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Depth-Resolved Near-Infrared Spectroscopy
Nadhamuni G. Nerella and James K. Drennen*
Division of Pharmaceutics
Graduate School of Pharmaceutical Sciences
Duquesne University
Pittsburgh, PA 15282.
(412) 396-5520 / drennen@nir.pharm.duq.edu
* Author to whom correspondence should be addressed
While there is substantial evidence proving the success of transdermal drug delivery, there have been few accomplishments in the area of depth-resolved prediction of drug concentration during diffusion through a matrix. Such a method for noninvasive quantitation of a diffusing species could assist in the development of new drugs, dosage forms and penetration enhancers. Near-IR depth-resolved measurements were accomplished by strategically controlling the amount of reflected light reaching the detectors using a combination of diaphragms with different diameter apertures. NIR spectra were collected from a set of cellulose and Silastic ® membranes to prove the possibility of depth-resolved near-IR measurements. Principal component regression was used to estimate the depth resolution of this method, yielding an average resolution of 31 µ m. Further, to demonstrate depth-resolved NIRS in a practical in vitro system, concentrations of salicylic acid (SA) in a hydrogel matrix were determined during diffusion experiments carried out for up to three hours. An artificial neural network based calibration model was developed which predicted SA concentrations accurately (R2 = 0.993, SEP = 123 µ g/ml).
Keywords: Near-IR Spectroscopy, depth resolution, diffusion kinetics, transdermal drug delivery
Transdermal drug delivery has been extensively investigated and shown to be an effective means of delivering a variety of drugs. Transdermal Drug Delivery Systems have several advantages over conventional drug delivery systems including ease of application, controlled systemic delivery, zero first-pass liver metabolism and improved patient compliance. A safe and non- invasive method for depth-resolved quantitation of chemical species during kinetic studies of drug transfer would be a valuable tool for the evaluation of new drugs, dosage forms and penetration enhancers. This work involved the development of a near-IR diffuse-reflectance method for depth-resolved quantitation of drug in vitro.
Numerous other instrumental methods have been utilized for characterizing human skin and the role of skin in the diffusional transport of chemicals. Solan and Laden [1] performed transmission studies of stratum corneum to prove that water will alter the transmission of uv light through skin.
Many methods are available for determination of skin hydration including electrical, mechanical, thermal and optical techniques. Potts et al. [2] have indicated that quantitative measurements of water content in vivo can be made using ATR-FT-IR instrumentation. Edwardson et al. [3] used this method to determine the effect of occlusion on stratum corneum hydration in vitro and in vivo. Walling and Dabney [4] have successfully distinguished bound and free water in excised porcine skin, developing near-IR prediction equations for each form of water.
While such studies relied on infrared methods for characterizing skin hydration, other techniques have been reported. For example, Warner et al. [5] have employed electron probe analysis to determine water concentration time profiles across frozen human skin.
Bommannan et al. [6] have examined the barrier function of the stratum corneum in vivo using Fourier-Transform Infrared-Spectroscopy (FT-IR) with an attenuated total reflection (ATR) accessory. Specifically, they wanted to determine if the barrier properties are uniformly distributed across the stratum corneum after tape stripping. Their results led to the conclusion that the stratum corneum is not homogenous with respect to its barrier function. The same group has also reported their findings characterizing the mode of action of percutaneous penetration enhancers using FT-IR. [7]
While these reports discuss spectroscopic characterization of the skin and stratum corneum, they do not address the kinetics of drug absorption or quantitation of a permeating chemical species. Analytical techniques such as electron microscope autoradiography and X-ray microanalysis have been employed in attempts to visualize the transfer of drug molecules across the skin. [8-9] Such methods, however, do not fit the description for a safe and noninvasive method that can be easily applied in vivo.
Confocal laser scanning microscopy (CLSM) was used effectively by Hoogstraate et al. [10] to study diffusion rates and transport pathways of fluorescein isothiocyanate (FITC) labeled dextrans through buccal epithelium. The FITC label allows fluorometric detection of permeating species by CLSM. This method allows optical sectioning of unfixed specimens, eliminating the tissue preparation, embedding and microtoming procedures required in the techniques discussed earlier. The plane of focus can be moved by focusing the microscope with a stepper motor. Nevertheless, the depth of optical sectioning is restricted by the working distance of the lens used, and is often very small for the microscopes useful in confocal microscopy. Hoogstraate et al. used a lens with a working distance of 0.13 mm.
