T₂ Relaxation Study to Evaluate the Crystalline State of Indomethacin Containing Solid Dispersions Using Time-Domain NMR

Abstract

The aim of this study was to demonstrate the usefulness of T₂ measurements conducted with a time-domain NMR (TD-NMR) for the characterization of active pharmaceutical ingredients (APIs) containing solid dosage forms. A solid dispersion (SD) and a physical mixture (PM) consisting of indomethacin (IMC) and polyvinylpyrrolidone (PVP) were prepared at different weight ratios as test samples, and then their T₂ relaxation curves were measured by TD-NMR. The T₂ relaxation curve of IMC was quite different from that of PVP by nature. T₂ values of the SD and PM samples became gradually shortened with increasing IMC content. No difference in T₂ relaxation curves was observed between SD and PM. By analyzing the T₂ relaxation curves in detail, we succeeded in precisely quantifying the IMC contents incorporated in the samples. Next, this study evaluated the T₂ relaxation curves of amorphous and crystalline states of powdered IMC. T₂ relaxation rate of crystalline IMC was slightly but significantly higher than that of amorphous IMC, proving that the T₂ measurement was sensitive enough to detect these differences. Finally, a thermal stress was imposed on SD and PM samples at 60°C for 7 d, and then an amorphous-to-crystalline transformation occurred in IMC in the PM sample and was successfully monitored by T₂ measurement. We believe that T₂ measurement by TD-NMR is a promising analysis for the characterization of APIs in solid dosage forms, including SD-based pharmaceuticals.

Introduction

Various technical approaches have been applied in the pharmaceutical industry to improve the solubility of active pharmaceutical ingredients (APIs).^1–5) Amorphization using the solid dispersion (SD) technique is regarded as a promising pharmaceutical technology.⁵⁾ We recently used the time-domain NMR (TD-NMR) method to evaluate the crystalline state of APIs incorporated into solid oral dosage forms including amorphous SDs.^6,7) TD-NMR is a benchtop instrument used for measuring the ¹H-NMR relaxation.⁸⁾ Instead of the molecular structure analysis performed with solid-state NMR spectroscopy,⁹⁾ TD-NMR enables easy and rapid measurement of the T₁ and T₂ relaxation times (T₁ and T₂, respectively) of the samples. Moreover, TD-NMR can be used to evaluate both solid and liquid samples.^10,11)

In a previous study, we demonstrated that T₁ was an effective parameter for distinguishing between amorphous and crystalline APIs (e.g., indomethacin (IMC) and carbamazepine). The crystalline state of APIs can be evaluated even if the APIs are incorporated into solid dosage forms such as SD. We further analyzed the T₁ relaxation curves of a physical mixture (PM) consisting of APIs and a carrier polymer for SD, and then precisely quantified the API contents in the samples.⁶⁾ In the course of the studies, we have investigated a wide range of aspects of T₁ measurement for use in the evaluation of the crystalline state of APIs. In contrast to the abundant knowledge on T₁ measurement, the study of T₂ measurement remains limited. In a previous study, we measured the T₂ of amorphous and crystalline APIs; however, these T₂ relaxation curves appeared to be similar to each other. Thus, at present, it remains uncertain whether T₂ is applicable for evaluating the crystalline state of APIs. Besides our work, there are several reports suggesting that T₂ measurement is effective for this purpose. For example, in polymer research, T₂ is frequently used to identify the amorphous and crystalline regions of polymers.¹²⁾ In pharmaceutical research, Yoshioka and colleagues¹³⁾ investigated the crystalline state of APIs containing F atoms based on the ¹⁹F T₂ measurement using low-frequency NMR. Moreover, they investigated the molecular mobility of hydrated water in various APIs based on T₁ and T₂ measurements,¹⁴⁾ and reported that the molecular states of sodium phosphates (Na₂HPO₄·12H₂O and Na₂HPO₄·2H₂O) differed from each other in terms of not only T₁, but also T₂. In general, it is considered that the regions of interest of T₁ and T₂ are different: the monitored area of T₂ is larger than that of T₁. Thus, it is our opinion that, like T₁, T₂ could be a sensitive parameter for characterizing the crystalline state of APIs; T₁ and T₂ are suitable for investigating “microscopic” and “macroscopic” molecular motions, respectively.

