Measuring how crystalline a drug powder is with FT-Raman: a two-band calibration for indomethacin

Background and motivation

Many processing steps, milling and compaction among them, can introduce disorder into a crystalline drug, from a disordered surface layer to complete loss of the lattice. C1 The amorphous material that results may be a problem, because it can raise solubility and hygroscopicity, change mechanical and flow properties and lower chemical stability. C1 Sometimes the amorphous state is the goal: its higher initial solubility can improve the bioavailability of poorly water-soluble drugs, and a sugar used as a lyoprotectant in freeze-dried proteins must sit in the same amorphous phase as the protein to protect it. C2 Either way, a formulator needs to know how much of a powder is amorphous.

In 1998 the most used quantitative tools were x-ray powder diffraction (XRD or XRPD), moisture sorption and microcalorimetry (refs 2–5). C3 They have different reach. XRD measures the average degree of crystalline order and detects about 10% amorphous content at best, whereas water vapour sorption and isothermal microcalorimetry, which respond to the higher energy of the disordered phase, can detect as little as 1% (Saleki-Gerhardt et al. 1994, ref 2; Briggner et al. 1994, ref 16). C28 The introduction singles out methods that can detect and quantify less than 5% amorphous material, and methods that work in situ or on line, as of particular interest. C3

FT-Raman spectroscopy had recently been used to quantify mixtures of crystal forms, either from one distinct peak per form (Langkilde et al. 1997, ref 6) or by factor analysis (Deeley et al. 1991, ref 7; Tudor et al. 1993, ref 8). C4 It is fast and needs no sample preparation, and Langkilde et al. had suggested that it could, "in theory", quantify amorphous content as well, provided the amorphous and crystalline spectra differ enough. C4 The authors' own earlier work (Taylor and Zografi 1997, ref 9) had characterised crystalline and amorphous indomethacin by FT-Raman: the drug is easily made amorphous by quench cooling its melt, and its amorphous and stable γ crystalline forms give distinguishable spectra. C5

The paper therefore asks a narrow, practical question: can FT-Raman put a number on the crystallinity of an indomethacin powder across the whole range, including small amounts of either form? A1·A2 The plan was to mix the two pure forms in known ratios, derive an equation that turns a measured Raman intensity ratio into percentage crystallinity, test it on further mixtures of known composition, and use it to estimate the crystallinity of milled indomethacin. A1·A2·A3 The authors also set out to find where the errors come from, following in part the error analysis of Bugay et al. for polymorph quantitation by diffuse reflectance infrared spectroscopy and XRPD (ref 10). P10

Background concepts

Degree of crystallinity. In this paper crystallinity is the fraction of the indomethacin in a sample that is crystalline, written $x_c$; the authors call it the mole fraction of the crystalline form, and $x_a=1-x_c$ is the amorphous fraction. E3 Because the standards are mixtures of one compound in two forms, a known weight ratio gives a known $x_c$. P4

Two-state and one-state disorder. A physical mixture of crystalline and amorphous powder is what the authors, citing Hüttenrauch et al. (ref 14), call a two-state system: each particle is either wholly crystalline or wholly amorphous. C17 Milled material is "likely" different: its particles may be partially crystalline throughout, an intermediate state called the one-state model. C17 A calibration made from two-state mixtures and then applied to a one-state solid gives a value that is "equivalent" to a mixture, which is how the authors report their milled samples. C20

What Raman measures here. In FT-Raman spectroscopy a near-infrared laser (here a Nd:YAG laser at 1064 nm) excites the sample, and the inelastically scattered light is recorded as a function of Raman shift in cm⁻¹. P6 The authors write the intensity of a Raman line as

where $I_0$ is the intensity of the exciting laser line, $\nu$ the Raman shift, $C$ the concentration of the scattering species, and $K(\nu )$ a factor that lumps together the response of the spectrometer, the self-absorption of the medium and the scattering properties of the molecules (Eq. 2). E2 In plain terms: the height of a band is proportional to how much of the species is present, scaled by a band-specific factor $K$. Because absolute intensities depend on laser power and sample placement, the authors work with ratios of $K$ factors, which they take to depend only on the scattering parameter of each band ("can be considered", following Kontoyannis et al., ref 13). C11