Jurdana and coworkers [11] performed depth profile analysis of keratin fibers using FT-IR photoacoustic spectroscopy. These investigators distinguished between the surface layer and interior matrix of intact keratin fibers, indicating a depth resolution of about 1 micron. Shick et al. [12] have discussed the theory that allows variable angle ATR to be used for depth profiling. Making certain assumptions and estimating the extinction coefficients allows identification of a concentration profile. The concentration profiles would be only on a microscopic scale however, and not useful for practical application to the study of drug diffusion through millimeters of skin and tissue.
Lodder [13] et al. have addressed the concept of depth-resolved measurements with diffuse reflectance near-IR spectroscopy in their study involving the NIR imaging of atheromas in arterial tissue. Lodder proposed controlling the solid angle of scattered light reaching the detector with a variable diaphragm. According to Lodder, depth-resolved measurements are possible by collecting spectra of a surface in multiple passes, increasing the angle of reflected light with each pass.
This work adapts the method proposed by Lodder to prove that near-IR spectroscopy may be used for the study of drug transfer. In a series of experiments using polymer membranes, depth- resolved near-infrared diffuse reflectance measurements have been proven possible. Further, the method has been practically applied to study the diffusion of salicylic acid from agarose gels.
Diffusely reflected light reaching the detectors of a near-IR instrument can be controlled by placing apertures of different sizes between the scattering sample and the detectors. One such typical arrangement is shown in Figure 1. Larger apertures tend to allow light that is diffusely reflected from all layers of the sample (including the surface and subsurface layers) to reach the detectors. In contrast, smaller apertures allow primarily that light reflected from more shallow surface layers to reach the detectors. Thus a difference spectrum (spectrum collected with larger aperture - spectrum collected with smaller aperture) provides a spectrum of the deeper layers of the sample. By using a series of apertures, and calculating the appropriate difference spectra, depth-resolved spectra may be selectively collected from various layers of the sample.
This work was carried out in two phases. In Phase I, the concept of depth-resolved diffuse reflectance measurements was proven valid and an approximate resolution determined using cellulose and Silastic polymer membranes. Phase II involved the application of this method to a more practical in vitro diffusion study where measurement of a diffusing species (salicylic acid) was performed.
Silastic sheets (polydimethyl siloxane, Rx medical grade, 0.02" thickness) were kindly provided by Dow Corning Corporation (Midland, MI 48640). Cellulose membranes, which are routinely used in drug diffusion experiments for the evaluation of topical dosage forms and transdermal systems, were obtained from Fisher Scientific, Inc., (Pittsburgh, PA 15282). Agarose (Enzyme grade) and salicylic acid (Reagent grade) were also acquired from Fisher Scientific, Inc. Apertures made of a diffusely reflective material (SpectralonTM) were obtained from Labsphere, Inc (North Sutton, NH 03260). A depth micrometer was obtained from Mitutoyo Corporation (Tokyo, Japan). The neural network development was accomplished using BrainMakerTM software (Standard version 3.0, California Scientific Software, Nevada City, CA).
Phase I: System of Polymeric Membranes
The experimental setup displayed inFigure 2 involved a sample matrix consisting of a variable number of cellulose membranes and one Silastic membrane. The thickness of the entire polymer system (~3 mm) was chosen in analogy to human skin. To simulate the migration of a chemical species across the skin, the position of the Silastic membrane was moved to various distances from the aperture by adding cellulose membranes. NIR spectra were acquired with 5 to 15 layers of cellulose membranes (0.075 mm each) as the sample matrix and one Silastic membrane (1.32 mm) as the chemical species of interest. Spectra were collected using no aperture and with apertures of 15, 20 and 25 mm diameters. Spectra collected with apertures of 5 mm and 10 mm diameter did not produce adequate absorbance to obtain a complete spectrum and were eliminated from the study.
Near-infrared spectra of all samples were collected in the range of 1200 - 2400 nm in one nm increments with an LT Industries, Inc. Quantum 1200 Plus near-IR spectrometer. The thin collection of polymers reflected little light to the detectors without a reflective back. Figure 2 illustrates the sample setup for spectral acquisition. The CAPCELLTM, not shown in Figure 2, was positioned on top of the Silastic membrane to enhance the signal.. Each time a layer of cellulose was added between the Silastic and the detectors, spectra were collected using no aperture, and with the 25 mm, 20 mm and 15 mm apertures.
