Fabrication and Characterization of Dissolving Microneedles for Transdermal Drug Delivery of Apomorphine Hydrochloride in Parkinson's Disease.

PURPOSE: We fabricated and characterized polyvinyl alcohol (PVA)-based dissolving microneedles (MNs) for transdermal drug delivery of apomorphine hydrochloride (APO), which is used in treating the wearing-off phenomenon observed in Parkinson's disease. METHODS: We fabricated MN arrays with 11 × 11 needles of four different lengths (300, 600, 900, and 1200 µm) by micromolding. The APO-loaded dissolving MNs were characterized in terms of their physicochemical and functional properties. We also compared the pharmacokinetic parameters after drug administration using MNs with those after subcutaneous injection by analyzing the blood concentration of APO in rats. RESULTS: PVA-based dissolving MNs longer than 600 µm could effectively puncture the stratum corneum of the rat skin with penetrability of approximately one-third of the needle length. Although APO is known to have chemical stability issues in aqueous solutions, the drug content in APO-loaded MNs was retained at 25°C for 12 weeks. The concentration of APO after the administration of APO-loaded 600-µm MNs that dissolved completely in skin within 60 min was 81%. The absorption of 200-µg APO delivered by MNs showed a Tmax of 20 min, Cmax of 76 ng/mL, and AUC0-120 min of 2,829 ng・min/mL, compared with a Tmax of 5 min, Cmax of 126 ng/mL, and AUC0-120 min of 3,224 ng・min/mL for subcutaneous injection. The bioavailability in terms of AUC0-120 min of APO delivered by MNs was 88%. CONCLUSION: APO-loaded dissolving MNs can deliver APO via skin into the systemic circulation with rapid absorption and high bioavailability.

Evaluation of Drug Sorption on Laboratory Materials with Abraham Solvation Parameters of Drugs and its Prevention.

PURPOSE: Undesired drug sorption on laboratory material surfaces reduces the performance of analytical methods and results in the generation of unreliable data. Hence, we characterized the sorption of drugs and evaluated the sorption extent using a linear free energy relationship (LFER) model with Abraham solvation parameters of drugs. Furthermore, to prevent sorption, the effects of additives, such as organic solvents and salts, were evaluated. METHODS: The sorption of fifteen model drugs (concentration: 2 µM), with various physicochemical properties, on materials in 0.2% dimethyl sulfoxide aqueous solutions was evaluated. Drug sorption extent on the materials was determined using high-performance liquid chromatography. The obtained results were analyzed using an LFER model with Abraham solvation parameters of the drugs. The effect of additives on the sorption of itraconazole, one of the most hydrophobic drugs among those tested in this study, was investigated. RESULTS: Sorption was dependent on the physicochemical properties of drugs, rather than the type of materials used, and additives altered the rate of drug sorption. Equations were developed to evaluate the sorption extent (nmol) of drugs to glass and polypropylene using the Abraham solvation parameters of the drugs. CONCLUSIONS: LFER modeling with Abraham solvation parameters of drugs enabled us to evaluate drug sorption on materials. All the additives altered the rate of drug sorption, and some organic solvents effectively prevented sorption. The developed LFER model would be useful for assessment of the sorption properties of compounds in in vitro evaluations in drug discovery research and various other biochemical fields.

Cold Flow Evaluation in Transdermal Drug Delivery Systems by Measuring the Width of the Oozed Adhesive.

The objective of this study was to develop a simpler and more practical quantitative evaluation method of cold flow (CF) in transdermal drug delivery systems (TDDSs). CF was forcibly induced by loading a weight on a punched-out sample (bisoprolol and tulobuterol tapes). When the extent of CF was analyzed using the area of oozed adhesive as following a previously reported method, the CF profiles were looked different between the samples 12 mm in diameter subjected to a 0.5-kg weight and samples 24 mm in diameter subjected to a 2.0-kg weight despite an equal load per unit area (4.42 g/mm2). The width of oozed adhesive around the original sample was suggested to be an index that properly describes the relationship between the load per unit area and the extent of CF. Further, it was clarified that the average CF width over the entire circumference of the sample was the same whether the samples were round or square as long as the sample area and load were the same. We also observed a linear relationship between the CF width and the aspect ratio of oval and rectangular samples. These results indicated that the CF properties of typical TDDS products lacking CF-proof processing at the edges could be determined by testing samples cut from the product rather than the whole TDDS patch. The proposed width measuring method was simple and useful for optimizing the composition of the adhesive and for testing the quality of the product.

