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Details of milk samples
A total of 13 different brands of milk pills were obtained from local grocery stores in Chiang Mai, Thailand. The relevant details of the milk tablets are summarized in Table 1. The samples were divided into three groups, namely training (T1–T3), internal validation (I1–I3) and external validation (E1–E7) samples. Each milk tablet is ground into a fine and homogeneous powder with a ceramic mortar. A central composite design (CCD) structure was used to generate systematic variations representing the sugar content of milk samples.22, containing nine experiments for each sample. For example, for samples T1, T2 and T3, amounts of sucrose (analytical grade, > 99% purity, RCI Labscan, Bangkok, Thailand) and lactose (analytical grade, > 99% purity, KEMAUS, NSW, Australia) were added. to powdered milk according to the coded values of the structure of PZS given in Table 2. A combination of the three CCD samples was then used to construct the training set, resulting in a total of 27 milk samples. The use of the CCD structure was to ensure that the variation in the recorded NIR spectra was related to the sugar concentration in the milk samples and that the number of training samples was sufficient to build predictive models.23. Samples I1, I2, and I3 were used to generate internal validation samples, and variations in sugar content were also modeled based on the CCD model. Therefore, 27 additional milk powder samples were used to construct the internal validation set. Samples E1–E7 were used as external samples to represent independent test sets. These were used to evaluate the performance of the calibration models when real samples were introduced.
It should be noted that two main types of milk tablets were used in this study. Samples E2 and E3 were non-dairy tablets or “cheap milk tablets” where artificial milk flavoring was added to achieve product satisfaction. On the other hand, the rest of the milk samples were produced from cow’s milk as raw material and were called “premium milk tablets”.
NIR spectral detection
NIR spectra of dry milk (9.00 g) using a NIR transport module (width × length × depth: 5.7 × 29.4 × 2.0 cm) equipped with a NIRSystem 6500 (Multi-Mode™ Analyzer, Foss, USA) has been taken. 400–2500 nm range at 2 nm sampling interval, providing 1050 data points per spectrum. An average of 64 scans was used for each sample. Samples of milk tablets are placed inside the NIR transport module. Layers of milk tablets were attached directly to the glass containing the powder samples according to the measurement conditions. Milk samples were stored at a controlled room temperature of 25 °C for at least 6 h before NIR detection. Prior to analysis, NIR spectra were preprocessed with standard normal variation (SNV) to eliminate errors caused by light scattering during NIR measurements. Then, they were mean-centered so that the analysis focused on variance from the data rather than absolute values.
HPLC analysis of sugar
The sugar content of the milk tablet samples was measured by high performance liquid chromatography (HPLC). To prepare the samples, 1.00 g of each crushed milk tablet was dissolved in 10 mL of ultrapure water and kept in a water bath (Julabo Labortechnik GMbH, Seelbach, Germany) at 55 °C for 5 min. Then, HPLC-grade acetonitrile was added for protein precipitation24,25. After denaturation, the sample solution was centrifuged at 10,000 rpm for 5 min. The clear solution was then filtered through a 0.45 μm capron syringe filter (Agilent Technologies, CA, USA).
Chromatographic analysis of sugar content in milk tablets was performed with an Agilent ZORBAX NH high-performance liquid chromatograph (Agilent 1100 HPLC system, CA, USA).2 column (5 µm, 4.6 mm inner diameter, 150 mm length) operated at 25 °C. Samples were automatically injected into the HPLC system with an injection volume of 10 μl. A mixture of HPLC grade acetonitrile and ultrapure water (75/25%v/v) was used as the mobile phase at a flow rate of 1.00 mL/min. The refractive index detector (RID) was operated at 25 °C. Sugar content was determined using an external standard calibration curve of sucrose and lactose standards, resulting in R2 values of 0.9907 and 0.9896, respectively. Table 1 summarizes the sugar concentration values in the studied milk tablet samples.
