Anal. Chem. 2003, 75, 1720-1725
Application of Frequency Domain Photon Migration to Particle Size Analysis and Monitoring of Pharmaceutical Powders Zhigang Sun,†,‡ Sharnay Torrance,‡ Fraser K McNeil-Watson,§ and Eva M. Sevick-Muraca*,‡
Malvern Instruments Inc., 10 Southville Road, Southborough, Massachusetts 01772, The Photon Migration Laboratory, Texas A&M University, College Station, Texas 77843-3573, and Malvern Instruments Ltd., Enigma Business Park, Grovewood Road, Malvern, Worcestershire WR14 1XZ, U.K.
The frequency domain photon migration (FDPM) technique was employed to determine mean particle size of pharmaceutical powders. Results show that the FDPMmeasured scattering coefficient increases linearly with reciprocal mean particle size of powdered samples. In contrast to near-infrared spectroscopy techniques, FDPM technique enables determination of scattering and absorption separately so that it does not require data pretreatment and chemometric calibration models. In addition, this unique advantage provides more detailed information about powder samples, which can be used as a potential tool for on-line monitoring of not only variation of active pharmaceutical ingredient concentrations from changes in the absorption coefficient but also variation of particle sizes from changes in the scattering coefficient. Analysis and determination of particle size of pharmaceutical powders is of central importance for monitoring and control of manufacturing processes as well as ultimate product quality in pharmaceutical industries. This is due to the fact that particle size has a strong influence on the behavior of pharmaceuticals (e.g., dissolution, flow properties, blending characteristics, and granulation). Currently, several particle sizing methods, such as sieve analysis, laser diffraction, and image analysis, have been applied to characterize dry powder systems.1,2 Some of these techniques, such as laser diffraction, have been applied to the on-line monitoring of dry milling of pharmaceutical materials in industries.3 However, these measurements require that the powder be presented in a relatively dilute form, to avoid multiple scattering, or excessive image overlap. Recently, near-infrared spectroscopy (NIRS) has been proven as a powerful on-line measurement technique in the pharmaceutical industries. Typically, NIRS is used as a powerful analytical tool * To whom correspondence should be addressed. Phone: 979-458-3206. Fax: 979-458-1011. E-mail:
[email protected]. † Malvern Instruments Inc. ‡ Texas A&M University. § Malvern Instruments Ltd. (1) Washington, C. Particle Size Analysis in Pharmaceutics and Other Industries; Ellis Horwood: New York, 1992. (2) Allen, T. Particle Size Measurement; Chapman & Hall: London, 1997. (3) Harvill, T. L.; Hoog, J. H.; Holve, D. J. Part. Part. Syst. Charact. 1995, 12, 309.
1720 Analytical Chemistry, Vol. 75, No. 7, April 1, 2003
to rapidly and nondestructively analyze chemical compositions of pharmaceutical powders by relating the sample reflectance to the concentration of a sample constituent.4 However, because NIRS reflectance is sensitive to particle sizes and shapes, as well as constituents of powders,5 NIRS reflectance spectra must be corrected in order to eliminate the effect of particle sizes for these conventional applications. Conversely, changes of spectra owing to particle size enable NIRS to measure particle size of powdered samples. Ciurczak et al.6 found that the measured absorbance changes linearly with reciprocal mean particle size by correlating particle size with NIRS data for four pure pharmaceutical products. In contrast, Ilari et al.7 demonstrated that the absorbance derived from NIRS data does not always change linearly with the reciprocal of particle size and that a calibration model is required to extract size information. Spectral data pretreatments (e.g., mean centering and second-derivative transformation) and chemometric methods (e.g., multiple linear regression and principle component regression) are often used for generating calibration models.8 For instance, O’Neil et al.9 used mean centering and a multiple linear regression model to determine the median particle size of drugs and pharmaceutical excipients. Frake et al.10 demonstrated that several calibration