The two bands and their overlap. Indomethacin carries a benzoyl carbonyl group. Its C=O stretching band lies at 1698 cm⁻¹ in the γ crystal and at 1680 cm⁻¹ in the glass (Figure 3), and these two bands were chosen for quantitation. R4·C9 The two bands are not completely resolved, which the authors attribute to the broadening of the carbonyl band in the amorphous spectrum. C10 The measured height at 1698 cm⁻¹ therefore contains some amorphous signal, and the height at 1680 cm⁻¹ some crystalline signal. Kontoyannis et al. had dealt with the same problem for calcium oxalate hydrates (ref 13), and their approach was adopted here (Eq. 3): C10·E3

Here $I_R$ is the measured ratio of the height at 1698 cm⁻¹ to the height at 1680 cm⁻¹; the subscripts c and a denote the crystalline and amorphous forms, and the superscripts the band position in cm⁻¹. E3 In plain terms: each measured height is the sum of the two forms' contributions at that wavenumber, each weighted by how much of that form is present. Of the four $K$ factors, only their ratios matter. Two of the ratios can be measured on the pure forms alone; the third, which links the crystalline band to the amorphous band, needs mixtures. R5·R6

Limits of detection and quantitation. Following Miller and Miller (ref 15), the limit of detection (LOD) is taken as three standard deviations, and the limit of quantitation (LOQ) as ten standard deviations, of the crystallinity measured repeatedly on a pure sample. E7·E8 In plain terms: the LOD is the smallest content that can be told apart from zero, and the LOQ the smallest that can be measured with acceptable precision. The relative standard deviation is defined in the usual way (Eq. 1): E1

where SD is the standard deviation and $\overline{x}$ the mean. In plain terms: the spread of repeated results as a percentage of their average. E1

Methods in detail

The work has four parts: preparing and checking the two reference forms and their mixtures; building the calibration from the two-band model; testing it on independent mixtures and taking apart its errors; and applying it to milled indomethacin. The flow below summarises them.

Part 1: reference materials and mixtures

Problem. A calibration is only as good as its standards: the crystalline reference must contain no amorphous material, the amorphous one no crystals, and the mixing step must not change either. C6·C7

What they did. γ-indomethacin from Sigma, a fine powder that passed a 150 µm sieve, was assumed to be 100% crystalline. M1·C6 Amorphous indomethacin was made by melting it at 165 °C for 5 minutes and quench cooling in liquid nitrogen; the glass was warmed to room temperature under vacuum to keep atmospheric moisture from condensing on it, lightly pulverised to below 150 µm and stored over phosphorus pentoxide at −20 °C. P1·M2 Both forms were checked by XRPD (10–40° 2θ, step 0.05°, 1.5 s per step) and by DSC (pinhole aluminium pans, 20 °C/min, dry nitrogen). P2·P3 Mixtures of known ratio were built up geometrically to 500 mg in a Wig-L-Bug stainless steel capsule without its ball, transferred whole to a sealed glass vial of about 1 cm diameter and kept at −20 °C and 0% RH until measured. P4 Agitating the crystalline powder in the capsule did not change its DSC enthalpy of fusion, so the mixing step was taken not to alter crystallinity. R2·C7

What they found about the references. The XRPD pattern of the γ form shows sharp peaks across 10–40° 2θ, and the authors report that it agrees with the published pattern (ref 11); the quench-cooled material shows no crystalline peaks, only a broad halo with its maximum at about 20–23° 2θ (read from Figure 1). R1 By DSC the glass has a Tg of 45 °C, while the crystal shows no glass transition and melts at 161 °C (peak) with a fusion enthalpy of 109 J/g. M1·M2 The authors call these values in "excellent agreement" with earlier characterisations (refs 11, 12) and take the two materials to represent 100% amorphous and 100% crystalline indomethacin. C8

Part 2: building the calibration

Problem. Equation 3 contains three independent $K$ ratios. Two can be read from the spectra of the pure forms, but the ratio that connects the crystalline band to the amorphous band cannot, because no single sample contains both bands at known amounts except a mixture. R5·R6

