On-Chip Optofluidic Single-Particle Method for Rapid Microscale

Letter pubs.acs.org/ac

On-Chip Optofluidic Single-Particle Method for Rapid Microscale Equilibrium Solubility Screening of Biologically Active Substances Sami Svanbac̈ k,* Henrik Ehlers, Osmo Antikainen, and Jouko Yliruusi Division of Pharmaceutical Chemistry and Technology, University of Helsinki, P.O. Box 56, FI-00014 Helsinki, Finland S Supporting Information *

ABSTRACT: Solubility is the primary physicochemical property determining the absorption and bioavailability of substances. Here, we present an optofluidic single-particle technique for microscale equilibrium solubility determination, based on on-chip hydrodynamic particle trapping and optical particle size monitoring. The method combines the rapidity, universality, and substance sparing nature of physical analysis, with the accuracy traditionally associated with chemical analysis. Applying the diffusion layer theory, we determined the equilibrium solubility from individual pure substance microparticles of as little as 14 μg in initial mass, in a matter of seconds to minutes. The reduction in time and substance consumption, when compared to the golden standard method, is above 2 orders of magnitude. With a simultaneous improvement above 3-fold in accuracy of the solubility data, the applicability of optofluidics based analytics for small-scale high-throughput quantitative solubility and biological activity screening is demonstrated.

S

sparing.4,6 Moreover, contrary to substance specific analytical techniques, particle detection can be seen as a universal analytical technique, applicable to all substances and transparent solvents as such. Thus, the need for time and substance consuming solute and solvent specific method development, calibration, and validation is avoided. However, these so-called kinetic solubility methods have been shown to be poor predictors of equilibrium solubility, with estimation errors up to 50 times that of the equilibrium value.4,7 In silico prediction is also used for rapid estimation of substance equilibrium solubility. However, despite considerable efforts to develop accurate computational methods for equilibrium solubility prediction, the root-mean-square error (RMSE) of these methods still generally remains around 0.8 log units.8 Analytical methods that combine the rapidity, universality, and substance sparing nature of physical analysis, with the accuracy traditionally associated with chemical analysis, could therefore have a significant impact on early bioavailability assessment of new chemical entities.

olubility and intestinal permeability are the two primary factors determining the absorption and biological activity of substances.1 In the case of drugs, the fundamental significance of solubility was epitomized by Curatolo: “An efficacious but nonabsorbed agent is no better than a well-absorbed but inefficacious one”.2 With up to 75% of current drug candidates demonstrating low aqueous solubility, the importance of in vitro solubility screening as a predictive tool for in vivo drug biological activity in early drug development is increasing.3 Thermodynamic solubility of a substance is an equilibrium event, and the standard way of determining this equilibrium is through time-consuming experiments that require incubation times above 24 h.4 Additionally, accurate determination demands substance specific analytical techniques with solute and solvent specific method development, calibration, and validation. Consequently, accurate determination of equilibrium solubility has traditionally been both time and substance consuming. The resource consuming nature of these techniques has prevented accurate solubility and bioavailability screening in early drug development, due to the large number and scarce amounts (less than a few milligrams) of compounds available for in vitro screening at this stage.4,5 On the other hand, physical analytical techniques, such as methods based on light scattering, are rapid and substance © 2015 American Chemical Society

Received: March 18, 2015 Accepted: April 26, 2015 Published: April 27, 2015 5041

DOI: 10.1021/acs.analchem.5b01033 Anal. Chem. 2015, 87, 5041−5045

Letter

Analytical Chemistry The synergistic fusion of photonics and fluidics in smart diagnostic systems, so-called optofluidic systems, provides promising new applications for small-scale life science analytics.9,10 The benefit of these miniaturized on-chip systems comes through allowing more simple and cost-effective analytical solutions. For example, optical and hydrodynamic single-cell manipulation and trapping has been widely used in miniaturization of biomedical studies.11 Here, we developed an on-chip optofluidic flow-through dissolution vessel incorporating a hydrodynamic particle trap for single-particle solubility and biological activity screening of substances. We designed and 3D-printed the flow-through cell, wherein the solvent flow creates a centrally positioned particle trapping vortex, allowing rapid noncontact particle focusing and, consequently, continuous monitoring by optical microscopy (Figure 1).

orientation, denying the possibility of a 3D estimation of the particle size from one detection angle.15 The same issue arises when studying fixed particles. In the hydrodynamic vortex formed in our dissolution vessel, the particle is allowed to rotate randomly within the particle trapping zone, as can be seen in the projection image series in Figure 2. An averaged 3D-shape

Figure 2. Dissolution of a randomly rotating single particle. The image demonstrates the concept of dissolution characterization based on particle size data. (a) Typical still image of a randomly rotating particle. (b) 96 binary images with equal intervals from a single-particle image series. The random rotation of the dissolving particle, which allows an average 3D particle size and shape determination from one detection angle only, is visualized. (c) Single-particle dissolution profiles of eight different substances in a mass released and time normalized plot. An equivalent volume approximation is made from the 2D particle projection micrographs, based on which the decrease in mass of the particle can be determined. The large amounts of data, of up to 22 000 images from a dissolution experiment, are analyzed with a custom-made MATLAB -script capable of real-time processing and analysis (for a more detailed description of image analysis, see the Supporting Information).