models can be applied to NIRS data to determine particle size of lactose powders. As an alternate method to NIRS, frequency domain photon migration (FDPM) was developed as a potential technique for online particle sizing as well as constituent monitoring of pharmaceutical powder blends. FDPM depends on launching intensitymodulated light (typically 30-200 MHz) within a turbid medium or a powder bed and then detecting the “photon density wave” (PDW) that propagates spherically to another point within the medium. The detected PDW is modulated at the same frequency as the incident wave but is amplitude attenuated and phase delayed relative to the incident light. Since the FDPM technique measures (4) Burns, D. A.; Ciurczak, E. W. Handbook of Near-Infrared Analysis; Marcel Dekker: New York, 1992. (5) Wendtlandt, W. W.; Hecht, H. G. Reflectance Spectroscopy; Interscience Publisher: New York, 1966. (6) Ciurczak, E. W.; Torlini, R. P.; Demkowicz, M. P. Spectroscopy 1986, 1, 36. (7) Ilari, J. L.; Martens, H.; Isaksson, T. Appl. Spectrosc. 1988, 42, 722. (8) Pasikatan, M. C.; Steele, J. L.; Spillman, C. K.; Haque, E. J. Near Infrared Spectrosc. 2001, 9, 153. (9) O’Neil, A. J.; Jee, R.; Moffatt, A. C. Analyst 1998, 123, 2297. (10) Frake, P.; Gill, I.; Luscombe, C. N.; Rudd, D. R.; Waterhouse, J.; Jayasooriya, U. A. Analyst 1998, 123, 2043. 10.1021/ac0261597 CCC: $25.00
© 2003 American Chemical Society Published on Web 02/22/2003
time-dependent propagation characteristics of light rather than the amount of light detected, it is self-calibrating and no external calibration is required. In contrast to the NIRS technique, FDPM allows determination of both absorption and scattering coefficients independently so that the absorption and scattering effects can be separated. In previous contributions, we have demonstrated that the FDPM-measured absorption coefficient can be successfully used to determine concentrations of absorbance in powder mixtures without a chemometric calibration model.11,12 In this contribution, we show that the FDPM-measured scattering coefficients can also be used to determine particle size of pharmaceutical powders without a chemometric calibration model. THEORY When light enters into a highly scattering but weakly absorbing medium (e.g., pharmaceutical powders), individual photons may be scattered a large number of times before eventually escaping from or being absorbed by the medium. Such light propagation, termed multiple scattering, can be modeled as a photon diffusion process due to the “random walk” of photons.13,14 In FDPM technique, the intensity of the light source is modulated sinusoidally and the propagating PDW is attenuated and phase-shifted relative to the incident light. By using the infinite boundary condition, the photon diffusion equation can be solved to yield the following analytical expressions:15,16
[ ]
ln
[
ln
]
rDC(r) ) - (r - r0)x3µa(µa + µs′) r0DC(r0)
rAC(r) ) r0AC(r0) - (r - r0)x3µa(µa + µs′)/2
PS(r) - PS(r0) ) (r - r0)x3µa(µa + µs′)/2
(1)
[x ( ) ]
(2)
[x ( ) ]
(3)
1+
1+
ω vµa
ω vµa
2
2
1/2
+1
1/2
-1
where DC is the time-invariant average intensity, AC is the amplitude of the photon density oscillation, PS is the phase shift of the photon density wave between detector and source, µa is the absorption coefficient, µ′s is the isotropic scattering coefficient, ν is the speed of light in the medium, and ω is the modulation frequency of light. To avoid unknown source contributions, DC, AC, and PS are measured at two different sourcedetector separations, namely, r and r0. The above equations indicate that light propagation within a powdered sample is characterized by the absorption coefficient, µa, and the isotropic (11) Shinde, R. R.; Balgi, G. V.; Nail, S. L.; Sevick-Muraca, E. M. J. Pharm. Sci. 1999, 88, 959. (12) Pan, T.; Barber, D.; Coffin-Beach, D.; Sun, Z.; Sevick-Muraca, E. M. J. Pharm. Sci., submitted. (13) Duderstadt, J. J.; Hamilton, L. J. Nuclear Reactor Analysis; Wiley: New York, 1976. (14) Ishimaru, A. Wave Propagation and Scattering in Random Media; Academic Press: New York, 1978. (15) Fishkin, J. B.; So, P. T. C.; Cerussi, A. E.; Fantini, S.; Franceschini, M. A.; Gratton, E. Appl. Opt. 1995, 34, 1143. (16) Sun, Z.; Huang, Y.; Sevick-Muraca, E. M. Rev. Sci. Instrum. 2002, 73, 383.