How the measurement was set up. Spectra were collected on a Bruker RFS 100 FT-Raman system with a Nd:YAG laser at 1064 nm, defocused to a spot of about 1 mm (the largest the instrument allows) at a power of about 450 mW. P6 Back-scattered light at 180° was collected with a liquid-nitrogen-cooled germanium detector and the Stokes spectrum reported; 100 scans over 4000–50 cm⁻¹ at 4 cm⁻¹ resolution were averaged for each spectrum, with the powder in a sealed, thin-walled glass vial. P6 Peak heights at 1698 and 1680 cm⁻¹ were used. P7·C24

Step 1: the pure-form ratios. From the spectrum of crystalline indomethacin, the height at 1680 cm⁻¹ is 0.052 of the height at 1698 cm⁻¹ ($K_c^{1680}/K_c^{1698}=0.052$); from the spectrum of the glass, the height at 1698 cm⁻¹ is 0.401 of the height at 1680 cm⁻¹ ($K_a^{1698}/K_a^{1680}=0.401$). R5 Each value is the mean of 10 measurements. R5 The authors read the small first ratio as the mark of a narrow crystalline band with little overlap, so the crystal contributes "relatively minor" intensity at the amorphous position; the larger second ratio "indicates" that the broad amorphous band adds more to the crystalline peak in mixtures. C12

Step 2: the rearranged equation. Inserting the two ratios into Eq. 3, with $x_a=1-x_c$, gives Eq. 4: E4·R5

In plain terms: for any mixture of known $x_c$ and measured $I_R$, the only unknown left is the ratio $K_c^{1698}/K_a^{1680}$. Multiplying out shows that $(x_c-1)(I_R-0.401)$ plotted against $x_c(0.052I_R-1)$ should give a straight line whose slope is that ratio, which is the plot of Figure 4. E6 (Note by the AI writer: the algebra from Eq. 3 to Eq. 4 checks out with the printed ratios, as recorded in the card. E4)

Step 3: the slope and the calibration equation. Intensity ratios were measured on mixtures covering 0–100% crystalline. A1 In the Figure 4 plot twelve points lie close to a least-squares line with a correlation coefficient of 0.993 and a slope of 2.72, which is $K_c^{1698}/K_a^{1680}$. R6 Putting this value into Eq. 4 gives the calibration equation, Eq. 5: E5

In plain terms: one measured band ratio gives the crystalline fraction directly. A ratio of 0.401, the value of the pure glass, gives zero, and the result rises toward one as the ratio grows. E5·R5 (Note by the AI writer: with the printed slope of 2.72 the two constants come out as 0.859 and 2.319; the printed 2.316 follows from an unrounded slope of 2.717, so the equation is consistent within the rounding of the slope. E5)

Part 3: validation and the error budget

Validation. "One way of determining the validity" of a calibration, the authors write, is to test samples of known composition that were not used to build it. R8 They prepared twelve such mixtures, at 99, 98, 97, 93, 96, 75, 55, 25, 7, 3, 2 and 1% crystalline, and measured each in 5 runs: three independent samples at 99, 98, 97 and 93%, six at 55%, and one at each other composition (Table 1 footnotes). P11·R9 The calculated crystallinity was plotted against the actual value (Figure 6) and tabulated with standard deviation and range (Table 1). R8·R9

Error budget. All error tests used 55% crystalline mixtures. (a) Laser power: three consecutive scans at each of 225, 450 and 900 mW. P8 (b) Instrument variability: 10 consecutive scans without moving the sample. P9 (c) Sample homogeneity: six independently prepared samples, each scanned, removed, shaken and rescanned five times, giving 30 values whose range was examined; the authors note that sample positioning also contributes here. P10 (d) Overall method error: the RSD of six independent mixtures, each scanned five times with shaking (Eq. 1). P10·E1 Tests (c) and (d) are described as separate procedures, but one data set (Table 2) is reported and used for both. X7 Detection and quantitation limits came from 10 measurements of each pure form. P12

Part 4: milled samples

To test the method on material made partly amorphous by processing, 500 mg of crystalline indomethacin was ground in the same Wig-L-Bug capsule, now with a metal ball, for 5, 15 and 30 minutes, and measured like the standards, with five determinations per sample. P5·R16 No other technique was applied to these samples in the paper. X9

