Chitosan cross-linked poly(acrylic acid) hydrogels: Drug release control and mechanism PDF

Colloids and Surfaces B: Biointerfaces 152 (2017) 252–259 Contents lists available at ScienceDirect Colloids and Surfaces B: Biointerfaces jour...

Colloids and Surfaces B: Biointerfaces 152 (2017) 252–259 Contents lists available at ScienceDirect Colloids and Surfaces B: Biointerfaces journal homepage: www.elsevier.com/locate/colsurfb Chitosan cross-linked poly(acrylic acid) hydrogels: Drug release control and mechanism Yiming Wang a,b , Jie Wang a,∗∗ , Zhenyu Yuan a , Haoya Han a,c , Tao Li a , Li Li a , Xuhong Guo a,d,∗ a State Key Laboratory of Chemical Engineering, East China University of Science and Technology, Meilong Road 130, 200237 Shanghai, China b Advanced Soft Matter Group, Department of Chemical Engineering, Delft University of Technology, van der Maasweg, 2629 HZ Delft, The Netherlands c Stranski-Laboratorium für Physikalische und Theoretische Chemie, Technische Universität Berlin, Strasse des 17. Juni 124, D-10623 Berlin, Germany d Engineering Research Center of Materials Chemical Engineering of Xinjiang Bingtuan, Shihezi University, Xinjiang 832000, China a r t i c l e i n f o a b s t r a c t Article history: Chitosan has been used to cross-link poly(acrylic acid) to give three pH-sensitive hydrogels designed Received 20 October 2016 to control the release of the drugs amoxicillin and meloxicam. The extent of cross-linking and solution Received in revised form 1 January 2017 pH was found to dominate the swelling behavior of these hydrogels as shown by scanning electron Accepted 6 January 2017 microscopy and swelling time dependencies. The rates of release of amoxicillin and meloxicam from the Available online 9 January 2017 loaded hydrogels increased with increase in pH consistent with the extent of hydrogen bonding between hydrogel components and between the hydrogel and the drugs being important determinants of release Keywords: rate. Both the Korsemeyer-Peppas and Weibull models fitted release data consistent with drug release Chitosan pH sensitive hydrogel occurred through a combination of drug diffusion and hydrogel relaxation processes. These hydrogels Drug delivery appear to provide an ideal basis for controlled drug delivery systems. Release mechanism © 2017 Elsevier B.V. All rights reserved. 1. Introduction release systems. Examples of such stimuli are light , temperature and pH change. Hydrogels are generally composed of hydrophilic organic net- Apart from being physically compatible with human physiology, works which incorporate large amounts of water into their hydrogels must also be biocompatible with body chemistry if they structures. This renders them both soft and elastic properties which are to be viable as drug delivery systems. Fortunately, there is range are compatible with human physiology. Many hydrogels are also of biocompatible polymers which may be converted to hydrogel able to load a wide variety of drugs into their structures and sub- networks through chemically cross-linking them. However, it must stantially protect them from physiological conditions, particularly be ensured that such cross-linking entities are not toxic [8–10]. those of the stomach were pH is low and enzyme concentrations While cross-linking through physical interactions such as hydro- are high; conditions under which many drugs are unstable. In addi- gen bonding or hydrophobic interactions has been proposed to tion to this protective characteristic, hydrogels may potentially be avoid toxicity problems [11–13], such cross-linking may be not be designed to selectively release drugs under the physiological condi- strong enough to produce a sufficiently stable hydrogel for effective tions at the disease site in the body, and thereby achieve a targeted drug loading. Fortunately, polysaccharides may be used as chemical drug release. Consequently, hydrogels have found wide application cross-linkers to produce biocompatible hydrogels which present in drug delivery studies [1–4]. In addition to these characteristics, attractive applications in drug delivery [14–17]. the introduction of stimuli dependent phase changes into hydrogels The naturally occurring polysaccharide chitosan (CS) has been offers the possibility of developing sophisticated controlled drug shown to be amenable to functionalization to produce a range of versatile materials