Phase II. Diffusion Studies
Salicylic acid was used as a model drug in a demonstration of the ability to study drug transfer from an agarose gel matrix using depth-resolved NIR spectroscopy. Gels were prepared by slowly dispersing agarose (2 % w/v) in boiling water. Salicylic acid (0.2 % w/v) was added while the gel remained at elevated temperature. Once the solution became transparent, the final volume was adjusted to 10 mL. While the contents were still warm, the solution was poured into the donor compartment of the diffusion cell and allowed to congeal for one hour. The cooled gels were cylindrical in shape due to the interior geometry of the diffusion cell and appeared opaque when inspected visually. The gels were placed on a clean glass plate and centered over the sample window of the NIR instrument for analysis. Immediately after collecting the zero time spectra, the gels were returned to the donor compartment of the diffusion cell and the diffusion experiment was carried out for a predetermined length of time [0.25, 0.5, 1, 2, and 3 hours].
Franz cells were used in these diffusion studies. However, this study employed custom fabricated donor chambers. The custom chambers offered the same nominal internal diameter and surface area of diffusion as the traditional Franz cell but more consistent dimensions than the glass cells. The outer geometry of the chamber was designed in such a way that the entire donor chamber could be securely clamped on a platform where a depth micrometer was used to push the gel cylinder out of the donor chamber. This assembly of the depth micrometer and the diffusion cell is shown in Figure 3.
In all diffusion experiments, the receptor solution was deionized water maintained at 32 C by a recirculating water bath. The contents in the receptor compartment of the diffusion cell were constantly stirred by a magnetic stirring unit to ensure proper mixing. A cellulose membrane with a molecular weight cutoff of 6000 Da was used as a barrier membrane between the donor and the receptor chambers of the Franz cell. After the completion of a diffusion run, the Franz cell was disassembled and the gel cylinder placed on a glass plate. An NIR spectrum was collected with no aperture, and with 25 mm, 20 mm, and 15 mm apertures. The gel cylinder was placed back in the diffusion cell and secured to the platform with a clamp. The depth micrometer was adjusted to push 500 mm of gel out of the diffusion cell. The projecting gel cylinder was sliced off and the amount of salicylic acid in that section was determined by UV spectrophotometry (at 296 nm) after redispersing the gel in a known amount of boiling water. Six such slices were collected for each sample. The estimated concentrations were further normalized against mass differences in the gel slices using the following formula:
Diffusion experiments were carried out for 5 different time intervals: 0.25, 0.5, 1, 2, and 3 hours. Each experiment was performed in triplicate. In each experiment, 6 gel sections with theoretical thickness of 500 µ m were collected, starting from the surface closest to the receptor.
Data Preprocessing and Analysis.
All data were processed using programs written in SPEAKEASY (Speakeasy Computing Corporation, Chicago, IL). A log (1/R) transformation was performed on all spectra. Spectral noise was reduced by using a cubic-spline smoothing routine. Multiplicative scatter correction [14] was performed on all spectra. Difference spectra were calculated by subtracting the spectrum collected with a smaller aperture from a spectrum collected with a larger aperture. The scheme in Table I has been used to identify each of the series of difference spectra in the subsequent text.
For example, series I represents the difference between spectra collected with no aperture and the corresponding spectra collected with a 15 mm aperture.
The actual spectra obtained from individual scans of Silastic and cellulose membranes are shown in Figure 4. Silastic shows peaks in the 1700 nm to 1800 nm region which are distinguishable from those of cellulose. The distances of the Silastic from the detectors in this study ranged from 1.675 mm (with 5 layers of cellulose) to 2.425 mm (with 15 layers of cellulose). The absorbance of Silastic alone (at 1750 nm), after subtraction of the spectrum of cellulose, is shown in Figure 5 for each of the apertures. Figure 5 shows that the Log (1/R) values at 1750 nm decrease, as expected, when Silastic is moved away from the detectors. This trend occurs for all the apertures and when no aperture was used.
Difference spectra (I - VI) were calculated as described earlier. The absorbance at 1750 nm for all the difference spectra (I - VI) is plotted in Figure 6. The absorbance is seen to increase for four of the plots, indicating that the difference spectra allow focusing to deeper layers of the sample. Consequently, a positive slope appears in the difference series I, II, III, and VI. Difference series IV and V focus on surface layers of the sample and give decreasing absorbance values as Silastic is moved away from the detectors and a negative slope results.