Against these issues, this study focused on the usefulness of T₂ measurements by TD-NMR for the evaluation of the crystalline state of APIs in solid dosage forms, including SD-based pharmaceuticals. The present study used IMC and polyvinylpyrrolidone (PVP) as a model API and a carrier polymer of SD. The first objective of the present study was to determine whether T₂ measurement could quantify the IMC contents in samples. The second objective was to determine whether T₂ measurement could characterize the crystalline state of APIs, such as the difference between the amorphous and crystalline forms. As a result of this study, we clarified that, like T₁, T₂ is a powerful tool for evaluating the crystalline state of APIs in solid dosage forms.

Experimental

Materials

IMC (minimum purity 98.0%) was purchased from Tokyo Chemical Industry (Tokyo, Japan). PVP K30 (Kollidon^® 30) was kindly supplied at no charge by BASF (Ludwigshafen, Germany). Other chemicals used were of reagent grades.

Sample Preparation of Amorphous IMC and PMs

Amorphous IMC was prepared by the melt-quenching method.¹⁵⁾ IMC crystals were placed on a heated Teflon-coated glass plate at ca. 190 and 160°C for a few minutes. The melts were then quench-cooled by immersion in liquid nitrogen. The resulting samples were lightly ground in a mortar, and then passed through a 500 µm sieve. For preparation of physical mixture samples, the amorphous APIs were mixed with PVP at weight ratios (w/w) of 20 : 80, 40 : 60, 60 : 40, and 80 : 20.

Sample Preparation of Amorphous SDs

SDs containing amorphous IMC were prepared by the melt-quenching method¹⁵⁾ following the solvent evaporation method. Designated amounts of IMC and PVP (20 : 80, 40 : 60, 60 : 40, 80 : 20, 85 : 15, 90 : 10, 95 : 5, and 99 : 1 (w/w)), were dissolved in ethanol–dichloromethane, 1 : 1 (v/v), at a total concentration of 100 mg/mL, and the solvent was removed using an evaporator (Rotavapor^® R-134; Büchi, Flawil, Switzerland) at 40–50°C. The resulting samples were further treated by the melt-quenching method to ensure that all incorporated IMC would be amorphous. Namely, all the obtained samples were placed on a heated polytetrafluoroethylene sheet at ca. 160°C for a few minutes, and then the melts were quench-cooled by immersion in liquid nitrogen. The resulting samples were lightly ground in a mortar, and then passed through a 500 µm sieve. As a comparative control, PVP and amorphous API were also prepared by the same method as for the SDs.

Powder X-Ray Diffraction (PXRD) Measurement

PXRD patterns of all samples were obtained using a D8 DISCOVER apparatus (Bruker BioSpin Corp., Billerica, MA, U.S.A.) with Cu-Kα radiation (λ = 0.154 nm). The count scanning rate was 10°/min and the scanning angle was from 2θ = 5° to 50°.

TD-NMR Measurement

The ¹H T₂ relaxation curves of the samples were measured by TD-NMR using a Bruker minispec mq20 instrument (Bruker BioSpin Corp.) at a ¹H frequency of 20 MHz at 25°C. The solid echo sequence was used for the measurement. The following parameters were applied: scans = 16, recycle delay = 10 s, gain = 60 dB, and dummy shots = 4. The ¹H T₂ relaxation time (T₂) was calculated from the free induction decay using TD-NMR Analyze software (Bruker BioSpin Corp.). After removing the offset value from intact T₂ relaxation curves, the T₂ relaxation data were calculated according to Gaussian curve fitting (Eq. 1)^13,14,16):

  

(1)

  

(2)

where M(t) and M₀ are the transverse magnetization at times t and 0 with Gaussian decay, t is the acquisition time, and T₂ is the T₂ relaxation time. The terms T_2(short) and T_2(long) are T₂s that have fast or slow relaxation speeds, respectively, and P_long is the fraction of protons with T_2(long).

