3.1. Simulations of Fluid Flow and Dissolution of a Single Particle
Dissolution measurements are frequently performed during the development of new pharmaceutical products. In compendial basket and paddle apparatuses, such as the USP 1 and USP 2 methods, the agitation rate is typically specified in terms of the number of revolutions per minute (rpm) and it is hence difficult to estimate the local fluid flow pattern and velocity around a solid product or fragments thereof [
24]. In a flow-through apparatus, such as the USP 4 method, the liquid flow velocity (mm/s) can be determined [
25,
26]. The advantage with a flow-through dissolution technique is that the sink condition is maintained during the experiment due to the constant introduction of new dissolution medium into the system [
27].
The flow rates have been suggested to be set between 4 to 16 mL/min in the flow-through (USP 4) dissolution apparatus [
26]. Depending on the diameter of the cell (12 mm or 22.6 mm) the corresponding average flow velocity values have been estimated [
27] to be approximately 0.33 mm/s and 2.4 mm/s for 8 mL/min and 16 mL/min, respectively. Those fluid velocities are considerable lower than the fluid velocities reported for the paddle apparatus, the basket apparatus and the µDISS Profiler [
27,
28]. At 50 rpm, simulated velocity values range from zero to values up to 67 mm/s in the paddle apparatus and 26 mm/s in the basket apparatus [
29]. Computational fluid dynamics (CFD) simulations assessing different agitator geometries and stirring rates in the µDISS Profiler show that the rotating disc is the least effective agitator with 17 mm/s per 100 rpm, whereas the cross stirrer is the most effective with an average flow velocity of 57 mm/s per 100 rpm [
28].
The fluid velocities in the single particle dissolution experiments were calculated by Equation (1). Since the velocity in the center of the micropipette is estimated to be twice the average velocity [
18], this was taken into consideration, and the fluid velocities in the vicinity of the particle were calculated to be 46, 66, 88 and 103 mm/s. These fluid velocities are hence similar to the velocities reported for the paddle apparatus, the basket apparatus and the µDISS Profiler, as discussed above. To confirm a laminar flow, the Reynolds number was calculated for the flow-pipette as well as the particles using Equation (2). It was calculated to be 21–46 for the flow-pipette, depending on fluid velocity (46–103 mm/s) and to be approximately 1–6 for the particles, depending on particle size and fluid velocity. Hence, the Reynolds numbers calculated are significantly lower than the cut-off value indicating a turbulent flow, which is estimated to be approximately 2300 for a tube [
30].
The fluid flow pattern in the experimental setup used in this work was assessed by CFD (
Figure 4 and
Figure 5). A gradient in flow velocity across the flow-pipette was obtained, i.e., a parabolic velocity profile which was similar for the two flow rates used in the simulation (46 mm/s and 103 mm/s). The continuous flow of fluid along the flow-pipette was disturbed around the micropipette and a marked gradient in flow velocity was obtained around the micropipette and the attached particle.
Simulations of the flow around the particle were done for two particle shapes, i.e., a sphere and a box, the latter mimicking the shape of the ibuprofen particles used as one of the model compounds in the dissolution experiments (see below), and magnified views of the fluid flow are provided in
Figure 5.
As expected, the finer details of the flow pattern were affected by the particle shape and the fluid velocity profile was more uniform for the sphere than for the box. However, the effect of particle geometry on the gross features of the liquid flow was small. Moreover, there were no indications of turbulent flow around either of the particles, i.e., a laminar flow around the particle was obtained.
In
Figure 6, the drug concentration (mol/m
3) around the particle during dissolution, as obtained from simulations, is depicted in the symmetry plane. For the box particle, the layer of fluid containing an appreciable amount of dissolved drug is thin, even along the particle surface facing the incoming fluid flow and along the surfaces parallel to the fluid flow. For the particle surface on the reverse side to the surface facing the incoming flow, a thicker and more uneven drug layer was obtained with a spike at one box corner. For the sphere, a similar overall pattern was obtained but with a less heterogeneous drug layer on the reverse side of the sphere to the incoming flow.