The resolution of the method was determined by first performing principal component analysis on all difference spectra. The first three principal components which contributed to more than 99% of the cumulative variance were selected for further use. Principal component regression was performed to develop a calibration model using the distance between the Silastic membrane and the detectors as the response variable and the first three principal components as independent variables. Standard error of regression (SER) for such a calibration is an indicator of the precision of the estimated values, which in this study is the depth resolution parameter, the theoretical resolution of the focusing system.
Table II summarizes the coefficient of determination and the depth resolution parameter for each difference spectrum. This data indicates depth resolution between 18 µ m and 36 µ m.
Phase II Studies - Salicylic Acid Diffusion from Agarose Gel Matrix.
In Phase II, depth-resolved spectroscopy was further investigated in a more practical experimental system. With salicylic acid as the diffusing species and agarose gel as the matrix, diffusion experiments were conducted for 0.25, 0.50, 1, 2, and 3 hours. The concentration of salicylic acid in various layers of the gel was estimated by UV spectroscopy, for reference purposes, after appropriate sample preparation. Figure 7 shows the actual spectra obtained from the raw materials of salicylic acid and agarose, both in the solid state.
Normalized concentrations of salicylic acid in each of the first six layers were calculated and the mean and standard errors are shown as a function of depth (Figure 8) and as a function of time (Figure 9). A two-way ANOVA was performed to test the statistical significance of the differences in the normalized concentrations between the layers and the times of diffusion. The results indicate that there was a statistically significant difference in the concentrations over the time (p < 0.05) and the layers (p < 0.05).
Calibration With Individual Wavelengths and Principal Components
Employing the six series of difference spectra, a calibration model was developed to correlate the concentrations observed in each of the six layers to the spectral features in the corresponding difference spectra. A two dimensional wavelength search was conducted across the time of diffusion [0.25, 0.5, 1, 2, and 3 hrs] and the wavelength domain [1200 to 2400 nm] to find wavelengths with good correlation to the concentration values. Maximum correlation was obtained at 2100 nm. Figure 7 shows that salicylic acid has an absorbance peak at that same wavelength. Therefore, 2100 nm was chosen for single wavelength calibration models.
In addition to a single point wavelength calibration, principal component calibration was also performed using the first 5 principal components. Individual calibrations were performed for the diffusion experiments at each time, and also when all data were combined (over all times). The results from these wavelength and principal component calibrations are summarized in Table III, revealing relatively poor correlation between the near-IR data and actual concentrations.
Theoretically, of the six series of difference spectra, only 3 are independent of any overlap from other difference spectra. These 3 non-overlapping difference spectra are difference series III, V, and VI. Considering the poor calibration results obtained when all difference spectra were used, it seemed appropriate to test calibrations using only the non-overlapping difference spectra. Because there were six concentrations of salicylic acid (from six different gel layers) available, of which only three concentrations could be effectively correlated to the three non-overlapping difference spectra, a search mechanism was employed to identify those three gel layers. Calibrations were performed using concentrations in each of the possible 20 (6C3) combinations of gel layers (such as, layers 6-5-3, layers 4-3-1 etc.) as the response variable. Using absorbance values at 2100 nm, layers 6, 4 and 1 provided optimum calibration statistics. With principal components, regression statistics were optimized using layers 6, 5 and 1. The results are summarized in Table IV. Principal component regression yielded better concentration estimates than single wavelength calibration allowing for prediction of drug concentration at three depths (3mm, 2.5 mm and 0.5mm corresponding to layers 6, 5, and 1) at any one time, but not over all times.
Linearity was apparent for the principal component calibration models developed with diffusion data at any one time; however, calibration models involving diffusion data from all times showed poor correlation coefficients. One would expect this to be due to the nonlinear nature of the concentration versus time profile common to first-order diffusion processes, but linearity was not obtained even with a traditional transformation to log concentration, evidently due to the depth factor.
Calibration with An Artificial Neural Network (ANN)
Because the objective of this work was to predict the concentration of salicylic acid at any time and at any depth for the system under study, another calibration method was required to account for the nonlinear relationships between concentration, time and depth. An artificial neural network based calibration model was developed for this purpose.
Using all six series of difference spectra and a simple backpropagation based algorithm with 121 spectral inputs, 1 time input, 1 depth input and 1 concentration output, a network was trained. The training group included 90% of the total data collected and the test group included 10%. The final network had 10 hidden nodes and was trained at a learning rate of 1.0 and a momentum factor of 0.9. The results of the neural network calibration and prediction are shown in Figure 10 and Figure 11 respectively. Calibration with the ANN yielded an R-squared of 0.935 with a standard error of 66 µ g/ml for the training group and a standard error of 123 µg/ml for the test group, proving the ANN was reasonably effective for prediction of salicylic acid concentration at any time and any depth in this experiment. The variances of the calibration and prediction samples were not significantly different in an F test (p < 0.05).