Results and Discussion

Quantification of IMC Contents in SDs and PMs by Analysis of T₂ Relaxation Curves

Figure 1 shows the T₂ relaxation curves of the samples consisting of amorphous IMC and PVP at the designated weight ratio. These curves have clearly changed with the change in the weight ratio of IMC and PVP; the decay of the NMR signal became slower with an increase in IMC content. The T₂ values were calculated from these curves. For this calculation, Gaussian curve fitting (Eq. 1) was used because of the better approximation. T₂ values increased with increasing IMC content: 8.4 ± 0.0 and 8.4 ± 0.0 µs for SD and PM containing 20% IMC and 11.8 ± 0.1 and 11.5 ± 0.0 µs for those containing 80% IMC, respectively (Table 1). The T₂ relaxation curves between SDs and PMs were completely consistent: almost the same T₂ values were observed from SD and PM for the same weight ratios of IMC and PVP. In addition to the single-Gaussian curve fitting, the present study analyzed the T₂ relaxation curves using bi-Gaussian curve fitting (Eq. 2) to estimate the IMC content in the samples. Based on our previous studies,^6,7) T_2(short) and T_2(long) were considered to correspond to the T₂ values of PVP and IMC incorporated into the samples, respectively. The IMC content was estimated from the fraction of protons with T_2(long) (P_long). Although the binary fitting was applicable to the obtained T₂ relaxation curves of Fig. 1, the precise estimation of IMC content appeared to be difficult in particular for the samples containing a lower amount of IMC. For instance, for the SD and PM samples containing 20% IMC, the estimated IMC contents were much lower than the actual contents—namely, 4.5 and 10.6%—and 99.8 and 131.4 µs of their T_2(long) values were much larger than the value obtained for amorphous IMC, 13.8 µs (Table 1). As is the case with single-Gaussian curve fitting analysis, almost the same T₂ values were calculated from the bi-Gaussian curve fitting analysis between SD and PM.

Fig. 1. T₂ Relaxation Curve of (a) Solid Dispersion (SD), (b) Physical Mixture (PM), Amorphous Indomethacin (IMC), and Polyvinylpyrrolidone (PVP)

Table 1. Gaussian Curve Fitting Analysis of T₂ Relaxation Curves for SDs and PMs

Samples	Designated IMC content	Single-Gaussian fitting analysisa)			Bi-Gaussian fitting analysisb)
		T2 (µs)	Plong	Estimated IMC content (%)	T2(short) (µs)	T2(long) (µs)	Plong	Estimated IMC content (%)
Solid dispersions (SDs)	20%	8.4 ± 0.0	0.14 ± 0.02	22.5 ± 2.3	8.3 ± 0.0	99.8 ± 9.1	0.03 ± 0.00	4.5 ± 0.3
	40%	9.1 ± 0.0	0.30 ± 0.00	44.3 ± 0.2	8.9 ± 0.0	53.9 ± 7.8	0.03 ± 0.00	5.1 ± 0.3
	60%	10.2 ± 0.0	0.53 ± 0.01	66.8 ± 0.9	9.5 ± 0.1	24.7 ± 2.4	0.08 ± 0.02	13.6 ± 2.5
	80%	11.8 ± 0.1	0.78 ± 0.01	86.2 ± 0.6	9.0 ± 0.5	16.1 ± 0.9	0.42 ± 0.09	56.1 ± 8.4
Physical mixtures (PMs)	20%	8.4 ± 0.0	0.15 ± 0.01	24.7 ± 0.9	8.3 ± 0.0	131.4 ± 4.3	0.06 ± 0.00	10.6 ± 0.1
	40%	9.2 ± 0.0	0.34 ± 0.02	48.4 ± 1.7	8.9 ± 0.0	36.5 ± 3.8	0.04 ± 0.00	7.6 ± 0.8
	60%	10.1 ± 0.0	0.54 ± 0.02	67.7 ± 1.4	9.2 ± 0.2	22.6 ± 3.5	0.11 ± 0.03	18.8 ± 4.4
	80%	11.5 ± 0.0	0.76 ± 0.01	85.0 ± 1.0	8.9 ± 0.2	16.5 ± 0.5	0.37 ± 0.02	51.6 ± 2.4
Amorphous IMC	100%	13.8 ± 0.0	—	—	—	—	—	—
PVP	0%	7.9 ± 0.0	—	—	—	—	—	—