Consistent with these observations, there were evident differences in simulated dissolution rates on the different faces of the particles, as seen in
Figure 7. For the box particle, the dissolution proceeded more rapidly at the edges and corners (
Figure 7a,b). As a result, an initially box-shaped particle is expected to become somewhat rounder in shape as dissolution proceeds. Dissolution was most rapid on the faces directed towards the incoming flow, intermediate for faces perpendicular to the flow and smallest on faces that opposed the incoming flow. Specifically, the following approximate average dissolution rates were obtained for a fluid velocity of 46 mm/s (
Figure 7a): left face: 13.0, bottom face: 11.0, side face (depicted in the middle of
Figure 7a): 9.6, right face: 8.8 and finally top face: 2.5 mg/(m
2s).
The rank order was the same for the higher fluid velocity. Taken together, these values indicate a similar rate of reduction in the length and breadth, which in turn is larger than the rate of reduction of the thickness. However, since the initial thickness was considerably smaller than the other main dimensions, the relative rate of change would be larger for the thickness than for the length and breadth (and of these, the relative change of the breadth would be somewhat larger than that of the length). For the equivalent sphere, a gradual reduction of the dissolution rate along the direction of the flow was obtained (
Figure 7c,d).
In
Figure 8, the Sherwood number, i.e., an indication of the overall dissolution rate, is presented as a function of inflow rate of fluid for the two types of particles. The dissolution rate increased non-linearly with increased fluid flow rate for both particle shapes. The curve shape is consistent with prior results obtained for convective enhancements of heat and mass transfer as expressed, e.g., by the Ranz−Marshall correlation [
31].
Despite the evident differences in local dissolution rates observed between the box particle and the equivalent sphere particle, the drug release-rate profiles were similar. This indicates that the single particle technique can be used to compare the dissolution of particles of different particle shape. The simulated dissolution rate−inflow rate relationship bent slightly but the relationship was nearly linear in the range of inflow rates used in the single particle dissolution experiments.
3.2. Determination of Dissolution Rate
Pharmaceutical preparations contain a large number of particles and multiparticulate dissolution represents a system property. Multiparticulate systems are, however, difficult to model since the fluid flow occurring around each particle is difficult to fully consider [
2,
16] and the contact area between fluid and particle is based on a single approximation of particle size and shape. In order to have more well-controlled experimental conditions regarding these aspects, i.e., the particle surface area is accurately determined in real-time and the flow of fluid around the dissolving particle is a controlled laminar flow of defined velocity, a single particle dissolution technique represents a more qualified situation.
Using the single particle technique presented in this paper makes it possible to evaluate different fundamental components, and how they affect the dissolution process. For example, various particle sizes and shapes, fluid velocities and dissolution media can be studied in different settings to assess what effect this might have on the IDR. This could assist in a better understanding of in vivo dissolution and to define the most suitable dissolution test conditions. Further, this technique is especially promising for poorly water-soluble compounds as previous studies have pointed out the difficulties of measuring the IDR from standardized dissolution methods, i.e., a compressed disc, since the dissolved material can be below the detection limit [
11,
32].
In recent decades, dissolution from single particles has been the subject of several studies, allowing the particle size and shape to be accurately observed [
2,
15,
16,
17,
33,
34,
35]. The methodology used in these experiments differed, some of which are described here below. Marabi et al. [
2] used a microscopy-based experimental method and image analysis algorithms to study sucrose particles (D (v,0.5) = 586 µm) of a spherical shape and homogeneous composition. Prasad et al. [
15] used paracetamol single crystals in the size of 3–5 mm grown in an aqueous solution containing 6.02%
w/
w p-acetoxyacetanilide (PAA). The paracetamol crystal was glued to a steel needle and positioned appropriately to the direction of the solution flow. Østergaard et al. [
34] used lidocaine single crystals (needle-shaped; 2–3.5 mm) obtained from the recrystallization of lidocaine in n-hexane. The single crystal of lidocaine was placed in a dissolution cell and the dissolution studies were performed using UV imaging. Svanbäck et al. [
17,
35] used an optofluidic flow cell and image analysis to study the dissolution of spherical pellets (14–747 µg) produced from micronized powders. They developed a flow-through cell, wherein the solvent flow did create a centrally positioned particle trapping vortex where the particle was allowed to rotate randomly. A general disadvantage of these methods are the procedures used to prepare the particles suitable for further dissolution investigation.