Figure 1. Schematic of the single-particle method (not to scale). Degassed distilled water (1) (22 ± 1 °C) was pumped (2) in a closed loop with a constant flow rate of 10 ± 0.05 mL/min through the dissolution cell (3) and back to the vial (1). Still images of the dissolving rotating particle (4) were acquired through a magnifying lense (5) by a CMOS image sensor (6) with a frame rate of 2−60 frames/min, using LED illumination (7) of the particle. Finally, the images were stored and analyzed on a computer.The inset on the top right shows a single-particle 3D-simulation of the diffusion layer dissolution rate model. According to the diffusion layer model, equilibrium solubility CS is assumed at the solid−liquid interface (black surface). A diffusion layer of thickness h (dots) exists immediately adjacent to the dissolving solid surface, outside of which a uniform bulk concentration Cb is assumed. The dots in the image represent dissolved molecules.

and -size characterization is therefore possible by the use of one image sensor and one detection angle only. An additional advantage of the noncontact particle trap is the avoidance of a particle fixing step. Apart from being time-consuming, particle fixing is likely to alter the surface morphology, intraparticle lattice energies and, thus, the dissolution kinetics of the particles. For this proof of concept study, we selected a set of 8 substances covering an equilibrium solubility range of 4.6 log units (15.9 μg/mL −592 mg/mL) (see the Supporting Information, Table S-1). The substances demonstrate a diverse range of properties, comprising neutral, acidic, basic, and ionic compounds. By means of a reorganized Hixson-Crowell (H-C) cube root law (for reorganization see the Supporting Information)

According to the generally accepted diffusion layer dissolution rate model, it is assumed that there exists a diffusion layer of thickness h around a dissolving surface, where saturation concentration is assumed at the solid−liquid interface (Figure 1).12,13 Consequently, when maintaining sink conditions during experiments, equilibrium solubility becomes the rate limiting factor of dissolution and can subsequently be determined. In order to accurately determine the diffusion layer of a particle, the size and shape of the particle have to be reliably determined. One way of achieving this is through single-particle analysis, thus avoiding population based estimations and other error sources arising from, e.g., aggregation and agglomeration of multiparticulate systems. Particle size analysis by photomicrography has previously been shown to be equivalent to chemical analysis in singleparticle dissolution studies, with a theoretical quantitation limit in the ng/L range.14 A common problem in particle size analysis is, however, the settling of particles in a preferential

CS =

5042

ρh(w01/3 − wt 1/3) 1/3

( 4πρ3 )

Dt

(1) DOI: 10.1021/acs.analchem.5b01033 Anal. Chem. 2015, 87, 5041−5045

Letter

Analytical Chemistry where w0 is the initial weight of the particle, wt is the weight of the particle at time t, D is the diffusion coefficient, CS is the equilibrium solubility of the substance, ρ is the density of the particle, and h is the diffusion layer thickness; we determined the equilibrium solubilities of the studied substances, on the basis of the random orientation 2D-projection images of the dissolving single particles (Figure 2).16 The high reproducibility of the single-particle equilibrium solubility data is shown by the small standard deviations of the individual measurements. All experiments were done in triplicate, and the average relative standard deviation (%RSD) of the solubility measurements was 10.7%. To validate the accuracy of the method, we compared the acquired singleparticle solubility data with reported experimental equilibrium solubility values. The result is visualized in Figure 3a, where a

Figure 4. Single-particle solubility profile. The dots show individual single-particle solubility values acquired through the reorganized H-C cube root law. Data points up to 290 s, with a higher range of fluctuation, are omitted in order to produce a more focused view. The moving average (n = 100) represents the buildup of the interfacial concentration, Ci, whereas the asymptote represents the equilibrium solubility, CS. In the inset, a closeup of the equilibration is visualized, with the dashed vertical line indicating the equilibration point. At this time point, the interfacial concentration is on average within 8% of equilibrium solubility, for all substances. Figure 3. Log−log correlation of literature equilibrium solubility with single-particle solubility and equilibration time. (a) Correlation between logarithmically transformed solubility (logS) calculated from single-particle dissolution rates and experimental logS values from literature. The high correlation is indicated by the R2 value of 0.998, with error bars showing the standard deviation of the single-particle equilibrium solubility values. (b) The decrease in equilibration time, T, with increasing solubility is visualized.