Mechanical Characterization of Dissolving Microneedles: Factors Affecting Physical Strength of Needles.

Dissolving microneedles (MNs) are novel transdermal drug delivery systems that can be painlessly self-administered. This study investigated the effects of experimental conditions on the mechanical characterization of dissolving MNs for quality evaluation. Micromolding was used to fabricate polyvinyl alcohol (PVA)-based dissolving MN patches with eight different cone-shaped geometries. Axial force mechanical characterization test conditions, in terms of compression speed and the number of compression needles per test, significantly affected the needle fracture force of dissolving MNs. Characterization using selected test conditions clearly showed differences in the needle fracture force of dissolving MNs prepared under various conditions. PVA-based MNs were divided into two groups that showed buckling and unbuckling deformation, which occurred at aspect ratios (needle height/base diameter) of 2.8 and 1.8, respectively. The needle fracture force of PVA-based MNs was negatively correlated with an increase in the needle's aspect ratio. Higher residual water or higher loading of lidocaine hydrochloride significantly decreased the needle fracture force. Therefore, setting appropriate methods and parameters for characterizing the mechanical properties of dissolving MNs should contribute to the development and supply of appropriate products.

Physicochemical profiling of nanomedicines using centrifugal field flow fractionation.

Nanomedicines comprise multiple components, and particle density is considered an important property that regulates the biodistribution of administered nanomedicines. The density of nanoparticles is characterized by centrifugal methods, such as analytical ultracentrifugation. Particle size and distribution are key physicochemical and quality attributes of nanomedicines. In this study, we developed a novel profiling method applicable to liposomes and lipid nanoparticles (LNPs), based on particle size and density, using centrifugal field-flow fractionation (CF3). We evaluated the elution profiles of PEGylated liposomes of different sizes with various doxorubicin (DOX)-loading amounts using CF3. This method was applied to evaluate the drug release of DOX-loaded liposomes, intra- and inter-batch variability, reconstitution reproducibility of AmBisome®, and elution characteristics of LNPs in COVID-19 vaccines (Comirnaty® and SpikevaxTM). The data obtained in the present study underscore the significance of the proposed methodology and highlight the importance of profiling and characterizing liposomes and LNPs using CF3 fractograms and a multi-angle light-scattering detector.

[Ion-pair HPLC analysis of B vitamins in syrup products in Indonesia].

A training course for analysis of B vitamins in syrup products was undertaken at the National Agency of Drug and Food Control at Jakarta as part of the project to deliver safe drugs to people in Indonesia by Japan International Cooperation Agency. Analytical methods have been developed for quantitative determination of B vitamins by ion-pair high-performance liquid chromatography using 1-hexanesulfonic acid sodium salt. Measurements were performed for two syrup products removed from a drug store in Jakarta to determine the amount of each vitamin B. The measured values of riboflavin 5'-phosphate sodium, nicotinamide and pyridoxine hydrochloride were almost the same with those of nominal content for both products. While the measured values of thiamine hydrochloride, pantothenol and cyanocobalamin were approximately twice the amount of nominal contents.

Real-time in situ X-ray micro-computed tomography study of the effect of impurities on the crystallization of amorphous nifedipine.

Controlling the physical stability of noncrystalline active pharmaceutical ingredients remains a major challenge in the development of amorphous formulations such as amorphous solid-dispersion (ASD) formulations. To establish new evaluation and formulation strategies, the spatial distribution of the crystal phase in bulk amorphous nifedipine (NFD) was investigated as a model. The crystallization of amorphous NFD and the effect of a deliberately added impurity were investigated using powder X-ray diffraction (PXRD), differential scanning calorimetry and real-time in situ X-ray micro-computed tomography (X-ray CT). The stability data of amorphous samples, i.e., NFD and a mixture of NFD with an oxidative degradation product of NFD, impurity A (Imp A), at a weight ratio of 90:10, presented as percent amorphous remaining, suggests that Imp A accelerates the bulk crystal growth of NFD. Real-time in situ X-ray CT results showed surface-enhanced crystal growth and cavity formation in solid NFD samples. Moreover, the crystals were heterogeneous in density. These results suggest that Imp A affects the physical stability of the amorphous NFD. X-ray CT equipped with a heating unit can aid in-situ evaluation and assessment of physicochemical properties and physical stability of amorphous samples and formulations.