a) Calculated according to Eq. 1 and 3. b) Calculated according to Eq. 2. Each value represents the mean ± standard deviation (S.D.) (n = 3).

We previously evaluated the T₁ relaxation curves of SDs and PMs consisting of IMC and PVP, and found a significant difference between them; SDs showed monophasic relaxation curves, whereas PMs showed biphasic curves. These differences were caused by the distinct mixed state of IMC and PVP in the samples. SD was produced by uniformly mixing IMC with PVP on a nanometer scale; thus, the monophasic behavior indicated that T₁ measurement recognized the SDs as having a homogeneous structure. Furthermore, the calculated T₁ values of the SDs were quite different from pure IMC and PVP, indicating that the uniform SD structures were regarded as being distinct from the pure components. By contrast, the T₁ measurement could distinguish between individual IMC and PVP particles incorporated into PM samples, because the initial rapid relaxation curve was close to that of PVP, while the slow relaxation curve of the latter was close to that of IMC. Furthermore, for each type of PM, the weight ratios of IMC and PVP calculated by the binary analysis were highly consistent with the actual ratios. We thought that both IMC and PVP particles in PMs were large enough to be recognized by the T₁ measurement, resulting in the biphasic relaxation curves.

It is our opinion that the T₂ measurement SD and PM was similar to the T₁ measurement of SD rather than that of PM. There was no obvious difference between the T₂ relaxation curves of SD and PM. This indicates that the T₂ measurement could not recognize IMC and PVP particles in PMs as the individual component because these particles were too small for T₂ measurement. Moreover, good fitting of the T₂ relaxation curves of SD and PM was achieved with the single-Gaussian approximation: the monophasic relaxation curve also indicated that the T₂ measurement recognized the both samples as having a uniform structure. Furthermore, the area monitored by the T₂ measurement was supposed to be much larger than that monitored by the T₁ measurement, because the proton resonance frequency of T₂ is lower than that of T₁. The binary analysis can be working under the condition that the sample consisted of two distinct domains, and they could be separately detected by the measurement. From these issues, we do not think that binary analysis is suitable for the T₂ measurement to evaluate the IMC contents in the test samples.

To estimate the IMC contents precisely, we next analyzed the T₂ values calculated from the single-Gaussian fitting in detail (Eq. 1). In NMR studies of a relative liquid, two distinct protons that are rapidly exchanging are frequently expressed as follows.¹⁷⁾

  

(3)

where T₂ is the observed overall T₂ relaxation time, T_2(short) and T_2(long) are the T₂ relaxation times of the distinct protons, and P_long is the fraction of proton having T_2(long). The reciprocal of T₂, 1/T₂, is defined as the T₂ relaxation rate. Thus, the T₂ relaxation rate is supposed to proportionally related to P_long.

Cooper et al.^18,19) used Eq. 3 to evaluate the molecular mobility of water molecules in a silica nanosuspension. They assumed that water molecules, solvent molecules of the test nanosuspension, were divided into two molecular states of free and bound water molecules interacting with the silica nanoparticles. As these water molecules were rapidly exchanged, the T₂ relaxation curve showed a monophasic relaxation behavior. From these experiments, the authors successfully identified the distinct water molecules in the suspension by using Eq. 3. As far as the present study is concerned, it is unlikely that protons of IMC and PVP were rapidly exchanged because of the solid sample; however, the observed T₂ relaxation curves appeared to have a monophasic behavior. Thus, we thought that there was a good possibility that this equation was applicable. Namely, T₂ relaxation rate was supposed to change proportionally as a function of the weight ratio of IMC and PVP.