with substantial potential for biomedical applications [18–22]. In this work, a chitosan derivative is used to cross-link poly(acrylic acid) (PAA) to give three pH sensi- ∗ Corresponding author at: State Key Laboratory of Chemical Engineering, East tive poly(acrylic acid)/chitosan hydrogels (PAACS-I, PAACS-II and China University of Science and Technology, Meilong Road 130, 200237 Shanghai, PAACS-III) in which the extent of chitosan cross-linking progres- China. ∗∗ Corresponding author. sively increases, and which are designed to control the release of the E-mail addresses: [email protected] (J. Wang), drugs amoxicillin and meloxicam (Scheme 1). These drug releases [email protected] (X. Guo). http://dx.doi.org/10.1016/j.colsurfb.2017.01.008 0927-7765/© 2017 Elsevier B.V. All rights reserved.  Y. Wang et al. / Colloids and Surfaces B: Biointerfaces 152 (2017) 252–259 253 Scheme 1. Molecular structures of amoxicillin and meloxicam. Table 1 stant weight in an oven at 60 ◦ C (hydrogel samples with 60 mg in Reactants amounts for the preparation of PAACS hydrogels. weight, 2.5 mm in diameter, and 20 mm in length). Hydrogel AA (g) CSMAH (g) APS (g) NaOH (g) Deionized Water (mL) 2.4. Determination of the hydrogel swelling ratios (SR) PAACS-I 2.8 0.05 0.01 1.4 40 PAACS-II 2.8 0.10 0.01 1.4 40 The dried hydrogel (0.5 g) was immersed in the 100 mL of aque- PAACS-III 2.8 0.15 0.01 1.4 40 ous phosphate buffer solutions at pH 1.2, 6.8, and 7.4. The hydrogels were taken out of solution and weighed after removing the resid- are analyzed through the Korsemeyer-Peppas and Weibull drug ual solutions on the surface at a pre-determined time interval. The release models [23,24] to gain insight into the drug release mecha- hydrogels were then returned to solution and the process was nism and thereby improved understanding for the design of more repeated until a constant SR was obtained as calculated through advanced and reliable hydrogel drug delivery systems. Eq. (1), in which ms and md are the weight of the hydrogel in the swollen and dry states, respectively. 2. Experimental ms − md SR = (1) md 2.1. Materials 2.5. Rheological measurements Chitosan (CS, degree of N-deacetylation = 95%, Mw = 200 kDa) was purchased from Aoxing Biotechnology Co. Ltd., China. Maleic The dynamic frequency sweep measurements were performed anhydride (MAH, 99%) was purchased from Acros Co. Ltd. Ammo- on a MCR501 rheometer (Anton-Paar Physical Company). A nium persulfate (APS, 99%) and acrylic acid (AA, 99%, distilled under parallel-plate made of stainless steel with a diameter of 25 mm was vacuum pressure prior to use) were provided by Sigma Aldrich. used. During all rheological measurements, the upper plate was set Amoxicillin and meloxicam were supplied by TCI, Japan. The water at a distance of 1 mm from the down plate. All the hydrogel sam- used in all experiments was purified by reverse osmosis (Shanghai ples were cut into a cylindrical shape with a thickness of 1 mm and RO Micro Q). All other reagents and solvents were used directly. a diameter of 25 mm for the measurement. The elastic modulus (G ) and viscous modulus (G ) over a frequency range of 0.1–10 Hz were 2.2. Synthesis of chitosan-g-(maleic anhydride) (CSMAH) recorded at a constant strain of 1%, which was in the linear range of the viscoelasticity. All measurements were performed at 37 ◦ C. An aqueous solution of chitosan was prepared by dissolving 0.5 g of chitosan in 40 mL of 2.5 wt% acetic acid aqueous solution under 2.6. Drug loading vigorous stirring. Subsequently, 2.5 g maleic anhydride in 1 mL ace- tone were added slowly into the pre-prepared chitosan solution Amoxicillin and meloxicam were loaded into the PAACS hydro- under ice cooling within 10 min. The reaction mixture was allowed gels by soaking and swelling the dried hydrogels in solutions of to warm to room temperature and stand for 8 h. Finally, the vis- drugs according to a reported method. This is exemplified by cous solution was poured into 500 mL of acetone to precipitate the the loading of amoxicillin for which 60 mg of the dry cylindrical product. The solid product was purified by extraction with acetone hydrogels were immersed into 50 mL of 200 ␮g mL−1 amoxicillin three times and subsequent drying under vacuum at 50 ◦ C for 48 h. solutions under moderate stirring for 24 h at 37 ◦ C. Thereafter, the drug-loaded hydrogels were taken out and rinsed