Experimental analysis

Result 1: the carbonyl region separates the two forms. The full spectra of the crystal and the glass differ across the whole plotted range, from the C–H stretching region near 3000 cm⁻¹ down to the low-wavenumber region (Figure 2); the authors refer to their earlier paper for the band-by-band differences (ref 9). R3 In the carbonyl region (Figure 3) the crystal shows one narrow band at 1698 cm⁻¹ and the glass one broader band at 1680 cm⁻¹. R4 As the amorphous content of a mixture rises from 20 to 50 to 80%, the 1680 cm⁻¹ band grows from a weak tail to a shoulder to a second maximum of about the same height as the 1698 cm⁻¹ band (read from Figure 3). R4 The peak positions do not move; what changes is the share of each band. R4

Result 2: the calibration is linear from 0 to 100% crystalline. With the slope of 2.72 inserted, Eq. 5 was applied back to the calibration mixtures. E5·R6 The calculated crystalline fractions stay within about 0.03 of the known values from about 0.05 to 1.0 (read from Figure 5), and a least-squares line through them has a slope of 1.01, an intercept of −0.01 and a correlation coefficient of 0.9996, which the authors present as "demonstrating the validity of equation 5". R7·C13 Note by the AI writer (not discussed in the paper): these are the same mixtures that set the slope, so Figure 5 shows that the fitted model reproduces its own calibration data; the independent test is the validation set below. X5

Result 3: independent mixtures follow the calibration. Table A reproduces Table 1 of the paper. R9

Table A. Known against measured crystallinity of the validation mixtures, in the order printed in Table 1 of the paper; the last column is the difference computed by the AI writer from the printed means. R9

Plotted against the actual values, the means fall on a line with a slope of 1.008 and an intercept "close to zero" at −0.0139 (Figure 6), which the authors read as showing that the assay is "reasonably rugged" and that calculated and input crystallinities are "in good agreement". R8·C14 They conclude that small percentages of both amorphous and crystalline material can be detected and quantified, as well as mid-range compositions ("It is apparent"). C15 They also note that the range of the runs is "quite large", so several measurements "must be averaged", and that accuracy improves when the number of measurements rises from 5 (one sample) to 15 (three samples) or 30 (six samples). C16

Two features of Table A deserve attention. First, the high end is tight: from 93 to 99% crystalline the means lie within 0.5 points of the true value, so 1–7% amorphous content is read well. R9.a–e Second, the low and middle range reads low: all seven compositions at or below 75% crystalline give means below the actual value, and at 25, 7, 3 and 2% even the highest of the five runs is below it (for example 25% crystalline read 21.3%, range 22.9–19.1%). R9.f–l·X4 The negative intercept of the validation line reflects this. R8·X4 Note by the AI writer: the 2% row cannot be internally consistent, because a mean of 1.0 with a range of 1.35–0.05 over five runs implies a standard deviation of at least 0.53, not 0.4; one of the three printed values is probably a misprint. X3 A least-squares fit of the twelve printed means also gives slope 1.010 and intercept −0.0134, close to but not exactly the stated 1.008 and −0.0139; which points the authors fitted is not stated. X8

Result 4: detection and quantitation limits. Ten measurements of pure crystalline indomethacin gave a crystallinity standard deviation of 0.2%, hence an LOD of 0.6% (3 SD) and an LOQ of about 2% (10 SD); pure amorphous indomethacin also gave a standard deviation of 0.2%, so similar limits apply to crystalline content in an amorphous sample. R14·E7·E8 From Table 1 the authors judge that a detection limit of around 1% amorphous or crystalline content "would seem reasonable" and is fairly close to the estimate, but that the variation in the mixture data "suggests" the estimated quantitation limit is too low. C21 The abstract states the result more plainly: "it was possible to detect down to either 1% amorphous or crystalline content". C15

Result 5: mixing, not the instrument, sets the error. Table B gathers the error tests, all on 55% crystalline mixtures. R10·R11·R12·R13

Table B. Error tests at 55% crystalline, from the text (Sources of Error) and Table 2 of the paper. R10·R11·R12·R13