The changes in T₂ relaxation rate as a function of IMC contents are shown in Fig. 2. As expected, the observed values of the SDs and PMs became proportionally shorter with increasing IMC content in a dose-dependent manner (Figs. 2a, b); their determination coefficients were very high (r² = 0.991 and 0.990). Next, the IMC content in the samples was estimated using Eq. 3. Namely, T₂ values of amorphous IMC and PVP were plugged in for T_2(long) and T_2(short), and then the P_long values, the fractions of the IMC proton, were calculated. Next, experimental IMC contents were estimated by taking the following parameters into account: P_long, proton mass, molecular weight, and the weight ratio of components in PMs (the parameters of PVP were calculated from its monomer unit, vinylpyrrolidone). As a result of the analysis, precise estimation of IMC contents in the sample was successfully achieved (Table 1). The estimated IMC content calculated from the results of PMs containing 20, 40, 60, and 80% IMC were 24.7, 48.4, 67.7, and 85.0%, respectively; the estimation was much higher than that obtained from the binary analysis (Table 1). We further stress that the same T₂ relaxation rates can be obtained regardless of SD or PM: e.g., 8.4 ± 0.0 and 8.4 ± 0.0 ms⁻¹ for SD and PM containing 20% IMC, compared with 11.8 ± 0.1 and 11.5 ± 0.0 ms⁻¹ for SD and PM containing 80% IMC, respectively. From these findings, we concluded that this analysis has achieved precise estimation of IMC contents in the test samples. As mentioned in the Introduction, TD-NMR enables the measurement of T₂ rapidly and easily. Furthermore, the measurement is carried out nondestructively. Thus, this technique could be powerful for component analysis of solid dosage forms, including SD-based pharmaceuticals.

Fig. 2. T₂ Relaxation Rate (1/T₂) of (a) SDs and (b) PMs as a Fraction of IMC Protons

Each value represents the mean ± S.D. (n = 3).

Evaluation of the Crystalline State of IMC Based on T₂ Relaxation Curves

In the next stage of this study, the crystalline state of IMC was evaluated. The T₂ relaxation curves of crystalline and amorphous IMC were measured, and the T₂ relaxation rates calculated by the single-Gaussian curve fitting (Eq. 1) were compared. Although the T₂ relaxation curves appeared to be almost the same (Fig. 3a), the calculated values of crystalline IMC were significantly higher than those for amorphous IMC: 76.2 ± 0.2 and 71.0 ± 0.3 ms⁻¹ for the crystalline and amorphous forms, respectively. We note that the same result was observed from carbamazepine and ursodeoxycholic acid (see Supplementary Materials, Fig. S1). It is well known that the relationship between relaxation time and rotational time reflects the molecular mobility of a compound.²⁰⁾ In general, the lower the molecular mobility, the shorter the T₂. Thus, the findings in this study are quite reasonable. As mentioned in Introduction, we have previously verified that the T₁ value measured by TD-NMR was an effective parameter for evaluating the crystalline state of API powders: the T₁ of crystalline APIs was clearly longer than that for amorphous forms. By contrast, at that time, from the T₂ measurement, we could not notice any difference between them. However, in the present study, we confirmed that there were slight but significant differences in T₂ relaxation rate between amorphous and crystalline APIs (Fig. 3b and Fig. S1). Our findings led us to suggest that the T₂ measurement is also useful for the evaluation of the crystalline state of API powers.

Fig. 3. (a) T₂ Relaxation and (b) T₂ Relaxation Rate (1/T₂) between Amorphous and Crystalline IMC

Each bar represents the mean ± S.D. (n = 3). ** p < 0.01.