scattering coefficient, µ′s. Hence, the optical properties, µa and µ′s, can be determined separately from DC, AC, and PS measurements by using eqs 1-3, which have been discussed in detail in the literature.16 On one hand, the FDPM technique can be used for monitoring of homogeneity of chemical constituents in powder mixtures without chemometric calibration owing to the linear relationship of the absorption coefficient with concentrations of absorbance.11,12 On the other hand, since the isotropic scattering coefficient is associated with particle size by light scattering theory, FDPM technique can be used for particle sizing. From classical Mie scattering theory, the isotropic scattering coefficient of a powder sample is given by
µ′s )
3m Q (n,x,λ)(1 - g) 2Fx Scat
(4)
where, QScat(n,x,λ) is the scattering efficiency for a particle of diameter, x, with relative refractive index of particle to medium, n, at wavelength, λ; g is the average of the cosine of the scattering angle, or the scattering anisotropy; m is the mass of powders per unit volume; and F is the particle density. The derivation of eq 4 is included in Supporting Information. If the particle size of powders is much larger than the wavelength of light, the values of QScat and g tend to be wavelength independent. Correspondently, if the mass of powders is kept constant, eq 4 reduces to
µ′s ∝ 1/x
(5)
Hence, for large particles in a powder bed or suspension, the mean particle size may be determined from FDPM-measured isotropic scattering coefficient. In contrast to NIRS, the FDPM-derived scattering coefficient is obtained independently and separately from the absorption coefficient. The major difference between the time-resolved FDPM technique and NIRS is that NIRS measures the attenuation of light using a time invariant light source (i.e., ω ) 0). The simpler instrumentation may provide an advantage of NIRS over FDPM. However, as shown in eq 1, since only the DC measurement is available from NIR technique, the two mechanisms of attenuation of light, absorption and scattering, cannot be determined separately. Nonetheless, the Kubelka-Munk (K-M) theory17 is often employed to determine particle size from reflectance measurement. The K-M formula can be written as
K/S ) (1 - R)2/2R
(6)
where S and K are K-M scattering and absorption coefficients, respectively, and R is measured diffuse reflectance of the sample. The coefficients K and S used in K-M theory are not directly comparable with µa and µ′s but instead are related using the following relationship:18,19
K/S ) (8/3)(µa/µ′s)
(7)
(17) Kubelka, P.; Munk, K. Z. Tech. Phys. 1931, 12, 593. (18) Mudgett, P. S.; Richards, L. W. Appl. Opt. 1971, 10, 1485. (19) Burger, T.; Kuhn, J.; Caps, R.; Fricke, J. Appl. Spectrosc. 1997, 51, 309.