In this study, a single particle dissolution technique is used which allows original unmanipulated drug particles to be studied, thus avoiding any preparation procedure such as spheronization. The particles used in this study had an initial mass of 0.06–0.88 µg and a calculated initial of 37.5–104.6 µm, which are considerably smaller, compared to the methods mentioned above. Even though we acknowledge the fact that a spheronization or a crystallization procedure may give a particle that is easier to study, such preprocessing procedures may change the physical properties of the drug in such a way that it affects the dissolution behavior. Moreover, the simulation discussed above indicates that the shape of the particle affects the local flow pattern of the dissolution fluid around the particle but has a limited effect on the dissolution rate profile.
The micropipette used during the single particle dissolution measurements had a tip of a Ø ≈ 50 µm and the particles selected for the dissolution experiments could not be smaller than about 50 µm. Hence, the particles selected were of similar size and the approximate average size used in the measurements was µm3 for carbamazepine, µm3 for ibuprofen and µm3 indomethacin (). During the experiment, one side of the particle was, to a relatively large extent, covered by the tip area of the micropipette which was compensated for in the derived dissolution data (see Equation (5)).
The particle shape of the tested compounds varied, i.e., carbamazepine had a more rounded shape (
Figure 9a,b) while the shapes of ibuprofen and indomethacin were flat and elongated (
Figure 9c–f). The particles did not have any visible open pores, as judged from SEM images, and the particles were considered to be dense. In the case of porous particles, the single particle technique could potentially be used to study the effect of particle porosity on the IDR. For each compound there was also a variation in the main particle dimensions (
and
) between each single particle sampled for dissolution measurement, as exemplified for ibuprofen (
Table 3). As can also be noticed in the SEM images, the finer particles were adsorbed to the surface of the larger particles (
Figure 9b,d,f). These fine particles could not be observed in the microscope used during dissolution testing. It is possible that these adsorbed fine particles can detach from the carrier particle while in contact with a fluid. If this happens when the actual dissolution experiment is started it may give rise to a, in relative terms, fast initial dissolution rate that is not representative of the overall dissolution process.
In
Figure 10, the position of an ibuprofen particle on the micropipette is shown. The
, the
and the
of each particle were measured before starting the experiment. Once the particle was attached to the micropipette and the experiment was commenced, the
and the
were measured regularly throughout the experiment. The micropipette kept the particle in a fixed position during the course of the dissolution process, enabling an accurate measurement of
and
. The third particle dimension (
) had to be calculated and to address the question of the accuracy of the calculated estimate of
, the final particle breath of ibuprofen was measured after the experiment was completed for two of the dissolution experiments (46 mm/s ‘measurement 3’ and 66 mm/s ‘measurement 3’). The estimated
values were 28.6 µm and 27.9 µm, while the final measured
values were 30.0 µm and 28.0 µm. It is concluded that the calculation used gave an acceptable approximation of
.
The data collected during a dissolution experiment are exemplified (
Table 3) for one of the compounds used, i.e., ibuprofen. The initial mass of the sampled ibuprofen particles varied between 0.07 µg and 0.28 µg and the initial
between 48.8 µm and 71.9 µm. The particle surface area (
) flakiness (
), and sphericity (
) also varied between the single particles. The dissolution measurement was performed as long as possible with the experimental set-up used. For ibuprofen, this occurred typically after about 15 min when the particle either detached, rearranged on the micropipette or the particle was broken into two pieces. For the dissolution measurement to be feasible, the particle has to be attached and retained on the micropipette for a sufficient time-period. For example, if the particle detached too soon, the measurements had to be restarted. By comparing the initial particle (0 min) to the same particle after 8 and 15 min of dissolution (
Figure 10) an obvious decrease of both the
and
of the particle was seen. From the measurements of
and
, the change in other indications of particle dimensions were derived and in
Figure 11, the change in
with dissolution time for ibuprofen is presented together with three other indications, i.e.,
,
and
. Results are presented for the individual particles measured for each fluid velocity.