Continuous Monitoring of the Crystalline State of IMC in PMs and SDs during the Thermal Stress Test

In the final phase of this study, we monitored the IMC amorphous-to-crystalline transformation accompanied by the change in T₂ relaxation rate behavior. A thermal stress test was conducted at 60°C for 7 d to enhance the crystalline transformation. SDs and PMs containing 20% of amorphous IMC were used for this experiment as a test sample. In a preliminary study, we conducted a thermal stress test at 60°C for several weeks on the same SD and PM samples. The SD was quite stable, and no crystalline transformation was observed throughout the experimental period. As for the PM sample, a clear crystalline amorphous-to-crystalline IMC transformation started to be detected after only 3 d of storage. Based on these findings, the present study considered the SD and PM as being stable and unstable samples, respectively. At the designated intervals, the T₂ relaxation rates and the PXRD spectra of the sample were continuously monitored.

From the continuous monitoring of PM, a clear prolongation of the T₂ relaxation rates could be observed during the thermal stress test; the values increased from 117.0 ± 0.4 to 120.9 ± 0.2 ms⁻¹ after storage for 7 d. By contrast, the T₂ relaxation rates of the SDs were almost constant throughout the experimental period; the values at the initial point and after 7 d of storage were 119.5 ± 0.4 and 119.7 ± 0.3 ms⁻¹, respectively (Fig. 4a). The amorphous IMC and PVP were also monitored as reference samples. Similar to PM, an obvious change in T₂ relaxation rate was observed from the amorphous IMC powder; the values expanded from 74.3 ± 0.4 to 76.2 ± 0.5 ms⁻¹ until the end of the 7-d experimental period (Fig. 4b). As for PVP, no change in T₂ relaxation rate was observed throughout the experimental period, similar to the SD sample: 127.1 ± 0.6 and 126.6 ± 0.4 ms⁻¹ for the samples at the initial point and after 7 d of storage, respectively (Fig. 4c).

Fig. 4. T₂ Relaxation Rate (1/T₂) Change of (a) SD and PM, (b) Amorphous IMC, and (c) Polyvinylpyrrolidone (PVP) during the Thermal Stress Test

Each value represents the mean ± S.D. (n = 3).

The PXRD patterns during the thermal stress test are shown in Fig. 5. The PM sample began to show clear crystalline diffraction peaks after 3 d of storage (Fig. 5b), and then the peak intensity clearly increased after 7 d of storage, indicating that a crystalline transformation steadily developed with prolonging storage period. By contrast, the SD showed a halo pattern during the test (Fig. 5a). In addition, a reasonable change can be observed from comparative controls, amorphous IMC and PVP. The amorphous IMC showed clear crystalline diffraction peaks after 3 d (Fig. 5c), whereas PVP showed a halo pattern during the test (Fig. 5d). From these findings, we concluded that the amorphous-to-crystalline transformation occurring in PM and SD samples of IMC can be evaluated by T₂ measurement.

Fig. 5. Powder X-Ray Diffraction (PXRD) Patterns Measured during the Thermal Stress Test at Regular Intervals

(a) SD, (b) PM, (c) amorphous IMC, and (d) PVP during the thermal stress test at 60°C.

In general, monitoring the crystalline state of APIs in SD by TD-NMR is very difficult with T₁ measurements because the spin diffusion of protons on average equals the T₁ relaxation of neighboring protons. However, T₂ is not affected by the spin diffusion of protons. This property of T₂ relaxation enables quantification of the API in both SD and PM (see Fig. 2). The APIs could be quantified regardless of the miscibility of the two components. For example, if a small amorphous domain appeared in the crystalline API powder because of some external factor, the T₁ relaxation would be averaged and could not be quantified. Additionally, even with conventional PXRD, the halo pattern would be too small to quantify the amorphous API. However, because the quantification of the T₂ relaxation does not depend on miscibility, the amorphous part can be quantified from the API powder by T₂ measurement. Moreover, compared with T₁ measurements, more detailed and precise data analysis can be achieved by T₂ measurements because they allow the acquisition of a massive amount of data points compared with the T₁ relaxation curves. In this study, we confirmed that the differences in T₂ between crystalline and amorphous APIs were slight but significant; thus, we believe that T₂ measurement could be a promising technique to evaluate the crystalline state of APIs incorporated into solid dosage forms as well as T₁ measurements.