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Table 1. Mean Particle Sizes of Lactose Samples Measured by Sieve Analysis, Laser Diffraction, and Image Analysis sample
sieve analysis (µm)
laser diffration (µm)
image analysis (µm)
50M 80M 90M 100M 110M 125M
290 180 135 130 105 55
402 236 180 167 150 70
273 196 155 144 126 81
From measurement of diffuse reflectance, eq 6 shows that the absorption and scattering coefficients cannot be determined independently. In this contribution, the time-invariant and FDPM measurements are compared at discrete wavelengths in order to demonstrate particle characterization with powders. EXPERIMENTAL SECTION Materials. A range of lactose monohydrate samples with different particle sizes (i.e., samples 50M, 80M, 90M, 100M, 110M, and 125M) were supplied by DMV International (Veghel, The Netherlands). All materials were used as received. Particle Size Measurement. The nominal mean particle sizes of these samples were measured using air jet sieve analysis conducted by the manufacturer. Particle sizes were also measured (dispersed in air) by laser diffraction (Mastersizer 2000, Malvern Instruments) and image analysis (Pharma-Vision System 830, Malvern Instruments). The mean particle sizes measured by these methods are listed in Table 1. Differences among the mean particle sizes measured by different techniques are expected.1 We used particle sizes measured by each of these methods to correlate FDPM-derived µ′s and NIRS parameter K/S. FDPM Measurement. FDPM measurements were performed on all lactose samples at three different wavelengths, 650, 785, and 828 nm. Details of the FDPM instrumentation are described elsewhere.16 The measurements consisted of measuring the phase shift (PS), attenuation of average of intensity (DC), and amplitude (AC) at six different source-detector distances ranging from 4 to 9 mm in response to the source modulation at six different frequencies ranging from 50 to 100 MHz. Measurements were conducted at the same depth within sample containers, and each of them contains ∼70 mg of lactose sample. The optical parameters, µa and µ′s, were then calculated using DC and PS data as a function of source-detector position and averaged across all modulation frequencies, as previously described.16 This procedure has been tested in colloidal suspensions, which yielded optical properties with high accuracy and precision (accuracy is ∼1.5% and precision is ∼1%16). The accuracy and precision of FDPM measurement has also been validated in other work (Gerken and Faris,20 and Pham et al.21). RESULTS AND DISCUSSION Error Analysis of FDPM Measurement. Table 2 illustrates typical errors in FDPM measurements of scattering and absorption (20) Gerken, M.; Faris, G. W. Opt. Lett. 1999, 24, 930. (21) Pham, T. H.; Coquoz, O.; Fishkin, J. B.; Anderson, E.; Tromberg, B. J. Rev. Sci. Instrum. 2000, 71, 2500.
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Figure 1. FDPM-measured isotropic scattering coefficient versus (a) lactose powder particle size and (b) reciprocal lactose powder particle size at 785 nm. Particle sizes are reported by sieve analysis, laser diffraction, and image analysis. Symbols denote scattering measurements (with error bars providing standard deviation (SD) of n ) 3) for each sample. Error bars for scattering measurements are the same, regardless of how particle size is reported. Lines in (b) denote linear regression results, where fitted equations and the coefficients of determination (R2) are also shown.
in the sample 110M at a wavelength of 785 nm. Locations a-c denote different locations of the detector fiber with fixed source position at each of six source-detector distances. At each location of detector fiber, three repeated measurements were performed. It can be seen that relative standard deviations (RSDs) of measured optical properties are below 0.6% at each fixed location, which are similar to that obtained from colloidal suspensions.16
Table 2. Error Analysis of Measured Isotropic Scattering Coefficients (a, Top) and Absorption Coefficients (b, Bottom) in Sample 110M at Wavelength of 785 nm µs′ (1/cm) location a location b location c
1 182.04 160.66 171.25
2 182.29 160.61 171.16
3
mean
Section a 181.39 160.33 169.58
mean
RSD (%)
0.46 0.18 0.94
0.26 0.11 0.55
3.81 × 10-5 1.59 × 10-5 1.34 × 10-5
0.43 0.20 0.17
171.03
deviation
10.69
RSD (%) location a location b location c
181.91 160.53 170.66
deviation
6.25 8.84 × 10-3 7.85 × 10-3 7.83 × 10-3
8.77 × 10-3 7.87 × 10-3 7.84 × 10-3
Section b 8.82 × 10-3 7.87 × 10-3 7.86 × 10-3
8.81 × 10-3 7.86 × 10-3 7.85 × 10-3
mean
8.17 × 10-3
deviation
5.50 × 10-4
RSD (%)
6.74