the diffusion layer, to the bulk solution. These factors can be expressed as

dm = −k i(CS − C i) dt

(2)

and dm = −k t(C i − C b) dt

log−log linear correlation is seen, having a R2 value of 0.998. While more data is retrieved from lower solubility substances, due to the longer dissolution times, an increased standard deviation with decreasing solubility was observed (Figure 3a, Table S-2, Supporting Information). A simple explanation is the relative increase in measurement error when studying smallscale changes. In a parallel experiment, we were unable to retrieve a dissolution curve for the low solubility single particles using chemical analysis. This was probably due to the adsorption and/or absorption of the low quantities of the hydrophobic substances to the tubing of the flow-through system and shows the critical importance of minimizing error sources when using miniaturized methods. This can be achieved through the use of physical analytical techniques, thus avoiding potential error sources such as liquid sample handling and the influence of adsorption or absorption of substances to hydrophobic surfaces of the apparatus and equipment. We extensively discussed the advantages of singleparticle studies using image analysis versus multiparticle studies using chemical analysis in a previous publication.14 A typical single-particle solubility profile obtained by the reorganized H-C cube root law is shown in Figure 4. It can be seen that a fluctuation around the equilibrium value takes place during the dissolution process, with the initially wide fluctuation equilibrating after a period of time. This can be explained through the biphasic interpretation of the diffusion layer dissolution rate theory.17 In the biphasic interpretation, the two factors determining the dissolution rate (dm/dt) are the rate of interfacial reaction and the rate of transport, through

(3)

where CS is the saturation concentration, Ci is the interfacial concentration, Cb is the bulk concentration, and ki and kt are the respective rate constants for the interfacial and the transport phases. Under sink conditions, Cb is negligible and the rate of transport becomes dependent on Ci only. The interfacial reaction rate, on the other hand, is dependent on the kinetic rates of dissolution and recrystallization. The fluctuation in the solubility data (Figure 4) indicates the alternation between these kinetic rates according to the Le Chatelier principle, i.e., the alternation between supersaturation and undersaturation caused by dissolution, nucleation, and recrystallization, until the thermodynamic equilibrium is reached. As Ci approaches CS, the interfacial reaction rate [see eq 2] reduces to zero and the dissolution rate becomes constant and dependent on the equilibrium solubility only, i.e.,

dm = −k tCs (4) dt In accordance with eq 2, we found that the equilibration time of the single-particle solubility measurements was inversely proportional to the solubility of the substance (Figure 3b), with lower solubility leading to prolonged equilibration times.17 In order to allow real-time estimation of the equilibrium solubility, the equilibration point of the oscillating solubility profile was determined. By representing the interfacial concentration Ci as a moving average (n = 100) and the equilibrium solubility CS as the asymptote, we found that a threshold of 5%RSD for 100 5043

DOI: 10.1021/acs.analchem.5b01033 Anal. Chem. 2015, 87, 5041−5045

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Analytical Chemistry

While equilibrium solubility is generally determined from bulk solutions, we have shown that it is possible to determine the equilibrium solubility from individual pure-substance particles based on the diffusion layer theory. We have also shown that, by replacing common analytical techniques with more unconventional ones, such as particle size analysis for solubility characterization, it is possible to combine the rapidity, universality, and substance sparing nature of physical analysis, with the accuracy traditionally associated with chemical analysis. Combining hydrodynamic trapping of individual particles with optical imaging in an optofluidic on-chip device, we were able to continuously monitor the unfixed sample in a liquid flow. Utilizing automated and real-time analysis of the large data sets, we were able to improve above 3-fold the accuracy and reproducibility of equilibrium solubility data, when compared to conventional methods. Thus, we demonstrate the synergistic benefit and applicability of this optofluidic method for rapid small-scale in vitro equilibrium solubility determination and, consequently, in vivo bioavailability prediction. The three main limiting factors of the current method are the initial micropellet production, the particle size quantitation limit of the analytical method, and the initial mass determination of the individual particle. Micropellet production has been miniaturized to approximately 300 μm, and the current limits of quantitation for mass and particle size are around 10 μg and 20 μm, respectively.14 Preliminary experiments using individual crystals have produced comparable results to micropellet data and, thus, we believe that micropellet dependency will not be an issue in the future. Regarding the two other current limiting factors, we anticipate significant advancements of the method capabilities, as techniques for the determination of particle size and mass on the nanometer and femtogram scale already exist.22−24

