions was cm/min in our previous study [25]. Therefore, the nanoparticle formulation of grise improved permeability by about 50% under non-sink conditions compared to tha sink conditions. (Figure 9) This effect under non-sink conditions has a significant on the absorption of nanoparticle formulations. Figure 9. Comparison of Papp of nanosuspension griseofulvin under non-sink conditions a conditions. The sink condition result is taken from our previous report [25]. The results r the average Papp ± SD (n = 3). Adapted from [25], MDPI, 2021.
Using the results of permeability measurements, we quantitatively estimated pact of nanoparticle formulations on permeability for small molecule compounds scribed in the Results section, the hUWL(app) was reported to be around 100 μm und conditions [23]. Under non-sink conditions, the hUWL(app) was calculated by the fo equation, using Daq(app), Papp and Pm(app) [25]: The Daq(app) of griseofulvin was 5.18 × 10 −6 cm 2 /s and the Pm(app) was 0.0284 cm stituting the measured Papp into Equation (6), the hUWL(app) was calculated to be aro μm for the microparticle samples and around 30 μm for the nanosuspensions und sink conditions (Figure 10). The nanonization of particle size significantly redu hUWL(app). When compounds are nanonized, the undissolved compounds can deepl trate the UWL, causing it to shrink. Considering this hUWL(app) reduction mechani micronization of griseofulvin may have improved the Papp. However, the S-micro griseofulvin and the L-microparticle griseofulvin did not show a clear difference Similar results showing the effect of micronization on Papp were reported previo vivo, but the mechanism has so far not been investigated in detail [34]. To und how micronization improves permeability, further research is necessary. Figure 9. Comparison of P app of nanosuspension griseofulvin under non-sink conditions and sink conditions. The sink condition result is taken from our previous report [25]. The results represent the average P app ± SD (n = 3). Adapted from [25], MDPI, 2021.
Using the results of permeability measurements, we quantitatively estimated the impact of nanoparticle formulations on permeability for small molecule compounds. As described in the Results section, the h UWL(app) was reported to be around 100 µm under sink conditions [23]. Under non-sink conditions, the h UWL(app) was calculated by the following equation, using D aq(app) , P app and P m(app) [25]: The D aq(app) of griseofulvin was 5.18 × 10 −6 cm 2 /s and the P m(app) was 0.0284 cm/s. Substituting the measured P app into Equation (6), the h UWL(app) was calculated to be around 70 µm for the microparticle samples and around 30 µm for the nanosuspensions under non-sink conditions ( Figure 10). The nanonization of particle size significantly reduced the h UWL(app) . When compounds are nanonized, the undissolved compounds can deeply penetrate the UWL, causing it to shrink. Considering this h UWL(app) reduction mechanism, the micronization of griseofulvin may have improved the P app . However, the S-microparticle griseofulvin and the L-microparticle griseofulvin did not show a clear difference in P app . Similar results showing the effect of micronization on P app were reported previously in vivo, but the mechanism has so far not been investigated in detail [34]. To understand how micronization improves permeability, further research is necessary. To evaluate the relationship between the lipophilicity of compounds and provement of Papp by nanonization, the Papp of microparticle and nanoparticle com with Pm(app) ranging from 0.001 cm/min to 1.0 cm/min was calculated under sink an sink conditions (Figure 11). The Papp can be calculated using Pm(app), hUWL (app) and D described in Equation (7) [25]: The Daq(app) of the model compounds (MW = ca.350) was calculated to be 5.2 cm 2 /s using Equation (5). Based on the measurements of griseofulvin permeabil hUWL(app) was estimated to be 100 μm under sink conditions, 70 μm for micropartic pounds under non-sink conditions, and 30 μm for nanoparticle compounds und sink conditions. The lipophilicity and membrane permeability of griseofulvin wer = 2.18 and Pm(app) = 0.0284 cm/min, respectively. When the Pm(app) of the compound i cm/min, its Papp under non-sink conditions for nanoparticle compounds was estim be about 50% higher than that under sink conditions. On the other hand, the lipop of hydrocortisone is Log P = 1.55 and its membrane permeability was estimate Pm(app) = 0.00259 cm/min. When the Pm(app) of the compound was 0.00259 cm/min, under non-sink conditions for nanoparticle compounds was estimated to be alm same as that under sink conditions. These results were consistent with the result permeability measurements. In addition, the effect of nanonization on the Papp higher lipophilic compound was also calculated. The lipophilicity of the neutr pound, progesterone, was Log P = 3.48 and its Papp using PAMPA was reported to times higher than that of griseofulvin [35]. When the Papp of the compound und conditions was twice as high as that of griseofulvin (Papp = 0.030 cm/min), its Pm( about 1.0 