Raising the laser power changed the peak-height ratio very little, although the absolute intensities rose, and the authors conclude that laser power introduced "little error". R10·C22 Ten consecutive scans of one spot spanned only half a point. R11 The reproducibility under higher power and repeated scanning "suggests that in this instance" heat from the laser did not crystallise the amorphous component. C23 Re-sampling the powder was another matter: the 30 values of Table 2 span 44.8 to 62.5%. R12 Within one sample, the standard deviation over its five shaken scans was 1.4 to 5.3 points; across the six samples at a given scan number it was 2.7 to 4.5 points; and the six sample means lay between 51.9 and 56.1%. R12 Because analysing one sample five times scatters about as much as analysing six samples once, and the means agree, the authors attribute the variation to non-homogeneous mixing within a sample rather than to poor reproducibility between preparations. C25 All 30 values give a mean of 54%, an SD of 4% and an RSD of 7.3% at this composition; since the standard deviations in Table 1 show no trend with crystallinity, the authors expect the RSD to depend on composition. R13·C26 Errors in reading the peak heights contribute to all of these figures. C24

Note by the AI writer on Table 2: the printed mean for scan 2 is 3.1, but the six scan-2 values average 53.08, so it should read 53.1. X1 Recomputing the RSD from the 30 printed values gives 7.2% (mean 54.03, SD 3.89) rather than 7.3%, a rounding difference. X2 The unlabelled corner cells of Table 2 (1.6 and 1.4) match the standard deviations of the six sample means and of the five scan means. X1

Result 6: milling lowers the Raman crystallinity. After milling, the intensity at 1680 cm⁻¹ increased, which the authors take as "indicating" that amorphous material had formed; the spectra otherwise looked like those of the calibration mixtures, with no change in peak positions. R15·C18 Table C gives the values read with Eq. 5. R16

Table C. Raman-equivalent crystallinity of milled crystalline indomethacin (500 mg, Wig-L-Bug with a metal ball), from the text (One State Versus Two State Model). R16

The authors describe these values as "estimated to be equivalent" to binary mixtures with that crystalline content, and the crystallinity "was observed to decrease" with milling time. C20 They add two qualifications: milled material is likely to be partially crystalline throughout (a one-state solid) rather than a two-state mixture like the standards, and milling reduces particle size, which can also affect the Raman intensity; the particle-size effect "was not evaluated in this study". C17·C19

Discussion

Where Raman fits. The authors place FT-Raman beside the existing methods rather than in place of them. C27 XRD sees the average crystalline order and misses less than about 10% amorphous material; sorption and microcalorimetry sense the excess energy of the disordered phase and reach about 1%; Raman, like infrared spectroscopy, reads molecular information from both phases at once and needs no phase transformation to do so. C28·C29 Here it detected about 1% of either form. C21 The authors list two practical advantages and one risk: no sample preparation is needed, which lowers the chance of changing the solid while preparing it; but the laser can heat the sample, "which could result in crystallisation if care is not taken", and cooling accessories may be used. C30

Why mixing dominates. The authors explain the dominance of mixing errors by the scale of what Raman samples. Different methods are sensitive to inhomogeneity over different scales, and the area of a powder bed seen by a Raman laser "can be small and can lead to sub-sampling". C31 Here the beam was already defocused to the largest spot the instrument allows, about 1 mm. P6 Particle size and mixing homogeneity then decide how representative one scan is, and the authors find it "easy to envisage" non-representative sampling in powders of large particles close to the spot size, of a wide range of sizes, or with clusters of one component. C31 Re-mixing by shaking before each spectrum, as done here, is "not an efficient method" compared with a rotating sample holder, and the homogeneity problem shows in the relatively high standard deviations. C33 Langkilde et al. had used a rotating holder that samples several areas, giving spectra more representative of the whole and less sample heating; Bugay et al. improved mixing with an acetone slurry, but the authors warn that "caution must be applied" with amorphous materials that may sorb solvent. C32 They expect that a device averaging data from different parts of the sample "would improve this method substantially" and lower the detection and quantitation limits, which depend on the variation. C34

Processed samples. For milled material the sampling question changes shape. If every particle had the same degree of disorder, a small sampling area would not matter; but the authors consider it "more likely" that milling creates a distribution of disorder depending on how much each particle has been reduced in size, so the same sampling concerns apply. C35 Particle size also matters directly: its influence on Raman intensity had not been examined in detail, and initial studies on inorganic materials found intensity rising as particle size falls, with changes of the order of 100 µm giving observable differences (Pellow-Jarman et al. 1996, ref 17). C36 The authors therefore recommend that the particle-size distribution of calibration standards be similar to that of the test samples, or that its influence be evaluated, and that the particle sizes of the two powders in binary standards be controlled. C37