Crystallization of Amorphous Nifedipine Under Isothermal Conditions: Inter-laboratory Reproducibility and Investigation of the Factors Affecting Reproducibility.

High inter-laboratory reproducibility is required for conducting collaborative experiments among several laboratories. The primary aim of our evaluation of the physical stability of amorphous drugs, conducted in co-operation with eight laboratories, was to establish a protocol for isothermal storage tests to obtain data of the same quality from all the participating laboratories. Sharing a protocol that contained the same level of detail as the experimental section of general papers was insufficient for high inter-laboratory reproducibility. We investigated the causes of variations in the data from the various laboratories and restricted the protocol step-by-step to achieve high inter-laboratory reproducibility. The various experimentalists had very different levels of awareness regarding how to control the temperature of a sample as the samples were transferred into and out of thermostatic chambers. Specific instructions on how to conduct this operation, such as regarding the time required for the transfer and thermal protection of the container during the transfer, helped to reduce variation. Improved inter-laboratory reproducibility revealed that the physical stabilities of amorphous drugs differed when samples were prepared in differently shaped aluminum pans designed for various differential scanning calorimeters.

[Studies on the food allergenic proteins contained in pharmaceutical excipients].

Most drugs contain pharmaceutical excipients. These are pharmacologically inactive substances used as vehicles for the active ingredients of a medication. Some of these pharmaceutical excipients are produced from allergenic foods (e.g., milk, egg, peanut, soybean, and sesame) and removing proteins completely from such excipients is difficult. Therefore, if individuals with food allergy consume drugs containing allergenic food-derived excipients, eliminating the risk of developing specific allergic symptoms induced by them may not be possible. We determined the levels of proteins in pharmaceutical excipients and ethical drugs (inhalants and injections) by spectrophotometric analyses. The level of protein in the pharmaceutical excipient lactose in each sample was approximately 1 mg/g. In the case of oils from soybeans, peanuts, and sesame in pharmaceutical excipients, proteins were detected in the range 7-9 microg/g sample. We also determined levels of allergenic proteins in pharmaceutical excipients and ethical drugs using commercial enzyme-linked immunosorbent assay systems. The milk proteins in lactose were detected in the range 1.39-13.07 microg/g. The results of this study suggest that physicians, patients with food allergies, pharmacists, and healthcare providers must pay attention to presence of potential impurities those may cause allergic symptoms in pharmaceutical products.

[Detection and Analysis of Drug Crystals in Medical Transdermal Patches by Using X-ray Diffraction Measurement].

The crystallization of active pharmaceutical ingredients (APIs) in matrix-type transdermal patches has implications for the rate of drug absorption through the skin and patch adhesion strength. Therefore, the presence or absence and the degree of API crystallinity must be controlled to guarantee the quality of patches. In this study, the utility of laboratory-level X-ray diffractometers for the detection and analysis of crystalline APIs in transdermal patches was investigated using medical patches of tulobuterol and isosorbide dinitrate. Several matrix-type patches employ a controlled drug delivery system containing intentionally crystallized API. Both benchtop and high-resolution laboratory X-ray diffractometers can detect several characteristic peaks of the APIs in these patches even if the patches are wrapped in an outer bag, although a benchtop model provides peak heights one-seventh to one-fifth that of a high-resolution instrument. An isosorbide dinitrate patch containing an unintentionally crystallized spot was wrapped in an outer bag, followed by measurements using both X-ray diffractometers. For both instruments, several isosorbide dinitrate-derived peaks were detected only at the crystallized spot, although the signal-to-noise ratio was poorer for the benchtop model. These results show that a high-resolution X-ray diffractometer is advantageous for high-detection sensitivity and offers a high degree of freedom of the measurement position on the sample. It was concluded that a laboratory-level high-resolution X-ray diffractometer can be used to examine the crystalline state of APIs in patches inside an unopened outer bag.

Influence of the crystallization tendencies of pharmaceutical glasses on the applicability of the Adam-Gibbs-Vogel and Vogel-Tammann-Fulcher equations in the prediction of their long-term physical stability.