However, the RSD of optical properties across spatial locations is ∼6%, which is larger than that at fixed location. In contrast to colloidal suspensions where mixing length scales, l, are small and the medium can be considered homogeneous, the mixing length scales of powders may be comparable to the distance between a source and detector fiber-optic pair. Consequently, the powder bed may not be considered as a truly homogeneous medium. For instance, percolation, a phenomenon in which fine particles trickle down through the gaps between the large ones, is a well-known segregation effect existing in dry powder samples.22 The volume of powders interrogated by FDPM may be of the same order of magnitude of volumetric scales (l3) of heterogeneity set up by percolation. The increase of RSD shown across spatial locations supports this hypothesis. Hence, study of RSD of optical properties in powdered samples provides an effective tool to understand the mixing process. Isotropic Scattering Coefficient of Lactose Samples. Figure 1a shows the FDPM-measured isotropic scattering coefficients at 785 nm as a function of particle size as measured by the various techniques. The error bar represents the RSD across spatial locations. It can be seen that the isotropic scattering coefficient decreases with increasing particle size, which is consistent with Mie scattering theory. To validate eq 5, the measured µ′s was plotted against the reciprocal of particle size as shown in Figure 1b. Linear regression of the measurement data to particle size was also performed, and the regressed lines, equations, and coefficients of determination (R2) are shown in Figure 1b. One can see that the measured isotropic scattering coefficient linearly changes with reciprocal of particle size with the slope depending upon the method used to represent particle size. It is noteworthy that owing to independent determination of scattering and absorption coefficients, data pretreatments or chemometric methods are not required by the FDPM technique to obtain the linear relationship between scattering coefficient and particle size (R2 > 0.98). Figure 2a shows the scattering coefficients at three wavelengths (650, 785, and 828 nm) as a function of particle size measured by image analysis and indicates that the scattering (22) Weinekotter, R.; Gericke, H. Mixing of Solids; Kluwer Academic Publisher: Dordrecht, The Netherlands, 2000.
coefficient is wavelength-insensitive for the large particles evaluated herein. For the smallest particle size (sample 125M), the scattering coefficient at 828 nm is different from that at 650 and 785 nm, due presumably to the smallest particle size that approaches the wavelength of light. Again, this is consistent with Mie scattering theory that predicts wavelength sensitivity when the size of the scatter approaches that of the wavelength of light. Similar results are obtained when particle sizes measured by other methods are used as the reference. Figure 2b illustrates the linear relationship between scattering coefficient at each wavelength and the reciprocal of particle size. The slopes at 650 and 785 nm are nearly identical, owing to the wavelength independence of scattering from particles where x . λ. The slope at 828 nm differs again due to the effects of smallest particle size. Absorption Coefficient of Lactose Samples. Figure 3a illustrates the measured absorption coefficients at 785 nm as a function of particle size for lactose powder samples. In contrast to the scattering coefficient, the variation of absorption coefficient with particle size is small (∼3.8% RSD). In previous contributions, we have demonstrated that the FDPM-measured absorption coefficient is sensitive to small variation of concentrations of active pharmaceutical ingredients in pharmaceutically relevant blends.11,12 In this study, we find that the absorption coefficient is insensitive to variation of particle size of the lactose excipient. The wavelength dependence on the absorption coefficient at varying particle size is shown in Figure 3b. For simplicity, we plot the absorption coefficient at three wavelengths (650, 785, and 828 nm) versus particle size as measured by image analysis. It can be seen that, while the absorption coefficient is sensitive to wavelength, it is insensitive to particle size at any of the three wavelengths. Time-Invariant Measurements. For time-invariant measurements (ω ) 0), the parameter P ) (µa(µa + µ′s))1/2 can be obtained from measured DC signals at various source-detector distances. Figure 4 illustrates the variation of parameter P with the reciprocal of particle size at three wavelengths. The nonlinear relationship between P and reciprocal of particle size indicates that time-invariant techniques are not suitable for particle sizing of powder samples without chemometric methods for calibration. Analytical Chemistry, Vol. 75, No. 7, April 1, 2003
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Figure 2. FDPM-measured isotropic scattering coefficient versus (a) lactose powder particle size and (b) reciprocal lactose powder particle size at three wavelengths, 650, 785, and 828 nm. Particle sizes are reported by image analysis. Symbols denote scattering measurements. Lines in (b) denote linear regression results, where fitted equations and the coefficients of determination (R2) are also shown.