moving average values was sufficient to estimate the equilibration point (Figure 4). For experiments where less than 200 data points were acquired, the end point of an experiment was considered as the equilibration time. At this time point, Ci was on average within 8% of CS, for all samples. Depending on the substance, we observed the equilibration between 21 s and 3.8 h (Table-S2, Supporting Information). Accordingly, we were able to determine the equilibrium solubilities of all substances in a maximum of 3.8 h, with a median of 7 min, demonstrating the rapidity of our method when compared to the minimum 24 h required for golden standard equilibrium solubility studies.4,18 One method that is capable of similar rapidity in producing equilibrium solubility data is the potentiometric method introduced by Stuart and Box.7 While reproducible data is achieved by this method, it requires on average 60 mg of substance for the individual experiments, compared to the average of 0.2 mg of our method. Additionally, as with other chemical property based techniques, the potentiometric method is limited by its analytics and the equilibrium solubility can only be determined for ionizable compounds. Other methods for small-scale solubility assessment with accompanying relevant data are presented in the Table S-3, Supporting Information. It is well-known that the diffusion layer thickness of a dissolving solid is affected by the hydrodynamic environment of the dissolution system.19 Therefore, the data obtained from a specific dissolution system will be dependent on the specific conditions of that system, such as flow rate of the solvent, which are reflected in a system constant. The system constant (k = 7.95 × 103) for our setup was acquired from the log−log linear correlation between single-particle solubility values and equilibrium solubility data from literature (see the Supporting Information). By inserting this value into the reorganized H-C cube root law [see eq 1], we were able to convert the measured solubility values into equilibrium solubility, achieving an average difference of 7.8% when compared to literature values (Table S-4, Supporting Information). CS = k

ρ(w01/3

− wt

1/3

ASSOCIATED CONTENT

S Supporting Information *

Supplementary text, detailed materials and methods, and Tables S-1 to S-4. The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/ acs.analchem.5b01033.

1/3

)MW

4πρ 1/3 t 3

( )

■ ■

(5)

A RMSE of the single-particle solubility determinations of 0.07 log units was achieved, which is significantly lower than the minimum RMSE of 0.6 log units associated with experimental determination of equilibrium solubility.8 Although the diffusion layer model has been the most prominent model used to describe the dissolution process, it has been criticized throughout its existence.20,21 The main point of criticism has been the assumption of a relatively instant formation of saturation concentration at the solid−liquid interface. In this study, we show that the single-particle solubility values, calculated on the basis of the diffusion layer theory, deviate linearly from literature equilibrium solubility values. This favors the assumption of a diffusion layer and indicates a direct dependency of the dissolution rate on the equilibrium solubility. However, we also show that saturation concentration is not instantly reached and that the interfacial concentration equilibrates at a rate dependent on the equilibrium solubility of the substance. As we have discussed, these results substantiate a biphasic interpretation of the diffusion layer dissolution rate theory.

AUTHOR INFORMATION

Corresponding Author

*E-mail: sami.svanback@helsinki.fi. Tel.: +358 504078190. Fax: +358 919159144. Author Contributions

M.Sc. Sami Svanbäck: Contribution to the conception and design of the study. Main contributor in theoretical and practical research, design of the Matlab-script, data analysis and writing of the article manuscript. Dr. Henrik Ehlers: Contribution to the conception and design of the study, design of the practical research and revision of the article manuscript. Dr. Osmo Antikainen: Main contributor in designing and coding the Matlab-script. Prof. Jouko Yliruusi: Contribution to the conception and design of the study and revision of the article manuscript. All authors have given approval to the final version of the manuscript. Notes

The authors declare the following competing financial interest(s): M.Sc. Sami Svanbäck has applied for the following patent: S. Svanbäck, Method and system for determining 5044

DOI: 10.1021/acs.analchem.5b01033 Anal. Chem. 2015, 87, 5041−5045

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Analytical Chemistry dissolution properties of matter, Finnish patents priority date August 29th 2014.

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ACKNOWLEDGMENTS Heikki Räikkönen is acknowledged for technical assistance. Ilkka Lassila, Göran Maconi, and Tor Paulin from the group of Prof. Edward Haeggström at the Division of Materials Physics, Department of Physics, University of Helsinki, are acknowledged for help in 3D-printing. Emmi Palomäki is acknowledged for assistance in X-ray characterization. Prof. Hannu Elo at the Division of Pharmaceutical Biosciences, Faculty of Pharmacy, University of Helsinki, is kindly acknowledged for allowing the use of the mass comparator. S. Svanbäck acknowledges the Drug Research Doctoral Programme funding of the Faculty of Pharmacy, University of Helsinki.

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