Amorphization is a powerful approach for improving the aqueous solubility and bioavailability of poorly water-soluble compounds. However, it can cause chemical and physical instability, the latter of which can lead to crystallization during storage, diminishing the solubility advantage of the amorphous state. As there is no standard method for predicting the physical stability of amorphous materials, a long-term stability study is needed in drug development. This study investigated the correlation between the physical stability of amorphous compounds and molecular mobility based on the assumption that physical stability is governed by the diffusional motion of a molecule. Model compounds were evaluated for crystallization onset time, structural relaxation time, fragility, and fictive temperature. The crystallization onset time of acetaminophen glass correlated with its relaxation time calculated from the Adam-Gibbs-Vogel equation; however, that of felodipine glass correlated with the relaxation time calculated from the Vogel-Tammann-Fulcher equation. The different crystallization tendencies of these compounds can be explained by the differences in the rate limiting steps in their crystallization processes, indicating the importance of distinguishing the critical process associated with crystallization. These findings will be useful for more accurate prediction of long-term physical stability of amorphous materials.

Chemical imaging analysis of active pharmaceutical ingredient in dissolving microneedle arrays by Raman spectroscopy.

The purpose of this study was to develop a quality evaluation method for dissolving microneedle arrays (DMNAs) and determine the spatial distribution pattern of drugs in DMNAs. Raman spectroscopy mapping was used to visualize the drug distribution in DMNAs and drug-loaded polymer films as a model. Powder X-ray diffraction (PXRD) and high-pressure liquid chromatography were also performed to characterize DMNAs. Drug-loaded polymer films and DMNAs were prepared by drying the aqueous solutions spread on the plates or casting. PXRD analysis suggested the crystallization of diclofenac sodium (DCF) in several forms depending on its amount in the sodium hyaluronate (HA)-based films. The Raman spectra of HA and DCF showed characteristic and non-overlapping peaks at 1376 and 1579 cm-1 Raman shifts, respectively. The intensity of the characteristic peak of DCF in the DCF-loaded films increased linearly with the increasing drug content in the range of 4.8 to 16.7% (DCF, w/w). Raman imaging analysis revealed a homogenous dispersion of small DCF crystals in these films. Raman imaging indicates the distribution of DCF on the surface of the DMNA needle. This work highlights the benefit of using Raman spectroscopy mapping to reveal the spatial distribution of drugs in DMNAs.

Isolation of N-nitrosodimethylamine from drug substances using solid-phase extraction-liquid chromatography-tandem mass spectrometry.

N-Nitrosodimethylamine (NDMA) has been detected in some drug substances and pharmaceutical products containing sartans, ranitidine and metformin, and a potential risk of NDMA contamination exists in other drug substances and their pharmaceutical products. To quantitate NDMA in various drugs having diverse physicochemical properties, a specific, sensitive, and reliable analytical method is required, in addition to methods that can be applied to a class of nitrosamines. We aimed to develop an off-line isolation method for NDMA in drug substances using SPE for quantification with LC-APCI-MS/MS. Impediments to accurate quantitation of NDMA in drug substances using LC-MS/MS and insufficient durability of the system are attributed to the extremely large amounts of active pharmaceutical ingredients (APIs) in sample solutions in comparison to the trace amount of NDMA. A reduced retention of NDMA and/or decreased separation from other substances in LC, matrix effect in MS detection, and undesirable contamination of instruments with API and other substances may be occasionally encountered, all of which consequently result in deterioration of system performance and generation of unreliable data, even in the cases where a divert valve is configured between the column and ion source of the MS instrument. To address these problems, an off-line NDMA isolation methodology from APIs exhibiting diverse physicochemical properties, namely ranitidine hydrochloride (ranitidine), metformin hydrochloride (metformin), nizatidine, valsartan, and telmisartan, was developed. The applicability of the method was confirmed by batch analysis of metformin and ranitidine. Furthermore, contrary to previous reports, NDMA was found to be stable over a wide pH range. The proposed methodology and data from this study would contribute to the control of NDMA contamination in various drugs to realize the safe delivery of pharmaceuticals to patients.

Discrimination of ranitidine hydrochloride crystals using X-ray micro-computed tomography for the evaluation of three-dimensional spatial distribution in solid dosage forms.