cm/min. Based on Figure 11, nanonization will increase its Papp by abou times. Nanonization has previously been reported to increase the in vivo permeab several highly lipophilic compounds by around 2-3 times [17]. Therefore, the est in Figure 11 is reasonable. To evaluate the relationship between the lipophilicity of compounds and the improvement of P app by nanonization, the P app of microparticle and nanoparticle compounds with P m(app) ranging from 0.001 cm/min to 1.0 cm/min was calculated under sink and non-sink conditions ( Figure 11). The P app can be calculated using P m(app) , h UWL (app) and D aq(app) as described in Equation (7) [25]: Pharmaceutics 2022, 14, x FOR PEER REVIEW 13 of 16 The in vivo absorption of compounds is proportional to their concentration and permeability in the human small intestine. Based on Figure 11, nanoparticle formulations greatly improve the permeability of highly lipophilic compounds. This improved permeability can significantly improve absorption. On the other hand, nanoparticle formulations have a very small effect on the permeability of low lipophilic compounds. As the effect of nanonization on solubility is also negligible, nanoparticle formulations will not improve the absorption of low lipophilic compounds. Our results explain the big differ- Figure 11. Calculated permeability improvement effect for microparticle and nanoparticle compounds under non-sink conditions. The permeability of model compounds ranges from P app,sink = 0.00097 cm/min to P app,sink = 0.029 cm/min. P app,sink and P app,non-sink represent the P app under sink conditions and under non-sink conditions, respectively.
The D aq(app) of the model compounds (MW = ca.350) was calculated to be 5.20 × 10 −6 cm 2 /s using Equation (5). Based on the measurements of griseofulvin permeability, the h UWL(app) was estimated to be 100 µm under sink conditions, 70 µm for microparticle compounds under non-sink conditions, and 30 µm for nanoparticle compounds under non-sink conditions. The lipophilicity and membrane permeability of griseofulvin were Log P = 2.18 and P m(app) = 0.0284 cm/min, respectively. When the P m(app) of the compound is 0.0284 cm/min, its P app under non-sink conditions for nanoparticle compounds was estimated to be about 50% higher than that under sink conditions. On the other hand, the lipophilicity of hydrocortisone is Log P = 1.55 and its membrane permeability was estimated to be P m(app) = 0.00259 cm/min. When the P m(app) of the compound was 0.00259 cm/min, its P app under non-sink conditions for nanoparticle compounds was estimated to be almost the same as that under sink conditions. These results were consistent with the results of the permeability measurements. In addition, the effect of nanonization on the P app of the higher lipophilic compound was also calculated. The lipophilicity of the neutral compound, progesterone, was Log P = 3.48 and its P app using PAMPA was reported to be 2-3 times higher than that of griseofulvin [35]. When the P app of the compound under sink conditions was twice as high as that of griseofulvin (P app = 0.030 cm/min), its P m(app) was about 1.0 cm/min. Based on Figure 11, nanonization will increase its P app by about three times. Nanonization has previously been reported to increase the in vivo permeability of several highly lipophilic compounds by around 2-3 times [17]. Therefore, the estimation in Figure 11 is reasonable.
The in vivo absorption of compounds is proportional to their concentration and permeability in the human small intestine. Based on Figure 11, nanoparticle formulations greatly improve the permeability of highly lipophilic compounds. This improved permeability can significantly improve absorption. On the other hand, nanoparticle formulations have a very small effect on the permeability of low lipophilic compounds. As the effect of nanonization on solubility is also negligible, nanoparticle formulations will not improve the absorption of low lipophilic compounds. Our results explain the big differences in absorption for each compound. Thus, knowledge of the relationship between lipophilicity and permeability improvement ( Figure 11) is critical for developing formulations for poorly watersoluble compounds.
Our proposed mechanism for how nanoparticle formulations improve permeability is illustrated in Figure 12. It explains why nanoparticle formulations improve the permeability of highly lipophilic compounds, but not low lipophilic compounds. Compared with sink conditions, h UWL(app) under non-sink conditions is smaller, becoming even smaller as particle size decreases. The reduction of h UWL(app) by nanonization greatly improves P UWL(app) . For highly lipophilic compounds, P m(app) is equal to or larger than P UWL(app) , and the improvement of P UWL(app) will in turn improve the P app ( Figure 12A). On the other hand, for the low lipophilic compounds, P m(app) is smaller than P UWL(app) , and the improvement of P UWL(app) will not improve the P app ( Figure 12B). The results of the permeability measurements successfully demonstrated the mechanism described in Figure 12.