Conclusion

In the first part of this study, we focused on the estimation of IMC contents in SD and PM samples. As a result of the detailed analysis of the T₂ relaxation curves measured by TD-NMR, a precise estimation of the IMC content in the sample was successfully achieved. In the latter part of this study, we confirmed that T₂ measurement could detect the difference between the amorphous and crystalline IMC; furthermore, it was effective in monitoring the transformation from amorphous to crystalline during a thermal stress test. In conclusion, the T₂ relaxation behaviors measured by TD-NMR could offer profound insights into the characterization of APIs incorporated in solid dosage forms.

Acknowledgments

This work was supported by JSPS KAKENHI Grant Number JP16K08192 and JSPS Core-to-Core Program, B. Asia-Africa Science Platforms.

Conflict of Interest

The authors declare no conflict of interest.

Supplementary Materials

The online version of this article contains supplementary materials.

References

• 1) Berge S. M., Bighley L. D., Monkhouse D. C., J. Pharm. Sci., 66, 1–19 (1977).
• 2) Rabinow B. E., Nat. Rev. Drug Discov., 3, 785–796 (2004).
• 3) Loftsson T., Duchêne D., Int. J. Pharm., 329, 1–11 (2007).
• 4) Rautio J., Kumpulainen H., Heimbach T., Oliyai R., Oh D., Järvinen T., Savolainen J., Nat. Rev. Drug Discov., 7, 255–270 (2008).
• 5) Vasconcelos T., Sarmento B., Costa P., Drug Discov. Today, 12, 1068–1075 (2007).
• 6) Okada K., Hirai D., Kumada S., Kosugi A., Hayashi Y., Onuki Y., J. Pharm. Sci., 108, 451–456 (2019).
• 7) Okada K., Hirai D., Hayashi Y., Kumada S., Kosugi A., Onuki Y., Chem. Pharm. Bull., 67, 265–270 (2019).
• 8) Metz H., Mäder K., Int. J. Pharm., 364, 170–175 (2008).
• 9) Yuan X., Sperger D., Munson E. J., Mol. Pharm., 11, 329–337 (2014).
• 10) Stueber D., Jehle S., J. Pharm. Sci., 106, 1828–1838 (2017).
• 11) Kuentz M., Rothenhäusler B., Röthlisberger D., Drug Dev. Ind. Pharm., 32, 1165–1173 (2006).
• 12) Spiess H. W., Macromolecules, 50, 1761–1777 (2017).
• 13) Aso Y., Yoshioka S., Miyazaki T., Kawanishi T., Chem. Pharm. Bull., 57, 61–64 (2009).
• 14) Yoshioka S., Aso Y., Osako T., Kawanishi T., J. Pharm. Sci., 97, 4258–4268 (2008).
• 15) Strachan C. J., Taday P. F., Newnham D. A., Gordon K. C., Zeitler J. A., Pepper M., Rades T., J. Pharm. Sci., 94, 837–846 (2005).
• 16) Schumacher S. U., Rothenhäusler B., Willmann A., Thun J., Moog R., Kuentz M., J. Pharm. Biomed. Anal., 137, 96–103 (2017).
• 17) Cooper C. L., Cosgrove T., van Duijneveldt J. S., Murray M., Prescott S. W., Soft Matter, 9, 7211–7228 (2013).
• 18) Cooper C. L., Cosgrove T., van Duijneveldt J. S., Murray M., Prescott S. W., Langmuir, 28, 16588–16595 (2012).
• 19) Cooper C. L., Cosgrove T., van Duijneveldt J. S., Murray M., Prescott S. W., Langmuir, 29, 12670–12678 (2013).
• 20) Bloembergen N., Purcell E. M., Pound R. V., Phys. Rev., 73, 679–712 (1948).