with deionized 2.3. Preparation of PAACS hydrogels water to remove any residual drugs from the surface. It should be noticed that meloxicam is poorly water soluble and accordingly a The three hydrogels, PAACS-I, PAACS-II and PAACS-III, were pre- small amount of methanol was added to improve solubility; other- pared through free radical polymerization, using APS as an initiator wise the procedure was as for that of amoxicillin. The loaded drug and the synthesized CSMAH as a cross-linker. Briefly, to a solu- amounts were determined by UV–vis spectroscopy (SHIMADZU tion of 1.4 g NaOH in 40 mL water at room temperature, either UV-2550 UV–vis) based on the decrease of the concentration of 0.05, 0.10 or 0.15 g of CSMAH were added (for PAACS-I, PAACS-II drug loading solutions determined from UV–vis calibration curves and PAACS-III, respectively) with stirring until a transparent solu- for amoxicillin and meloxicam at 228 nm and 361 nm, respectively. tion was obtained, whereupon 0.01 g APS was added (Table 1). The encapsulation efficiency (EE) and loading content (LC) of the These mixtures were each transferred into a reaction vessel and drugs were calculated through Eqs. (2) and (3) where me is the a N2 stream was passed through for 30 min to eliminate dissolved amount of encapsulated drug, mo is the total amount of added oxygen. The copolymerizations were carried out at 70 ◦ C for 2 h. drug, and md is the amount of the dried hydrogel. The EE and LC The gained hydrogels were placed in 500 mL of methanol/water determined are listed in Table S1. (v/v = 7/3) for 24 h to remove the residual reactants. Finally, the me EE(%) = × 100 (2) purified hydrogels were cut into thin cylindersand dried to con- mo 254 Y. Wang et al. / Colloids and Surfaces B: Biointerfaces 152 (2017) 252–259 defined as the number of grafted MAH per 100 pyranose units, was determined to be 27.3 ± 0.1% based on the proton integration (Eq. (4)), where I6.32ppm and I3.2–4.2ppm are the integrated peak area ratios of protons of the MAH and CS components, respectively. It is anticipated that GD varies over a small range between individual chains. 5 × I6.32 ppm GD = × 100% (4) I3.2−4.2 ppm FTIR spectra of PAA, CS, CSMAH, and PAACS hydrogels are dis- played in Fig. 1B. For PAA, a broad absorption band from 3000 to 3600 cm−1 is stemmed from the O H stretching vibration. The peaks appeared at 1637 and 1151 cm−1 are contributed by the stretching vibration of C O and C O of the carboxylic group. Another two peaks appeared at 1454 and 1409 cm−1 are caused by the O H bending vibration of PAA. The characteristic peaks of CS located at 3346 cm−1 (O H and N H stretching), 2921 and Scheme 2. Preparation of PAACS hydrogels. 2854 cm−1 (C H stretching), and 1654 cm−1 (NH CO (I) stretch- ing) can be observed clearly in the FT-IR spectrum. In the CSMAH me spectrum, the new peaks appeared at 1658 and 1564 cm−1 are LC(%) = × 100 (3) attributed to C O groups of the opened MAH, it further approves md the successful modification of CS. The peak at 1700 cm−1 is caused by the carboxyl stretching vibration of carboxylic acid. With regard 2.7. Drug release study to the spectrum of PAACS hydrogel, some absorption peaks are changed by comparing with CSMAH and PAA. A broad peak at The release of amoxicillin and meloxicam from PAACS hydrogels the range of 3000–3500 cm−1 arises from the overlapping of the was carried out in aqueous phosphate buffer solutions at pH 1.2, 6.8, O H stretching vibrations of PAA and N H stretching vibrations and 7.4 at 37 ◦ C. Basically, either amoxicillin or meloxicam loaded of CSMAH. The characteristic stretching absorption band of C O hydrogel was placed into 60 mL of moderately stirred aqueous in PAA presents at 1637 cm−1. In particular, the characteristic buffer solution. At appropriate time intervals, 2.0 mL samples of the absorption bands of CS at 2921 and 2854 cm−1 consistent with the aqueous buffer solutions were withdrawn and replaced by 2.0 mL participation of CSMAH in the polymerization to for PAACS hydro- fresh aqueous buffer solutions. The amount of the released drugs gels. in the withdrawn sample was determined by UV–vis absorbance at 228 nm for amoxicillin and 361 nm for meloxicam according to the molar absorbance calibration curves of amoxicillin and meloxicam. 