We can quantitatively evaluate the impact of nanonization on permeability by measuring permeability under non-sink conditions, enabling the more accurate prediction of absorption. Permeability measured by PAMPA, which was used in the permeation compartment for MicroFlux™, is highly correlated with human jejunal permeability, but only for compounds that are not affected by transporters [35,36]. Though MicroFlux™ and the PAMPA system are apparently different, the mechanism underlying the measurement of the passive diffusion is the same, and important features, such as membrane composition and the donor/acceptor chambers, are similar, suggesting that the permeability measured using MicroFlux™ can also be correlated with human jejunal permeability. Several studies have also reported that MicroFlux™ results are well-correlated with in vivo absorption [22,23,37,38], and that P UWL(app) affects permeability in the human small intestine [39,40]. Therefore, we concluded that the improvement of permeability by nanonization observed in this study can be correlated with permeability in in vivo contexts. We can quantitatively evaluate the impact of nanonization on permeability by measuring permeability under non-sink conditions, enabling the more accurate prediction of absorption. Permeability measured by PAMPA, which was used in the permeation compartment for MicroFlux TM , is highly correlated with human jejunal permeability, but only for compounds that are not affected by transporters [35,36]. Though MicroFlux TM and the PAMPA system are apparently different, the mechanism underlying the measurement of the passive diffusion is the same, and important features, such as membrane composition and the donor/acceptor chambers, are similar, suggesting that the permeability measured using MicroFlux TM can also be correlated with human jejunal permeability. Several studies have also reported that MicroFlux TM results are well-correlated with in vivo absorption [22,23,37,38], and that PUWL(app) affects permeability in the human small intestine [39,40]. Therefore, we concluded that the improvement of permeability by nanonization observed in this study can be correlated with permeability in in vivo contexts.

Conclusions
This is the first report to quantitatively study the impact of nanoparticle formulations on permeability. Furthermore, it was not clear what type of compounds could have their absorption improved by nanoparticle formulations. Thus, we proposed a mechanism explaining how nanoparticle formulations improve permeability. We successfully demonstrated this mechanism by measuring permeability under non-sink conditions, wherein compounds are not completely dissolved. We found that nanoparticle formulations of highly lipophilic compounds can greatly improve permeability under non-sink conditions, resulting in the improvement of absorption. Nanoparticle formulations will improve the absorption of compounds with Log P ≥ ca.3.5 more than three-fold. On the other hand, they do not effectively improve the permeability of low lipophilic compounds. Nanoparticle formulations will not improve the absorption of compounds with Log P ≤ ca.1.5. Based on these findings, the absorption of nanoparticle formulations is affected by both permeability and dissolution. Furthermore, our research suggests that we should investigate technologies other than nanoparticle formulations for low lipophilic compounds. It is critical that permeability is measured under conditions that reflect clinical characteristics, such as dosage and non-sink/sink conditions, in order to accurately predict the absorption of nanoparticle formulations.

Conclusions
This is the first report to quantitatively study the impact of nanoparticle formulations on permeability. Furthermore, it was not clear what type of compounds could have their absorption improved by nanoparticle formulations. Thus, we proposed a mechanism explaining how nanoparticle formulations improve permeability. We successfully demonstrated this mechanism by measuring permeability under non-sink conditions, wherein compounds are not completely dissolved. We found that nanoparticle formulations of highly lipophilic compounds can greatly improve permeability under non-sink conditions, resulting in the improvement of absorption. Nanoparticle formulations will improve the absorption of compounds with Log P ≥ ca.3.5 more than three-fold. On the other hand, they do not effectively improve the permeability of low lipophilic compounds. Nanoparticle formulations will not improve the absorption of compounds with Log P ≤ ca.1.5. Based on these findings, the absorption of nanoparticle formulations is affected by both permeability and dissolution. Furthermore, our research suggests that we should investigate technologies other than nanoparticle formulations for low lipophilic compounds. It is critical that permeability is measured under conditions that reflect clinical characteristics, such as dosage and non-sink/sink conditions, in order to accurately predict the absorption of nanoparticle formulations.

Data Availability Statement:
The data presented in this study are available in this article.