A non-destructive discrimination method for crystals in solid dosage drug forms was first developed using a combination of Raman spectroscopy and X-ray micro-computed tomography (X-ray CT). Identification of the crystal form of an active pharmaceutical ingredient (API) at the appropriate pharmaceutical dosage is crucial, as the crystal form is a determinant of the quality and performance of the final formulation. To develop a non-destructive analytical methodology for the discrimination of solid API crystals in a solid dosage form, we utilized a combination of Raman spectroscopy and X-ray CT to differentiate between ranitidine crystal polymorphs (forms 1 and 2) in tablet formulations containing three excipients. The difference in electron density correlated with the true density between ranitidine polymorphs, thereby enabling the discrimination of crystal forms and visualization of their three-dimensional spatial localization inside the tablets through X-ray CT imaging. Furthermore, X-ray CT imaging revealed that the crystal particles were of varying densities, sizes, and shapes within the same batch. These findings suggest that X-ray CT is not only an imaging tool but also a unique method for quantitative physicochemical characterization to study crystal polymorphs and solid dosage forms.

[Comparison of Adhesive Properties of Transdermal Patches Distributing in Japan-Tack and Peel Strength].

Forty-four brands of transdermal patches for twelve kinds of active pharmaceutical ingredients (APIs) are available in Japan as of April 30, 2018. Although approximately one-third of the corresponding pharmaceutical interview forms lack information on how to evaluate the adhesive properties of the patches, the peel test, probe tack test, or inclined ball tack test have generally been adopted. This means that it might be difficult to simply compare the adhesive properties among the patches because the testing methods are not unified in some cases. In this study, measurements of the adhesive properties of 38 transdermal patches of ten different APIs were performed using several unified testing methods (180° peel test, 90° peel test, self-adhesion test, and probe tack test) under unified experimental conditions. The adhesive properties were found to be quite different among the patches, even for the same API, dose, and size. For example, the ratios of the maximum to minimum measured values of tack and 180° peel strength for tulobuterol patches were 5 and 29, respectively. In the case of generic products for which the bioequivalence to a brand-name product is assured, the variation in adhesive properties can extend the range of choices for patients, which is advantageous. Providing information to medical experts on adhesive properties through, for example, pharmaceutical interview forms and package inserts, is considered to be useful for helping patients to make better choices.

Crystallization rate of amorphous nifedipine analogues unrelated to the glass transition temperature.

To examine the relative contributions of molecular mobility and thermodynamic factor, the relationship between glass transition temperature (T(g)) and the crystallization rate was examined using amorphous dihydropyridines (nifedipine (NFD), m-nifedipine (m-NFD), nitrendipine (NTR) and nilvadipine (NLV)) with differing T(g) values. The time required for 10% crystallization, t(90), was calculated from the time course of decreases in the heat capacity change at T(g). The t(90) of NLV and NTR decreased with decreases in T(g) associated with water sorption. The t(90) versus T(g)/T plots almost overlapped for samples of differing water contents, indicating that the crystallization rate is determined by molecular mobility as indicated by T(g). In contrast, differences in the crystallization rate between these four drugs cannot be explained only by molecular mobility, since the t(90) values at a given T(g)/T were in the order: NLV>NTR>NFD approximately m-NFD. A lower rate was obtained for amorphous drugs with lower structural symmetry and more bulky functional groups, suggesting that these factors are also important. Furthermore, the crystallization rate of NTR in solid dispersions with poly(vinylpyrrolidone) (PVP) and hydroxypropyl methylcellulose (HPMC) decreased to a greater extent than expected from the increased T(g). This also suggests that factors other than molecular mobility affect the crystallization rate.

Degradation rate of lyophilized insulin, exhibiting an apparent Arrhenius behavior around glass transition temperature regardless of significant contribution of molecular mobility.