Chemometric analysis
Standardization of NIR spectra using DS and PDS calibration transfers
Although both forms of milk samples (tablet and powder) were considered solid, there were differences in, for example, particle size and tablet compaction pressure. These physical variations resulted in significant deviations in the recorded NIR spectra26. Calibration shifts are multivariate correction methods that can be used to stabilize variations caused by different instrumentation and measurement conditions. In this study, they were used to account for any signal differences between the spectra obtained from tablet samples and powder samples. Particle Direct Standardization (PDS) is an algorithm extension of the conventional method known as Direct Standardization DS27,28. The DS method describes the correlation between two data matrices (Xm the and Xs by referencing the master and slave data) by computing the transformation matrix (F) using multiple linear regression models such as MLR, PCR and PLS:
$${\varvec{X}}_{m} = {\varvec{X}}_{s} \times {\varvec{F}}$$
An extension in the PDS algorithm is that each spectral point of the basic data (Xm,j) especially related to the spectral part of slave data (Xs.j). The PDS algorithm includes the following steps:
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Step 1: Select spectral points of master data (Xm, y) in wavelength j.
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Step 2: Define the slave data subspectrum (Xs.j) near wavelength j create an index j – k before the j + k
$${\varvec{X}}_{s,j} { = [}{\varvec{x}}_{s,j – k} \cdot {\varvec{x}}_{s,j – k + 1} {, } \ldots {, }{\varvec{x}}_{s,j + k – 1} \cdot {\varvec{x}}_{s,j + k} ]$$
where iskwindow size, which controls the amount of spectral data to be used in the calculation.
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Step 3: Construct the regression coefficient
$${\varvec{X}}_{m,j} = {\varvec{X}}_{s,j} \times {\varvec{b}}_{j}$$
where is bi is a vector containing regression coefficients.
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Step 4: Create the transformation matrix (F) by organization bj to a diagonal matrix
$$\varvec{F }={\text{diag}}\;{(}{\varvec{b}}_{{1}}^{T} {,}\;{\varvec{b}}_ {{2}}^{T} {,} \ldots \;{\varvec{b}}_{j}^{T} {,} \ldots \;{\text{b}}_{n}^ {T} )$$
where ispis the number of spectral channels included.
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Step 5: Standardize the spectra of unknown samples (Xs, un) to use F to obtain the modified spectrum (Xs, PDS)
$${\varvec{X}}_{s,PDS} = {\varvec{F}} \times {\varvec{X}}_{s,un}$$
In this study, DS and PDS transformations were used to account for discrepancies between spectra obtained from powder samples and tablet samples. These transformation methods examine the correlation between two data sets. Then, the obtained correlation information was used to adjust the NIR spectra of the milk tablet samples. Therefore, using a calibration model generated from the NIR spectra of powder samples without the need to recalibrate the model, the adjusted data can be consistent with the prediction.
Model optimization is based on a previously published report21. Both DS and PLS correlation matrices were determined using PLS regression, which was calculated with training samples and optimized based on internal validation samples.
PLS for quantitative analyses
Partial least squares (PLS) regression is one of the most powerful methods for analyzing multivariate calibration models.29. An important advantage of the PLS algorithm is that the variances obtained from the predictor and response parameters are simultaneously extracted and then used to build the prediction model. By using a PLS model, the correlation between these data blocks can be maximized. In most cases, PLS can successfully offer an optimal predictor for predicting NIR spectral data11.30.
In this study, NIR spectrum and sugar content were used as predictor and response parameters for PLS models, respectively. PLS calculation was performed according to the procedure described in previously published literature29. A leave-one-out cross-validation method was used to determine the optimal number of PLS latent variables.31. According to Table 1 , PLS models were developed using training (T1–T3) samples as calibration data. To test the models, internal validation (I1–I3) and external validation (E1–E7) samples were used for validation and prediction, respectively.
Estimates of the prediction accuracy of the PLS models are reported using root mean square error of calibration (RMSEC) and root mean square error of prediction (RMSEP). Determination coefficients for calibration (R2) and prediction (Q2) values were calculated to determine the robustness of the models. In addition, standard error of cross-validation (SECV) and ratio of prediction deviation (RPD) were used to compare the different predictive performance of the calibration models.32. PLS model calculations, PDS calibration transfer, and statistical analyzes were performed using in-house MATLAB scripts (MATLAB, The Math Works Inc., Natick).
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