3.2. X-Ray powder diffraction (XRD) All release data were performed in triplicate and averaged. XRD was employed to reveal the crystallinity of CS, CSMAH, PAA, PAACS-I, PAACS-II and PAACS-III. As shown in Fig. 1C, the XRD pat- 2.8. Characterization tern of CS shows two major peaks at 10◦ and 19◦ which transforms into a single broad peak at 20◦ in the XRD pattern of CSMAH caused All infrared spectra were obtained from dried samples in KBr by the grafting of MAH onto CS. Upon polymerization with AA, a pellets using a Nicolet 6700 FTIR spectrophotometer. 1 H NMR spec- substantial decrease in intensity occurs in the region centered at tra was taken by a 500 MHz Bruker DRX500 spectrometer at 25 ◦ C 10◦ where both CS and CSMAH absorb, and the broad peaks of PAA using D2 O as the solvent. The SEM was performed using a Nova appear in the range 15◦ –40◦. This is consistent with the copoly- Nano SEM 50 field emission scanning electron microscope (FE- merization of CSMAH and AA progressing in a random way and a SEM) at an acceleration voltage of 3 kV. consequent decrease in crystallinity by comparison with that of CS, and also a decrease in inter- and intra-molecular hydrogen bonding. 3. Results and discussion 3.3. Rheology As shown in Scheme 2, CSMAH was synthesized by grafting MAH onto the main chain of CS. Subsequently, CSMAH was employed The rheological properties are important indicators of soft mate- to copolymerize with AA to create the three hydrogels in which rials performances. As shown in Fig. 1D, for each of the three the extent of CS cross-linking increase in the sequence PAACS- hydrogels, PAACS-I, PAACS-II and PAACS-III, the elastic modulus, G’, I < PAACS-II < PAACS-III as a consequence of the three-fold increase was higher than their viscous modulus, G”, over the measured fre- in CSMAH concentration used in their respective preparations quency range. This is consistent with the hydrogels being present as (Table 1). solids under the measuring conditions; thereby constituting a sta- ble structure for drug loading. It is also observed that G’ increases 3.1. Structure characterization in the sequence PAACS-I < PAACS-II < PAACS-III coincident with the increasing CS cross-linker content. Additionally, the reacted ratio Fig. 1A shows the 1 H NMR spectrum of CSMAH. The broad peaks of MAH groups in CSMAH was estimated by Eq. (5), where  is the at 3.2–4.2 ppm arise from the hydrogens of the pyranose units of density of PAA, R is the ideal gas constant, T is temperature, and CS (H3, H4, H5, and H6), the peak at 3.05 ppm arises from H2, and M̄c is the average molecular weight of PAA between two adjacent the peak of methyl hydrogen of the N-acetyl groups is located at cross-linking points , here we hypothesize a complete copoly- 2.12 ppm. The two peaks at 5.85 and 6.32 ppm which are referred merization is achieved. to H7 and H8 of the grafted MAH. Thus, the 1 H NMR characteriza- tion indicates that MAH modified CS was successfully synthesized. RT G= (5) The averaging grafting degree (GD) of MAH onto CS in CSMAH, M̄c  Y. Wang et al. / Colloids and Surfaces B: Biointerfaces 152 (2017) 252–259 255 Fig. 1. 1 H NMR spectrum of CSMAH (A); FTIR spectra (B) and XRD patterns (C) of CS, CSMAH, PAA and PAACS hydrogels; Elastic modulus G’ and viscous modulus G” of PAACS hydrogels as a function of frequency (D). The calculation results demonstrated that the cross-linking effi- 3.4. Morphology of PAACS hydrogels ciency is not very high which might stem from the big molecular volume of chitosan, for instance, only ∼0.5% MAH groups in CSMAH The micro-morphologies of the freeze-dried PAACS hydrogels was presented in cross-linking PAA chains (Fig. 1D). This is also were shown to possess well-defined network structures by SEM responsible for the low elastic modulus of these hydrogels. (Fig. 2). A statistical analyses of the pore size of these hydrogels Fig. 2. The network structures and the pore size distributions of the hydrogels: A) PAACS-I; B) PAACS-II; C) PAACS-III (each statistical result was obtained by counting 100 pores from the SEM image). 