On-line use. The authors close the discussion with process monitoring. Near-infrared spectroscopy was drawing attention for non-destructive in situ and on-line testing (refs 18, 19); FT-Raman analysis of a drug inside an intact dosage form had been proposed because polymeric excipients scatter weakly compared with drug substances (refs 20, 21); and Raman can be used with fibre-optic probes for remote sampling. C38 It is "thus conceivable", they write, that FT-Raman could be used on line, for example to assess how a milling step affects the polymorphic form or crystallinity of a drug. C39

What it suggests for formulation (note by the AI writer, not stated in the paper). The paper offers a template that still applies: choose one band per solid form, measure on the pure forms how much each band leaks into the other's position, fix the remaining ratio with mixtures, and validate with independent mixtures across the range. For indomethacin this reached about 1% detection without any sample preparation. The weak point is sampling: with a millimetre spot on a powder, single readings at low amorphous content should be averaged and reported with their spread, and values for milled or otherwise processed material should be treated as equivalents on a physical-mixture scale until checked by a second method.

Limitations

Limitations stated by the authors. The authors call the work a "preliminary study". C27 They state that errors in measuring peak heights contribute to all the errors discussed; that the effect of particle size on the milled samples "was not evaluated"; that their estimated quantitation limit is probably too low; and that further investigations are needed to establish correlations with existing techniques for processed samples, where the measured response "may depend" on which property of the amorphous or crystalline state each technique senses. C24·C19·C21·C40 The heating test is framed as holding "in this instance". C23

The AI writer's own judgement (1): what the validation does and does not show. The validation with mixtures not used in the calibration is the strongest part of the paper, and the separation of error sources is clear. R8·R9·R10·R11·R12 Three points weaken it. Figure 5, presented as demonstrating the validity of Eq. 5, re-plots the calibration mixtures that set its slope, so it is a consistency check only. X5 The validation is not uniform across the range: above 90% crystalline it is tight, but from 2 to 25% crystalline the means read 0.8 to 3.7 points low, with ranges that exclude the true value. X4 And some printed values do not hold together: the 2% row of Table 1, the scan-2 mean of Table 2 and, to a lesser degree, the 7.3% RSD. X3·X1·X2 The claim that averaging 15 or 30 measurements improves accuracy is supported by Table 2 at 55% crystalline but is not shown for any other composition, since the 15-run and 5-run groups of Table 1 are different compositions. X6

The AI writer's own judgement (2): the milled samples and the heating test. The milled-sample values are read on a calibration built from two-state physical mixtures, while the authors themselves expect milled indomethacin to be a one-state solid with a distribution of disorder, and particle size, which milling reduces, was not controlled; no XRPD or DSC was run on these samples. X9·C17·C19 The values show that the band ratio moves in the expected direction with milling time, but they are not yet amorphous contents in the sense that a calorimetric or diffraction method would give. The heating test rests on a single 55% mixture, with crystallinity spreads of 54.4–56.6% across laser powers and 55.8–56.3% over ten scans, and without a measured sample temperature. X10

Conclusion

The paper shows that FT-Raman spectroscopy can quantify the degree of crystallinity of indomethacin across the whole composition range. C41 The key step is the two-band model: because the crystalline (1698 cm⁻¹) and amorphous (1680 cm⁻¹) carbonyl bands overlap, the two pure-form leakage ratios (0.052 and 0.401) and one fitted ratio (2.72) are combined into a single equation that turns a measured band ratio into a crystalline fraction. R5·R6·E5 Independent mixtures from 1 to 99% crystalline followed it with a slope of 1.008, about 1% of either form could be detected, and the overall RSD at 55% crystalline was 7.3%, set mainly by inhomogeneous mixing seen through a laser spot of about 1 mm. R8·R9·C21·R13·C25 Milled crystalline indomethacin lost Raman-measured crystallinity with milling time, to an equivalent of 63.5% after 30 minutes. R16·C20 The authors' own summary is modest, a "potentially useful method to complement existing techniques", and their two open items, particle size and correlation with other techniques for processed material, are the ones a user of the method still needs to settle. C27·C19·C40