The and the of the particles decreased throughout the experiments approximately linearly with time and the decrease became more rapid with a higher fluid velocity, i.e., the average slope of the line (), calculated by linear regression, increased with an increase in flow velocity. The absolute surface area of the particle decreased with a reduction in particle diameter but the specific surface area increased during the dissolution process. The specific surface area profiles were nearly linear but tended to bend upwards with increased dissolution time.
The sphericity (
Figure 11) decreased slightly with dissolution time and the flakiness (i.e.,
) changed from a range of 2.7 and 5.0 before dissolution to a range between 3.4 and 5.8 as the dissolution measurements proceeded. It seems, therefore, that the particles became flakier as the dissolution measurement proceeded in the set-up used. One possible explanation is that the side of the particle facing the incoming fluid dissolved faster. This is consistent with the CFD simulations (
Figure 6) where a thicker stagnant layer was seen on the part of the particle that was not facing the incoming flow. However, compared to the change in
and
of the particles, the change in particle shape was small and thus, the particle shape was almost retained during the course of dissolution.
The highest fluid flow velocity used in this study was 103 mm/s. At this flow velocity, some of the particles detached from the micropipette when the flowing fluid came in contact with the particle, i.e., the suction applied was not always strong enough to hold the particle firmly attached to the micropipette. It is thus also possible that a tendency for a reorientation of the particle at the tip of the pipette during the course of dissolution increased at the highest flow velocity. For the same reason, the minimum final
of carbamazepine, ibuprofen and indomethacin that could be determined was approximately 30 µm (
Figure 12), since below this particle size, the particles became too small to be firmly attached to the micropipette. If there is a need to measure dissolution of even smaller particles, i.e., a
below 30 µm, a smaller tip diameter would need to be used. Since the measurement proceeded until this limit of
, the measurement time varied between the compounds, depending on their solubility (
Figure 12). For carbamazepine, the single particles dissolved relatively rapidly, i.e., in about 4–5 min, while for indomethacin, the particle dissolution measurements were maintained for 60 min in all flow velocities.
One of the compounds used in this study, carbamazepine, is reported to have several different anhydrous polymorphs and a dihydrate form, which exhibit different melting points, solubility and compactability [
20]. The most common forms of carbamazepine are the anhydrous form III and the dihydrate form. The anhydrous form III is thermodynamically stable at room temperature, while carbamazepine dihydrate is the most stable form in aqueous solution. Hence, all polymorphs convert to the dihydrate form in aqueous solution through a solution-mediated mechanism [
36].
In a previous study where disc IDR was performed [
20], it was shown that particle size and morphology affected the appearance of the surface of the compacts. To minimize this problem, carbamazepine samples were sieved into fractions and a size fraction of 250–355 µm was selected. When measuring IDR, the slop of the curve changed because of a phase transformation from anhydrous into the dihydrate form. During the IDR measurement, crystallization of carbamazepine dihydrate occurred at the surface of the disc, resulting in a decrease of IDR and in two distinct slopes. The initial slope represented the dissolution of the anhydrous phase and the second slope described the dissolution of the dihydrate phase. In another study [
37], where disc dissolution of poorly soluble weak acids was investigated, a similar morphological transformation was observed during the experiment. As one example, naproxen exhibited surface heterogeneity to start with, but the appearance of the surface changed during dissolution, where hydrate formation was suggested as an explanation.
In this study, a change in the appearance of the particles was observed while held in water, giving the formation of a large number of small aggregated needles (
Figure 13a). This indicates a phase transformation into the dihydrate form of carbamazepine. However, during single particle dissolution in a continuous aqueous fluid flow, a similar change in the appearance of the studied particle was not observed (
Figure 13b). Thus, the phase transformation did not occur during the actual dissolution measurements. The type of single particle dissolution technique used in this study, with a continuous monitoring of the particle appearance, could be a complementary technique to other dissolution experiments to detect phase transformations occurring during dissolution and determine any consequent effect on the dissolution rate.