256 Y. Wang et al. / Colloids and Surfaces B: Biointerfaces 152 (2017) 252–259 Fig. 3. Swelling kinetics of PAACS hydrogels at different pH, error bars are the standard error of the mean taken from three samples. indicated that increase in the extent of CS cross-linking significantly and swelling is reduced [31–34]. However, at pH 7.4, the carboxylic decreased pore size. The average pore size of PAACS-I is around groups were deprotonated and hydrogen-bonding between them ∼126 ␮m, while those of PAACS-II and PAACS-III are smaller, ∼86 is absent while their negative charges cause electrostatic repulsion and ∼51 ␮m, respectively. While it has been proposed that the pore between the PAA chains. The overall effect is that the hydrogel size of the hydrogel depends on the size of the ice crystals which network has a looser structure at pH 7.4 than that at pH 1.2 which are formed during the freeze-drying treatment of the samples , permits an increased diffusion of water into the hydrogel and an the greater the extent of CS cross-linking the greater will be the increased swelling. restraint on the capacity of the hydrogel to swell with water absorp- The effect of pH change on hydrogel swelling superimposes tion. As a result, the size of the ice crystals and hydrogel pores will on the increase in the extent CS of cross-linking in the sequence: decrease with increase in CS cross-linking [29,30]. PAACS-I < PAACS-II < PAACS-III and the corresponding decrease in SR in the sequence: PAACS-I > PAACS-II > PAACS-III at the three pH conditions studied. Thus, an increase in CS cross-linking tightens 3.5. Swelling behavior the hydrogel network thereby impeding diffusion of water into it and decreasing the SR. The swelling properties of PAACS hydrogels were investigated by soaking the freeze-dried hydrogels in aqueous buffer solutions at pH 1.2, 6.8 and 7.7 and recording the weight changes with time 3.6. Study of pH triggered drug release at 37 ◦ C. It is seen from Fig. 3 that PAACS-I, PAACS-II and PAACS-III each exhibits an increase in swelling ratio (SR) as pH increases. It is The release curves for amoxicillin and meloxicam are displayed also seen that at a given pH SR decreases in the sequence PAACS- in Fig. 4. It demonstrated drug release rate decreases in the hydrogel I > PAACS-II > PAACS-III as the extent of CS cross-linking increases. sequence PAACS-I > PAACS-II > PAACS-III and that for each hydrogel At pH 1.2, the carboxylic acid groups in PAA chains are almost pro- the release rate increases with increase in pH. This pattern bears a tonated and substantial hydrogen-bonding occurs between them striking similarity to that for the hydrogel SR shown in Fig. 3 and and the repulsion force between polymer chains in the networks suggests that the increase in drug mobility is directly related the is reduced so that the water diffusion into the hydrogel is impeded increase in hydrogel pore size as pH increases. Fig. 4. The release curves of amoxicillin and meloxicam at different pH, error bars are the standard error of the mean taken from three samples.  Y. Wang et al. / Colloids and Surfaces B: Biointerfaces 152 (2017) 252–259 257 Fig. 5. Schemetic illustration of the process of drug release from hydrogel. For PAACS-I, ∼30%, ∼60% and ∼80% of amoxillin is released after release up to the stage where 60% of the drug is released through Eq. 800 min at pH 1.2, 6.8 and 7.4, respectively (Fig. 4). The analogous (6) where Mt and M∞ are the amounts of drug released at time t and values for meloxicam are ∼20%, ∼70% and ∼90% at pH 1.2, 6.8 and when equilibrium is reached, respectively; k is a kinetic constant, 7.4, respectively. Both drugs are released more slowly from PAACS- and n is an exponent typifying the release mechanism. II and PAACS-III, and release from both hydrogels shows an increase Mt in rate with increase in pH. It has been suggested that many drugs = kt n (6) M∞ are released from hydrogels through a diffusion process which is dominated by the swelling behavior of the hydrogel. Thus, the The release data for both amoxicillin and meloxicam is well- lower release rate of amoxicillin and meloxicam at pH 1.2 is prob- fitted by Eq. (6) for up to 60% of drug release as shown in Fig. S1a ably largely contributed by the pore size decrease (Fig. S1) due to and c). These fittings correspond to n values in the range beween greater hydrogen bonding between the PAA and CS chains in hydro- 0.51 and 0.85 for amoxicillin and between 0.63 and 0.87 for meloxi- gel networks (Scheme 1) and a consequent decrease in hydrogel cam (Table S2) consistent with the drugs being released through flexibility and an inhibition of both drug and water diffusion. The so-called anomalous diffusion, in which the effects of drug diffu- hyrogel flexibility is further decreased as cross-linking increases sion