Modeling of Diffusion Data
To effectively model the diffusion data as a function of time and distance, and to estimate the diffusion coefficient of salicylic acid through an agarose gel matrix, Fick's first and second laws of diffusion must be utilized. The following equations describe Fick's laws of diffusion.
eq 2
eq 3
where C is the concentration, x is the distance or depth, D is the diffusion coefficient, J is flux, and t is the time.
Solutions to Fick's laws are obtained by applying boundary conditions known from the experimental system. By using a method of separation of variables as described below, a generalized function relating the concentration as a function of time and distance is obtained. Assuming that, C (x,t) = f(t)*g(x), the following equations can be derived, where f(t) and g(x) are functions of time and depth, respectively.
eq 4
eq 5
Substituting Eq (4) and Eq (5) into Eq (3) and rearranging the resultant terms leads to the following:
eq 6
From this equality, functions g(x) and f(t) can be estimated by equating
the left hand side and the right hand side to a constant such as -
and
solving the resulting differential equations.
eq 7
eq 8
Finally an equation for concentration as a function of time and distance of the following form is obtained,
eq 9
where , A, and B are constants, and D is the diffusion coefficient.
Equation 9 was used in conjunction with a nonlinear modeling program
(TableCurve 3D, Jandel Scientific, Inc., San Rafael, CA) to estimate all
of the parameters (, A, B and D). Using this equation relating the concentration
to time and distance, the diffusion coefficient of SA in an agarose matrix
was determined to be 25.7 x 10
cm
/sec. Coefficients , A, and B are
1.41 x 10
sec
, 1524.2 µg/ml, and 1575.1 µg/ml respectively. The correlation
coefficient for the nonlinear regression equation was estimated to be 0.9641.
At the 95% confidence level, the model shown in Eq (9) was statistically
significant (p < 0.05). A surface fit of Eq. (9) to the actual data is
seen in Figure 12, which displays correlation of
the model to the data.
This technique may prove to be of value for noninvasive / in vivo measurements of diffusing species in biological tissue or for biological imaging. Use of this method for depth-resolved analysis of biological tissue, in vitro or in vivo, will present a new series of questions to answer. The method and any resulting calibrations are instrument/optics sensitive and the theoretical and practical limits have yet to be determined. For example, although the theoretical depth resolution of this method was determined to be approximately 31 µm, actual resolution of the method is practically limited to the thickness of the mechanically sliced sections used for reference analysis.
However, these studies illustrate the concept of depth-resolved near-IR diffuse reflectance spectroscopy with a system of polymer membranes and the application of this method to the analysis of a specific diffusing species in a practical in vitro setting. Advantages over other techniques include the nondestructive nature of near-IR spectroscopy, the potential for collecting spectra of nearly any organic molecule without the need for labelling, the ability for macroscopic or microscopic resolution, and the need for only traditional and relatively inexpensive near-IR instrumentation.
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Figure 1 Schematic representation of the optical system used for depth resolution
Figure 2 Experimental setup for scanning Silastic and cellulose polymers
Figure 3 Experimental setup for harvesting salicylic acid laden gel slices
Figure 4 Representative NIR spectra of Silastic and cellulose
Figure 5 Absorbance values of Silastic at 1750 nm obtained from each of the apertures as a function of its distance from the detectors
Figure 6 Absorbance values of Silastic at 1750 nm obtained from the difference spectra as a function of its distance from the detectors
Figure 7 Spectra of solid salicylic acid and agarose
Figure 8 Post diffusion normalized salicylic acid concentrations (µg/mL) estimated in each of the first 6 layers of agarose gel, shown as a function of depth
Figure 9 Post diffusion normalized salicylic acid concentrations (µg/mL) estimated in each of the first 6 layers of agarose gel, shown as a function of time
Figure 10 Predicted vs. actual concentrations of salicylic acid for training
group, obtained from a neural network (123 inputs, 10 hidden and 1 output)
based calibration (R = 0.935, SER = 66 mg/ml)
Figure 11 Predicted vs. actual concentrations of salicylic acid estimated for test group obtained from a neural network (123 inputs, 10 hidden and 1 output) based calibration (SEP = 123 µg/ml)
Figure 12 Eq. (9) fit to UV determined salicylic acid concentrations