3.3. Intrinsic Dissolution Rate
From the dissolution data for single particles of carbamazepine, ibuprofen and indomethacin, a surface area normalized dissolution rate (SAND), hereafter denoted IDR, was derived at four fluid velocities. The IDR values were calculated firstly, by Equation (9) and secondly, as the slope of the plot of the cumulative dissolved amount of compound per surface area (µg/cm
2) against time (min). The latter procedure gave lower standard deviations of IDR in all cases except for ibuprofen 103 mm/s and indomethacin 46 mm/s and 103 mm/s (
Table 4).
The average relative standard deviations (%RSD) of the dissolution measurements were 8.4% for carbamazepine, 12.8% for ibuprofen and 14.5% for indomethacin, comparable to a %RSD of 9.4 reported by Svanbäck et al. [
17]. The measurements performed in the highest fluid velocity (103 mm/s) gave the highest variability in dissolution data, explained by a tendency to a reorientation of the particle at the tip of the pipette during the course of dissolution, as discussed above.
The IDR was relatively constant during the dissolution process (
Figure 14) and the variations obtained thus seemed stochastic with one exception, i.e., relatively high IDR values were obtained during the first minutes (about 3 min) of dissolution in some cases. These initial high values may be due to the detachment of small drug particles attached to the surface of the particle (
Figure 9) and thus affecting the measurement of L and T, as discussed above. An alternative explanation is that a slight reorientation of the particle occurred when the dissolution experiment started. Another explanation is that the IDR values calculated by Equation (9) fluctuate more in the beginning as the distance between the data points are narrow which gives rise to more uncertain data. As the distance between the initial
/
and the data points collected at time ‘
’ increases, the fluctuation eventually evens out.
The cumulative amount of dissolved drug (µg/cm
2) was plotted against time (min) to demonstrate the dissolution process of the single particles (
Figure 15). The particles dissolved in a nearly linear way, and with an increase in dissolved amount per time with an increase in fluid velocity. However, as mentioned earlier, one limitation was the difficulty in measuring the dissolution in the highest fluid velocity (103 mm/s). For example, carbamazepine could be measured for only a few minutes, which made the results somewhat uncertain in this fluid velocity. The most poorly soluble drug, indomethacin, could be measured for a time period of 60 min in all fluid velocities.
The IDR increased with an increase in fluid flow velocity in a slightly bent way (
Figure 16). In the same range of flow velocity, the simulations gave a similar type of relationship between Sherwood number and flow velocity (
Figure 8), supporting that a controlled laminar flow occurred during the dissolution experiment. For ibuprofen, an IDR was also determined by a rotating disc method using a µDISS profiler. The IDR thus obtained was 9.0 ± 1.9 µg/min/cm
2, which was markedly lower than the IDR obtained by the single particle dissolution technique. The fluid flow velocity in the µDISS Profiler using a disc stirrer has been estimated to be [
28] about 17 mm/s which is considerably lower than for the single particle technique used here, i.e., 46–103 mm/s. Assuming that the type of bent relationship between IDR and flow velocity obtained by simulation (
Figure 8) applies also to the experimental relationship, the IDR obtained by the disc method is somewhat lower than the extrapolated single particle results. This may indicate that the fluid flow conditions in the vicinity of the rotating disc is less well defined than in the single particle set-up used in this study. As a future study, it would be interesting to compare the results obtained in this study to dissolution data obtained by an USP 4 dissolution apparatus which has a similar fluid flow pattern, provided that an accurate solid-to-liquid contact area can be determined for a polydisperse powder.
The IDR increased with an increased solubility of the compounds, albeit not in a linear way. Since laminar flow occurred around the particle, an effective transport rate constant describing the transport of dissolved molecules in the stagnant water layer can be calculated as the ratio between IDR and solubility (
Figure 17). The qualified measurement conditions used in this study make it possible to decipher the dissolution curve into two physically sound descriptors of the dissolution process, i.e., the IDR and effective transport rate constant. Hence, the relative contribution of drug solubility and drug transport properties on the IDR can be assessed. The high IDR of carbamazepine is a consequence of both a high solubility and a high transport rate, while the relatively low IDR of ibuprofen in relationship to the solubility is due to a low transport rate.
The effective transport rate constant increased for all compounds nearly linearly with flow velocity in the range of velocities used, reflecting a decreased thickness of the aqueous boundary layer and hence, a reduced effective diffusion distance of the solute with increased flow velocity.