and hydrogel relaxation are comparable. [36,39–42]. It can also with the consequence that drug release is further slowed as seen be seen clearly that at a given pH value, the n values more closely from Fig. 4. approach 0.89 at which only the relaxation of hydrogel governs the It has been revealed that the chemical structure of both the drug release as the extent of cross-linking increases in the sequence drug and the hydrogel determine the nature and extent of inter- PAACS-I < PAACS-II < PAACS-III in the hydrogels [39–42]. That is actions between them and that this impinges on the magnitude of because increases in cross-linking decrease the hydrogel flexibility drug release rates. From the release curves for amoxicillin and such that the hydrogel relaxation process becomes the control- meloxicam (Fig. 4), we can see obviously that the release rate of ling factor for drug release. The n values characterizing amoxicillin amoxicillin is higher than that of meloxicam at pH 1.2 whereas the release are smaller than those for meloxicam release which may reverse is the case at pH 6.8 and 7.4. This reflects the variation of indicate that amoxicillin interacts more strongly with the hydro- the effects of hydrogen bonding between the hydrogel PAA and CS gels and is therefore less dependent upon hydrogel relaxation for chains and probably between them and the two drugs. Amoxicillin release. This can also be seen from the diffusion coefficients of is more hydrophilc than is meloxicam as assessed on the basis of the amoxicillin (D1 ) and meloxicam (D2 ) in the hydrogels (Fig. S3 and higher water solubility of amoxicillin. This is likely to diffentiate the Table S3). At higher pH (pH 6.8 and 7.4), we found that the hydrogels behavior of the two drugs within the hydrogel but a more detailed relaxed completely within ∼300 min, after which the drugs were analysis is not possible on the basis of the currently available data. released in a stable diffusion process. By estimating the diffusion coefficient, we found that D1 was smaller than D2 demonstrating the higher interation between amoxicillin and hydrogel. Conse- 3.7. Mechanism of drug release from hydrogels quently, the n values for amoxicillin release more closely approach 0.45 (at which only diffusion controls drug release) than is the case The mechanism of drug released from hydrogels may be envis- for meloxicam. However, the overall conclusion is that both amox- aged as occurring in three main steps as shown in Fig. 5. In the initial icillin and meloxicam are released from the hydrogels through a step, a), the drug-loaded hydrogel contains a minimum amount combination of diffusion and hydrogel relaxation under the condi- of water, the hydrogel exhibits it minimum flexibility, pore size is tions of this study. small and drug mobility is limited. In the second step, b), water As we mentioned previously, Korsemeyer-Peppas equation is diffuses into the hydrogel which undergoes relaxation to become only valid for the first 60% of the release curve. In order to give a more flexible, pore size grows and drug mobility increases with more reliable mechanism revealing, another model, Weibull model, increased hydration. In the final stage, c), the hydrogel is fully which covers the entire drug release process, is described through relaxed and hydrated and pore size is at a maximum, as is the rate Eq. (7), where a is a constant, and b is an exponent which reflects of drug diffusion from the hydrogel [38,39]. the underlying release mechanism. A value of b in the range of The mathematical modeling of drug release from hydrogel is 0.35–0.75 signifies a diffusion dominated drug release process and a facile and an important approach to understand the elusive a b value in the range 0.75–1.0 indicates a combined diffusion and release mechanism [24,39–44]. Accordingly, We have employed hydrogel relaxation mechanism. both Korsemeyer-Peppas [39–42] and Weibull models to elu- cidate the release mechanism of amoxicillin and meloxicam. The Mt = 1 − exp(−at b ) (7) widely used Korsemeyer-Peppas model expresses the rate of drug M∞ 258 Y. Wang et al. / Colloids and Surfaces B: Biointerfaces 152 (2017) 252–259 It can be seen from Fig. S2b and d that Eq. (7) can fit the drug E.A. Appel, R.A. Forster, M.J. Rowland, O.A. Scherman, The control of cargo release data very well. 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