Based upon K-M theory (eq 6), the ratio of absorption and scattering coefficients can be obtained from diffuse reflectance measurements in the NIRS technique. Typically, the absorbance, log(1/R), was plotted with reciprocal particle size in NIRS analysis.4 In this study, we calculated the absorbance from FDPMmeasured scattering and absorption coefficients using eqs 6 and 7. Figure 5 illustrates the nonlinear relationship between log(1/R) and reciprocal particle size at three wavelengths. It 1724 Analytical Chemistry, Vol. 75, No. 7, April 1, 2003
Figure 3. FDPM-measured absorption coefficient versus lactose powder particle size at (a) 785 nm and at (b) at three wavelengths, 650, 785, and 828 nm. Particle sizes are reported by sieve analysis, laser diffraction, and image analysis. Symbols denote absorption measurements (with error bars providing SD of n ) 3) for each sample. Error bars for scattering measurements are the same, regardless of how particle size is reported.
clearly shows that the absorbance, log(1/R), is influenced by both scattering and absorption coefficients in powder samples, and data pretreatment and chemometric methods must be used for calibration before information of particle size can be ascertained. For example, using time-invariant attenuation measurement across the surface of a colloidal scattering solution, Farrell et al.23 showed they could obtain optical property values with accuracy on the order of 5-10% but required neural networks to further improve accuracy. (23) Farrell, T. J.; Wilson, B. C.; Patterson, M. S. Phys. Med. Biol. 1992, 37, 2281.
Figure 4. Nonlinear relationship of parameter P with reciprocal lactose powder particle size at three wavelengths, 650, 785, and 828 nm. Particle sizes are reported by image analysis. Values of P are calculated from time-invariant (DC) measurements by eq 1.
In summary, the advantages of FDPM technique over timeinvariant techniques lie in the independent determination of the scattering and absorption coefficients. Correspondingly, the scattering coefficients measured accurately by the FDPM technique can match the scattering theory (eq 5) without chemometric calibration. CONCLUSIONS In this work, the FDPM technique was employed for particle sizing of pharmaceutical powders when the particle size was larger than the wavelength of light employed. The results illustrate that the FDPM-measured scattering coefficient increases linearly with reciprocal mean particle size of powdered samples, in agreement with the light scattering theory. Consequently, the FDPM technique does not require any data pretreatment or chemometric calibration, which is often required by NIRS or time-invariant techniques. In addition, the FDPM technique does not require sample preparation and provides a potential tool for undiluted online powder measurement in industrial pharmaceutical applications. Separate and simultaneous determination of the scattering and absorption coefficients provides more detailed information about
Figure 5. Nonlinear relationship of absorbance (log(1/R)) with reciprocal lactose powder particle size at three wavelengths, 650, 785, and 828 nm. Particle sizes are measured by image analysis. Values of absorbance are calculated from time-invariant (DC) measurements by K-M theory.
powder samples and a better understanding of powder mixing processes. This unique advantage opens many opportunities for on-line monitoring of powder manufacturing processes. For example, in a powder blending process, only one FDPM sensor is needed to monitor both homogeneity of chemical constituents and particle segregation phenomena, owing to the high sensitivity of the absorption coefficient to powder absorbance11,12 and the high sensitivity of scattering coefficient to particle size. Further work is under way to adapt FDPM technique as an in situ sensor for monitoring of blend homogeneity. ACKNOWLEDGMENT This work is supported in part by the National Science Foundation (CTS-9876583, CTS-0213280) and Malvern Instruments, Ltd. SUPPORTING INFORMATION AVAILABLE Additional information as noted in text. This material is available free of charge via the Internet at http://pubs.acs.org. Received for review September 22, 2002. Accepted January 28, 2003. AC0261597
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