The relative influences of chemical activation energy and molecular mobility in determining chemical reactivity were evaluated for insulin lyophilized with alpha,beta-poly(N-hydroxyethyl)-L-aspartamide (PHEA), and compared with that for insulin lyophilized with trehalose, which had been found to have the ability to decrease the molecular mobility of insulin at low humidity. The ratio of the observed rate constant k(obs) to the chemical activation energy-controlled rate constant k(act) (k(obs)/k(act)) at glass transition temperature (T(g)) was estimated to be approximately 0.6 and 0.8 at 6% RH and 12% RH, respectively, indicating that the degradation rate is significantly affected by molecular mobility at lower humidity conditions. However, these k(obs)/k(act) values at T(g) were larger than those for the insulin-trehalose system, and changes in the temperature-dependent slope around T(g) were less obvious than those for the insulin-trehalose system. Thus, the contribution of molecular mobility to the degradation rate in the insulin-PHEA system appeared to be less intense than that in the insulin-trehalose system. The subtle change in the temperature-dependent slope around T(g) observed in the insulin-PHEA system brought about a significant bias in shelf-life estimation when the reaction rate was extrapolated from temperatures above T(g) according to the Arrhenius equation.

Negligible contribution of molecular mobility to the degradation rate of insulin lyophilized with poly(vinylpyrrolidone).

The purpose of this study is to confirm the speculation which arose in our previous study that the degradation rate of insulin lyophilized with poly(vinylpyrrolidone) is mainly governed by the chemical activational barrier rather than molecular mobility. This speculation was based on the degradation data of insulin lyophilized with poly(vinylpyrrolidone) K-30 (PVP K-30), which was obtained at temperatures well below the glass transition temperature (T(g)). In this study, the degradation rate of insulin at temperatures below and above T(g) was determined using PVP 10k as an excipient, instead of PVP K-30, in order to examine whether or not the temperature dependence of the degradation rate changes around T(g). The relative contributions of molecular mobility and the activational barrier, calculated from the temperature- and T(g)-dependence of the degradation rate, indicated that the contribution of molecular mobility to the degradation rate was negligible. Furthermore, the negligible contribution of molecular mobility was confirmed by the lack of significant change observed in the temperature- and T(g)-dependence of the rate around T(g).

Ability of polyvinylpyrrolidone and polyacrylic acid to inhibit the crystallization of amorphous acetaminophen.

The inhibition of crystallization of amorphous acetaminophen (ACTA) by polyvinylpyrrolidone (PVP) and polyacrylic acid (PAA) was studied using amorphous solid dispersions prepared by melt quenching. Co-melting with PVP and PAA decreased the average molecular mobility, as indicated by increases in glass transition temperature and enthalpy relaxation time. The ACTA/PAA dispersion exhibited much slower crystallization than the ACTA/PVP dispersion with a similar glass transition temperature value, indicating that interaction between ACTA and polymers also contributed to the stabilizing effect of these polymers. The carboxyl group of PAA may interact with the hydroxyl group of ACTA more intensely than the carbonyl group of PVP does, resulting in the stronger stabilizing effect of PAA. Dielectric relaxation spectroscopy showed that the number of water molecules tightly binding to PVP per monomer unit was larger than that to PAA. Furthermore, a small amount of absorbed water decreased the stabilizing effect of PVP, but not that of PAA. These findings suggest that the stronger stabilizing effect of PAA is due to the stronger interaction with ACTA. The ability of PAA to decrease the molecular mobility of solid dispersion was also larger than that of PVP, as indicated by the longer enthalpy relaxation time.

Feasibility of atomic force microscopy for determining crystal growth rates of nifedipine at the surface of amorphous solids with and without polymers.

Amorphous nifedipine (NFD), which has a smooth surface immediately after preparation, was shown to have structures resembling clusters of curling and branching fibers approximately 1 µm wide by atomic force microscopy (AFM) after storage at 25°C. The size of the cluster-like structures increased with storage over time, implying crystal growth. The average elongation rate of the fibers determined by AFM at ambient room temperature was 1.1 × 10(-9) m/s, and this agreed well with the crystal growth rate of 1.6 × 10(-9) m/s determined by polarized light microscopy. The crystal growth rate of NFD in solid dispersions with 5% polyethylene glycol (PEG) was found to be 5.0 × 10(-8) m/s by AFM. Although this value was approximately the same as that obtained by polarized light microscopy, three-dimensional information obtained by AFM for the crystallization of NFD in a solid dispersion with PEG revealed that the changes in topography were not a consequence of surface crystal growth, but rather attributable to the growth of crystals formed in the amorphous bulk. For solid dispersions with α,ß-poly(N-5-hydroxypentyl)-l-aspartamide, acceleration of NFD crystallization by tapping with an AFM probe was observed. The present study has demonstrated the feasibility and application of AFM for interpretation of surface crystallization data.